Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [14,14,Mod(1,14)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(14, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("14.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 14 = 2 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 14.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: | \(15.0123300533\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{100129}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 25032 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(158.716\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 14.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −64.0000 | −0.707107 | ||||||||
\(3\) | −156.863 | −0.124232 | −0.0621160 | − | 0.998069i | \(-0.519785\pi\) | ||||
−0.0621160 | + | 0.998069i | \(0.519785\pi\) | |||||||
\(4\) | 4096.00 | 0.500000 | ||||||||
\(5\) | −23868.4 | −0.683153 | −0.341577 | − | 0.939854i | \(-0.610961\pi\) | ||||
−0.341577 | + | 0.939854i | \(0.610961\pi\) | |||||||
\(6\) | 10039.3 | 0.0878453 | ||||||||
\(7\) | 117649. | 0.377964 | ||||||||
\(8\) | −262144. | −0.353553 | ||||||||
\(9\) | −1.56972e6 | −0.984566 | ||||||||
\(10\) | 1.52758e6 | 0.483062 | ||||||||
\(11\) | −7.69356e6 | −1.30941 | −0.654704 | − | 0.755886i | \(-0.727207\pi\) | ||||
−0.654704 | + | 0.755886i | \(0.727207\pi\) | |||||||
\(12\) | −642512. | −0.0621160 | ||||||||
\(13\) | 3.39648e7 | 1.95163 | 0.975814 | − | 0.218604i | \(-0.0701501\pi\) | ||||
0.975814 | + | 0.218604i | \(0.0701501\pi\) | |||||||
\(14\) | −7.52954e6 | −0.267261 | ||||||||
\(15\) | 3.74408e6 | 0.0848694 | ||||||||
\(16\) | 1.67772e7 | 0.250000 | ||||||||
\(17\) | 2.76685e7 | 0.278014 | 0.139007 | − | 0.990291i | \(-0.455609\pi\) | ||||
0.139007 | + | 0.990291i | \(0.455609\pi\) | |||||||
\(18\) | 1.00462e8 | 0.696194 | ||||||||
\(19\) | 3.67896e8 | 1.79402 | 0.897009 | − | 0.442013i | \(-0.145736\pi\) | ||||
0.897009 | + | 0.442013i | \(0.145736\pi\) | |||||||
\(20\) | −9.77649e7 | −0.341577 | ||||||||
\(21\) | −1.84548e7 | −0.0469553 | ||||||||
\(22\) | 4.92388e8 | 0.925891 | ||||||||
\(23\) | 1.11611e9 | 1.57208 | 0.786040 | − | 0.618176i | \(-0.212128\pi\) | ||||
0.786040 | + | 0.618176i | \(0.212128\pi\) | |||||||
\(24\) | 4.11208e7 | 0.0439226 | ||||||||
\(25\) | −6.51003e8 | −0.533302 | ||||||||
\(26\) | −2.17375e9 | −1.38001 | ||||||||
\(27\) | 4.96322e8 | 0.246547 | ||||||||
\(28\) | 4.81890e8 | 0.188982 | ||||||||
\(29\) | 1.26815e9 | 0.395899 | 0.197950 | − | 0.980212i | \(-0.436572\pi\) | ||||
0.197950 | + | 0.980212i | \(0.436572\pi\) | |||||||
\(30\) | −2.39621e8 | −0.0600118 | ||||||||
\(31\) | −1.12245e9 | −0.227153 | −0.113576 | − | 0.993529i | \(-0.536231\pi\) | ||||
−0.113576 | + | 0.993529i | \(0.536231\pi\) | |||||||
\(32\) | −1.07374e9 | −0.176777 | ||||||||
\(33\) | 1.20684e9 | 0.162670 | ||||||||
\(34\) | −1.77078e9 | −0.196586 | ||||||||
\(35\) | −2.80809e9 | −0.258208 | ||||||||
\(36\) | −6.42956e9 | −0.492283 | ||||||||
\(37\) | 6.44073e9 | 0.412690 | 0.206345 | − | 0.978479i | \(-0.433843\pi\) | ||||
0.206345 | + | 0.978479i | \(0.433843\pi\) | |||||||
\(38\) | −2.35453e10 | −1.26856 | ||||||||
\(39\) | −5.32783e9 | −0.242454 | ||||||||
\(40\) | 6.25696e9 | 0.241531 | ||||||||
\(41\) | −2.85618e10 | −0.939052 | −0.469526 | − | 0.882919i | \(-0.655575\pi\) | ||||
−0.469526 | + | 0.882919i | \(0.655575\pi\) | |||||||
\(42\) | 1.18111e9 | 0.0332024 | ||||||||
\(43\) | 3.62003e10 | 0.873309 | 0.436654 | − | 0.899629i | \(-0.356163\pi\) | ||||
0.436654 | + | 0.899629i | \(0.356163\pi\) | |||||||
\(44\) | −3.15128e10 | −0.654704 | ||||||||
\(45\) | 3.74666e10 | 0.672610 | ||||||||
\(46\) | −7.14308e10 | −1.11163 | ||||||||
\(47\) | 6.27841e10 | 0.849599 | 0.424799 | − | 0.905288i | \(-0.360345\pi\) | ||||
0.424799 | + | 0.905288i | \(0.360345\pi\) | |||||||
\(48\) | −2.63173e9 | −0.0310580 | ||||||||
\(49\) | 1.38413e10 | 0.142857 | ||||||||
\(50\) | 4.16642e10 | 0.377101 | ||||||||
\(51\) | −4.34017e9 | −0.0345383 | ||||||||
\(52\) | 1.39120e11 | 0.975814 | ||||||||
\(53\) | 2.48076e11 | 1.53742 | 0.768708 | − | 0.639600i | \(-0.220900\pi\) | ||||
0.768708 | + | 0.639600i | \(0.220900\pi\) | |||||||
\(54\) | −3.17646e10 | −0.174335 | ||||||||
\(55\) | 1.83633e11 | 0.894526 | ||||||||
\(56\) | −3.08410e10 | −0.133631 | ||||||||
\(57\) | −5.77094e10 | −0.222874 | ||||||||
\(58\) | −8.11618e10 | −0.279943 | ||||||||
\(59\) | −3.81015e11 | −1.17599 | −0.587995 | − | 0.808865i | \(-0.700082\pi\) | ||||
−0.587995 | + | 0.808865i | \(0.700082\pi\) | |||||||
\(60\) | 1.53357e10 | 0.0424347 | ||||||||
\(61\) | 3.52805e11 | 0.876780 | 0.438390 | − | 0.898785i | \(-0.355549\pi\) | ||||
0.438390 | + | 0.898785i | \(0.355549\pi\) | |||||||
\(62\) | 7.18371e10 | 0.160621 | ||||||||
\(63\) | −1.84676e11 | −0.372131 | ||||||||
\(64\) | 6.87195e10 | 0.125000 | ||||||||
\(65\) | −8.10684e11 | −1.33326 | ||||||||
\(66\) | −7.72376e10 | −0.115025 | ||||||||
\(67\) | −1.39117e12 | −1.87886 | −0.939429 | − | 0.342744i | \(-0.888644\pi\) | ||||
−0.939429 | + | 0.342744i | \(0.888644\pi\) | |||||||
\(68\) | 1.13330e11 | 0.139007 | ||||||||
\(69\) | −1.75076e11 | −0.195302 | ||||||||
\(70\) | 1.79718e11 | 0.182580 | ||||||||
\(71\) | 8.06319e11 | 0.747012 | 0.373506 | − | 0.927628i | \(-0.378155\pi\) | ||||
0.373506 | + | 0.927628i | \(0.378155\pi\) | |||||||
\(72\) | 4.11492e11 | 0.348097 | ||||||||
\(73\) | −1.13789e12 | −0.880035 | −0.440018 | − | 0.897989i | \(-0.645028\pi\) | ||||
−0.440018 | + | 0.897989i | \(0.645028\pi\) | |||||||
\(74\) | −4.12207e11 | −0.291816 | ||||||||
\(75\) | 1.02119e11 | 0.0662531 | ||||||||
\(76\) | 1.50690e12 | 0.897009 | ||||||||
\(77\) | −9.05139e11 | −0.494909 | ||||||||
\(78\) | 3.40981e11 | 0.171441 | ||||||||
\(79\) | 3.95957e11 | 0.183262 | 0.0916308 | − | 0.995793i | \(-0.470792\pi\) | ||||
0.0916308 | + | 0.995793i | \(0.470792\pi\) | |||||||
\(80\) | −4.00445e11 | −0.170788 | ||||||||
\(81\) | 2.42478e12 | 0.953937 | ||||||||
\(82\) | 1.82795e12 | 0.664010 | ||||||||
\(83\) | 1.41067e11 | 0.0473608 | 0.0236804 | − | 0.999720i | \(-0.492462\pi\) | ||||
0.0236804 | + | 0.999720i | \(0.492462\pi\) | |||||||
\(84\) | −7.55909e10 | −0.0234776 | ||||||||
\(85\) | −6.60402e11 | −0.189926 | ||||||||
\(86\) | −2.31682e12 | −0.617523 | ||||||||
\(87\) | −1.98927e11 | −0.0491833 | ||||||||
\(88\) | 2.01682e12 | 0.462945 | ||||||||
\(89\) | 3.02962e12 | 0.646180 | 0.323090 | − | 0.946368i | \(-0.395278\pi\) | ||||
0.323090 | + | 0.946368i | \(0.395278\pi\) | |||||||
\(90\) | −2.39786e12 | −0.475607 | ||||||||
\(91\) | 3.99592e12 | 0.737646 | ||||||||
\(92\) | 4.57157e12 | 0.786040 | ||||||||
\(93\) | 1.76072e11 | 0.0282196 | ||||||||
\(94\) | −4.01818e12 | −0.600757 | ||||||||
\(95\) | −8.78108e12 | −1.22559 | ||||||||
\(96\) | 1.68431e11 | 0.0219613 | ||||||||
\(97\) | 6.73995e12 | 0.821562 | 0.410781 | − | 0.911734i | \(-0.365256\pi\) | ||||
0.410781 | + | 0.911734i | \(0.365256\pi\) | |||||||
\(98\) | −8.85842e11 | −0.101015 | ||||||||
\(99\) | 1.20767e13 | 1.28920 | ||||||||
\(100\) | −2.66651e12 | −0.266651 | ||||||||
\(101\) | −9.08439e12 | −0.851543 | −0.425772 | − | 0.904831i | \(-0.639997\pi\) | ||||
−0.425772 | + | 0.904831i | \(0.639997\pi\) | |||||||
\(102\) | 2.77771e11 | 0.0244222 | ||||||||
\(103\) | 1.26254e12 | 0.104185 | 0.0520924 | − | 0.998642i | \(-0.483411\pi\) | ||||
0.0520924 | + | 0.998642i | \(0.483411\pi\) | |||||||
\(104\) | −8.90366e12 | −0.690005 | ||||||||
\(105\) | 4.40487e11 | 0.0320776 | ||||||||
\(106\) | −1.58768e13 | −1.08712 | ||||||||
\(107\) | −1.91740e13 | −1.23515 | −0.617573 | − | 0.786514i | \(-0.711884\pi\) | ||||
−0.617573 | + | 0.786514i | \(0.711884\pi\) | |||||||
