Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,38,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 38, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 38);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 38 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.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: | \(86.7140381246\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1222518952080 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.10568e6\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 262144. | 0.707107 | ||||||||
\(3\) | −6.89815e8 | −1.02799 | −0.513996 | − | 0.857793i | \(-0.671835\pi\) | ||||
−0.513996 | + | 0.857793i | \(0.671835\pi\) | |||||||
\(4\) | 6.87195e10 | 0.500000 | ||||||||
\(5\) | 3.81470e12 | 0.447214 | ||||||||
\(6\) | −1.80831e14 | −0.726900 | ||||||||
\(7\) | 3.29617e15 | 0.765060 | 0.382530 | − | 0.923943i | \(-0.375053\pi\) | ||||
0.382530 | + | 0.923943i | \(0.375053\pi\) | |||||||
\(8\) | 1.80144e16 | 0.353553 | ||||||||
\(9\) | 2.55614e16 | 0.0567672 | ||||||||
\(10\) | 1.00000e18 | 0.316228 | ||||||||
\(11\) | −1.36311e19 | −0.739205 | −0.369603 | − | 0.929190i | \(-0.620506\pi\) | ||||
−0.369603 | + | 0.929190i | \(0.620506\pi\) | |||||||
\(12\) | −4.74038e19 | −0.513996 | ||||||||
\(13\) | −1.75195e20 | −0.432085 | −0.216043 | − | 0.976384i | \(-0.569315\pi\) | ||||
−0.216043 | + | 0.976384i | \(0.569315\pi\) | |||||||
\(14\) | 8.64071e20 | 0.540979 | ||||||||
\(15\) | −2.63144e21 | −0.459732 | ||||||||
\(16\) | 4.72237e21 | 0.250000 | ||||||||
\(17\) | −8.98224e20 | −0.0154910 | −0.00774550 | − | 0.999970i | \(-0.502465\pi\) | ||||
−0.00774550 | + | 0.999970i | \(0.502465\pi\) | |||||||
\(18\) | 6.70076e21 | 0.0401405 | ||||||||
\(19\) | 1.81344e23 | 0.399542 | 0.199771 | − | 0.979843i | \(-0.435980\pi\) | ||||
0.199771 | + | 0.979843i | \(0.435980\pi\) | |||||||
\(20\) | 2.62144e23 | 0.223607 | ||||||||
\(21\) | −2.27375e24 | −0.786475 | ||||||||
\(22\) | −3.57330e24 | −0.522697 | ||||||||
\(23\) | −8.96395e24 | −0.576149 | −0.288074 | − | 0.957608i | \(-0.593015\pi\) | ||||
−0.288074 | + | 0.957608i | \(0.593015\pi\) | |||||||
\(24\) | −1.24266e25 | −0.363450 | ||||||||
\(25\) | 1.45519e25 | 0.200000 | ||||||||
\(26\) | −4.59263e25 | −0.305530 | ||||||||
\(27\) | 2.92980e26 | 0.969636 | ||||||||
\(28\) | 2.26511e26 | 0.382530 | ||||||||
\(29\) | 8.10751e26 | 0.715360 | 0.357680 | − | 0.933844i | \(-0.383568\pi\) | ||||
0.357680 | + | 0.933844i | \(0.383568\pi\) | |||||||
\(30\) | −6.89815e26 | −0.325080 | ||||||||
\(31\) | 1.17491e27 | 0.301865 | 0.150933 | − | 0.988544i | \(-0.451772\pi\) | ||||
0.150933 | + | 0.988544i | \(0.451772\pi\) | |||||||
\(32\) | 1.23794e27 | 0.176777 | ||||||||
\(33\) | 9.40292e27 | 0.759897 | ||||||||
\(34\) | −2.35464e26 | −0.0109538 | ||||||||
\(35\) | 1.25739e28 | 0.342145 | ||||||||
\(36\) | 1.75656e27 | 0.0283836 | ||||||||
\(37\) | 1.05137e29 | 1.02335 | 0.511673 | − | 0.859180i | \(-0.329026\pi\) | ||||
0.511673 | + | 0.859180i | \(0.329026\pi\) | |||||||
\(38\) | 4.75384e28 | 0.282519 | ||||||||
\(39\) | 1.20852e29 | 0.444180 | ||||||||
\(40\) | 6.87195e28 | 0.158114 | ||||||||
\(41\) | −7.89765e29 | −1.15079 | −0.575396 | − | 0.817875i | \(-0.695152\pi\) | ||||
−0.575396 | + | 0.817875i | \(0.695152\pi\) | |||||||
\(42\) | −5.96049e29 | −0.556122 | ||||||||
\(43\) | −2.46365e30 | −1.48735 | −0.743675 | − | 0.668541i | \(-0.766919\pi\) | ||||
−0.743675 | + | 0.668541i | \(0.766919\pi\) | |||||||
\(44\) | −9.36720e29 | −0.369603 | ||||||||
\(45\) | 9.75088e28 | 0.0253871 | ||||||||
\(46\) | −2.34985e30 | −0.407399 | ||||||||
\(47\) | −4.05145e30 | −0.471846 | −0.235923 | − | 0.971772i | \(-0.575811\pi\) | ||||
−0.235923 | + | 0.971772i | \(0.575811\pi\) | |||||||
\(48\) | −3.25756e30 | −0.256998 | ||||||||
\(49\) | −7.69740e30 | −0.414683 | ||||||||
\(50\) | 3.81470e30 | 0.141421 | ||||||||
\(51\) | 6.19609e29 | 0.0159246 | ||||||||
\(52\) | −1.20393e31 | −0.216043 | ||||||||
\(53\) | −7.63383e31 | −0.963027 | −0.481514 | − | 0.876439i | \(-0.659913\pi\) | ||||
−0.481514 | + | 0.876439i | \(0.659913\pi\) | |||||||
\(54\) | 7.68030e31 | 0.685636 | ||||||||
\(55\) | −5.19984e31 | −0.330583 | ||||||||
\(56\) | 5.93785e31 | 0.270490 | ||||||||
\(57\) | −1.25094e32 | −0.410726 | ||||||||
\(58\) | 2.12534e32 | 0.505836 | ||||||||
\(59\) | 5.16782e30 | 0.00896489 | 0.00448245 | − | 0.999990i | \(-0.498573\pi\) | ||||
0.00448245 | + | 0.999990i | \(0.498573\pi\) | |||||||
\(60\) | −1.80831e32 | −0.229866 | ||||||||
\(61\) | −3.70977e32 | −0.347332 | −0.173666 | − | 0.984805i | \(-0.555561\pi\) | ||||
−0.173666 | + | 0.984805i | \(0.555561\pi\) | |||||||
\(62\) | 3.07996e32 | 0.213451 | ||||||||
\(63\) | 8.42545e31 | 0.0434303 | ||||||||
\(64\) | 3.24519e32 | 0.125000 | ||||||||
\(65\) | −6.68315e32 | −0.193234 | ||||||||
\(66\) | 2.46492e33 | 0.537328 | ||||||||
\(67\) | −4.33067e33 | −0.714778 | −0.357389 | − | 0.933956i | \(-0.616333\pi\) | ||||
−0.357389 | + | 0.933956i | \(0.616333\pi\) | |||||||
\(68\) | −6.17255e31 | −0.00774550 | ||||||||
\(69\) | 6.18347e33 | 0.592276 | ||||||||
\(70\) | 3.29617e33 | 0.241933 | ||||||||
\(71\) | −5.77653e31 | −0.00326128 | −0.00163064 | − | 0.999999i | \(-0.500519\pi\) | ||||
−0.00163064 | + | 0.999999i | \(0.500519\pi\) | |||||||
\(72\) | 4.60472e32 | 0.0200702 | ||||||||
\(73\) | −2.08780e34 | −0.705043 | −0.352522 | − | 0.935804i | \(-0.614676\pi\) | ||||
−0.352522 | + | 0.935804i | \(0.614676\pi\) | |||||||
\(74\) | 2.75610e34 | 0.723615 | ||||||||
\(75\) | −1.00381e34 | −0.205598 | ||||||||
\(76\) | 1.24619e34 | 0.199771 | ||||||||
\(77\) | −4.49303e34 | −0.565536 | ||||||||
\(78\) | 3.16807e34 | 0.314083 | ||||||||
\(79\) | 1.43759e35 | 1.12599 | 0.562994 | − | 0.826461i | \(-0.309650\pi\) | ||||
0.562994 | + | 0.826461i | \(0.309650\pi\) | |||||||
\(80\) | 1.80144e34 | 0.111803 | ||||||||
\(81\) | −2.13612e35 | −1.05354 | ||||||||
\(82\) | −2.07032e35 | −0.813732 | ||||||||
\(83\) | −4.18848e35 | −1.31556 | −0.657782 | − | 0.753208i | \(-0.728505\pi\) | ||||
−0.657782 | + | 0.753208i | \(0.728505\pi\) | |||||||
\(84\) | −1.56251e35 | −0.393238 | ||||||||
\(85\) | −3.42645e33 | −0.00692779 | ||||||||
\(86\) | −6.45832e35 | −1.05172 | ||||||||
\(87\) | −5.59269e35 | −0.735384 | ||||||||
\(88\) | −2.45555e35 | −0.261349 | ||||||||
\(89\) | −8.24770e35 | −0.712226 | −0.356113 | − | 0.934443i | \(-0.615898\pi\) | ||||
−0.356113 | + | 0.934443i | \(0.615898\pi\) | |||||||
\(90\) | 2.55614e34 | 0.0179514 | ||||||||
\(91\) | −5.77472e35 | −0.330571 | ||||||||
\(92\) | −6.15998e35 | −0.288074 | ||||||||
\(93\) | −8.10471e35 | −0.310315 | ||||||||
\(94\) | −1.06206e36 | −0.333645 | ||||||||
\(95\) | 6.91774e35 | 0.178681 | ||||||||
\(96\) | −8.53950e35 | −0.181725 | ||||||||
\(97\) | 6.35165e36 | 1.11586 | 0.557930 | − | 0.829888i | \(-0.311596\pi\) | ||||
0.557930 | + | 0.829888i | \(0.311596\pi\) | |||||||
\(98\) | −2.01783e36 | −0.293225 | ||||||||
\(99\) | −3.48428e35 | −0.0419626 | ||||||||
\(100\) | 1.00000e36 | 0.100000 | ||||||||
\(101\) | −6.22694e36 | −0.518000 | −0.259000 | − | 0.965877i | \(-0.583393\pi\) | ||||
−0.259000 | + | 0.965877i | \(0.583393\pi\) | |||||||
\(102\) | 1.62427e35 | 0.0112604 | ||||||||
\(103\) | −2.97899e37 | −1.72417 | −0.862085 | − | 0.506764i | \(-0.830842\pi\) | ||||
−0.862085 | + | 0.506764i | \(0.830842\pi\) | |||||||
\(104\) | −3.15603e36 | −0.152765 | ||||||||
\(105\) | −8.67366e36 | −0.351723 | ||||||||
\(106\) | −2.00116e37 | −0.680963 | ||||||||
\(107\) | −5.21404e37 | −1.49133 | −0.745666 | − | 0.666320i | \(-0.767869\pi\) | ||||