\(108\) | 2.03293e12 | 0.123273 | ||||||||
\(109\) | 3.17798e13 | 1.81501 | 0.907505 | − | 0.420040i | \(-0.137984\pi\) | ||||
0.907505 | + | 0.420040i | \(0.137984\pi\) | |||||||
\(110\) | −1.17525e13 | −0.632525 | ||||||||
\(111\) | −1.01031e12 | −0.0512693 | ||||||||
\(112\) | 1.97382e12 | 0.0944911 | ||||||||
\(113\) | 7.26494e12 | 0.328263 | 0.164132 | − | 0.986438i | \(-0.447518\pi\) | ||||
0.164132 | + | 0.986438i | \(0.447518\pi\) | |||||||
\(114\) | 3.69340e12 | 0.157596 | ||||||||
\(115\) | −2.66396e13 | −1.07397 | ||||||||
\(116\) | 5.19436e12 | 0.197950 | ||||||||
\(117\) | −5.33151e13 | −1.92151 | ||||||||
\(118\) | 2.43849e13 | 0.831550 | ||||||||
\(119\) | 3.25517e12 | 0.105080 | ||||||||
\(120\) | −9.81487e11 | −0.0300059 | ||||||||
\(121\) | 2.46681e13 | 0.714547 | ||||||||
\(122\) | −2.25795e13 | −0.619977 | ||||||||
\(123\) | 4.48029e12 | 0.116660 | ||||||||
\(124\) | −4.59757e12 | −0.113576 | ||||||||
\(125\) | 4.46746e13 | 1.04748 | ||||||||
\(126\) | 1.18192e13 | 0.263136 | ||||||||
\(127\) | 2.95105e13 | 0.624098 | 0.312049 | − | 0.950066i | \(-0.398985\pi\) | ||||
0.312049 | + | 0.950066i | \(0.398985\pi\) | |||||||
\(128\) | −4.39805e12 | −0.0883883 | ||||||||
\(129\) | −5.67851e12 | −0.108493 | ||||||||
\(130\) | 5.18838e13 | 0.942758 | ||||||||
\(131\) | −1.77852e13 | −0.307465 | −0.153732 | − | 0.988113i | \(-0.549129\pi\) | ||||
−0.153732 | + | 0.988113i | \(0.549129\pi\) | |||||||
\(132\) | 4.94320e12 | 0.0813351 | ||||||||
\(133\) | 4.32826e13 | 0.678075 | ||||||||
\(134\) | 8.90349e13 | 1.32855 | ||||||||
\(135\) | −1.18464e13 | −0.168429 | ||||||||
\(136\) | −7.25312e12 | −0.0982929 | ||||||||
\(137\) | 1.05369e14 | 1.36153 | 0.680767 | − | 0.732500i | \(-0.261647\pi\) | ||||
0.680767 | + | 0.732500i | \(0.261647\pi\) | |||||||
\(138\) | 1.12049e13 | 0.138100 | ||||||||
\(139\) | −5.89997e13 | −0.693831 | −0.346915 | − | 0.937896i | \(-0.612771\pi\) | ||||
−0.346915 | + | 0.937896i | \(0.612771\pi\) | |||||||
\(140\) | −1.15019e13 | −0.129104 | ||||||||
\(141\) | −9.84853e12 | −0.105547 | ||||||||
\(142\) | −5.16044e13 | −0.528217 | ||||||||
\(143\) | −2.61310e14 | −2.55547 | ||||||||
\(144\) | −2.63355e13 | −0.246142 | ||||||||
\(145\) | −3.02688e13 | −0.270460 | ||||||||
\(146\) | 7.28247e13 | 0.622279 | ||||||||
\(147\) | −2.17119e12 | −0.0177474 | ||||||||
\(148\) | 2.63812e13 | 0.206345 | ||||||||
\(149\) | −1.56999e14 | −1.17540 | −0.587700 | − | 0.809079i | \(-0.699967\pi\) | ||||
−0.587700 | + | 0.809079i | \(0.699967\pi\) | |||||||
\(150\) | −6.53558e12 | −0.0468480 | ||||||||
\(151\) | 6.48245e13 | 0.445030 | 0.222515 | − | 0.974929i | \(-0.428573\pi\) | ||||
0.222515 | + | 0.974929i | \(0.428573\pi\) | |||||||
\(152\) | −9.64417e13 | −0.634281 | ||||||||
\(153\) | −4.34317e13 | −0.273724 | ||||||||
\(154\) | 5.79289e13 | 0.349954 | ||||||||
\(155\) | 2.67912e13 | 0.155180 | ||||||||
\(156\) | −2.18228e13 | −0.121227 | ||||||||
\(157\) | −4.47531e12 | −0.0238493 | −0.0119246 | − | 0.999929i | \(-0.503796\pi\) | ||||
−0.0119246 | + | 0.999929i | \(0.503796\pi\) | |||||||
\(158\) | −2.53412e13 | −0.129586 | ||||||||
\(159\) | −3.89140e13 | −0.190996 | ||||||||
\(160\) | 2.56285e13 | 0.120766 | ||||||||
\(161\) | 1.31309e14 | 0.594190 | ||||||||
\(162\) | −1.55186e14 | −0.674536 | ||||||||
\(163\) | −7.19194e13 | −0.300349 | −0.150175 | − | 0.988659i | \(-0.547984\pi\) | ||||
−0.150175 | + | 0.988659i | \(0.547984\pi\) | |||||||
\(164\) | −1.16989e14 | −0.469526 | ||||||||
\(165\) | −2.88053e13 | −0.111129 | ||||||||
\(166\) | −9.02831e12 | −0.0334891 | ||||||||
\(167\) | 1.24252e14 | 0.443246 | 0.221623 | − | 0.975132i | \(-0.428864\pi\) | ||||
0.221623 | + | 0.975132i | \(0.428864\pi\) | |||||||
\(168\) | 4.83782e12 | 0.0166012 | ||||||||
\(169\) | 8.50731e14 | 2.80885 | ||||||||
\(170\) | 4.22657e13 | 0.134298 | ||||||||
\(171\) | −5.77492e14 | −1.76633 | ||||||||
\(172\) | 1.48277e14 | 0.436654 | ||||||||
\(173\) | 4.99887e14 | 1.41766 | 0.708830 | − | 0.705380i | \(-0.249224\pi\) | ||||
0.708830 | + | 0.705380i | \(0.249224\pi\) | |||||||
\(174\) | 1.27313e13 | 0.0347779 | ||||||||
\(175\) | −7.65899e13 | −0.201569 | ||||||||
\(176\) | −1.29076e14 | −0.327352 | ||||||||
\(177\) | 5.97672e13 | 0.146095 | ||||||||
\(178\) | −1.93896e14 | −0.456919 | ||||||||
\(179\) | 2.16915e14 | 0.492883 | 0.246442 | − | 0.969158i | \(-0.420739\pi\) | ||||
0.246442 | + | 0.969158i | \(0.420739\pi\) | |||||||
\(180\) | 1.53463e14 | 0.336305 | ||||||||
\(181\) | 5.44744e14 | 1.15155 | 0.575774 | − | 0.817609i | \(-0.304701\pi\) | ||||
0.575774 | + | 0.817609i | \(0.304701\pi\) | |||||||
\(182\) | −2.55739e14 | −0.521594 | ||||||||
\(183\) | −5.53421e13 | −0.108924 | ||||||||
\(184\) | −2.92580e14 | −0.555814 | ||||||||
\(185\) | −1.53730e14 | −0.281930 | ||||||||
\(186\) | −1.12686e13 | −0.0199543 | ||||||||
\(187\) | −2.12869e14 | −0.364034 | ||||||||
\(188\) | 2.57164e14 | 0.424799 | ||||||||
\(189\) | 5.83918e13 | 0.0931858 | ||||||||
\(190\) | 5.61989e14 | 0.866622 | ||||||||
\(191\) | −4.16278e14 | −0.620393 | −0.310197 | − | 0.950672i | \(-0.600395\pi\) | ||||
−0.310197 | + | 0.950672i | \(0.600395\pi\) | |||||||
\(192\) | −1.07796e13 | −0.0155290 | ||||||||
\(193\) | −2.53824e14 | −0.353517 | −0.176759 | − | 0.984254i | \(-0.556561\pi\) | ||||
−0.176759 | + | 0.984254i | \(0.556561\pi\) | |||||||
\(194\) | −4.31357e14 | −0.580932 | ||||||||
\(195\) | 1.27167e14 | 0.165634 | ||||||||
\(196\) | 5.66939e13 | 0.0714286 | ||||||||
\(197\) | −4.45065e14 | −0.542491 | −0.271246 | − | 0.962510i | \(-0.587436\pi\) | ||||
−0.271246 | + | 0.962510i | \(0.587436\pi\) | |||||||
\(198\) | −7.72909e14 | −0.911601 | ||||||||
\(199\) | 6.21823e14 | 0.709777 | 0.354888 | − | 0.934909i | \(-0.384519\pi\) | ||||
0.354888 | + | 0.934909i | \(0.384519\pi\) | |||||||
\(200\) | 1.70657e14 | 0.188551 | ||||||||
\(201\) | 2.18224e14 | 0.233414 | ||||||||
\(202\) | 5.81401e14 | 0.602132 | ||||||||
\(203\) | 1.49197e14 | 0.149636 | ||||||||
\(204\) | −1.77773e13 | −0.0172691 | ||||||||
\(205\) | 6.81723e14 | 0.641517 | ||||||||
\(206\) | −8.08028e13 | −0.0736698 | ||||||||
\(207\) | −1.75197e15 | −1.54782 | ||||||||
\(208\) | 5.69834e14 | 0.487907 | ||||||||
\(209\) | −2.83043e15 | −2.34910 | ||||||||
\(210\) | −2.81911e13 | −0.0226823 | ||||||||
\(211\) | −1.76477e14 | −0.137674 | −0.0688370 | − | 0.997628i | \(-0.521929\pi\) | ||||
−0.0688370 | + | 0.997628i | \(0.521929\pi\) | |||||||
\(212\) | 1.01612e15 | 0.768708 | ||||||||
\(213\) | −1.26482e14 | −0.0928028 | ||||||||
\(214\) | 1.22714e15 | 0.873380 | ||||||||
\(215\) | −8.64044e14 | −0.596604 | ||||||||
\(216\) | −1.30108e14 | −0.0871674 | ||||||||
\(217\) | −1.32056e14 | −0.0858556 | ||||||||
\(218\) | −2.03391e15 | −1.28341 | ||||||||
\(219\) | 1.78493e14 | 0.109328 | ||||||||
\(220\) | 7.52160e14 | 0.447263 | ||||||||
\(221\) | 9.39753e14 | 0.542580 | ||||||||
\(222\) | 6.46601e13 | 0.0362529 | ||||||||
\(223\) | −9.89687e14 | −0.538910 | −0.269455 | − | 0.963013i | \(-0.586844\pi\) | ||||
−0.269455 | + | 0.963013i | \(0.586844\pi\) | |||||||
\(224\) | −1.26325e14 | −0.0668153 | ||||||||
\(225\) | 1.02189e15 | 0.525071 | ||||||||
\(226\) | −4.64956e14 | −0.232117 | ||||||||
\(227\) | 1.13962e15 | 0.552832 | 0.276416 | − | 0.961038i | \(-0.410853\pi\) | ||||
0.276416 | + | 0.961038i | \(0.410853\pi\) | |||||||
\(228\) | −2.36378e14 | −0.111437 | ||||||||
\(229\) | 2.34581e15 | 1.07489 | 0.537443 | − | 0.843300i | \(-0.319390\pi\) | ||||
0.537443 | + | 0.843300i | \(0.319390\pi\) | |||||||
\(230\) | 1.70494e15 | 0.759412 | ||||||||
\(231\) | 1.41983e14 | 0.0614836 | ||||||||
\(232\) | −3.32439e14 | −0.139972 | ||||||||