−0.745666 | + | 0.666320i | \(0.767869\pi\) | |||||||
\(108\) | 2.01334e37 | 0.484818 | ||||||||
\(109\) | −6.52849e37 | −1.32563 | −0.662815 | − | 0.748783i | \(-0.730639\pi\) | ||||
−0.662815 | + | 0.748783i | \(0.730639\pi\) | |||||||
\(110\) | −1.36311e37 | −0.233757 | ||||||||
\(111\) | −7.25250e37 | −1.05199 | ||||||||
\(112\) | 1.55657e37 | 0.191265 | ||||||||
\(113\) | 2.53181e37 | 0.263925 | 0.131963 | − | 0.991255i | \(-0.457872\pi\) | ||||
0.131963 | + | 0.991255i | \(0.457872\pi\) | |||||||
\(114\) | −3.27927e37 | −0.290427 | ||||||||
\(115\) | −3.41948e37 | −0.257661 | ||||||||
\(116\) | 5.57144e37 | 0.357680 | ||||||||
\(117\) | −4.47822e36 | −0.0245283 | ||||||||
\(118\) | 1.35471e36 | 0.00633914 | ||||||||
\(119\) | −2.96070e36 | −0.0118515 | ||||||||
\(120\) | −4.74038e37 | −0.162540 | ||||||||
\(121\) | −1.54234e38 | −0.453576 | ||||||||
\(122\) | −9.72493e37 | −0.245601 | ||||||||
\(123\) | 5.44792e38 | 1.18300 | ||||||||
\(124\) | 8.07392e37 | 0.150933 | ||||||||
\(125\) | 5.55112e37 | 0.0894427 | ||||||||
\(126\) | 2.20868e37 | 0.0307099 | ||||||||
\(127\) | 6.80429e38 | 0.817361 | 0.408681 | − | 0.912678i | \(-0.365989\pi\) | ||||
0.408681 | + | 0.912678i | \(0.365989\pi\) | |||||||
\(128\) | 8.50706e37 | 0.0883883 | ||||||||
\(129\) | 1.69947e39 | 1.52898 | ||||||||
\(130\) | −1.75195e38 | −0.136637 | ||||||||
\(131\) | −1.33635e39 | −0.904487 | −0.452243 | − | 0.891895i | \(-0.649376\pi\) | ||||
−0.452243 | + | 0.891895i | \(0.649376\pi\) | |||||||
\(132\) | 6.46164e38 | 0.379948 | ||||||||
\(133\) | 5.97742e38 | 0.305674 | ||||||||
\(134\) | −1.13526e39 | −0.505424 | ||||||||
\(135\) | 1.11763e39 | 0.433634 | ||||||||
\(136\) | −1.61810e37 | −0.00547690 | ||||||||
\(137\) | 2.14881e39 | 0.635138 | 0.317569 | − | 0.948235i | \(-0.397134\pi\) | ||||
0.317569 | + | 0.948235i | \(0.397134\pi\) | |||||||
\(138\) | 1.62096e39 | 0.418802 | ||||||||
\(139\) | 6.21195e39 | 1.40428 | 0.702141 | − | 0.712038i | \(-0.252228\pi\) | ||||
0.702141 | + | 0.712038i | \(0.252228\pi\) | |||||||
\(140\) | 8.64071e38 | 0.171073 | ||||||||
\(141\) | 2.79475e39 | 0.485054 | ||||||||
\(142\) | −1.51428e37 | −0.00230607 | ||||||||
\(143\) | 2.38809e39 | 0.319400 | ||||||||
\(144\) | 1.20710e38 | 0.0141918 | ||||||||
\(145\) | 3.09277e39 | 0.319919 | ||||||||
\(146\) | −5.47304e39 | −0.498541 | ||||||||
\(147\) | 5.30978e39 | 0.426291 | ||||||||
\(148\) | 7.22494e39 | 0.511673 | ||||||||
\(149\) | −1.54514e40 | −0.966100 | −0.483050 | − | 0.875593i | \(-0.660471\pi\) | ||||
−0.483050 | + | 0.875593i | \(0.660471\pi\) | |||||||
\(150\) | −2.63144e39 | −0.145380 | ||||||||
\(151\) | −2.44879e40 | −1.19640 | −0.598202 | − | 0.801345i | \(-0.704118\pi\) | ||||
−0.598202 | + | 0.801345i | \(0.704118\pi\) | |||||||
\(152\) | 3.26681e39 | 0.141260 | ||||||||
\(153\) | −2.29598e37 | −0.000879381 0 | ||||||||
\(154\) | −1.17782e40 | −0.399895 | ||||||||
\(155\) | 4.48193e39 | 0.134998 | ||||||||
\(156\) | 8.30489e39 | 0.222090 | ||||||||
\(157\) | −5.93872e40 | −1.41107 | −0.705536 | − | 0.708674i | \(-0.749294\pi\) | ||||
−0.705536 | + | 0.708674i | \(0.749294\pi\) | |||||||
\(158\) | 3.76855e40 | 0.796193 | ||||||||
\(159\) | 5.26593e40 | 0.989984 | ||||||||
\(160\) | 4.72237e39 | 0.0790569 | ||||||||
\(161\) | −2.95467e40 | −0.440788 | ||||||||
\(162\) | −5.59971e40 | −0.744969 | ||||||||
\(163\) | 1.27298e41 | 1.51131 | 0.755653 | − | 0.654972i | \(-0.227320\pi\) | ||||
0.755653 | + | 0.654972i | \(0.227320\pi\) | |||||||
\(164\) | −5.42722e40 | −0.575396 | ||||||||
\(165\) | 3.58693e40 | 0.339836 | ||||||||
\(166\) | −1.09799e41 | −0.930245 | ||||||||
\(167\) | −1.13007e41 | −0.856742 | −0.428371 | − | 0.903603i | \(-0.640912\pi\) | ||||
−0.428371 | + | 0.903603i | \(0.640912\pi\) | |||||||
\(168\) | −4.09602e40 | −0.278061 | ||||||||
\(169\) | −1.33708e41 | −0.813302 | ||||||||
\(170\) | −8.98224e38 | −0.00489868 | ||||||||
\(171\) | 4.63541e39 | 0.0226809 | ||||||||
\(172\) | −1.69301e41 | −0.743675 | ||||||||
\(173\) | 2.46449e41 | 0.972464 | 0.486232 | − | 0.873830i | \(-0.338371\pi\) | ||||
0.486232 | + | 0.873830i | \(0.338371\pi\) | |||||||
\(174\) | −1.46609e41 | −0.519995 | ||||||||
\(175\) | 4.79655e40 | 0.153012 | ||||||||
\(176\) | −6.43709e40 | −0.184801 | ||||||||
\(177\) | −3.56484e39 | −0.00921584 | ||||||||
\(178\) | −2.16208e41 | −0.503620 | ||||||||
\(179\) | −1.68898e41 | −0.354685 | −0.177343 | − | 0.984149i | \(-0.556750\pi\) | ||||
−0.177343 | + | 0.984149i | \(0.556750\pi\) | |||||||
\(180\) | 6.70076e39 | 0.0126935 | ||||||||
\(181\) | −6.06854e41 | −1.03760 | −0.518801 | − | 0.854895i | \(-0.673621\pi\) | ||||
−0.518801 | + | 0.854895i | \(0.673621\pi\) | |||||||
\(182\) | −1.51381e41 | −0.233749 | ||||||||
\(183\) | 2.55905e41 | 0.357054 | ||||||||
\(184\) | −1.61480e41 | −0.203699 | ||||||||
\(185\) | 4.01065e41 | 0.457655 | ||||||||
\(186\) | −2.12460e41 | −0.219426 | ||||||||
\(187\) | 1.22437e40 | 0.0114510 | ||||||||
\(188\) | −2.78414e41 | −0.235923 | ||||||||
\(189\) | 9.65712e41 | 0.741829 | ||||||||
\(190\) | 1.81344e41 | 0.126346 | ||||||||
\(191\) | 1.09994e42 | 0.695429 | 0.347714 | − | 0.937600i | \(-0.386958\pi\) | ||||
0.347714 | + | 0.937600i | \(0.386958\pi\) | |||||||
\(192\) | −2.23858e41 | −0.128499 | ||||||||
\(193\) | 3.18819e42 | 1.66240 | 0.831198 | − | 0.555977i | \(-0.187656\pi\) | ||||
0.831198 | + | 0.555977i | \(0.187656\pi\) | |||||||
\(194\) | 1.66505e42 | 0.789032 | ||||||||
\(195\) | 4.61014e41 | 0.198643 | ||||||||
\(196\) | −5.28961e41 | −0.207342 | ||||||||
\(197\) | 2.35999e42 | 0.841948 | 0.420974 | − | 0.907073i | \(-0.361688\pi\) | ||||
0.420974 | + | 0.907073i | \(0.361688\pi\) | |||||||
\(198\) | −9.13384e40 | −0.0296720 | ||||||||
\(199\) | 5.36739e42 | 1.58848 | 0.794238 | − | 0.607606i | \(-0.207870\pi\) | ||||
0.794238 | + | 0.607606i | \(0.207870\pi\) | |||||||
\(200\) | 2.62144e41 | 0.0707107 | ||||||||
\(201\) | 2.98736e42 | 0.734786 | ||||||||
\(202\) | −1.63236e42 | −0.366281 | ||||||||
\(203\) | 2.67237e42 | 0.547293 | ||||||||
\(204\) | 4.25792e40 | 0.00796231 | ||||||||
\(205\) | −3.01271e42 | −0.514649 | ||||||||
\(206\) | −7.80924e42 | −1.21917 | ||||||||
\(207\) | −2.29131e41 | −0.0327063 | ||||||||
\(208\) | −8.27334e41 | −0.108021 | ||||||||
\(209\) | −2.47192e42 | −0.295344 | ||||||||
\(210\) | −2.27375e42 | −0.248705 | ||||||||
\(211\) | 6.79782e42 | 0.680996 | 0.340498 | − | 0.940245i | \(-0.389404\pi\) | ||||
0.340498 | + | 0.940245i | \(0.389404\pi\) | |||||||
\(212\) | −5.24592e42 | −0.481514 | ||||||||
\(213\) | 3.98474e40 | 0.00335257 | ||||||||
\(214\) | −1.36683e43 | −1.05453 | ||||||||
\(215\) | −9.39810e42 | −0.665163 | ||||||||
\(216\) | 5.27786e42 | 0.342818 | ||||||||
\(217\) | 3.87270e42 | 0.230945 | ||||||||
\(218\) | −1.71140e43 | −0.937363 | ||||||||
\(219\) | 1.44020e43 | 0.724778 | ||||||||
\(220\) | −3.57330e42 | −0.165291 | ||||||||
\(221\) | 1.57364e41 | 0.00669343 | ||||||||
\(222\) | −1.90120e43 | −0.743871 | ||||||||
\(223\) | −3.83398e42 | −0.138042 | −0.0690208 | − | 0.997615i | \(-0.521987\pi\) | ||||
−0.0690208 | + | 0.997615i | \(0.521987\pi\) | |||||||
\(224\) | 4.08046e42 | 0.135245 | ||||||||
\(225\) | 3.71967e41 | 0.0113534 | ||||||||
\(226\) | 6.63700e42 | 0.186623 | ||||||||
\(227\) | 1.43677e42 | 0.0372313 | 0.0186157 | − | 0.999827i | \(-0.494074\pi\) | ||||
0.0186157 | + | 0.999827i | \(0.494074\pi\) | |||||||
\(228\) | −8.59641e42 | −0.205363 | ||||||||
\(229\) | 2.80830e43 | 0.618710 | 0.309355 | − | 0.950947i | \(-0.399887\pi\) | ||||
0.309355 | + | 0.950947i | \(0.399887\pi\) | |||||||
\(230\) | −8.96395e42 | −0.182194 | ||||||||
\(231\) | 3.09936e43 | 0.581367 | ||||||||
\(232\) | 1.46052e43 | 0.252918 | ||||||||
\(233\) | −1.02012e44 | −1.63143 | −0.815716 | − | 0.578453i | \(-0.803657\pi\) | ||||
−0.815716 | + | 0.578453i | \(0.803657\pi\) | |||||||
\(234\) | −1.17394e42 | −0.0173441 | ||||||||
\(235\) | −1.54551e43 | −0.211016 | ||||||||
\(236\) | 3.55130e41 | 0.00448245 | ||||||||
\(237\) | −9.91671e43 | −1.15751 | ||||||||
\(238\) | −7.76129e41 | −0.00838031 | ||||||||
\(239\) | 1.19632e43 | 0.119532 | 0.0597661 | − | 0.998212i | \(-0.480965\pi\) | ||||
0.0597661 | + | 0.998212i | \(0.480965\pi\) | |||||||
\(240\) | −1.24266e43 | −0.114933 | ||||||||
\(241\) | −2.33793e43 | −0.200224 | −0.100112 | − | 0.994976i | \(-0.531920\pi\) | ||||
−0.100112 | + | 0.994976i | \(0.531920\pi\) | |||||||
\(242\) | −4.04314e43 | −0.320726 | ||||||||
\(243\) | 1.54287e43 | 0.113400 | ||||||||
\(244\) | −2.54933e43 | −0.173666 | ||||||||
\(245\) | −2.93632e43 | −0.185452 | ||||||||
\(246\) | 1.42814e44 | 0.836510 | ||||||||
\(247\) | −3.17706e43 | −0.172636 | ||||||||
\(248\) | 2.11653e43 | 0.106726 | ||||||||
\(249\) | 2.88928e44 | 1.35239 | ||||||||
\(250\) | 1.45519e43 | 0.0632456 | ||||||||
\(251\) | 1.57065e44 | 0.634040 | 0.317020 | − | 0.948419i | \(-0.397318\pi\) | ||||
0.317020 | + | 0.948419i | \(0.397318\pi\) | |||||||
\(252\) | 5.78993e42 | 0.0217152 | ||||||||
\(253\) | 1.22188e44 | 0.425892 | ||||||||
\(254\) | 1.78370e44 | 0.577962 | ||||||||
\(255\) | 2.36362e42 | 0.00712171 | ||||||||
\(256\) | 2.23007e43 | 0.0625000 | ||||||||
\(257\) | −6.40421e44 | −1.66995 | −0.834973 | − | 0.550291i | \(-0.814517\pi\) | ||||
−0.834973 | + | 0.550291i | \(0.814517\pi\) | |||||||
\(258\) | 4.45505e44 | 1.08116 | ||||||||
\(259\) | 3.46548e44 | 0.782922 | ||||||||
\(260\) | −4.59263e43 | −0.0966172 | ||||||||
\(261\) | 2.07239e43 | 0.0406090 | ||||||||
\(262\) | −3.50317e44 | −0.639569 | ||||||||
\(263\) | 6.42820e44 | 1.09372 | 0.546862 | − | 0.837223i | \(-0.315822\pi\) | ||||
0.546862 | + | 0.837223i | \(0.315822\pi\) | |||||||
\(264\) | 1.69388e44 | 0.268664 | ||||||||
\(265\) | −2.91207e44 | −0.430679 | ||||||||
\(266\) | 1.56694e44 | 0.216144 | ||||||||
\(267\) | 5.68939e44 | 0.732162 | ||||||||
\(268\) | −2.97601e44 | −0.357389 | ||||||||
\(269\) | −4.52122e44 | −0.506803 | −0.253401 | − | 0.967361i | \(-0.581549\pi\) | ||||
−0.253401 | + | 0.967361i | \(0.581549\pi\) | |||||||
\(270\) | 2.92980e44 | 0.306626 | ||||||||
\(271\) | −5.63666e44 | −0.550922 | −0.275461 | − | 0.961312i | \(-0.588830\pi\) | ||||
−0.275461 | + | 0.961312i | \(0.588830\pi\) | |||||||
\(272\) | −4.24174e42 | −0.00387275 | ||||||||
\(273\) | 3.98349e44 | 0.339824 | ||||||||
\(274\) | 5.63298e44 | 0.449110 | ||||||||
\(275\) | −1.98358e44 | −0.147841 | ||||||||
\(276\) | 4.24925e44 | 0.296138 | ||||||||
\(277\) | −8.72981e44 | −0.569022 | −0.284511 | − | 0.958673i | \(-0.591831\pi\) | ||||
−0.284511 | + | 0.958673i | \(0.591831\pi\) | |||||||
\(278\) | 1.62843e45 | 0.992977 | ||||||||
\(279\) | 3.00323e43 | 0.0171361 | ||||||||
\(280\) | 2.26511e44 | 0.120967 | ||||||||
\(281\) | −3.74401e45 | −1.87184 | −0.935922 | − | 0.352206i | \(-0.885432\pi\) | ||||
−0.935922 | + | 0.352206i | \(0.885432\pi\) | |||||||
\(282\) | 7.32628e44 | 0.342985 | ||||||||
\(283\) | 1.09059e45 | 0.478204 | 0.239102 | − | 0.970994i | \(-0.423147\pi\) | ||||
0.239102 | + | 0.970994i | \(0.423147\pi\) | |||||||
\(284\) | −3.96960e42 | −0.00163064 | ||||||||
\(285\) | −4.77197e44 | −0.183682 | ||||||||
\(286\) | 6.26024e44 | 0.225850 | ||||||||
\(287\) | −2.60320e45 | −0.880424 | ||||||||
\(288\) | 3.16434e43 | 0.0100351 | ||||||||
\(289\) | −3.36129e45 | −0.999760 | ||||||||
\(290\) | 8.10751e44 | 0.226217 | ||||||||
\(291\) | −4.38147e45 | −1.14709 | ||||||||
\(292\) | −1.43472e45 | −0.352522 | ||||||||
\(293\) | −1.50027e45 | −0.346033 | −0.173017 | − | 0.984919i | \(-0.555351\pi\) | ||||
−0.173017 | + | 0.984919i | \(0.555351\pi\) | |||||||
\(294\) | 1.39193e45 | 0.301433 | ||||||||
\(295\) | 1.97137e43 | 0.00400922 | ||||||||
\(296\) | 1.89398e45 | 0.361808 | ||||||||
\(297\) | −3.99363e45 | −0.716760 | ||||||||
\(298\) | −4.05049e45 | −0.683136 | ||||||||
\(299\) | 1.57044e45 | 0.248945 | ||||||||
\(300\) | −6.89815e44 | −0.102799 | ||||||||
\(301\) | −8.12062e45 | −1.13791 | ||||||||
\(302\) | −6.41936e45 | −0.845986 | ||||||||
\(303\) | 4.29544e45 | 0.532500 | ||||||||
\(304\) | 8.56375e44 | 0.0998856 | ||||||||
\(305\) | −1.41516e45 | −0.155332 | ||||||||
\(306\) | −6.01878e42 | −0.000621816 0 | ||||||||
\(307\) | 8.88941e45 | 0.864595 | 0.432298 | − | 0.901731i | \(-0.357703\pi\) | ||||
0.432298 | + | 0.901731i | \(0.357703\pi\) | |||||||
\(308\) | −3.08758e45 | −0.282768 | ||||||||
\(309\) | 2.05495e46 | 1.77243 | ||||||||
\(310\) | 1.17491e45 | 0.0954582 | ||||||||
\(311\) | 1.86301e46 | 1.42609 | 0.713045 | − | 0.701118i | \(-0.247316\pi\) | ||||
0.713045 | + | 0.701118i | \(0.247316\pi\) | |||||||
\(312\) | 2.17708e45 | 0.157041 | ||||||||
\(313\) | −1.03471e46 | −0.703476 | −0.351738 | − | 0.936098i | \(-0.614409\pi\) | ||||
−0.351738 | + | 0.936098i | \(0.614409\pi\) | |||||||
\(314\) | −1.55680e46 | −0.997779 | ||||||||
\(315\) | 3.21405e44 | 0.0194226 | ||||||||
\(316\) | 9.87903e45 | 0.562994 | ||||||||
\(317\) | 3.08721e46 | 1.65947 | 0.829736 | − | 0.558157i | \(-0.188491\pi\) | ||||
0.829736 | + | 0.558157i | \(0.188491\pi\) | |||||||
\(318\) | 1.38043e46 | 0.700025 | ||||||||
\(319\) | −1.10514e46 | −0.528798 | ||||||||
\(320\) | 1.23794e45 | 0.0559017 | ||||||||
\(321\) | 3.59672e46 | 1.53308 | ||||||||
\(322\) | −7.74549e45 | −0.311684 | ||||||||
\(323\) | −1.62888e44 | −0.00618931 | ||||||||
\(324\) | −1.46793e46 | −0.526772 | ||||||||
\(325\) | −2.54942e45 | −0.0864170 | ||||||||
\(326\) | 3.33705e46 | 1.06865 | ||||||||
\(327\) | 4.50345e46 | 1.36274 | ||||||||
\(328\) | −1.42271e46 | −0.406866 | ||||||||
\(329\) | −1.33543e46 | −0.360990 | ||||||||
\(330\) | 9.40292e45 | 0.240301 | ||||||||
\(331\) | −3.83499e46 | −0.926716 | −0.463358 | − | 0.886171i | \(-0.653356\pi\) | ||||
−0.463358 | + | 0.886171i | \(0.653356\pi\) | |||||||
\(332\) | −2.87830e46 | −0.657782 | ||||||||
\(333\) | 2.68744e45 | 0.0580925 | ||||||||
\(334\) | −2.96241e46 | −0.605808 | ||||||||
\(335\) | −1.65202e46 | −0.319658 | ||||||||
\(336\) | −1.07375e46 | −0.196619 | ||||||||
\(337\) | 3.97446e46 | 0.688850 | 0.344425 | − | 0.938814i | \(-0.388074\pi\) | ||||
0.344425 | + | 0.938814i | \(0.388074\pi\) | |||||||
\(338\) | −3.50506e46 | −0.575092 | ||||||||
\(339\) | −1.74648e46 | −0.271313 | ||||||||
\(340\) | −2.35464e44 | −0.00346389 | ||||||||
\(341\) | −1.60153e46 | −0.223141 | ||||||||
\(342\) | 1.21514e45 | 0.0160378 | ||||||||
\(343\) | −8.65557e46 | −1.08232 | ||||||||
\(344\) | −4.43813e46 | −0.525858 | ||||||||
\(345\) | 2.35881e46 | 0.264874 | ||||||||
\(346\) | 6.46050e46 | 0.687636 | ||||||||
\(347\) | 1.01071e47 | 1.01983 | 0.509917 | − | 0.860223i | \(-0.329676\pi\) | ||||
0.509917 | + | 0.860223i | \(0.329676\pi\) | |||||||
\(348\) | −3.84326e46 | −0.367692 | ||||||||
\(349\) | 6.03446e46 | 0.547480 | 0.273740 | − | 0.961804i | \(-0.411739\pi\) | ||||
0.273740 | + | 0.961804i | \(0.411739\pi\) | |||||||
\(350\) | 1.25739e46 | 0.108196 | ||||||||
\(351\) | −5.13286e46 | −0.418965 | ||||||||
\(352\) | −1.68744e46 | −0.130674 | ||||||||
\(353\) | 6.49991e46 | 0.477612 | 0.238806 | − | 0.971067i | \(-0.423244\pi\) | ||||
0.238806 | + | 0.971067i | \(0.423244\pi\) | |||||||
\(354\) | −9.34502e44 | −0.00651658 | ||||||||
\(355\) | −2.20357e44 | −0.00145849 | ||||||||
\(356\) | −5.66777e46 | −0.356113 | ||||||||
\(357\) | 2.04233e45 | 0.0121833 | ||||||||