\(233\) | 2.61893e14 | 0.107229 | 0.0536143 | − | 0.998562i | \(-0.482926\pi\) | ||||
0.0536143 | + | 0.998562i | \(0.482926\pi\) | |||||||
\(234\) | 3.41217e15 | 1.35871 | ||||||||
\(235\) | −1.49856e15 | −0.580406 | ||||||||
\(236\) | −1.56064e15 | −0.587995 | ||||||||
\(237\) | −6.21111e13 | −0.0227669 | ||||||||
\(238\) | −2.08331e14 | −0.0743025 | ||||||||
\(239\) | 4.55614e14 | 0.158129 | 0.0790644 | − | 0.996870i | \(-0.474807\pi\) | ||||
0.0790644 | + | 0.996870i | \(0.474807\pi\) | |||||||
\(240\) | 6.28152e13 | 0.0212174 | ||||||||
\(241\) | 2.83710e15 | 0.932746 | 0.466373 | − | 0.884588i | \(-0.345561\pi\) | ||||
0.466373 | + | 0.884588i | \(0.345561\pi\) | |||||||
\(242\) | −1.57876e15 | −0.505261 | ||||||||
\(243\) | −1.17166e15 | −0.365056 | ||||||||
\(244\) | 1.44509e15 | 0.438390 | ||||||||
\(245\) | −3.30369e14 | −0.0975933 | ||||||||
\(246\) | −2.86739e14 | −0.0824913 | ||||||||
\(247\) | 1.24955e16 | 3.50125 | ||||||||
\(248\) | 2.94245e14 | 0.0803106 | ||||||||
\(249\) | −2.21283e13 | −0.00588372 | ||||||||
\(250\) | −2.85918e15 | −0.740680 | ||||||||
\(251\) | −5.04809e15 | −1.27423 | −0.637115 | − | 0.770769i | \(-0.719873\pi\) | ||||
−0.637115 | + | 0.770769i | \(0.719873\pi\) | |||||||
\(252\) | −7.56431e14 | −0.186066 | ||||||||
\(253\) | −8.58682e15 | −2.05849 | ||||||||
\(254\) | −1.88867e15 | −0.441304 | ||||||||
\(255\) | 1.03593e14 | 0.0235949 | ||||||||
\(256\) | 2.81475e14 | 0.0625000 | ||||||||
\(257\) | 1.58419e15 | 0.342959 | 0.171480 | − | 0.985188i | \(-0.445145\pi\) | ||||
0.171480 | + | 0.985188i | \(0.445145\pi\) | |||||||
\(258\) | 3.63424e14 | 0.0767160 | ||||||||
\(259\) | 7.57746e14 | 0.155982 | ||||||||
\(260\) | −3.32056e15 | −0.666630 | ||||||||
\(261\) | −1.99064e15 | −0.389789 | ||||||||
\(262\) | 1.13825e15 | 0.217411 | ||||||||
\(263\) | −6.88068e14 | −0.128209 | −0.0641046 | − | 0.997943i | \(-0.520419\pi\) | ||||
−0.0641046 | + | 0.997943i | \(0.520419\pi\) | |||||||
\(264\) | −3.16365e14 | −0.0575126 | ||||||||
\(265\) | −5.92117e15 | −1.05029 | ||||||||
\(266\) | −2.77009e15 | −0.479471 | ||||||||
\(267\) | −4.75237e14 | −0.0802762 | ||||||||
\(268\) | −5.69823e15 | −0.939429 | ||||||||
\(269\) | 7.45199e15 | 1.19917 | 0.599587 | − | 0.800310i | \(-0.295331\pi\) | ||||
0.599587 | + | 0.800310i | \(0.295331\pi\) | |||||||
\(270\) | 7.58170e14 | 0.119097 | ||||||||
\(271\) | −8.43521e14 | −0.129359 | −0.0646793 | − | 0.997906i | \(-0.520602\pi\) | ||||
−0.0646793 | + | 0.997906i | \(0.520602\pi\) | |||||||
\(272\) | 4.64200e14 | 0.0695036 | ||||||||
\(273\) | −6.26814e14 | −0.0916392 | ||||||||
\(274\) | −6.74361e15 | −0.962750 | ||||||||
\(275\) | 5.00853e15 | 0.698309 | ||||||||
\(276\) | −7.17112e14 | −0.0976512 | ||||||||
\(277\) | −1.28498e16 | −1.70914 | −0.854572 | − | 0.519334i | \(-0.826180\pi\) | ||||
−0.854572 | + | 0.519334i | \(0.826180\pi\) | |||||||
\(278\) | 3.77598e15 | 0.490612 | ||||||||
\(279\) | 1.76194e15 | 0.223647 | ||||||||
\(280\) | 7.36125e14 | 0.0912902 | ||||||||
\(281\) | 8.51626e15 | 1.03195 | 0.515974 | − | 0.856604i | \(-0.327430\pi\) | ||||
0.515974 | + | 0.856604i | \(0.327430\pi\) | |||||||
\(282\) | 6.30306e14 | 0.0746332 | ||||||||
\(283\) | 8.22266e15 | 0.951482 | 0.475741 | − | 0.879585i | \(-0.342180\pi\) | ||||
0.475741 | + | 0.879585i | \(0.342180\pi\) | |||||||
\(284\) | 3.30268e15 | 0.373506 | ||||||||
\(285\) | 1.37743e15 | 0.152257 | ||||||||
\(286\) | 1.67238e16 | 1.80699 | ||||||||
\(287\) | −3.36026e15 | −0.354928 | ||||||||
\(288\) | 1.68547e15 | 0.174048 | ||||||||
\(289\) | −9.13903e15 | −0.922708 | ||||||||
\(290\) | 1.93720e15 | 0.191244 | ||||||||
\(291\) | −1.05725e15 | −0.102064 | ||||||||
\(292\) | −4.66078e15 | −0.440018 | ||||||||
\(293\) | −8.61473e15 | −0.795430 | −0.397715 | − | 0.917509i | \(-0.630197\pi\) | ||||
−0.397715 | + | 0.917509i | \(0.630197\pi\) | |||||||
\(294\) | 1.38956e14 | 0.0125493 | ||||||||
\(295\) | 9.09420e15 | 0.803381 | ||||||||
\(296\) | −1.68840e15 | −0.145908 | ||||||||
\(297\) | −3.81848e15 | −0.322830 | ||||||||
\(298\) | 1.00479e16 | 0.831134 | ||||||||
\(299\) | 3.79083e16 | 3.06811 | ||||||||
\(300\) | 4.18277e14 | 0.0331266 | ||||||||
\(301\) | 4.25893e15 | 0.330080 | ||||||||
\(302\) | −4.14877e15 | −0.314684 | ||||||||
\(303\) | 1.42501e15 | 0.105789 | ||||||||
\(304\) | 6.17227e15 | 0.448504 | ||||||||
\(305\) | −8.42088e15 | −0.598975 | ||||||||
\(306\) | 2.77963e15 | 0.193552 | ||||||||
\(307\) | −2.20767e16 | −1.50499 | −0.752496 | − | 0.658597i | \(-0.771150\pi\) | ||||
−0.752496 | + | 0.658597i | \(0.771150\pi\) | |||||||
\(308\) | −3.70745e15 | −0.247455 | ||||||||
\(309\) | −1.98047e14 | −0.0129431 | ||||||||
\(310\) | −1.71464e15 | −0.109729 | ||||||||
\(311\) | −2.38285e16 | −1.49333 | −0.746663 | − | 0.665203i | \(-0.768345\pi\) | ||||
−0.746663 | + | 0.665203i | \(0.768345\pi\) | |||||||
\(312\) | 1.39666e15 | 0.0857206 | ||||||||
\(313\) | −2.62444e16 | −1.57760 | −0.788802 | − | 0.614648i | \(-0.789298\pi\) | ||||
−0.788802 | + | 0.614648i | \(0.789298\pi\) | |||||||
\(314\) | 2.86420e14 | 0.0168640 | ||||||||
\(315\) | 4.40791e15 | 0.254223 | ||||||||
\(316\) | 1.62184e15 | 0.0916308 | ||||||||
\(317\) | 2.62984e16 | 1.45561 | 0.727805 | − | 0.685785i | \(-0.240541\pi\) | ||||
0.727805 | + | 0.685785i | \(0.240541\pi\) | |||||||
\(318\) | 2.49050e15 | 0.135055 | ||||||||
\(319\) | −9.75661e15 | −0.518393 | ||||||||
\(320\) | −1.64022e15 | −0.0853941 | ||||||||
\(321\) | 3.00770e15 | 0.153445 | ||||||||
\(322\) | −8.40376e15 | −0.420156 | ||||||||
\(323\) | 1.01791e16 | 0.498762 | ||||||||
\(324\) | 9.93190e15 | 0.476969 | ||||||||
\(325\) | −2.21112e16 | −1.04081 | ||||||||
\(326\) | 4.60284e15 | 0.212379 | ||||||||
\(327\) | −4.98509e15 | −0.225482 | ||||||||
\(328\) | 7.48729e15 | 0.332005 | ||||||||
\(329\) | 7.38649e15 | 0.321118 | ||||||||
\(330\) | 1.84354e15 | 0.0785798 | ||||||||
\(331\) | −3.32594e16 | −1.39005 | −0.695027 | − | 0.718983i | \(-0.744608\pi\) | ||||
−0.695027 | + | 0.718983i | \(0.744608\pi\) | |||||||
\(332\) | 5.77812e14 | 0.0236804 | ||||||||
\(333\) | −1.01101e16 | −0.406321 | ||||||||
\(334\) | −7.95211e15 | −0.313423 | ||||||||
\(335\) | 3.32050e16 | 1.28355 | ||||||||
\(336\) | −3.09620e14 | −0.0117388 | ||||||||
\(337\) | 1.94532e16 | 0.723429 | 0.361715 | − | 0.932289i | \(-0.382191\pi\) | ||||
0.361715 | + | 0.932289i | \(0.382191\pi\) | |||||||
\(338\) | −5.44468e16 | −1.98616 | ||||||||
\(339\) | −1.13960e15 | −0.0407808 | ||||||||
\(340\) | −2.70501e15 | −0.0949632 | ||||||||
\(341\) | 8.63566e15 | 0.297435 | ||||||||
\(342\) | 3.69595e16 | 1.24898 | ||||||||
\(343\) | 1.62841e15 | 0.0539949 | ||||||||
\(344\) | −9.48970e15 | −0.308761 | ||||||||
\(345\) | 4.17878e15 | 0.133421 | ||||||||
\(346\) | −3.19927e16 | −1.00244 | ||||||||
\(347\) | 3.23704e16 | 0.995421 | 0.497711 | − | 0.867343i | \(-0.334174\pi\) | ||||
0.497711 | + | 0.867343i | \(0.334174\pi\) | |||||||
\(348\) | −8.14804e14 | −0.0245917 | ||||||||
\(349\) | −5.23174e16 | −1.54982 | −0.774909 | − | 0.632073i | \(-0.782204\pi\) | ||||
−0.774909 | + | 0.632073i | \(0.782204\pi\) | |||||||
\(350\) | 4.90175e15 | 0.142531 | ||||||||
\(351\) | 1.68575e16 | 0.481167 | ||||||||
\(352\) | 8.26089e15 | 0.231473 | ||||||||
\(353\) | −2.57219e16 | −0.707565 | −0.353783 | − | 0.935328i | \(-0.615105\pi\) | ||||
−0.353783 | + | 0.935328i | \(0.615105\pi\) | |||||||
\(354\) | −3.82510e15 | −0.103305 | ||||||||
\(355\) | −1.92455e16 | −0.510324 | ||||||||
\(356\) | 1.24093e16 | 0.323090 | ||||||||
\(357\) | −5.10617e14 | −0.0130542 | ||||||||
\(358\) | −1.38825e16 | −0.348521 | ||||||||
\(359\) | 3.04674e16 | 0.751141 | 0.375571 | − | 0.926794i | \(-0.377447\pi\) | ||||
0.375571 | + | 0.926794i | \(0.377447\pi\) | |||||||