\(358\) | −4.42756e46 | −0.250801 | ||||||||
\(359\) | −1.34716e47 | −0.724724 | −0.362362 | − | 0.932038i | \(-0.618030\pi\) | ||||
−0.362362 | + | 0.932038i | \(0.618030\pi\) | |||||||
\(360\) | 1.75656e45 | 0.00897568 | ||||||||
\(361\) | −1.73122e47 | −0.840366 | ||||||||
\(362\) | −1.59083e47 | −0.733695 | ||||||||
\(363\) | 1.06393e47 | 0.466272 | ||||||||
\(364\) | −3.96835e46 | −0.165286 | ||||||||
\(365\) | −7.96432e46 | −0.315305 | ||||||||
\(366\) | 6.70841e46 | 0.252476 | ||||||||
\(367\) | 1.76042e47 | 0.629934 | 0.314967 | − | 0.949103i | \(-0.398007\pi\) | ||||
0.314967 | + | 0.949103i | \(0.398007\pi\) | |||||||
\(368\) | −4.23311e46 | −0.144037 | ||||||||
\(369\) | −2.01875e46 | −0.0653272 | ||||||||
\(370\) | 1.05137e47 | 0.323611 | ||||||||
\(371\) | −2.51624e47 | −0.736774 | ||||||||
\(372\) | −5.56952e46 | −0.155158 | ||||||||
\(373\) | 3.37762e47 | 0.895359 | 0.447679 | − | 0.894194i | \(-0.352251\pi\) | ||||
0.447679 | + | 0.894194i | \(0.352251\pi\) | |||||||
\(374\) | 3.20962e45 | 0.00809710 | ||||||||
\(375\) | −3.82924e46 | −0.0919464 | ||||||||
\(376\) | −7.29844e46 | −0.166823 | ||||||||
\(377\) | −1.42039e47 | −0.309096 | ||||||||
\(378\) | 2.53156e47 | 0.524553 | ||||||||
\(379\) | −6.92554e47 | −1.36656 | −0.683279 | − | 0.730157i | \(-0.739447\pi\) | ||||
−0.683279 | + | 0.730157i | \(0.739447\pi\) | |||||||
\(380\) | 4.75384e46 | 0.0893404 | ||||||||
\(381\) | −4.69370e47 | −0.840240 | ||||||||
\(382\) | 2.88343e47 | 0.491743 | ||||||||
\(383\) | 2.21003e47 | 0.359105 | 0.179553 | − | 0.983748i | \(-0.442535\pi\) | ||||
0.179553 | + | 0.983748i | \(0.442535\pi\) | |||||||
\(384\) | −5.86830e46 | −0.0908625 | ||||||||
\(385\) | −1.71395e47 | −0.252916 | ||||||||
\(386\) | 8.35765e47 | 1.17549 | ||||||||
\(387\) | −6.29743e46 | −0.0844327 | ||||||||
\(388\) | 4.36482e47 | 0.557930 | ||||||||
\(389\) | 3.20256e47 | 0.390328 | 0.195164 | − | 0.980771i | \(-0.437476\pi\) | ||||
0.195164 | + | 0.980771i | \(0.437476\pi\) | |||||||
\(390\) | 1.20852e47 | 0.140462 | ||||||||
\(391\) | 8.05163e45 | 0.00892512 | ||||||||
\(392\) | −1.38664e47 | −0.146613 | ||||||||
\(393\) | 9.21837e47 | 0.929805 | ||||||||
\(394\) | 6.18657e47 | 0.595347 | ||||||||
\(395\) | 5.48396e47 | 0.503557 | ||||||||
\(396\) | −2.39438e46 | −0.0209813 | ||||||||
\(397\) | 2.55758e47 | 0.213897 | 0.106948 | − | 0.994265i | \(-0.465892\pi\) | ||||
0.106948 | + | 0.994265i | \(0.465892\pi\) | |||||||
\(398\) | 1.40703e48 | 1.12322 | ||||||||
\(399\) | −4.12331e47 | −0.314230 | ||||||||
\(400\) | 6.87195e46 | 0.0500000 | ||||||||
\(401\) | 2.29575e48 | 1.59498 | 0.797488 | − | 0.603334i | \(-0.206161\pi\) | ||||
0.797488 | + | 0.603334i | \(0.206161\pi\) | |||||||
\(402\) | 7.83119e47 | 0.519572 | ||||||||
\(403\) | −2.05838e47 | −0.130432 | ||||||||
\(404\) | −4.27912e47 | −0.259000 | ||||||||
\(405\) | −8.14865e47 | −0.471160 | ||||||||
\(406\) | 7.00546e47 | 0.386995 | ||||||||
\(407\) | −1.43313e48 | −0.756463 | ||||||||
\(408\) | 1.11619e46 | 0.00563020 | ||||||||
\(409\) | −1.23961e48 | −0.597592 | −0.298796 | − | 0.954317i | \(-0.596585\pi\) | ||||
−0.298796 | + | 0.954317i | \(0.596585\pi\) | |||||||
\(410\) | −7.89765e47 | −0.363912 | ||||||||
\(411\) | −1.48228e48 | −0.652916 | ||||||||
\(412\) | −2.04714e48 | −0.862085 | ||||||||
\(413\) | 1.70340e46 | 0.00685868 | ||||||||
\(414\) | −6.00652e46 | −0.0231269 | ||||||||
\(415\) | −1.59778e48 | −0.588338 | ||||||||
\(416\) | −2.16881e47 | −0.0763826 | ||||||||
\(417\) | −4.28510e48 | −1.44359 | ||||||||
\(418\) | −6.47998e47 | −0.208840 | ||||||||
\(419\) | 3.37300e48 | 1.04006 | 0.520029 | − | 0.854149i | \(-0.325921\pi\) | ||||
0.520029 | + | 0.854149i | \(0.325921\pi\) | |||||||
\(420\) | −5.96049e47 | −0.175861 | ||||||||
\(421\) | 2.03580e48 | 0.574798 | 0.287399 | − | 0.957811i | \(-0.407209\pi\) | ||||
0.287399 | + | 0.957811i | \(0.407209\pi\) | |||||||
\(422\) | 1.78201e48 | 0.481537 | ||||||||
\(423\) | −1.03561e47 | −0.0267854 | ||||||||
\(424\) | −1.37519e48 | −0.340482 | ||||||||
\(425\) | −1.30709e46 | −0.00309820 | ||||||||
\(426\) | 1.04458e46 | 0.00237062 | ||||||||
\(427\) | −1.22280e48 | −0.265730 | ||||||||
\(428\) | −3.58306e48 | −0.745666 | ||||||||
\(429\) | −1.64734e48 | −0.328340 | ||||||||
\(430\) | −2.46365e48 | −0.470342 | ||||||||
\(431\) | 6.24281e48 | 1.14170 | 0.570848 | − | 0.821056i | \(-0.306615\pi\) | ||||
0.570848 | + | 0.821056i | \(0.306615\pi\) | |||||||
\(432\) | 1.38356e48 | 0.242409 | ||||||||
\(433\) | −4.71991e48 | −0.792333 | −0.396166 | − | 0.918179i | \(-0.629660\pi\) | ||||
−0.396166 | + | 0.918179i | \(0.629660\pi\) | |||||||
\(434\) | 1.01521e48 | 0.163303 | ||||||||
\(435\) | −2.13344e48 | −0.328874 | ||||||||
\(436\) | −4.48635e48 | −0.662815 | ||||||||
\(437\) | −1.62556e48 | −0.230196 | ||||||||
\(438\) | 3.77539e48 | 0.512496 | ||||||||
\(439\) | −7.57651e48 | −0.985997 | −0.492999 | − | 0.870030i | \(-0.664099\pi\) | ||||
−0.492999 | + | 0.870030i | \(0.664099\pi\) | |||||||
\(440\) | −9.36720e47 | −0.116879 | ||||||||
\(441\) | −1.96756e47 | −0.0235404 | ||||||||
\(442\) | 4.12521e46 | 0.00473297 | ||||||||
\(443\) | 8.83812e48 | 0.972503 | 0.486252 | − | 0.873819i | \(-0.338364\pi\) | ||||
0.486252 | + | 0.873819i | \(0.338364\pi\) | |||||||
\(444\) | −4.98388e48 | −0.525996 | ||||||||
\(445\) | −3.14625e48 | −0.318517 | ||||||||
\(446\) | −1.00505e48 | −0.0976101 | ||||||||
\(447\) | 1.06586e49 | 0.993143 | ||||||||
\(448\) | 1.06967e48 | 0.0956325 | ||||||||
\(449\) | −2.01986e49 | −1.73286 | −0.866429 | − | 0.499300i | \(-0.833590\pi\) | ||||
−0.866429 | + | 0.499300i | \(0.833590\pi\) | |||||||
\(450\) | 9.75088e46 | 0.00802809 | ||||||||
\(451\) | 1.07653e49 | 0.850671 | ||||||||
\(452\) | 1.73985e48 | 0.131963 | ||||||||
\(453\) | 1.68921e49 | 1.22989 | ||||||||
\(454\) | 3.76640e47 | 0.0263265 | ||||||||
\(455\) | −2.20288e48 | −0.147836 | ||||||||
\(456\) | −2.25350e48 | −0.145214 | ||||||||
\(457\) | 6.61916e48 | 0.409594 | 0.204797 | − | 0.978804i | \(-0.434347\pi\) | ||||
0.204797 | + | 0.978804i | \(0.434347\pi\) | |||||||
\(458\) | 7.36180e48 | 0.437494 | ||||||||
\(459\) | −2.63162e47 | −0.0150206 | ||||||||
\(460\) | −2.34985e48 | −0.128831 | ||||||||
\(461\) | 2.46377e49 | 1.29758 | 0.648788 | − | 0.760969i | \(-0.275276\pi\) | ||||
0.648788 | + | 0.760969i | \(0.275276\pi\) | |||||||
\(462\) | 8.12478e48 | 0.411088 | ||||||||
\(463\) | 3.33469e49 | 1.62109 | 0.810546 | − | 0.585675i | \(-0.199171\pi\) | ||||
0.810546 | + | 0.585675i | \(0.199171\pi\) | |||||||
\(464\) | 3.82866e48 | 0.178840 | ||||||||
\(465\) | −3.09170e48 | −0.138777 | ||||||||
\(466\) | −2.67420e49 | −1.15360 | ||||||||
\(467\) | 9.90311e48 | 0.410591 | 0.205295 | − | 0.978700i | \(-0.434184\pi\) | ||||
0.205295 | + | 0.978700i | \(0.434184\pi\) | |||||||
\(468\) | −3.07741e47 | −0.0122641 | ||||||||
\(469\) | −1.42746e49 | −0.546848 | ||||||||
\(470\) | −4.05145e48 | −0.149211 | ||||||||
\(471\) | 4.09662e49 | 1.45057 | ||||||||
\(472\) | 9.30952e46 | 0.00316957 | ||||||||
\(473\) | 3.35822e49 | 1.09946 | ||||||||
\(474\) | −2.59961e49 | −0.818480 | ||||||||
\(475\) | 2.63891e48 | 0.0799084 | ||||||||
\(476\) | −2.03457e47 | −0.00592577 | ||||||||
\(477\) | −1.95131e48 | −0.0546684 | ||||||||
\(478\) | 3.13607e48 | 0.0845221 | ||||||||
\(479\) | −3.54457e49 | −0.919086 | −0.459543 | − | 0.888156i | \(-0.651987\pi\) | ||||
−0.459543 | + | 0.888156i | \(0.651987\pi\) | |||||||
\(480\) | −3.25756e48 | −0.0812699 | ||||||||
\(481\) | −1.84194e49 | −0.442173 | ||||||||
\(482\) | −6.12874e48 | −0.141580 | ||||||||