\(360\) | −9.82165e15 | −0.237803 | ||||||||
\(361\) | 9.32944e16 | 2.21850 | ||||||||
\(362\) | −3.48636e16 | −0.814267 | ||||||||
\(363\) | −3.86952e15 | −0.0887696 | ||||||||
\(364\) | 1.63673e16 | 0.368823 | ||||||||
\(365\) | 2.71595e16 | 0.601199 | ||||||||
\(366\) | 3.54190e15 | 0.0770210 | ||||||||
\(367\) | −1.73795e16 | −0.371285 | −0.185643 | − | 0.982617i | \(-0.559437\pi\) | ||||
−0.185643 | + | 0.982617i | \(0.559437\pi\) | |||||||
\(368\) | 1.87251e16 | 0.393020 | ||||||||
\(369\) | 4.48339e16 | 0.924559 | ||||||||
\(370\) | 9.83871e15 | 0.199355 | ||||||||
\(371\) | 2.91859e16 | 0.581088 | ||||||||
\(372\) | 7.21191e14 | 0.0141098 | ||||||||
\(373\) | −4.63979e15 | −0.0892053 | −0.0446026 | − | 0.999005i | \(-0.514202\pi\) | ||||
−0.0446026 | + | 0.999005i | \(0.514202\pi\) | |||||||
\(374\) | 1.36236e16 | 0.257411 | ||||||||
\(375\) | −7.00781e15 | −0.130130 | ||||||||
\(376\) | −1.64585e16 | −0.300378 | ||||||||
\(377\) | 4.30725e16 | 0.772648 | ||||||||
\(378\) | −3.73707e15 | −0.0658923 | ||||||||
\(379\) | −8.74316e15 | −0.151535 | −0.0757676 | − | 0.997126i | \(-0.524141\pi\) | ||||
−0.0757676 | + | 0.997126i | \(0.524141\pi\) | |||||||
\(380\) | −3.59673e16 | −0.612794 | ||||||||
\(381\) | −4.62912e15 | −0.0775329 | ||||||||
\(382\) | 2.66418e16 | 0.438684 | ||||||||
\(383\) | −7.53155e16 | −1.21925 | −0.609625 | − | 0.792690i | \(-0.708680\pi\) | ||||
−0.609625 | + | 0.792690i | \(0.708680\pi\) | |||||||
\(384\) | 6.89892e14 | 0.0109807 | ||||||||
\(385\) | 2.16042e16 | 0.338099 | ||||||||
\(386\) | 1.62447e16 | 0.249974 | ||||||||
\(387\) | −5.68243e16 | −0.859830 | ||||||||
\(388\) | 2.76068e16 | 0.410781 | ||||||||
\(389\) | −2.25509e16 | −0.329983 | −0.164991 | − | 0.986295i | \(-0.552760\pi\) | ||||
−0.164991 | + | 0.986295i | \(0.552760\pi\) | |||||||
\(390\) | −8.13867e15 | −0.117121 | ||||||||
\(391\) | 3.08809e16 | 0.437061 | ||||||||
\(392\) | −3.62841e15 | −0.0505076 | ||||||||
\(393\) | 2.78985e15 | 0.0381970 | ||||||||
\(394\) | 2.84842e16 | 0.383599 | ||||||||
\(395\) | −9.45084e15 | −0.125196 | ||||||||
\(396\) | 4.94662e16 | 0.644599 | ||||||||
\(397\) | −3.26995e16 | −0.419182 | −0.209591 | − | 0.977789i | \(-0.567213\pi\) | ||||
−0.209591 | + | 0.977789i | \(0.567213\pi\) | |||||||
\(398\) | −3.97967e16 | −0.501888 | ||||||||
\(399\) | −6.78945e15 | −0.0842385 | ||||||||
\(400\) | −1.09220e16 | −0.133325 | ||||||||
\(401\) | 3.07711e16 | 0.369577 | 0.184789 | − | 0.982778i | \(-0.440840\pi\) | ||||
0.184789 | + | 0.982778i | \(0.440840\pi\) | |||||||
\(402\) | −1.39663e16 | −0.165049 | ||||||||
\(403\) | −3.81239e16 | −0.443317 | ||||||||
\(404\) | −3.72097e16 | −0.425772 | ||||||||
\(405\) | −5.78756e16 | −0.651685 | ||||||||
\(406\) | −9.54860e15 | −0.105809 | ||||||||
\(407\) | −4.95521e16 | −0.540379 | ||||||||
\(408\) | 1.13775e15 | 0.0122111 | ||||||||
\(409\) | −1.56215e17 | −1.65014 | −0.825071 | − | 0.565029i | \(-0.808865\pi\) | ||||
−0.825071 | + | 0.565029i | \(0.808865\pi\) | |||||||
\(410\) | −4.36303e16 | −0.453621 | ||||||||
\(411\) | −1.65285e16 | −0.169146 | ||||||||
\(412\) | 5.17138e15 | 0.0520924 | ||||||||
\(413\) | −4.48260e16 | −0.444482 | ||||||||
\(414\) | 1.12126e17 | 1.09447 | ||||||||
\(415\) | −3.36705e15 | −0.0323547 | ||||||||
\(416\) | −3.64694e16 | −0.345002 | ||||||||
\(417\) | 9.25489e15 | 0.0861959 | ||||||||
\(418\) | 1.81147e17 | 1.66106 | ||||||||
\(419\) | −1.46057e17 | −1.31865 | −0.659327 | − | 0.751856i | \(-0.729159\pi\) | ||||
−0.659327 | + | 0.751856i | \(0.729159\pi\) | |||||||
\(420\) | 1.80423e15 | 0.0160388 | ||||||||
\(421\) | 9.63368e16 | 0.843255 | 0.421627 | − | 0.906769i | \(-0.361459\pi\) | ||||
0.421627 | + | 0.906769i | \(0.361459\pi\) | |||||||
\(422\) | 1.12945e16 | 0.0973503 | ||||||||
\(423\) | −9.85533e16 | −0.836486 | ||||||||
\(424\) | −6.50316e16 | −0.543558 | ||||||||
\(425\) | −1.80123e16 | −0.148266 | ||||||||
\(426\) | 8.09484e15 | 0.0656215 | ||||||||
\(427\) | 4.15071e16 | 0.331392 | ||||||||
\(428\) | −7.85367e16 | −0.617573 | ||||||||
\(429\) | 4.09899e16 | 0.317472 | ||||||||
\(430\) | 5.52988e16 | 0.421862 | ||||||||
\(431\) | −1.43677e16 | −0.107965 | −0.0539826 | − | 0.998542i | \(-0.517192\pi\) | ||||
−0.0539826 | + | 0.998542i | \(0.517192\pi\) | |||||||
\(432\) | 8.32690e15 | 0.0616366 | ||||||||
\(433\) | 2.68630e17 | 1.95877 | 0.979385 | − | 0.202002i | \(-0.0647446\pi\) | ||||
0.979385 | + | 0.202002i | \(0.0647446\pi\) | |||||||
\(434\) | 8.45156e15 | 0.0607091 | ||||||||
\(435\) | 4.74806e15 | 0.0335998 | ||||||||
\(436\) | 1.30170e17 | 0.907505 | ||||||||
\(437\) | 4.10611e17 | 2.82034 | ||||||||
\(438\) | −1.14235e16 | −0.0773069 | ||||||||
\(439\) | 5.75567e16 | 0.383775 | 0.191887 | − | 0.981417i | \(-0.438539\pi\) | ||||
0.191887 | + | 0.981417i | \(0.438539\pi\) | |||||||
\(440\) | −4.81382e16 | −0.316263 | ||||||||
\(441\) | −2.17269e16 | −0.140652 | ||||||||
\(442\) | −6.01442e16 | −0.383662 | ||||||||
\(443\) | −1.08881e17 | −0.684428 | −0.342214 | − | 0.939622i | \(-0.611177\pi\) | ||||
−0.342214 | + | 0.939622i | \(0.611177\pi\) | |||||||
\(444\) | −4.13825e15 | −0.0256346 | ||||||||
\(445\) | −7.23123e16 | −0.441440 | ||||||||
\(446\) | 6.33400e16 | 0.381067 | ||||||||
\(447\) | 2.46274e16 | 0.146022 | ||||||||
\(448\) | 8.08478e15 | 0.0472456 | ||||||||
\(449\) | −1.23522e16 | −0.0711449 | −0.0355725 | − | 0.999367i | \(-0.511325\pi\) | ||||
−0.0355725 | + | 0.999367i | \(0.511325\pi\) | |||||||
\(450\) | −6.54010e16 | −0.371281 | ||||||||
\(451\) | 2.19741e17 | 1.22960 | ||||||||
\(452\) | 2.97572e16 | 0.164132 | ||||||||
\(453\) | −1.01686e16 | −0.0552869 | ||||||||
\(454\) | −7.29359e16 | −0.390911 | ||||||||
\(455\) | −9.53762e16 | −0.503925 | ||||||||
\(456\) | 1.51282e16 | 0.0787979 | ||||||||
\(457\) | −2.23133e16 | −0.114580 | −0.0572901 | − | 0.998358i | \(-0.518246\pi\) | ||||
−0.0572901 | + | 0.998358i | \(0.518246\pi\) | |||||||
\(458\) | −1.50132e17 | −0.760059 | ||||||||
\(459\) | 1.37325e16 | 0.0685435 | ||||||||
\(460\) | −1.09116e17 | −0.536985 | ||||||||
\(461\) | 2.25114e17 | 1.09231 | 0.546156 | − | 0.837683i | \(-0.316091\pi\) | ||||
0.546156 | + | 0.837683i | \(0.316091\pi\) | |||||||
\(462\) | −9.08692e15 | −0.0434754 | ||||||||
\(463\) | −2.32113e17 | −1.09502 | −0.547511 | − | 0.836798i | \(-0.684425\pi\) | ||||
−0.547511 | + | 0.836798i | \(0.684425\pi\) | |||||||
\(464\) | 2.12761e16 | 0.0989748 | ||||||||
\(465\) | −4.20255e15 | −0.0192783 | ||||||||
\(466\) | −1.67612e16 | −0.0758221 | ||||||||
\(467\) | 4.08601e17 | 1.82280 | 0.911402 | − | 0.411518i | \(-0.135001\pi\) | ||||
0.911402 | + | 0.411518i | \(0.135001\pi\) | |||||||
\(468\) | −2.18379e17 | −0.960753 | ||||||||
\(469\) | −1.63670e17 | −0.710142 | ||||||||
\(470\) | 9.59076e16 | 0.410409 | ||||||||
\(471\) | 7.02011e14 | 0.00296284 | ||||||||
\(472\) | 9.98807e16 | 0.415775 | ||||||||
\(473\) | −2.78509e17 | −1.14352 | ||||||||
\(474\) | 3.97511e15 | 0.0160987 | ||||||||
\(475\) | −2.39501e17 | −0.956752 | ||||||||
\(476\) | 1.33332e16 | 0.0525398 | ||||||||
\(477\) | −3.89409e17 | −1.51369 | ||||||||
\(478\) | −2.91593e16 | −0.111814 | ||||||||
\(479\) | 2.05872e17 | 0.778783 | 0.389391 | − | 0.921072i | \(-0.372685\pi\) | ||||
0.389391 | + | 0.921072i | \(0.372685\pi\) | |||||||
\(480\) | −4.02017e15 | −0.0150029 | ||||||||
\(481\) | 2.18758e17 | 0.805417 | ||||||||
\(482\) | −1.81574e17 | −0.659551 | ||||||||
\(483\) | −2.05975e16 | −0.0738174 | ||||||||
\(484\) | 1.01041e17 | 0.357274 | ||||||||
\(485\) | −1.60872e17 | −0.561252 | ||||||||
\(486\) | 7.49860e16 | 0.258134 | ||||||||
\(487\) | 2.42234e17 | 0.822806 | 0.411403 | − | 0.911454i | \(-0.365039\pi\) | ||||
0.411403 | + | 0.911454i | \(0.365039\pi\) | |||||||
\(488\) | −9.24857e16 | −0.309989 | ||||||||
\(489\) | 1.12815e16 | 0.0373130 | ||||||||
\(490\) | 2.11436e16 | 0.0690089 | ||||||||
\(491\) | −2.00232e17 | −0.644916 | −0.322458 | − | 0.946584i | \(-0.604509\pi\) | ||||
−0.322458 | + | 0.946584i | \(0.604509\pi\) | |||||||
\(492\) | 1.83513e16 | 0.0583301 | ||||||||
\(493\) | 3.50879e16 | 0.110066 | ||||||||
\(494\) | −7.99712e17 | −2.47576 | ||||||||
\(495\) | −2.88252e17 | −0.880720 | ||||||||
\(496\) | −1.88317e16 | −0.0567881 | ||||||||
\(497\) | 9.48626e16 | 0.282344 | ||||||||
\(498\) | 1.41621e15 | 0.00416042 | ||||||||
\(499\) | 3.10865e17 | 0.901402 | 0.450701 | − | 0.892675i | \(-0.351174\pi\) | ||||
0.450701 | + | 0.892675i | \(0.351174\pi\) | |||||||
\(500\) | 1.82987e17 | 0.523740 | ||||||||
\(501\) | −1.94905e16 | −0.0550654 | ||||||||
\(502\) | 3.23078e17 | 0.901017 | ||||||||
\(503\) | 3.90092e17 | 1.07393 | 0.536964 | − | 0.843605i | \(-0.319571\pi\) | ||||
0.536964 | + | 0.843605i | \(0.319571\pi\) | |||||||
\(504\) | 4.84116e16 | 0.131568 | ||||||||
\(505\) | 2.16830e17 | 0.581735 | ||||||||
\(506\) | 5.49557e17 | 1.45557 | ||||||||
\(507\) | −1.33448e17 | −0.348949 | ||||||||
\(508\) | 1.20875e17 | 0.312049 | ||||||||
\(509\) | −4.02933e17 | −1.02699 | −0.513497 | − | 0.858092i | \(-0.671650\pi\) | ||||
−0.513497 | + | 0.858092i | \(0.671650\pi\) | |||||||
\(510\) | −6.62994e15 | −0.0166841 | ||||||||
\(511\) | −1.33871e17 | −0.332622 | ||||||||
\(512\) | −1.80144e16 | −0.0441942 | ||||||||
\(513\) | 1.82595e17 | 0.442309 | ||||||||
\(514\) | −1.01388e17 | −0.242509 | ||||||||
\(515\) | −3.01349e16 | −0.0711742 | ||||||||
\(516\) | −2.32592e16 | −0.0542464 | ||||||||
\(517\) | −4.83033e17 | −1.11247 | ||||||||
\(518\) | −4.84957e16 | −0.110296 | ||||||||
\(519\) | −7.84139e16 | −0.176119 | ||||||||
\(520\) | 2.12516e17 | 0.471379 | ||||||||
\(521\) | 6.24074e17 | 1.36707 | 0.683536 | − | 0.729917i | \(-0.260441\pi\) | ||||
0.683536 | + | 0.729917i | \(0.260441\pi\) | |||||||
\(522\) | 1.27401e17 | 0.275623 | ||||||||
\(523\) | −6.81767e17 | −1.45672 | −0.728358 | − | 0.685196i | \(-0.759716\pi\) | ||||
−0.728358 | + | 0.685196i | \(0.759716\pi\) | |||||||
\(524\) | −7.28482e16 | −0.153732 | ||||||||
\(525\) | 1.20141e16 | 0.0250413 | ||||||||
\(526\) | 4.40363e16 | 0.0906575 | ||||||||
\(527\) | −3.10566e16 | −0.0631517 | ||||||||
\(528\) | 2.02474e16 | 0.0406675 | ||||||||
\(529\) | 7.41656e17 | 1.47143 | ||||||||
\(530\) | 3.78955e17 | 0.742667 | ||||||||
\(531\) | 5.98085e17 | 1.15784 | ||||||||
\(532\) | 1.77285e17 | 0.339037 | ||||||||
\(533\) | −9.70093e17 | −1.83268 | ||||||||
\(534\) | 3.04152e16 | 0.0567639 | ||||||||
\(535\) | 4.57653e17 | 0.843794 | ||||||||
\(536\) | 3.64687e17 | 0.664277 | ||||||||
\(537\) | −3.40260e16 | −0.0612319 | ||||||||
\(538\) | −4.76927e17 | −0.847944 | ||||||||
\(539\) | −1.06489e17 | −0.187058 | ||||||||
\(540\) | −4.85229e16 | −0.0842145 | ||||||||
\(541\) | −4.36270e17 | −0.748122 | −0.374061 | − | 0.927404i | \(-0.622035\pi\) | ||||
−0.374061 | + | 0.927404i | \(0.622035\pi\) | |||||||
\(542\) | 5.39854e16 | 0.0914704 | ||||||||
\(543\) | −8.54504e16 | −0.143059 | ||||||||
\(544\) | −2.97088e16 | −0.0491465 | ||||||||
\(545\) | −7.58533e17 | −1.23993 | ||||||||
\(546\) | 4.01161e16 | 0.0647987 | ||||||||
\(547\) | 8.65775e17 | 1.38193 | 0.690967 | − | 0.722886i | \(-0.257185\pi\) | ||||
0.690967 | + | 0.722886i | \(0.257185\pi\) | |||||||
\(548\) | 4.31591e17 | 0.680767 | ||||||||
\(549\) | −5.53804e17 | −0.863248 | ||||||||
\(550\) | −3.20546e17 | −0.493779 | ||||||||
\(551\) | 4.66548e17 | 0.710250 | ||||||||
\(552\) | 4.58951e16 | 0.0690498 | ||||||||
\(553\) | 4.65839e16 | 0.0692664 | ||||||||
\(554\) | 8.22388e17 | 1.20855 | ||||||||
\(555\) | 2.41146e16 | 0.0350248 | ||||||||
\(556\) | −2.41663e17 | −0.346915 | ||||||||
\(557\) | −2.37958e17 | −0.337630 | −0.168815 | − | 0.985648i | \(-0.553994\pi\) | ||||
−0.168815 | + | 0.985648i | \(0.553994\pi\) | |||||||
\(558\) | −1.12764e17 | −0.158142 | ||||||||
\(559\) | 1.22954e18 | 1.70437 | ||||||||
\(560\) | −4.71120e16 | −0.0645519 | ||||||||
\(561\) | 3.33913e16 | 0.0452246 | ||||||||
\(562\) | −5.45040e17 | −0.729697 | ||||||||
\(563\) | −4.98751e17 | −0.660054 | −0.330027 | − | 0.943971i | \(-0.607058\pi\) | ||||
−0.330027 | + | 0.943971i | \(0.607058\pi\) | |||||||
\(564\) | −4.03396e16 | −0.0527736 | ||||||||
\(565\) | −1.73403e17 | −0.224254 | ||||||||
\(566\) | −5.26250e17 | −0.672799 | ||||||||
\(567\) | 2.85273e17 | 0.360554 | ||||||||
\(568\) | −2.11372e17 | −0.264109 | ||||||||
\(569\) | −1.27035e17 | −0.156926 | −0.0784629 | − | 0.996917i | \(-0.525001\pi\) | ||||
−0.0784629 | + | 0.996917i | \(0.525001\pi\) | |||||||
\(570\) | −8.81555e16 | −0.107662 | ||||||||
\(571\) | −6.42693e17 | −0.776013 | −0.388006 | − | 0.921657i | \(-0.626836\pi\) | ||||
−0.388006 | + | 0.921657i | \(0.626836\pi\) | |||||||
\(572\) | −1.07033e18 | −1.27774 | ||||||||
\(573\) | 6.52988e16 | 0.0770727 | ||||||||
\(574\) | 2.15057e17 | 0.250972 | ||||||||
\(575\) | −7.26588e17 | −0.838393 | ||||||||
\(576\) | −1.07870e17 | −0.123071 | ||||||||
\(577\) | −3.21707e17 | −0.362926 | −0.181463 | − | 0.983398i | \(-0.558083\pi\) | ||||
−0.181463 | + | 0.983398i | \(0.558083\pi\) | |||||||
\(578\) | 5.84898e17 | 0.652453 | ||||||||
\(579\) | 3.98157e16 | 0.0439181 | ||||||||
\(580\) | −1.23981e17 | −0.135230 | ||||||||
\(581\) | 1.65964e16 | 0.0179007 | ||||||||
\(582\) | 6.76640e16 | 0.0721703 | ||||||||
\(583\) | −1.90858e18 | −2.01310 | ||||||||
\(584\) | 2.98290e17 | 0.311139 | ||||||||
\(585\) | 1.27255e18 | 1.31268 | ||||||||
\(586\) | 5.51343e17 | 0.562454 | ||||||||
\(587\) | 5.64618e17 | 0.569649 | 0.284825 | − | 0.958580i | \(-0.408065\pi\) | ||||
0.284825 | + | 0.958580i | \(0.408065\pi\) | |||||||
\(588\) | −8.89320e15 | −0.00887371 | ||||||||
\(589\) | −4.12946e17 | −0.407516 | ||||||||
\(590\) | −5.82029e17 | −0.568076 | ||||||||
\(591\) | 6.98144e16 | 0.0673948 | ||||||||
\(592\) | 1.08058e17 | 0.103173 | ||||||||
\(593\) | −7.34438e17 | −0.693585 | −0.346792 | − | 0.937942i | \(-0.612729\pi\) | ||||
−0.346792 | + | 0.937942i | \(0.612729\pi\) | |||||||
\(594\) | 2.44383e17 | 0.228275 | ||||||||
\(595\) | −7.76956e16 | −0.0717854 | ||||||||
\(596\) | −6.43067e17 | −0.587700 | ||||||||
\(597\) | −9.75412e16 | −0.0881769 | ||||||||
\(598\) | −2.42613e18 | −2.16948 | ||||||||
\(599\) | 1.62460e18 | 1.43705 | 0.718526 | − | 0.695500i | \(-0.244817\pi\) | ||||
0.718526 | + | 0.695500i | \(0.244817\pi\) | |||||||
\(600\) | −2.67698e16 | −0.0234240 | ||||||||
\(601\) | 1.35612e18 | 1.17385 | 0.586927 | − | 0.809640i | \(-0.300338\pi\) | ||||
0.586927 | + | 0.809640i | \(0.300338\pi\) | |||||||
\(602\) | −2.72572e17 | −0.233402 | ||||||||
\(603\) | 2.18374e18 | 1.84986 | ||||||||
\(604\) | 2.65521e17 | 0.222515 | ||||||||
\(605\) | −5.88788e17 | −0.488145 | ||||||||
\(606\) | −9.12005e16 | −0.0748040 | ||||||||
\(607\) | 2.18499e17 | 0.177306 | 0.0886528 | − | 0.996063i | \(-0.471744\pi\) | ||||
0.0886528 | + | 0.996063i | \(0.471744\pi\) | |||||||
\(608\) | −3.95025e17 | −0.317140 | ||||||||
\(609\) | −2.34035e16 | −0.0185896 | ||||||||
\(610\) | 5.38937e17 | 0.423539 | ||||||||
\(611\) | 2.13245e18 | 1.65810 | ||||||||
\(612\) | −1.77896e17 | −0.136862 | ||||||||
\(613\) | −1.30291e18 | −0.991797 | −0.495898 | − | 0.868380i | \(-0.665161\pi\) | ||||
−0.495898 | + | 0.868380i | \(0.665161\pi\) | |||||||
\(614\) | 1.41291e18 | 1.06419 | ||||||||
\(615\) | −1.06937e17 | −0.0796968 | ||||||||
\(616\) | 2.37277e17 | 0.174977 | ||||||||
\(617\) | 2.22565e18 | 1.62406 | 0.812031 | − | 0.583614i | \(-0.198362\pi\) | ||||