\(483\) | 2.03818e49 | 0.453127 | ||||||||
\(484\) | −1.05989e49 | −0.226788 | ||||||||
\(485\) | 2.42296e49 | 0.499028 | ||||||||
\(486\) | 4.04453e48 | 0.0801857 | ||||||||
\(487\) | −5.61975e49 | −1.07258 | −0.536292 | − | 0.844032i | \(-0.680175\pi\) | ||||
−0.536292 | + | 0.844032i | \(0.680175\pi\) | |||||||
\(488\) | −6.68292e48 | −0.122800 | ||||||||
\(489\) | −8.78124e49 | −1.55361 | ||||||||
\(490\) | −7.69740e48 | −0.131134 | ||||||||
\(491\) | −6.73087e49 | −1.10424 | −0.552120 | − | 0.833764i | \(-0.686181\pi\) | ||||
−0.552120 | + | 0.833764i | \(0.686181\pi\) | |||||||
\(492\) | 3.74378e49 | 0.591502 | ||||||||
\(493\) | −7.28236e47 | −0.0110816 | ||||||||
\(494\) | −8.32848e48 | −0.122072 | ||||||||
\(495\) | −1.32915e48 | −0.0187662 | ||||||||
\(496\) | 5.54836e48 | 0.0754664 | ||||||||
\(497\) | −1.90404e47 | −0.00249507 | ||||||||
\(498\) | 7.57408e49 | 0.956284 | ||||||||
\(499\) | −1.57170e50 | −1.91209 | −0.956045 | − | 0.293221i | \(-0.905273\pi\) | ||||
−0.956045 | + | 0.293221i | \(0.905273\pi\) | |||||||
\(500\) | 3.81470e48 | 0.0447214 | ||||||||
\(501\) | 7.79539e49 | 0.880724 | ||||||||
\(502\) | 4.11738e49 | 0.448334 | ||||||||
\(503\) | 8.33167e49 | 0.874429 | 0.437214 | − | 0.899357i | \(-0.355965\pi\) | ||||
0.437214 | + | 0.899357i | \(0.355965\pi\) | |||||||
\(504\) | 1.51779e48 | 0.0153549 | ||||||||
\(505\) | −2.37539e49 | −0.231657 | ||||||||
\(506\) | 3.20309e49 | 0.301151 | ||||||||
\(507\) | 9.22336e49 | 0.836068 | ||||||||
\(508\) | 4.67587e49 | 0.408681 | ||||||||
\(509\) | −1.50351e50 | −1.26715 | −0.633575 | − | 0.773682i | \(-0.718413\pi\) | ||||
−0.633575 | + | 0.773682i | \(0.718413\pi\) | |||||||
\(510\) | 6.19609e47 | 0.00503581 | ||||||||
\(511\) | −6.88173e49 | −0.539400 | ||||||||
\(512\) | 5.84601e48 | 0.0441942 | ||||||||
\(513\) | 5.31303e49 | 0.387410 | ||||||||
\(514\) | −1.67882e50 | −1.18083 | ||||||||
\(515\) | −1.13639e50 | −0.771072 | ||||||||
\(516\) | 1.16786e50 | 0.764492 | ||||||||
\(517\) | 5.52256e49 | 0.348791 | ||||||||
\(518\) | 9.08456e49 | 0.553609 | ||||||||
\(519\) | −1.70004e50 | −0.999685 | ||||||||
\(520\) | −1.20393e49 | −0.0683187 | ||||||||
\(521\) | 5.18958e49 | 0.284207 | 0.142103 | − | 0.989852i | \(-0.454613\pi\) | ||||
0.142103 | + | 0.989852i | \(0.454613\pi\) | |||||||
\(522\) | 5.43264e48 | 0.0287149 | ||||||||
\(523\) | −1.48076e50 | −0.755445 | −0.377723 | − | 0.925919i | \(-0.623293\pi\) | ||||
−0.377723 | + | 0.925919i | \(0.623293\pi\) | |||||||
\(524\) | −9.18335e49 | −0.452243 | ||||||||
\(525\) | −3.30874e49 | −0.157295 | ||||||||
\(526\) | 1.68511e50 | 0.773380 | ||||||||
\(527\) | −1.05533e48 | −0.00467620 | ||||||||
\(528\) | 4.44040e49 | 0.189974 | ||||||||
\(529\) | −1.61711e50 | −0.668053 | ||||||||
\(530\) | −7.63383e49 | −0.304536 | ||||||||
\(531\) | 1.32096e47 | 0.000508912 0 | ||||||||
\(532\) | 4.10765e49 | 0.152837 | ||||||||
\(533\) | 1.38363e50 | 0.497240 | ||||||||
\(534\) | 1.49144e50 | 0.517717 | ||||||||
\(535\) | −1.98900e50 | −0.666944 | ||||||||
\(536\) | −7.80144e49 | −0.252712 | ||||||||
\(537\) | 1.16508e50 | 0.364614 | ||||||||
\(538\) | −1.18521e50 | −0.358364 | ||||||||
\(539\) | 1.04924e50 | 0.306536 | ||||||||
\(540\) | 7.68030e49 | 0.216817 | ||||||||
\(541\) | 5.01469e50 | 1.36803 | 0.684013 | − | 0.729470i | \(-0.260233\pi\) | ||||
0.684013 | + | 0.729470i | \(0.260233\pi\) | |||||||
\(542\) | −1.47762e50 | −0.389561 | ||||||||
\(543\) | 4.18617e50 | 1.06665 | ||||||||
\(544\) | −1.11195e48 | −0.00273845 | ||||||||
\(545\) | −2.49042e50 | −0.592840 | ||||||||
\(546\) | 1.04425e50 | 0.240292 | ||||||||
\(547\) | 4.97650e50 | 1.10703 | 0.553513 | − | 0.832840i | \(-0.313287\pi\) | ||||
0.553513 | + | 0.832840i | \(0.313287\pi\) | |||||||
\(548\) | 1.47665e50 | 0.317569 | ||||||||
\(549\) | −9.48266e48 | −0.0197171 | ||||||||
\(550\) | −5.19984e49 | −0.104539 | ||||||||
\(551\) | 1.47025e50 | 0.285816 | ||||||||
\(552\) | 1.11392e50 | 0.209401 | ||||||||
\(553\) | 4.73853e50 | 0.861448 | ||||||||
\(554\) | −2.28847e50 | −0.402359 | ||||||||
\(555\) | −2.76661e50 | −0.470465 | ||||||||
\(556\) | 4.26882e50 | 0.702141 | ||||||||
\(557\) | 6.67759e49 | 0.106243 | 0.0531213 | − | 0.998588i | \(-0.483083\pi\) | ||||
0.0531213 | + | 0.998588i | \(0.483083\pi\) | |||||||
\(558\) | 7.87279e48 | 0.0121170 | ||||||||
\(559\) | 4.31620e50 | 0.642662 | ||||||||
\(560\) | 5.93785e49 | 0.0855363 | ||||||||
\(561\) | −8.44592e48 | −0.0117716 | ||||||||
\(562\) | −9.81469e50 | −1.32359 | ||||||||
\(563\) | 1.01553e51 | 1.32522 | 0.662610 | − | 0.748964i | \(-0.269449\pi\) | ||||
0.662610 | + | 0.748964i | \(0.269449\pi\) | |||||||
\(564\) | 1.92054e50 | 0.242527 | ||||||||
\(565\) | 9.65810e49 | 0.118031 | ||||||||
\(566\) | 2.85892e50 | 0.338142 | ||||||||
\(567\) | −7.04101e50 | −0.806025 | ||||||||
\(568\) | −1.04061e48 | −0.00115304 | ||||||||
\(569\) | −4.88120e50 | −0.523540 | −0.261770 | − | 0.965130i | \(-0.584306\pi\) | ||||
−0.261770 | + | 0.965130i | \(0.584306\pi\) | |||||||
\(570\) | −1.25094e50 | −0.129883 | ||||||||
\(571\) | −6.10676e49 | −0.0613822 | −0.0306911 | − | 0.999529i | \(-0.509771\pi\) | ||||
−0.0306911 | + | 0.999529i | \(0.509771\pi\) | |||||||
\(572\) | 1.64108e50 | 0.159700 | ||||||||
\(573\) | −7.58757e50 | −0.714895 | ||||||||
\(574\) | −6.82413e50 | −0.622554 | ||||||||
\(575\) | −1.30443e50 | −0.115230 | ||||||||
\(576\) | 8.29513e48 | 0.00709590 | ||||||||
\(577\) | −5.54304e50 | −0.459193 | −0.229597 | − | 0.973286i | \(-0.573741\pi\) | ||||
−0.229597 | + | 0.973286i | \(0.573741\pi\) | |||||||
\(578\) | −8.81142e50 | −0.706937 | ||||||||
\(579\) | −2.19926e51 | −1.70893 | ||||||||
\(580\) | 2.12534e50 | 0.159959 | ||||||||
\(581\) | −1.38059e51 | −1.00649 | ||||||||
\(582\) | −1.14858e51 | −0.811118 | ||||||||
\(583\) | 1.04057e51 | 0.711875 | ||||||||
\(584\) | −3.76104e50 | −0.249270 | ||||||||
\(585\) | −1.70830e49 | −0.0109694 | ||||||||
\(586\) | −3.93286e50 | −0.244682 | ||||||||
\(587\) | 7.00286e50 | 0.422154 | 0.211077 | − | 0.977469i | \(-0.432303\pi\) | ||||
0.211077 | + | 0.977469i | \(0.432303\pi\) | |||||||
\(588\) | 3.64885e50 | 0.213145 | ||||||||
\(589\) | 2.13064e50 | 0.120608 | ||||||||
\(590\) | 5.16782e48 | 0.00283495 | ||||||||
\(591\) | −1.62796e51 | −0.865515 | ||||||||
\(592\) | 4.96494e50 | 0.255837 | ||||||||
\(593\) | 3.03179e51 | 1.51421 | 0.757106 | − | 0.653292i | \(-0.226613\pi\) | ||||
0.757106 | + | 0.653292i | \(0.226613\pi\) | |||||||
\(594\) | −1.04691e51 | −0.506826 | ||||||||
\(595\) | −1.12942e49 | −0.00530017 | ||||||||
\(596\) | −1.06181e51 | −0.483050 | ||||||||
\(597\) | −3.70251e51 | −1.63294 | ||||||||
\(598\) | 4.11681e50 | 0.176031 | ||||||||
\(599\) | 3.37693e51 | 1.39999 | 0.699997 | − | 0.714145i | \(-0.253184\pi\) | ||||
0.699997 | + | 0.714145i | \(0.253184\pi\) | |||||||
\(600\) | −1.80831e50 | −0.0726900 | ||||||||
\(601\) | 3.37420e51 | 1.31521 | 0.657603 | − | 0.753365i | \(-0.271571\pi\) | ||||
0.657603 | + | 0.753365i | \(0.271571\pi\) | |||||||
\(602\) | −2.12877e51 | −0.804626 | ||||||||
\(603\) | −1.10698e50 | −0.0405759 | ||||||||
\(604\) | −1.68280e51 | −0.598202 | ||||||||
\(605\) | −5.88355e50 | −0.202845 | ||||||||
\(606\) | 1.12602e51 | 0.376534 | ||||||||
\(607\) | 5.86428e51 | 1.90206 | 0.951029 | − | 0.309101i | \(-0.100028\pi\) | ||||
0.951029 | + | 0.309101i | \(0.100028\pi\) | |||||||
\(608\) | 2.24494e50 | 0.0706298 | ||||||||
\(609\) | −1.84344e51 | −0.562613 | ||||||||
\(610\) | −3.70977e50 | −0.109836 | ||||||||
\(611\) | 7.09793e50 | 0.203878 | ||||||||
\(612\) | −1.57779e48 | −0.000439690 0 | ||||||||