0.812031 | + | 0.583614i | \(0.198362\pi\) | |||||||
\(618\) | 1.26750e16 | 0.00915215 | ||||||||
\(619\) | −1.86509e18 | −1.33263 | −0.666317 | − | 0.745668i | \(-0.732130\pi\) | ||||
−0.666317 | + | 0.745668i | \(0.732130\pi\) | |||||||
\(620\) | 1.09737e17 | 0.0775900 | ||||||||
\(621\) | 5.53948e17 | 0.387591 | ||||||||
\(622\) | 1.52503e18 | 1.05594 | ||||||||
\(623\) | 3.56432e17 | 0.244233 | ||||||||
\(624\) | −8.93861e16 | −0.0606136 | ||||||||
\(625\) | −2.71630e17 | −0.182288 | ||||||||
\(626\) | 1.67964e18 | 1.11553 | ||||||||
\(627\) | 4.43990e17 | 0.291833 | ||||||||
\(628\) | −1.83309e16 | −0.0119246 | ||||||||
\(629\) | 1.78205e17 | 0.114734 | ||||||||
\(630\) | −2.82106e17 | −0.179763 | ||||||||
\(631\) | 1.09793e18 | 0.692445 | 0.346222 | − | 0.938152i | \(-0.387464\pi\) | ||||
0.346222 | + | 0.938152i | \(0.387464\pi\) | |||||||
\(632\) | −1.03798e17 | −0.0647928 | ||||||||
\(633\) | 2.76828e16 | 0.0171035 | ||||||||
\(634\) | −1.68310e18 | −1.02927 | ||||||||
\(635\) | −7.04369e17 | −0.426354 | ||||||||
\(636\) | −1.59392e17 | −0.0954980 | ||||||||
\(637\) | 4.70116e17 | 0.278804 | ||||||||
\(638\) | 6.24423e17 | 0.366559 | ||||||||
\(639\) | −1.26569e18 | −0.735483 | ||||||||
\(640\) | 1.04974e17 | 0.0603828 | ||||||||
\(641\) | −1.03316e18 | −0.588290 | −0.294145 | − | 0.955761i | \(-0.595035\pi\) | ||||
−0.294145 | + | 0.955761i | \(0.595035\pi\) | |||||||
\(642\) | −1.92493e17 | −0.108502 | ||||||||
\(643\) | −2.84730e18 | −1.58877 | −0.794386 | − | 0.607413i | \(-0.792207\pi\) | ||||
−0.794386 | + | 0.607413i | \(0.792207\pi\) | |||||||
\(644\) | 5.37841e17 | 0.297095 | ||||||||
\(645\) | 1.35537e17 | 0.0741172 | ||||||||
\(646\) | −6.51464e17 | −0.352678 | ||||||||
\(647\) | −2.96154e18 | −1.58723 | −0.793616 | − | 0.608419i | \(-0.791804\pi\) | ||||
−0.793616 | + | 0.608419i | \(0.791804\pi\) | |||||||
\(648\) | −6.35642e17 | −0.337268 | ||||||||
\(649\) | 2.93136e18 | 1.53985 | ||||||||
\(650\) | 1.41512e18 | 0.735961 | ||||||||
\(651\) | 2.07147e16 | 0.0106660 | ||||||||
\(652\) | −2.94582e17 | −0.150175 | ||||||||
\(653\) | −1.76423e18 | −0.890471 | −0.445236 | − | 0.895413i | \(-0.646880\pi\) | ||||
−0.445236 | + | 0.895413i | \(0.646880\pi\) | |||||||
\(654\) | 3.19046e17 | 0.159440 | ||||||||
\(655\) | 4.24504e17 | 0.210046 | ||||||||
\(656\) | −4.79187e17 | −0.234763 | ||||||||
\(657\) | 1.78616e18 | 0.866453 | ||||||||
\(658\) | −4.72735e17 | −0.227065 | ||||||||
\(659\) | −2.97544e18 | −1.41513 | −0.707565 | − | 0.706648i | \(-0.750207\pi\) | ||||
−0.707565 | + | 0.706648i | \(0.750207\pi\) | |||||||
\(660\) | −1.17986e17 | −0.0555643 | ||||||||
\(661\) | −2.68609e18 | −1.25260 | −0.626298 | − | 0.779584i | \(-0.715431\pi\) | ||||
−0.626298 | + | 0.779584i | \(0.715431\pi\) | |||||||
\(662\) | 2.12860e18 | 0.982917 | ||||||||
\(663\) | −1.47413e17 | −0.0674058 | ||||||||
\(664\) | −3.69800e16 | −0.0167446 | ||||||||
\(665\) | −1.03309e18 | −0.463229 | ||||||||
\(666\) | 6.47048e17 | 0.287312 | ||||||||
\(667\) | 1.41539e18 | 0.622385 | ||||||||
\(668\) | 5.08935e17 | 0.221623 | ||||||||
\(669\) | 1.55246e17 | 0.0669498 | ||||||||
\(670\) | −2.12512e18 | −0.907605 | ||||||||
\(671\) | −2.71432e18 | −1.14806 | ||||||||
\(672\) | 1.98157e16 | 0.00830060 | ||||||||
\(673\) | −4.74026e17 | −0.196655 | −0.0983273 | − | 0.995154i | \(-0.531349\pi\) | ||||
−0.0983273 | + | 0.995154i | \(0.531349\pi\) | |||||||
\(674\) | −1.24500e18 | −0.511542 | ||||||||
\(675\) | −3.23107e17 | −0.131484 | ||||||||
\(676\) | 3.48459e18 | 1.40442 | ||||||||
\(677\) | 3.87922e16 | 0.0154853 | 0.00774263 | − | 0.999970i | \(-0.497535\pi\) | ||||
0.00774263 | + | 0.999970i | \(0.497535\pi\) | |||||||
\(678\) | 7.29346e16 | 0.0288364 | ||||||||
\(679\) | 7.92948e17 | 0.310521 | ||||||||
\(680\) | 1.73120e17 | 0.0671491 | ||||||||
\(681\) | −1.78765e17 | −0.0686794 | ||||||||
\(682\) | −5.52683e17 | −0.210318 | ||||||||
\(683\) | −9.31461e17 | −0.351099 | −0.175550 | − | 0.984471i | \(-0.556170\pi\) | ||||
−0.175550 | + | 0.984471i | \(0.556170\pi\) | |||||||
\(684\) | −2.36541e18 | −0.883165 | ||||||||
\(685\) | −2.51499e18 | −0.930137 | ||||||||
\(686\) | −1.04218e17 | −0.0381802 | ||||||||
\(687\) | −3.67972e17 | −0.133535 | ||||||||
\(688\) | 6.07341e17 | 0.218327 | ||||||||
\(689\) | 8.42584e18 | 3.00046 | ||||||||
\(690\) | −2.67442e17 | −0.0943432 | ||||||||
\(691\) | −2.86951e18 | −1.00277 | −0.501384 | − | 0.865225i | \(-0.667176\pi\) | ||||
−0.501384 | + | 0.865225i | \(0.667176\pi\) | |||||||
\(692\) | 2.04754e18 | 0.708830 | ||||||||
\(693\) | 1.42081e18 | 0.487271 | ||||||||
\(694\) | −2.07171e18 | −0.703869 | ||||||||
\(695\) | 1.40823e18 | 0.473993 | ||||||||
\(696\) | 5.21474e16 | 0.0173889 | ||||||||
\(697\) | −7.90260e17 | −0.261070 | ||||||||
\(698\) | 3.34831e18 | 1.09589 | ||||||||
\(699\) | −4.10815e16 | −0.0133212 | ||||||||
\(700\) | −3.13712e17 | −0.100785 | ||||||||
\(701\) | 1.12523e17 | 0.0358158 | 0.0179079 | − | 0.999840i | \(-0.494299\pi\) | ||||
0.0179079 | + | 0.999840i | \(0.494299\pi\) | |||||||
\(702\) | −1.07888e18 | −0.340236 | ||||||||
\(703\) | 2.36952e18 | 0.740373 | ||||||||
\(704\) | −5.28697e17 | −0.163676 | ||||||||
\(705\) | 2.35068e17 | 0.0721050 | ||||||||
\(706\) | 1.64620e18 | 0.500324 | ||||||||
\(707\) | −1.06877e18 | −0.321853 | ||||||||
\(708\) | 2.44806e17 | 0.0730477 | ||||||||
\(709\) | 3.66046e18 | 1.08227 | 0.541134 | − | 0.840937i | \(-0.317995\pi\) | ||||
0.541134 | + | 0.840937i | \(0.317995\pi\) | |||||||
\(710\) | 1.23171e18 | 0.360853 | ||||||||
\(711\) | −6.21540e17 | −0.180433 | ||||||||
\(712\) | −7.94198e17 | −0.228459 | ||||||||
\(713\) | −1.25278e18 | −0.357102 | ||||||||
\(714\) | 3.26795e16 | 0.00923074 | ||||||||
\(715\) | 6.23705e18 | 1.74578 | ||||||||
\(716\) | 8.88482e17 | 0.246442 | ||||||||
\(717\) | −7.14691e16 | −0.0196446 | ||||||||
\(718\) | −1.94991e18 | −0.531137 | ||||||||
\(719\) | 1.97154e18 | 0.532190 | 0.266095 | − | 0.963947i | \(-0.414266\pi\) | ||||
0.266095 | + | 0.963947i | \(0.414266\pi\) | |||||||
\(720\) | 6.28585e17 | 0.168152 | ||||||||
\(721\) | 1.48537e17 | 0.0393782 | ||||||||
\(722\) | −5.97084e18 | −1.56871 | ||||||||
\(723\) | −4.45036e17 | −0.115877 | ||||||||
\(724\) | 2.23127e18 | 0.575774 | ||||||||
\(725\) | −8.25572e17 | −0.211134 | ||||||||
\(726\) | 2.47649e17 | 0.0627696 | ||||||||
\(727\) | −7.34060e17 | −0.184399 | −0.0921994 | − | 0.995741i | \(-0.529390\pi\) | ||||
−0.0921994 | + | 0.995741i | \(0.529390\pi\) | |||||||
\(728\) | −1.04751e18 | −0.260797 | ||||||||
\(729\) | −3.68209e18 | −0.908586 | ||||||||
\(730\) | −1.73821e18 | −0.425112 | ||||||||
\(731\) | 1.00161e18 | 0.242792 | ||||||||
\(732\) | −2.26681e17 | −0.0544620 | ||||||||
\(733\) | −1.48745e18 | −0.354215 | −0.177108 | − | 0.984192i | \(-0.556674\pi\) | ||||
−0.177108 | + | 0.984192i | \(0.556674\pi\) | |||||||
\(734\) | 1.11229e18 | 0.262538 | ||||||||
\(735\) | 5.18228e16 | 0.0121242 | ||||||||
\(736\) | −1.19841e18 | −0.277907 | ||||||||
\(737\) | 1.07030e19 | 2.46019 | ||||||||
\(738\) | −2.86937e18 | −0.653762 | ||||||||
\(739\) | 1.88091e18 | 0.424796 | 0.212398 | − | 0.977183i | \(-0.431873\pi\) | ||||
0.212398 | + | 0.977183i | \(0.431873\pi\) | |||||||
\(740\) | −6.29678e17 | −0.140965 | ||||||||
\(741\) | −1.96009e18 | −0.434967 | ||||||||
\(742\) | −1.86790e18 | −0.410891 | ||||||||
\(743\) | −5.79526e18 | −1.26371 | −0.631853 | − | 0.775088i | \(-0.717705\pi\) | ||||
−0.631853 | + | 0.775088i | \(0.717705\pi\) | |||||||
\(744\) | −4.61562e16 | −0.00997714 | ||||||||
\(745\) | 3.74731e18 | 0.802979 | ||||||||
\(746\) | 2.96946e17 | 0.0630777 | ||||||||
\(747\) | −2.21436e17 | −0.0466298 | ||||||||