\(613\) | −6.86486e50 | −0.185615 | −0.0928075 | − | 0.995684i | \(-0.529584\pi\) | ||||
−0.0928075 | + | 0.995684i | \(0.529584\pi\) | |||||||
\(614\) | 2.33031e51 | 0.611361 | ||||||||
\(615\) | 2.07822e51 | 0.529055 | ||||||||
\(616\) | −8.09392e50 | −0.199947 | ||||||||
\(617\) | −2.90878e51 | −0.697326 | −0.348663 | − | 0.937248i | \(-0.613364\pi\) | ||||
−0.348663 | + | 0.937248i | \(0.613364\pi\) | |||||||
\(618\) | 5.38693e51 | 1.25330 | ||||||||
\(619\) | 4.53284e51 | 1.02351 | 0.511756 | − | 0.859131i | \(-0.328995\pi\) | ||||
0.511756 | + | 0.859131i | \(0.328995\pi\) | |||||||
\(620\) | 3.07996e50 | 0.0674992 | ||||||||
\(621\) | −2.62626e51 | −0.558654 | ||||||||
\(622\) | 4.88376e51 | 1.00840 | ||||||||
\(623\) | −2.71858e51 | −0.544895 | ||||||||
\(624\) | 5.70708e50 | 0.111045 | ||||||||
\(625\) | 2.11758e50 | 0.0400000 | ||||||||
\(626\) | −2.71244e51 | −0.497433 | ||||||||
\(627\) | 1.70517e51 | 0.303611 | ||||||||
\(628\) | −4.08106e51 | −0.705536 | ||||||||
\(629\) | −9.44363e49 | −0.0158527 | ||||||||
\(630\) | 8.42545e49 | 0.0137339 | ||||||||
\(631\) | −4.30708e50 | −0.0681772 | −0.0340886 | − | 0.999419i | \(-0.510853\pi\) | ||||
−0.0340886 | + | 0.999419i | \(0.510853\pi\) | |||||||
\(632\) | 2.58973e51 | 0.398097 | ||||||||
\(633\) | −4.68924e51 | −0.700058 | ||||||||
\(634\) | 8.09293e51 | 1.17342 | ||||||||
\(635\) | 2.59563e51 | 0.365535 | ||||||||
\(636\) | 3.61872e51 | 0.494992 | ||||||||
\(637\) | 1.34854e51 | 0.179178 | ||||||||
\(638\) | −2.89706e51 | −0.373916 | ||||||||
\(639\) | −1.47656e48 | −0.000185133 0 | ||||||||
\(640\) | 3.24519e50 | 0.0395285 | ||||||||
\(641\) | −3.95135e51 | −0.467597 | −0.233799 | − | 0.972285i | \(-0.575116\pi\) | ||||
−0.233799 | + | 0.972285i | \(0.575116\pi\) | |||||||
\(642\) | 9.42860e51 | 1.08405 | ||||||||
\(643\) | −1.17106e52 | −1.30821 | −0.654103 | − | 0.756406i | \(-0.726954\pi\) | ||||
−0.654103 | + | 0.756406i | \(0.726954\pi\) | |||||||
\(644\) | −2.03043e51 | −0.220394 | ||||||||
\(645\) | 6.48295e51 | 0.683783 | ||||||||
\(646\) | −4.27001e49 | −0.00437650 | ||||||||
\(647\) | 2.47032e51 | 0.246051 | 0.123025 | − | 0.992404i | \(-0.460740\pi\) | ||||
0.123025 | + | 0.992404i | \(0.460740\pi\) | |||||||
\(648\) | −3.84809e51 | −0.372484 | ||||||||
\(649\) | −7.04429e49 | −0.00662690 | ||||||||
\(650\) | −6.68315e50 | −0.0611061 | ||||||||
\(651\) | −2.67145e51 | −0.237410 | ||||||||
\(652\) | 8.74788e51 | 0.755653 | ||||||||
\(653\) | −1.97344e52 | −1.65703 | −0.828513 | − | 0.559970i | \(-0.810812\pi\) | ||||
−0.828513 | + | 0.559970i | \(0.810812\pi\) | |||||||
\(654\) | 1.18055e52 | 0.963601 | ||||||||
\(655\) | −5.09778e51 | −0.404499 | ||||||||
\(656\) | −3.72956e51 | −0.287698 | ||||||||
\(657\) | −5.33669e50 | −0.0400233 | ||||||||
\(658\) | −3.50074e51 | −0.255259 | ||||||||
\(659\) | −1.00529e52 | −0.712711 | −0.356355 | − | 0.934351i | \(-0.615981\pi\) | ||||
−0.356355 | + | 0.934351i | \(0.615981\pi\) | |||||||
\(660\) | 2.46492e51 | 0.169918 | ||||||||
\(661\) | 1.30458e52 | 0.874468 | 0.437234 | − | 0.899348i | \(-0.355958\pi\) | ||||
0.437234 | + | 0.899348i | \(0.355958\pi\) | |||||||
\(662\) | −1.00532e52 | −0.655287 | ||||||||
\(663\) | −1.08552e50 | −0.00688079 | ||||||||
\(664\) | −7.54530e51 | −0.465122 | ||||||||
\(665\) | 2.28020e51 | 0.136701 | ||||||||
\(666\) | 7.04496e50 | 0.0410776 | ||||||||
\(667\) | −7.26753e51 | −0.412154 | ||||||||
\(668\) | −7.76577e51 | −0.428371 | ||||||||
\(669\) | 2.64474e51 | 0.141906 | ||||||||
\(670\) | −4.33067e51 | −0.226033 | ||||||||
\(671\) | 5.05681e51 | 0.256750 | ||||||||
\(672\) | −2.81476e51 | −0.139031 | ||||||||
\(673\) | −2.06557e52 | −0.992570 | −0.496285 | − | 0.868160i | \(-0.665303\pi\) | ||||
−0.496285 | + | 0.868160i | \(0.665303\pi\) | |||||||
\(674\) | 1.04188e52 | 0.487091 | ||||||||
\(675\) | 4.26342e51 | 0.193927 | ||||||||
\(676\) | −9.18832e51 | −0.406651 | ||||||||
\(677\) | −1.48357e52 | −0.638876 | −0.319438 | − | 0.947607i | \(-0.603494\pi\) | ||||
−0.319438 | + | 0.947607i | \(0.603494\pi\) | |||||||
\(678\) | −4.57830e51 | −0.191847 | ||||||||
\(679\) | 2.09361e52 | 0.853700 | ||||||||
\(680\) | −6.17255e49 | −0.00244934 | ||||||||
\(681\) | −9.91105e50 | −0.0382735 | ||||||||
\(682\) | −4.19831e51 | −0.157784 | ||||||||
\(683\) | −1.63537e51 | −0.0598183 | −0.0299092 | − | 0.999553i | \(-0.509522\pi\) | ||||
−0.0299092 | + | 0.999553i | \(0.509522\pi\) | |||||||
\(684\) | 3.18543e50 | 0.0113404 | ||||||||
\(685\) | 8.19706e51 | 0.284042 | ||||||||
\(686\) | −2.26901e52 | −0.765314 | ||||||||
\(687\) | −1.93721e52 | −0.636029 | ||||||||
\(688\) | −1.16343e52 | −0.371838 | ||||||||
\(689\) | 1.33741e52 | 0.416110 | ||||||||
\(690\) | 6.18347e51 | 0.187294 | ||||||||
\(691\) | −2.87913e51 | −0.0849018 | −0.0424509 | − | 0.999099i | \(-0.513517\pi\) | ||||
−0.0424509 | + | 0.999099i | \(0.513517\pi\) | |||||||
\(692\) | 1.69358e52 | 0.486232 | ||||||||
\(693\) | −1.14848e51 | −0.0321039 | ||||||||
\(694\) | 2.64951e52 | 0.721132 | ||||||||
\(695\) | 2.36967e52 | 0.628014 | ||||||||
\(696\) | −1.00749e52 | −0.259998 | ||||||||
\(697\) | 7.09386e50 | 0.0178269 | ||||||||
\(698\) | 1.58190e52 | 0.387127 | ||||||||
\(699\) | 7.03698e52 | 1.67710 | ||||||||
\(700\) | 3.29617e51 | 0.0765060 | ||||||||
\(701\) | −4.36552e52 | −0.986852 | −0.493426 | − | 0.869788i | \(-0.664256\pi\) | ||||
−0.493426 | + | 0.869788i | \(0.664256\pi\) | |||||||
\(702\) | −1.34555e52 | −0.296253 | ||||||||
\(703\) | 1.90660e52 | 0.408870 | ||||||||
\(704\) | −4.42353e51 | −0.0924007 | ||||||||
\(705\) | 1.06611e52 | 0.216923 | ||||||||
\(706\) | 1.70391e52 | 0.337723 | ||||||||
\(707\) | −2.05251e52 | −0.396301 | ||||||||
\(708\) | −2.44974e50 | −0.00460792 | ||||||||
\(709\) | 6.12553e52 | 1.12251 | 0.561253 | − | 0.827645i | \(-0.310320\pi\) | ||||
0.561253 | + | 0.827645i | \(0.310320\pi\) | |||||||
\(710\) | −5.77653e49 | −0.00103131 | ||||||||
\(711\) | 3.67467e51 | 0.0639191 | ||||||||
\(712\) | −1.48577e52 | −0.251810 | ||||||||
\(713\) | −1.05318e52 | −0.173919 | ||||||||
\(714\) | 5.35385e50 | 0.00861489 | ||||||||
\(715\) | 9.10985e51 | 0.142840 | ||||||||
\(716\) | −1.16066e52 | −0.177343 | ||||||||
\(717\) | −8.25238e51 | −0.122878 | ||||||||
\(718\) | −3.53150e52 | −0.512457 | ||||||||
\(719\) | 6.31848e52 | 0.893569 | 0.446784 | − | 0.894642i | \(-0.352569\pi\) | ||||
0.446784 | + | 0.894642i | \(0.352569\pi\) | |||||||
\(720\) | 4.60472e50 | 0.00634677 | ||||||||
\(721\) | −9.81924e52 | −1.31909 | ||||||||
\(722\) | −4.53828e52 | −0.594228 | ||||||||
\(723\) | 1.61274e52 | 0.205829 | ||||||||
\(724\) | −4.17027e52 | −0.518801 | ||||||||
\(725\) | 1.17980e52 | 0.143072 | ||||||||
\(726\) | 2.78902e52 | 0.329704 | ||||||||
\(727\) | 5.46946e52 | 0.630316 | 0.315158 | − | 0.949039i | \(-0.397943\pi\) | ||||
0.315158 | + | 0.949039i | \(0.397943\pi\) | |||||||
\(728\) | −1.04028e52 | −0.116875 | ||||||||
\(729\) | 8.55432e52 | 0.936971 | ||||||||
\(730\) | −2.08780e52 | −0.222954 | ||||||||
\(731\) | 2.21291e51 | 0.0230405 | ||||||||
\(732\) | 1.75857e52 | 0.178527 | ||||||||
\(733\) | 3.01068e52 | 0.298017 | 0.149008 | − | 0.988836i | \(-0.452392\pi\) | ||||
0.149008 | + | 0.988836i | \(0.452392\pi\) | |||||||
\(734\) | 4.61485e52 | 0.445431 | ||||||||
\(735\) | 2.02552e52 | 0.190643 | ||||||||
\(736\) | −1.10968e52 | −0.101850 | ||||||||
\(737\) | 5.90316e52 | 0.528367 | ||||||||
\(738\) | −5.29202e51 | −0.0461933 | ||||||||
\(739\) | 1.55405e53 | 1.32295 | 0.661476 | − | 0.749967i | \(-0.269930\pi\) | ||||
0.661476 | + | 0.749967i | \(0.269930\pi\) | |||||||
\(740\) | 2.75610e52 | 0.228827 | ||||||||
\(741\) | 2.19159e52 | 0.177469 | ||||||||