\(748\) | −8.71911e17 | −0.182017 | ||||||||
\(749\) | −2.25580e18 | −0.466841 | ||||||||
\(750\) | 4.48500e17 | 0.0920161 | ||||||||
\(751\) | −4.05166e15 | −0.000824087 0 | −0.000412043 | − | 1.00000i | \(-0.500131\pi\) | ||||
−0.000412043 | 1.00000i | \(0.500131\pi\) | ||||||||
\(752\) | 1.05334e18 | 0.212400 | ||||||||
\(753\) | 7.91860e17 | 0.158300 | ||||||||
\(754\) | −2.75664e18 | −0.546345 | ||||||||
\(755\) | −1.54726e18 | −0.304023 | ||||||||
\(756\) | 2.39173e17 | 0.0465929 | ||||||||
\(757\) | 6.86221e17 | 0.132538 | 0.0662691 | − | 0.997802i | \(-0.478890\pi\) | ||||
0.0662691 | + | 0.997802i | \(0.478890\pi\) | |||||||
\(758\) | 5.59562e17 | 0.107152 | ||||||||
\(759\) | 1.34696e18 | 0.255730 | ||||||||
\(760\) | 2.30191e18 | 0.433311 | ||||||||
\(761\) | 2.75544e18 | 0.514269 | 0.257135 | − | 0.966376i | \(-0.417222\pi\) | ||||
0.257135 | + | 0.966376i | \(0.417222\pi\) | |||||||
\(762\) | 2.96264e17 | 0.0548240 | ||||||||
\(763\) | 3.73886e18 | 0.686010 | ||||||||
\(764\) | −1.70508e18 | −0.310197 | ||||||||
\(765\) | 1.03664e18 | 0.186995 | ||||||||
\(766\) | 4.82019e18 | 0.862139 | ||||||||
\(767\) | −1.29411e19 | −2.29509 | ||||||||
\(768\) | −4.41531e16 | −0.00776450 | ||||||||
\(769\) | −4.07852e18 | −0.711183 | −0.355592 | − | 0.934641i | \(-0.615721\pi\) | ||||
−0.355592 | + | 0.934641i | \(0.615721\pi\) | |||||||
\(770\) | −1.38267e18 | −0.239072 | ||||||||
\(771\) | −2.48502e17 | −0.0426065 | ||||||||
\(772\) | −1.03966e18 | −0.176759 | ||||||||
\(773\) | −8.60493e17 | −0.145071 | −0.0725355 | − | 0.997366i | \(-0.523109\pi\) | ||||
−0.0725355 | + | 0.997366i | \(0.523109\pi\) | |||||||
\(774\) | 3.63676e18 | 0.607992 | ||||||||
\(775\) | 7.30721e17 | 0.121141 | ||||||||
\(776\) | −1.76684e18 | −0.290466 | ||||||||
\(777\) | −1.18862e17 | −0.0193780 | ||||||||
\(778\) | 1.44326e18 | 0.233333 | ||||||||
\(779\) | −1.05078e19 | −1.68468 | ||||||||
\(780\) | 5.20875e17 | 0.0828168 | ||||||||
\(781\) | −6.20346e18 | −0.978143 | ||||||||
\(782\) | −1.97638e18 | −0.309048 | ||||||||
\(783\) | 6.29412e17 | 0.0976076 | ||||||||
\(784\) | 2.32218e17 | 0.0357143 | ||||||||
\(785\) | 1.06818e17 | 0.0162927 | ||||||||
\(786\) | −1.78550e17 | −0.0270093 | ||||||||
\(787\) | 2.29610e18 | 0.344473 | 0.172236 | − | 0.985056i | \(-0.444901\pi\) | ||||
0.172236 | + | 0.985056i | \(0.444901\pi\) | |||||||
\(788\) | −1.82299e18 | −0.271246 | ||||||||
\(789\) | 1.07933e17 | 0.0159277 | ||||||||
\(790\) | 6.04854e17 | 0.0885267 | ||||||||
\(791\) | 8.54713e17 | 0.124072 | ||||||||
\(792\) | −3.16584e18 | −0.455800 | ||||||||
\(793\) | 1.19829e19 | 1.71115 | ||||||||
\(794\) | 2.09277e18 | 0.296406 | ||||||||
\(795\) | 9.28814e17 | 0.130480 | ||||||||
\(796\) | 2.54699e18 | 0.354888 | ||||||||
\(797\) | −1.04185e19 | −1.43988 | −0.719938 | − | 0.694039i | \(-0.755830\pi\) | ||||
−0.719938 | + | 0.694039i | \(0.755830\pi\) | |||||||
\(798\) | 4.34525e17 | 0.0595656 | ||||||||
\(799\) | 1.73714e18 | 0.236201 | ||||||||
\(800\) | 6.99009e17 | 0.0942753 | ||||||||
\(801\) | −4.75565e18 | −0.636207 | ||||||||
\(802\) | −1.96935e18 | −0.261331 | ||||||||
\(803\) | 8.75439e18 | 1.15232 | ||||||||
\(804\) | 8.93844e17 | 0.116707 | ||||||||
\(805\) | −3.13413e18 | −0.405923 | ||||||||
\(806\) | 2.43993e18 | 0.313473 | ||||||||
\(807\) | −1.16894e18 | −0.148976 | ||||||||
\(808\) | 2.38142e18 | 0.301066 | ||||||||
\(809\) | −5.32128e18 | −0.667345 | −0.333673 | − | 0.942689i | \(-0.608288\pi\) | ||||
−0.333673 | + | 0.942689i | \(0.608288\pi\) | |||||||
\(810\) | 3.70404e18 | 0.460811 | ||||||||
\(811\) | 1.29734e18 | 0.160110 | 0.0800550 | − | 0.996790i | \(-0.474490\pi\) | ||||
0.0800550 | + | 0.996790i | \(0.474490\pi\) | |||||||
\(812\) | 6.11111e17 | 0.0748179 | ||||||||
\(813\) | 1.32318e17 | 0.0160705 | ||||||||
\(814\) | 3.17134e18 | 0.382106 | ||||||||
\(815\) | 1.71660e18 | 0.205185 | ||||||||
\(816\) | −7.28159e16 | −0.00863457 | ||||||||
\(817\) | 1.33180e19 | 1.56673 | ||||||||
\(818\) | 9.99776e18 | 1.16683 | ||||||||
\(819\) | −6.27247e18 | −0.726261 | ||||||||
\(820\) | 2.79234e18 | 0.320758 | ||||||||
\(821\) | −9.96562e18 | −1.13573 | −0.567863 | − | 0.823123i | \(-0.692230\pi\) | ||||
−0.567863 | + | 0.823123i | \(0.692230\pi\) | |||||||
\(822\) | 1.05782e18 | 0.119604 | ||||||||
\(823\) | 1.59169e19 | 1.78549 | 0.892747 | − | 0.450558i | \(-0.148775\pi\) | ||||
0.892747 | + | 0.450558i | \(0.148775\pi\) | |||||||
\(824\) | −3.30968e17 | −0.0368349 | ||||||||
\(825\) | −7.85655e17 | −0.0867523 | ||||||||
\(826\) | 2.86886e18 | 0.314296 | ||||||||
\(827\) | 3.63722e18 | 0.395352 | 0.197676 | − | 0.980267i | \(-0.436661\pi\) | ||||
0.197676 | + | 0.980267i | \(0.436661\pi\) | |||||||
\(828\) | −7.17607e18 | −0.773908 | ||||||||
\(829\) | 1.00664e18 | 0.107713 | 0.0538567 | − | 0.998549i | \(-0.482849\pi\) | ||||
0.0538567 | + | 0.998549i | \(0.482849\pi\) | |||||||
\(830\) | 2.15491e17 | 0.0228782 | ||||||||
\(831\) | 2.01567e18 | 0.212330 | ||||||||
\(832\) | 2.33404e18 | 0.243953 | ||||||||
\(833\) | 3.82967e17 | 0.0397163 | ||||||||
\(834\) | −5.92313e17 | −0.0609497 | ||||||||
\(835\) | −2.96569e18 | −0.302805 | ||||||||
\(836\) | −1.15934e19 | −1.17455 | ||||||||
\(837\) | −5.57099e17 | −0.0560037 | ||||||||
\(838\) | 9.34764e18 | 0.932429 | ||||||||
\(839\) | 1.17697e19 | 1.16496 | 0.582481 | − | 0.812844i | \(-0.302082\pi\) | ||||
0.582481 | + | 0.812844i | \(0.302082\pi\) | |||||||
\(840\) | −1.15471e17 | −0.0113412 | ||||||||
\(841\) | −8.65242e18 | −0.843264 | ||||||||
\(842\) | −6.16556e18 | −0.596271 | ||||||||
\(843\) | −1.33589e18 | −0.128201 | ||||||||
\(844\) | −7.22850e17 | −0.0688370 | ||||||||
\(845\) | −2.03056e19 | −1.91887 | ||||||||
\(846\) | 6.30741e18 | 0.591485 | ||||||||
\(847\) | 2.90218e18 | 0.270073 | ||||||||
\(848\) | 4.16202e18 | 0.384354 | ||||||||
\(849\) | −1.28983e18 | −0.118204 | ||||||||
\(850\) | 1.15278e18 | 0.104840 | ||||||||
\(851\) | 7.18854e18 | 0.648781 | ||||||||
\(852\) | −5.18070e17 | −0.0464014 | ||||||||
\(853\) | 6.77053e18 | 0.601803 | 0.300901 | − | 0.953655i | \(-0.402713\pi\) | ||||
0.300901 | + | 0.953655i | \(0.402713\pi\) | |||||||
\(854\) | −2.65646e18 | −0.234329 | ||||||||
\(855\) | 1.37838e19 | 1.20667 | ||||||||
\(856\) | 5.02635e18 | 0.436690 | ||||||||
\(857\) | 1.30576e19 | 1.12587 | 0.562933 | − | 0.826503i | \(-0.309673\pi\) | ||||
0.562933 | + | 0.826503i | \(0.309673\pi\) | |||||||
\(858\) | −2.62336e18 | −0.224486 | ||||||||
\(859\) | −1.06213e19 | −0.902034 | −0.451017 | − | 0.892515i | \(-0.648939\pi\) | ||||
−0.451017 | + | 0.892515i | \(0.648939\pi\) | |||||||
\(860\) | −3.53912e18 | −0.298302 | ||||||||
\(861\) | 5.27102e17 | 0.0440934 | ||||||||
\(862\) | 9.19530e17 | 0.0763429 | ||||||||
\(863\) | 1.70375e19 | 1.40390 | 0.701949 | − | 0.712227i | \(-0.252314\pi\) | ||||
0.701949 | + | 0.712227i | \(0.252314\pi\) | |||||||
\(864\) | −5.32922e17 | −0.0435837 | ||||||||
\(865\) | −1.19315e19 | −0.968478 | ||||||||
\(866\) | −1.71923e19 | −1.38506 | ||||||||
\(867\) | 1.43358e18 | 0.114630 | ||||||||
\(868\) | −5.40900e17 | −0.0429278 | ||||||||
\(869\) | −3.04631e18 | −0.239964 | ||||||||
\(870\) | −3.03876e17 | −0.0237586 | ||||||||
\(871\) | −4.72508e19 | −3.66683 | ||||||||
\(872\) | −8.33089e18 | −0.641703 | ||||||||
\(873\) | −1.05798e19 | −0.808882 | ||||||||
\(874\) | −2.62791e19 | −1.99428 | ||||||||
\(875\) | 5.25592e18 | 0.395910 | ||||||||
\(876\) | 7.31105e17 | 0.0546642 | ||||||||
\(877\) | −1.26202e19 | −0.936633 | −0.468316 | − | 0.883561i | \(-0.655139\pi\) | ||||
−0.468316 | + | 0.883561i | \(0.655139\pi\) | |||||||
\(878\) | −3.68363e18 | −0.271370 | ||||||||
\(879\) | 1.35134e18 | 0.0988179 | ||||||||
\(880\) | 3.08085e18 | 0.223631 | ||||||||