\(742\) | −6.59616e52 | −0.520978 | ||||||||
\(743\) | 1.58003e53 | 1.21723 | 0.608613 | − | 0.793467i | \(-0.291726\pi\) | ||||
0.608613 | + | 0.793467i | \(0.291726\pi\) | |||||||
\(744\) | −1.46002e52 | −0.109713 | ||||||||
\(745\) | −5.89424e52 | −0.432053 | ||||||||
\(746\) | 8.85422e52 | 0.633114 | ||||||||
\(747\) | −1.07063e52 | −0.0746809 | ||||||||
\(748\) | 8.41384e50 | 0.00572551 | ||||||||
\(749\) | −1.71863e53 | −1.14096 | ||||||||
\(750\) | −1.00381e52 | −0.0650159 | ||||||||
\(751\) | −7.41700e52 | −0.468694 | −0.234347 | − | 0.972153i | \(-0.575295\pi\) | ||||
−0.234347 | + | 0.972153i | \(0.575295\pi\) | |||||||
\(752\) | −1.91324e52 | −0.117961 | ||||||||
\(753\) | −1.08346e53 | −0.651788 | ||||||||
\(754\) | −3.72348e52 | −0.218564 | ||||||||
\(755\) | −9.34139e52 | −0.535048 | ||||||||
\(756\) | 6.63632e52 | 0.370915 | ||||||||
\(757\) | −2.14270e53 | −1.16866 | −0.584329 | − | 0.811517i | \(-0.698642\pi\) | ||||
−0.584329 | + | 0.811517i | \(0.698642\pi\) | |||||||
\(758\) | −1.81549e53 | −0.966303 | ||||||||
\(759\) | −8.42873e52 | −0.437814 | ||||||||
\(760\) | 1.24619e52 | 0.0631732 | ||||||||
\(761\) | −4.02061e53 | −1.98919 | −0.994594 | − | 0.103844i | \(-0.966886\pi\) | ||||
−0.994594 | + | 0.103844i | \(0.966886\pi\) | |||||||
\(762\) | −1.23043e53 | −0.594140 | ||||||||
\(763\) | −2.15190e53 | −1.01419 | ||||||||
\(764\) | 7.55875e52 | 0.347714 | ||||||||
\(765\) | −8.75847e49 | −0.000393271 0 | ||||||||
\(766\) | 5.79347e52 | 0.253926 | ||||||||
\(767\) | −9.05375e50 | −0.00387360 | ||||||||
\(768\) | −1.53834e52 | −0.0642495 | ||||||||
\(769\) | −1.75938e53 | −0.717335 | −0.358667 | − | 0.933465i | \(-0.616769\pi\) | ||||
−0.358667 | + | 0.933465i | \(0.616769\pi\) | |||||||
\(770\) | −4.49303e52 | −0.178838 | ||||||||
\(771\) | 4.41772e53 | 1.71669 | ||||||||
\(772\) | 2.19091e53 | 0.831198 | ||||||||
\(773\) | −2.25368e53 | −0.834781 | −0.417390 | − | 0.908727i | \(-0.637055\pi\) | ||||
−0.417390 | + | 0.908727i | \(0.637055\pi\) | |||||||
\(774\) | −1.65083e52 | −0.0597029 | ||||||||
\(775\) | 1.70972e52 | 0.0603731 | ||||||||
\(776\) | 1.14421e53 | 0.394516 | ||||||||
\(777\) | −2.39054e53 | −0.804837 | ||||||||
\(778\) | 8.39531e52 | 0.276003 | ||||||||
\(779\) | −1.43219e53 | −0.459790 | ||||||||
\(780\) | 3.16807e52 | 0.0993217 | ||||||||
\(781\) | 7.87402e50 | 0.00241075 | ||||||||
\(782\) | 2.11069e51 | 0.00631101 | ||||||||
\(783\) | 2.37534e53 | 0.693638 | ||||||||
\(784\) | −3.63499e52 | −0.103671 | ||||||||
\(785\) | −2.26544e53 | −0.631051 | ||||||||
\(786\) | 2.41654e53 | 0.657471 | ||||||||
\(787\) | 5.34066e53 | 1.41926 | 0.709631 | − | 0.704574i | \(-0.248862\pi\) | ||||
0.709631 | + | 0.704574i | \(0.248862\pi\) | |||||||
\(788\) | 1.62177e53 | 0.420974 | ||||||||
\(789\) | −4.43427e53 | −1.12434 | ||||||||
\(790\) | 1.43759e53 | 0.356068 | ||||||||
\(791\) | 8.34528e52 | 0.201918 | ||||||||
\(792\) | −6.27673e51 | −0.0148360 | ||||||||
\(793\) | 6.49932e52 | 0.150077 | ||||||||
\(794\) | 6.70453e52 | 0.151248 | ||||||||
\(795\) | 2.00879e53 | 0.442734 | ||||||||
\(796\) | 3.68844e53 | 0.794238 | ||||||||
\(797\) | 6.52917e53 | 1.37366 | 0.686830 | − | 0.726818i | \(-0.259002\pi\) | ||||
0.686830 | + | 0.726818i | \(0.259002\pi\) | |||||||
\(798\) | −1.08090e53 | −0.222194 | ||||||||
\(799\) | 3.63911e51 | 0.00730937 | ||||||||
\(800\) | 1.80144e52 | 0.0353553 | ||||||||
\(801\) | −2.10822e52 | −0.0404311 | ||||||||
\(802\) | 6.01818e53 | 1.12782 | ||||||||
\(803\) | 2.84589e53 | 0.521171 | ||||||||
\(804\) | 2.05290e53 | 0.367393 | ||||||||
\(805\) | −1.12712e53 | −0.197127 | ||||||||
\(806\) | −5.39593e52 | −0.0922291 | ||||||||
\(807\) | 3.11881e53 | 0.520989 | ||||||||
\(808\) | −1.12175e53 | −0.183141 | ||||||||
\(809\) | −5.66679e53 | −0.904252 | −0.452126 | − | 0.891954i | \(-0.649334\pi\) | ||||
−0.452126 | + | 0.891954i | \(0.649334\pi\) | |||||||
\(810\) | −2.13612e53 | −0.333160 | ||||||||
\(811\) | 4.52502e53 | 0.689818 | 0.344909 | − | 0.938636i | \(-0.387910\pi\) | ||||
0.344909 | + | 0.938636i | \(0.387910\pi\) | |||||||
\(812\) | 1.83644e53 | 0.273647 | ||||||||
\(813\) | 3.88826e53 | 0.566343 | ||||||||
\(814\) | −3.75685e53 | −0.534900 | ||||||||
\(815\) | 4.85605e53 | 0.675877 | ||||||||
\(816\) | 2.92602e51 | 0.00398116 | ||||||||
\(817\) | −4.46770e53 | −0.594259 | ||||||||
\(818\) | −3.24957e53 | −0.422561 | ||||||||
\(819\) | −1.47610e52 | −0.0187656 | ||||||||
\(820\) | −2.07032e53 | −0.257325 | ||||||||
\(821\) | −1.11490e54 | −1.35484 | −0.677419 | − | 0.735597i | \(-0.736902\pi\) | ||||
−0.677419 | + | 0.735597i | \(0.736902\pi\) | |||||||
\(822\) | −3.88572e53 | −0.461681 | ||||||||
\(823\) | 1.69605e54 | 1.97034 | 0.985171 | − | 0.171575i | \(-0.0548855\pi\) | ||||
0.985171 | + | 0.171575i | \(0.0548855\pi\) | |||||||
\(824\) | −5.36647e53 | −0.609586 | ||||||||
\(825\) | 1.36830e53 | 0.151979 | ||||||||
\(826\) | 4.46536e51 | 0.00484982 | ||||||||
\(827\) | −4.68182e53 | −0.497236 | −0.248618 | − | 0.968602i | \(-0.579976\pi\) | ||||
−0.248618 | + | 0.968602i | \(0.579976\pi\) | |||||||
\(828\) | −1.57457e52 | −0.0163532 | ||||||||
\(829\) | −6.57785e53 | −0.668075 | −0.334037 | − | 0.942560i | \(-0.608411\pi\) | ||||
−0.334037 | + | 0.942560i | \(0.608411\pi\) | |||||||
\(830\) | −4.18848e53 | −0.416018 | ||||||||
\(831\) | 6.02196e53 | 0.584950 | ||||||||
\(832\) | −5.68540e52 | −0.0540106 | ||||||||
\(833\) | 6.91398e51 | 0.00642386 | ||||||||
\(834\) | −1.12331e54 | −1.02077 | ||||||||
\(835\) | −4.31087e53 | −0.383147 | ||||||||
\(836\) | −1.69869e53 | −0.147672 | ||||||||
\(837\) | 3.44225e53 | 0.292700 | ||||||||
\(838\) | 8.84213e53 | 0.735432 | ||||||||
\(839\) | −1.37838e54 | −1.12143 | −0.560714 | − | 0.828009i | \(-0.689473\pi\) | ||||
−0.560714 | + | 0.828009i | \(0.689473\pi\) | |||||||
\(840\) | −1.56251e53 | −0.124353 | ||||||||
\(841\) | −6.27159e53 | −0.488260 | ||||||||
\(842\) | 5.33672e53 | 0.406444 | ||||||||
\(843\) | 2.58267e54 | 1.92424 | ||||||||
\(844\) | 4.67143e53 | 0.340498 | ||||||||
\(845\) | −5.10054e53 | −0.363720 | ||||||||
\(846\) | −2.71478e52 | −0.0189401 | ||||||||
\(847\) | −5.08380e53 | −0.347013 | ||||||||
\(848\) | −3.60497e53 | −0.240757 | ||||||||
\(849\) | −7.52308e53 | −0.491590 | ||||||||
\(850\) | −3.42645e51 | −0.00219076 | ||||||||
\(851\) | −9.42441e53 | −0.589600 | ||||||||
\(852\) | 2.73829e51 | 0.00167628 | ||||||||
\(853\) | 3.21106e54 | 1.92350 | 0.961748 | − | 0.273937i | \(-0.0883260\pi\) | ||||
0.961748 | + | 0.273937i | \(0.0883260\pi\) | |||||||
\(854\) | −3.20550e53 | −0.187899 | ||||||||
\(855\) | 1.76827e52 | 0.0101432 | ||||||||
\(856\) | −9.39278e53 | −0.527265 | ||||||||
\(857\) | −3.02093e54 | −1.65957 | −0.829784 | − | 0.558085i | \(-0.811536\pi\) | ||||
−0.829784 | + | 0.558085i | \(0.811536\pi\) | |||||||
\(858\) | −4.31841e53 | −0.232172 | ||||||||
\(859\) | −1.03473e54 | −0.544444 | −0.272222 | − | 0.962235i | \(-0.587758\pi\) | ||||
−0.272222 | + | 0.962235i | \(0.587758\pi\) | |||||||
\(860\) | −6.45832e53 | −0.332582 | ||||||||
\(861\) | 1.79573e54 | 0.905069 | ||||||||
\(862\) | 1.63651e54 | 0.807301 | ||||||||
\(863\) | −2.58733e54 | −1.24926 | −0.624629 | − | 0.780921i | \(-0.714750\pi\) | ||||
−0.624629 | + | 0.780921i | \(0.714750\pi\) | |||||||
\(864\) | 3.62692e53 | 0.171409 | ||||||||
\(865\) | 9.40127e53 | 0.434899 | ||||||||
\(866\) | −1.23730e54 | −0.560264 | ||||||||
\(867\) | 2.31867e54 | 1.02775 | ||||||||
\(868\) | 2.66130e53 | 0.115473 | ||||||||
\(869\) | −1.95959e54 | −0.832336 | ||||||||
\(870\) | −5.59269e53 | −0.232549 | ||||||||
\(871\) | 7.58711e53 | 0.308845 | ||||||||