\(881\) | 8.97828e18 | 0.646919 | 0.323459 | − | 0.946242i | \(-0.395154\pi\) | ||||
0.323459 | + | 0.946242i | \(0.395154\pi\) | |||||||
\(882\) | 1.39052e18 | 0.0994562 | ||||||||
\(883\) | 1.09184e19 | 0.775201 | 0.387601 | − | 0.921827i | \(-0.373304\pi\) | ||||
0.387601 | + | 0.921827i | \(0.373304\pi\) | |||||||
\(884\) | 3.84923e18 | 0.271290 | ||||||||
\(885\) | −1.42655e18 | −0.0998056 | ||||||||
\(886\) | 6.96838e18 | 0.483964 | ||||||||
\(887\) | 9.88099e18 | 0.681235 | 0.340618 | − | 0.940202i | \(-0.389364\pi\) | ||||
0.340618 | + | 0.940202i | \(0.389364\pi\) | |||||||
\(888\) | 2.64848e17 | 0.0181264 | ||||||||
\(889\) | 3.47188e18 | 0.235887 | ||||||||
\(890\) | 4.62798e18 | 0.312145 | ||||||||
\(891\) | −1.86552e19 | −1.24909 | ||||||||
\(892\) | −4.05376e18 | −0.269455 | ||||||||
\(893\) | 2.30980e19 | 1.52419 | ||||||||
\(894\) | −1.57615e18 | −0.103253 | ||||||||
\(895\) | −5.17740e18 | −0.336715 | ||||||||
\(896\) | −5.17426e17 | −0.0334077 | ||||||||
\(897\) | −5.94642e18 | −0.381158 | ||||||||
\(898\) | 7.90542e17 | 0.0503071 | ||||||||
\(899\) | −1.42344e18 | −0.0899295 | ||||||||
\(900\) | 4.18566e18 | 0.262535 | ||||||||
\(901\) | 6.86388e18 | 0.427423 | ||||||||
\(902\) | −1.40635e19 | −0.869460 | ||||||||
\(903\) | −6.68071e17 | −0.0410064 | ||||||||
\(904\) | −1.90446e18 | −0.116059 | ||||||||
\(905\) | −1.30022e19 | −0.786683 | ||||||||
\(906\) | 6.50790e17 | 0.0390938 | ||||||||
\(907\) | 2.22017e19 | 1.32416 | 0.662078 | − | 0.749435i | \(-0.269675\pi\) | ||||
0.662078 | + | 0.749435i | \(0.269675\pi\) | |||||||
\(908\) | 4.66790e18 | 0.276416 | ||||||||
\(909\) | 1.42599e19 | 0.838401 | ||||||||
\(910\) | 6.10408e18 | 0.356329 | ||||||||
\(911\) | 4.58123e18 | 0.265530 | 0.132765 | − | 0.991148i | \(-0.457615\pi\) | ||||
0.132765 | + | 0.991148i | \(0.457615\pi\) | |||||||
\(912\) | −9.68203e17 | −0.0557186 | ||||||||
\(913\) | −1.08531e18 | −0.0620146 | ||||||||
\(914\) | 1.42805e18 | 0.0810204 | ||||||||
\(915\) | 1.32093e18 | 0.0744118 | ||||||||
\(916\) | 9.60844e18 | 0.537443 | ||||||||
\(917\) | −2.09241e18 | −0.116211 | ||||||||
\(918\) | −8.78878e17 | −0.0484676 | ||||||||
\(919\) | 2.38248e19 | 1.30460 | 0.652302 | − | 0.757959i | \(-0.273803\pi\) | ||||
0.652302 | + | 0.757959i | \(0.273803\pi\) | |||||||
\(920\) | 6.98342e18 | 0.379706 | ||||||||
\(921\) | 3.46302e18 | 0.186968 | ||||||||
\(922\) | −1.44073e19 | −0.772381 | ||||||||
\(923\) | 2.73864e19 | 1.45789 | ||||||||
\(924\) | 5.81563e17 | 0.0307418 | ||||||||
\(925\) | −4.19294e18 | −0.220088 | ||||||||
\(926\) | 1.48552e19 | 0.774298 | ||||||||
\(927\) | −1.98184e18 | −0.102577 | ||||||||
\(928\) | −1.36167e18 | −0.0699858 | ||||||||
\(929\) | −6.20632e18 | −0.316761 | −0.158381 | − | 0.987378i | \(-0.550627\pi\) | ||||
−0.158381 | + | 0.987378i | \(0.550627\pi\) | |||||||
\(930\) | 2.68963e17 | 0.0136318 | ||||||||
\(931\) | 5.09215e18 | 0.256288 | ||||||||
\(932\) | 1.07272e18 | 0.0536143 | ||||||||
\(933\) | 3.73782e18 | 0.185519 | ||||||||
\(934\) | −2.61505e19 | −1.28892 | ||||||||
\(935\) | 5.08084e18 | 0.248691 | ||||||||
\(936\) | 1.39762e19 | 0.679355 | ||||||||
\(937\) | −6.23647e18 | −0.301045 | −0.150523 | − | 0.988607i | \(-0.548096\pi\) | ||||
−0.150523 | + | 0.988607i | \(0.548096\pi\) | |||||||
\(938\) | 1.04749e19 | 0.502146 | ||||||||
\(939\) | 4.11678e18 | 0.195989 | ||||||||
\(940\) | −6.13809e18 | −0.290203 | ||||||||
\(941\) | 2.44374e19 | 1.14742 | 0.573710 | − | 0.819059i | \(-0.305504\pi\) | ||||
0.573710 | + | 0.819059i | \(0.305504\pi\) | |||||||
\(942\) | −4.49287e16 | −0.00209504 | ||||||||
\(943\) | −3.18779e19 | −1.47626 | ||||||||
\(944\) | −6.39236e18 | −0.293997 | ||||||||
\(945\) | −1.39372e18 | −0.0636602 | ||||||||
\(946\) | 1.78246e19 | 0.808588 | ||||||||
\(947\) | −3.75329e19 | −1.69097 | −0.845487 | − | 0.533996i | \(-0.820690\pi\) | ||||
−0.845487 | + | 0.533996i | \(0.820690\pi\) | |||||||
\(948\) | −2.54407e17 | −0.0113835 | ||||||||
\(949\) | −3.86480e19 | −1.71750 | ||||||||
\(950\) | 1.53281e19 | 0.676526 | ||||||||
\(951\) | −4.12526e18 | −0.180833 | ||||||||
\(952\) | −8.53323e17 | −0.0371512 | ||||||||
\(953\) | 2.13125e19 | 0.921573 | 0.460786 | − | 0.887511i | \(-0.347567\pi\) | ||||
0.460786 | + | 0.887511i | \(0.347567\pi\) | |||||||
\(954\) | 2.49222e19 | 1.07034 | ||||||||
\(955\) | 9.93590e18 | 0.423824 | ||||||||
\(956\) | 1.86619e18 | 0.0790644 | ||||||||
\(957\) | 1.53045e18 | 0.0644010 | ||||||||
\(958\) | −1.31758e19 | −0.550683 | ||||||||
\(959\) | 1.23965e19 | 0.514612 | ||||||||
\(960\) | 2.57291e17 | 0.0106087 | ||||||||
\(961\) | −2.31576e19 | −0.948402 | ||||||||
\(962\) | −1.40005e19 | −0.569516 | ||||||||
\(963\) | 3.00978e19 | 1.21608 | ||||||||
\(964\) | 1.16207e19 | 0.466373 | ||||||||
\(965\) | 6.05837e18 | 0.241506 | ||||||||
\(966\) | 1.31824e18 | 0.0521968 | ||||||||
\(967\) | −1.72188e19 | −0.677222 | −0.338611 | − | 0.940926i | \(-0.609957\pi\) | ||||
−0.338611 | + | 0.940926i | \(0.609957\pi\) | |||||||
\(968\) | −6.46659e18 | −0.252631 | ||||||||
\(969\) | −1.59673e18 | −0.0619622 | ||||||||
\(970\) | 1.02958e19 | 0.396865 | ||||||||
\(971\) | −4.71671e19 | −1.80598 | −0.902992 | − | 0.429656i | \(-0.858635\pi\) | ||||
−0.902992 | + | 0.429656i | \(0.858635\pi\) | |||||||
\(972\) | −4.79911e18 | −0.182528 | ||||||||
\(973\) | −6.94125e18 | −0.262243 | ||||||||
\(974\) | −1.55030e19 | −0.581812 | ||||||||
\(975\) | 3.46843e18 | 0.129301 | ||||||||
\(976\) | 5.91908e18 | 0.219195 | ||||||||
\(977\) | 3.68129e19 | 1.35421 | 0.677105 | − | 0.735887i | \(-0.263234\pi\) | ||||
0.677105 | + | 0.735887i | \(0.263234\pi\) | |||||||
\(978\) | −7.22017e17 | −0.0263843 | ||||||||
\(979\) | −2.33086e19 | −0.846113 | ||||||||
\(980\) | −1.35319e18 | −0.0487967 | ||||||||
\(981\) | −4.98853e19 | −1.78700 | ||||||||
\(982\) | 1.28148e19 | 0.456024 | ||||||||
\(983\) | −5.24638e19 | −1.85465 | −0.927325 | − | 0.374258i | \(-0.877898\pi\) | ||||
−0.927325 | + | 0.374258i | \(0.877898\pi\) | |||||||
\(984\) | −1.17448e18 | −0.0412456 | ||||||||
\(985\) | 1.06230e19 | 0.370605 | ||||||||
\(986\) | −2.24562e18 | −0.0778282 | ||||||||
\(987\) | −1.15867e18 | −0.0398931 | ||||||||
\(988\) | 5.11816e19 | 1.75063 | ||||||||
\(989\) | 4.04034e19 | 1.37291 | ||||||||
\(990\) | 1.84481e19 | 0.622763 | ||||||||
\(991\) | −2.94165e19 | −0.986535 | −0.493268 | − | 0.869878i | \(-0.664198\pi\) | ||||
−0.493268 | + | 0.869878i | \(0.664198\pi\) | |||||||
\(992\) | 1.20523e18 | 0.0401553 | ||||||||
\(993\) | 5.21717e18 | 0.172689 | ||||||||
\(994\) | −6.07121e18 | −0.199647 | ||||||||
\(995\) | −1.48419e19 | −0.484886 | ||||||||
\(996\) | −9.06375e16 | −0.00294186 | ||||||||
\(997\) | 2.42460e19 | 0.781847 | 0.390924 | − | 0.920423i | \(-0.372156\pi\) | ||||
0.390924 | + | 0.920423i | \(0.372156\pi\) | |||||||
\(998\) | −1.98954e19 | −0.637387 | ||||||||
\(999\) | 3.19668e18 | 0.101747 |
(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 | 14.14.a.c.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 126.14.a.l.1.2 | 2 | |||
4.3 | odd | 2 | 112.14.a.d.1.2 | 2 | |||
7.2 | even | 3 | 98.14.c.l.67.2 | 4 | |||
7.3 | odd | 6 | 98.14.c.m.79.1 | 4 | |||
7.4 | even | 3 | 98.14.c.l.79.2 | 4 | |||
7.5 | odd | 6 | 98.14.c.m.67.1 | 4 | |||
7.6 | odd | 2 | 98.14.a.e.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.14.a.c.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
98.14.a.e.1.2 | 2 | 7.6 | odd | 2 | |||
98.14.c.l.67.2 | 4 | 7.2 | even | 3 | |||
98.14.c.l.79.2 | 4 | 7.4 | even | 3 | |||
98.14.c.m.67.1 | 4 | 7.5 | odd | 6 | |||
98.14.c.m.79.1 | 4 | 7.3 | odd | 6 | |||
112.14.a.d.1.2 | 2 | 4.3 | odd | 2 | |||
126.14.a.l.1.2 | 2 | 3.2 | odd | 2 |