\(872\) | −1.17607e54 | −0.468681 | ||||||||
\(873\) | 1.62357e53 | 0.0633442 | ||||||||
\(874\) | −4.26132e53 | −0.162773 | ||||||||
\(875\) | 1.82974e53 | 0.0684291 | ||||||||
\(876\) | 9.89695e53 | 0.362389 | ||||||||
\(877\) | −1.33643e54 | −0.479132 | −0.239566 | − | 0.970880i | \(-0.577005\pi\) | ||||
−0.239566 | + | 0.970880i | \(0.577005\pi\) | |||||||
\(878\) | −1.98614e54 | −0.697205 | ||||||||
\(879\) | 1.03491e54 | 0.355719 | ||||||||
\(880\) | −2.45555e53 | −0.0826457 | ||||||||
\(881\) | 1.19179e54 | 0.392776 | 0.196388 | − | 0.980526i | \(-0.437079\pi\) | ||||
0.196388 | + | 0.980526i | \(0.437079\pi\) | |||||||
\(882\) | −5.15784e52 | −0.0166456 | ||||||||
\(883\) | 2.32196e54 | 0.733805 | 0.366903 | − | 0.930259i | \(-0.380418\pi\) | ||||
0.366903 | + | 0.930259i | \(0.380418\pi\) | |||||||
\(884\) | 1.08140e52 | 0.00334672 | ||||||||
\(885\) | −1.35988e52 | −0.00412145 | ||||||||
\(886\) | 2.31686e54 | 0.687664 | ||||||||
\(887\) | −2.27100e54 | −0.660131 | −0.330065 | − | 0.943958i | \(-0.607071\pi\) | ||||
−0.330065 | + | 0.943958i | \(0.607071\pi\) | |||||||
\(888\) | −1.30649e54 | −0.371935 | ||||||||
\(889\) | 2.24281e54 | 0.625330 | ||||||||
\(890\) | −8.24770e53 | −0.225226 | ||||||||
\(891\) | 2.91176e54 | 0.778786 | ||||||||
\(892\) | −2.63469e53 | −0.0690208 | ||||||||
\(893\) | −7.34708e53 | −0.188522 | ||||||||
\(894\) | 2.79409e54 | 0.702258 | ||||||||
\(895\) | −6.44295e53 | −0.158620 | ||||||||
\(896\) | 2.80407e53 | 0.0676224 | ||||||||
\(897\) | −1.08331e54 | −0.255914 | ||||||||
\(898\) | −5.29493e54 | −1.22532 | ||||||||
\(899\) | 9.52560e53 | 0.215942 | ||||||||
\(900\) | 2.55614e52 | 0.00567672 | ||||||||
\(901\) | 6.85688e52 | 0.0149183 | ||||||||
\(902\) | 2.82207e54 | 0.601515 | ||||||||
\(903\) | 5.60173e54 | 1.16976 | ||||||||
\(904\) | 4.56091e53 | 0.0933116 | ||||||||
\(905\) | −2.31497e54 | −0.464030 | ||||||||
\(906\) | 4.42817e54 | 0.869666 | ||||||||
\(907\) | 9.99936e53 | 0.192414 | 0.0962072 | − | 0.995361i | \(-0.469329\pi\) | ||||
0.0962072 | + | 0.995361i | \(0.469329\pi\) | |||||||
\(908\) | 9.87340e52 | 0.0186157 | ||||||||
\(909\) | −1.59169e53 | −0.0294054 | ||||||||
\(910\) | −5.77472e53 | −0.104536 | ||||||||
\(911\) | 8.26172e52 | 0.0146548 | 0.00732741 | − | 0.999973i | \(-0.497668\pi\) | ||||
0.00732741 | + | 0.999973i | \(0.497668\pi\) | |||||||
\(912\) | −5.90741e53 | −0.102682 | ||||||||
\(913\) | 5.70935e54 | 0.972472 | ||||||||
\(914\) | 1.73517e54 | 0.289627 | ||||||||
\(915\) | 9.76202e53 | 0.159680 | ||||||||
\(916\) | 1.92985e54 | 0.309355 | ||||||||
\(917\) | −4.40484e54 | −0.691987 | ||||||||
\(918\) | −6.89863e52 | −0.0106212 | ||||||||
\(919\) | 5.97032e54 | 0.900867 | 0.450433 | − | 0.892810i | \(-0.351269\pi\) | ||||
0.450433 | + | 0.892810i | \(0.351269\pi\) | |||||||
\(920\) | −6.15998e53 | −0.0910971 | ||||||||
\(921\) | −6.13205e54 | −0.888797 | ||||||||
\(922\) | 6.45862e54 | 0.917524 | ||||||||
\(923\) | 1.01202e52 | 0.00140915 | ||||||||
\(924\) | 2.12986e54 | 0.290683 | ||||||||
\(925\) | 1.52994e54 | 0.204669 | ||||||||
\(926\) | 8.74170e54 | 1.14628 | ||||||||
\(927\) | −7.61470e53 | −0.0978763 | ||||||||
\(928\) | 1.00366e54 | 0.126459 | ||||||||
\(929\) | −1.17859e55 | −1.45571 | −0.727853 | − | 0.685734i | \(-0.759482\pi\) | ||||
−0.727853 | + | 0.685734i | \(0.759482\pi\) | |||||||
\(930\) | −8.10471e53 | −0.0981303 | ||||||||
\(931\) | −1.39588e54 | −0.165683 | ||||||||
\(932\) | −7.01025e54 | −0.815716 | ||||||||
\(933\) | −1.28513e55 | −1.46601 | ||||||||
\(934\) | 2.59604e54 | 0.290332 | ||||||||
\(935\) | 4.67062e52 | 0.00512106 | ||||||||
\(936\) | −8.06724e52 | −0.00867205 | ||||||||
\(937\) | −1.35568e54 | −0.142881 | −0.0714405 | − | 0.997445i | \(-0.522760\pi\) | ||||
−0.0714405 | + | 0.997445i | \(0.522760\pi\) | |||||||
\(938\) | −3.74200e54 | −0.386680 | ||||||||
\(939\) | 7.13761e54 | 0.723168 | ||||||||
\(940\) | −1.06206e54 | −0.105508 | ||||||||
\(941\) | −1.66103e55 | −1.61796 | −0.808981 | − | 0.587835i | \(-0.799980\pi\) | ||||
−0.808981 | + | 0.587835i | \(0.799980\pi\) | |||||||
\(942\) | 1.07390e55 | 1.02571 | ||||||||
\(943\) | 7.07941e54 | 0.663027 | ||||||||
\(944\) | 2.44043e52 | 0.00224122 | ||||||||
\(945\) | 3.68390e54 | 0.331756 | ||||||||
\(946\) | 8.80338e54 | 0.777434 | ||||||||
\(947\) | −5.07081e54 | −0.439139 | −0.219570 | − | 0.975597i | \(-0.570465\pi\) | ||||
−0.219570 | + | 0.975597i | \(0.570465\pi\) | |||||||
\(948\) | −6.81471e54 | −0.578753 | ||||||||
\(949\) | 3.65772e54 | 0.304639 | ||||||||
\(950\) | 6.91774e53 | 0.0565038 | ||||||||
\(951\) | −2.12960e55 | −1.70592 | ||||||||
\(952\) | −5.33352e52 | −0.00419015 | ||||||||
\(953\) | −1.58180e55 | −1.21880 | −0.609401 | − | 0.792862i | \(-0.708590\pi\) | ||||
−0.609401 | + | 0.792862i | \(0.708590\pi\) | |||||||
\(954\) | −5.11524e53 | −0.0386564 | ||||||||
\(955\) | 4.19595e54 | 0.311005 | ||||||||
\(956\) | 8.22103e53 | 0.0597661 | ||||||||
\(957\) | 7.62342e54 | 0.543600 | ||||||||
\(958\) | −9.29187e54 | −0.649892 | ||||||||
\(959\) | 7.08284e54 | 0.485918 | ||||||||
\(960\) | −8.53950e53 | −0.0574665 | ||||||||
\(961\) | −1.37685e55 | −0.908877 | ||||||||
\(962\) | −4.82854e54 | −0.312663 | ||||||||
\(963\) | −1.33278e54 | −0.0846587 | ||||||||
\(964\) | −1.60661e54 | −0.100112 | ||||||||
\(965\) | 1.21620e55 | 0.743446 | ||||||||
\(966\) | 5.34296e54 | 0.320409 | ||||||||
\(967\) | 1.47153e55 | 0.865724 | 0.432862 | − | 0.901460i | \(-0.357504\pi\) | ||||
0.432862 | + | 0.901460i | \(0.357504\pi\) | |||||||
\(968\) | −2.77843e54 | −0.160363 | ||||||||
\(969\) | 1.12363e53 | 0.00636256 | ||||||||
\(970\) | 6.35165e54 | 0.352866 | ||||||||
\(971\) | −3.18652e55 | −1.73684 | −0.868422 | − | 0.495825i | \(-0.834866\pi\) | ||||
−0.868422 | + | 0.495825i | \(0.834866\pi\) | |||||||
\(972\) | 1.06025e54 | 0.0566999 | ||||||||
\(973\) | 2.04756e55 | 1.07436 | ||||||||
\(974\) | −1.47318e55 | −0.758432 | ||||||||
\(975\) | 1.75863e54 | 0.0888360 | ||||||||
\(976\) | −1.75189e54 | −0.0868330 | ||||||||
\(977\) | −1.74536e55 | −0.848857 | −0.424428 | − | 0.905462i | \(-0.639525\pi\) | ||||
−0.424428 | + | 0.905462i | \(0.639525\pi\) | |||||||
\(978\) | −2.30195e55 | −1.09857 | ||||||||
\(979\) | 1.12425e55 | 0.526481 | ||||||||
\(980\) | −2.01783e54 | −0.0927260 | ||||||||
\(981\) | −1.66877e54 | −0.0752523 | ||||||||
\(982\) | −1.76446e55 | −0.780816 | ||||||||
\(983\) | −7.48657e54 | −0.325119 | −0.162560 | − | 0.986699i | \(-0.551975\pi\) | ||||
−0.162560 | + | 0.986699i | \(0.551975\pi\) | |||||||
\(984\) | 9.81410e54 | 0.418255 | ||||||||
\(985\) | 9.00265e54 | 0.376530 | ||||||||
\(986\) | −1.90903e53 | −0.00783590 | ||||||||
\(987\) | 9.21197e54 | 0.371095 | ||||||||
\(988\) | −2.18326e54 | −0.0863181 | ||||||||
\(989\) | 2.20841e55 | 0.856935 | ||||||||
\(990\) | −3.48428e53 | −0.0132697 | ||||||||
\(991\) | −1.50174e55 | −0.561349 | −0.280674 | − | 0.959803i | \(-0.590558\pi\) | ||||
−0.280674 | + | 0.959803i | \(0.590558\pi\) | |||||||
\(992\) | 1.45447e54 | 0.0533628 | ||||||||
\(993\) | 2.64544e55 | 0.952656 | ||||||||
\(994\) | −4.99133e52 | −0.00176428 | ||||||||
\(995\) | 2.04750e55 | 0.710388 | ||||||||
\(996\) | 1.98550e55 | 0.676195 | ||||||||
\(997\) | 2.10810e55 | 0.704743 | 0.352371 | − | 0.935860i | \(-0.385375\pi\) | ||||
0.352371 | + | 0.935860i | \(0.385375\pi\) | |||||||
\(998\) | −4.12010e55 | −1.35205 | ||||||||
\(999\) | 3.08030e55 | 0.992273 |
(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 | 10.38.a.a.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.38.a.a.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial |