Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [197,10,Mod(1,197)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(197, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("197.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 197 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 197.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: | \(101.462059724\) |
Analytic rank: | \(0\) |
Dimension: | \(76\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 197.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −37.7253 | −1.66724 | −0.833618 | − | 0.552341i | \(-0.813735\pi\) | ||||
−0.833618 | + | 0.552341i | \(0.813735\pi\) | |||||||
\(3\) | −206.276 | −1.47029 | −0.735144 | − | 0.677911i | \(-0.762885\pi\) | ||||
−0.735144 | + | 0.677911i | \(0.762885\pi\) | |||||||
\(4\) | 911.195 | 1.77968 | ||||||||
\(5\) | −2075.65 | −1.48521 | −0.742607 | − | 0.669727i | \(-0.766411\pi\) | ||||
−0.742607 | + | 0.669727i | \(0.766411\pi\) | |||||||
\(6\) | 7781.80 | 2.45132 | ||||||||
\(7\) | −5253.06 | −0.826934 | −0.413467 | − | 0.910519i | \(-0.635682\pi\) | ||||
−0.413467 | + | 0.910519i | \(0.635682\pi\) | |||||||
\(8\) | −15059.7 | −1.29991 | ||||||||
\(9\) | 22866.6 | 1.16175 | ||||||||
\(10\) | 78304.4 | 2.47620 | ||||||||
\(11\) | −12772.0 | −0.263021 | −0.131511 | − | 0.991315i | \(-0.541983\pi\) | ||||
−0.131511 | + | 0.991315i | \(0.541983\pi\) | |||||||
\(12\) | −187957. | −2.61664 | ||||||||
\(13\) | 107848. | 1.04729 | 0.523647 | − | 0.851935i | \(-0.324571\pi\) | ||||
0.523647 | + | 0.851935i | \(0.324571\pi\) | |||||||
\(14\) | 198173. | 1.37869 | ||||||||
\(15\) | 428156. | 2.18369 | ||||||||
\(16\) | 101600. | 0.387573 | ||||||||
\(17\) | −149863. | −0.435187 | −0.217593 | − | 0.976040i | \(-0.569821\pi\) | ||||
−0.217593 | + | 0.976040i | \(0.569821\pi\) | |||||||
\(18\) | −862649. | −1.93690 | ||||||||
\(19\) | 434522. | 0.764928 | 0.382464 | − | 0.923970i | \(-0.375076\pi\) | ||||
0.382464 | + | 0.923970i | \(0.375076\pi\) | |||||||
\(20\) | −1.89132e6 | −2.64320 | ||||||||
\(21\) | 1.08358e6 | 1.21583 | ||||||||
\(22\) | 481826. | 0.438519 | ||||||||
\(23\) | 1.41689e6 | 1.05575 | 0.527874 | − | 0.849323i | \(-0.322989\pi\) | ||||
0.527874 | + | 0.849323i | \(0.322989\pi\) | |||||||
\(24\) | 3.10645e6 | 1.91123 | ||||||||
\(25\) | 2.35520e6 | 1.20586 | ||||||||
\(26\) | −4.06861e6 | −1.74609 | ||||||||
\(27\) | −656706. | −0.237812 | ||||||||
\(28\) | −4.78656e6 | −1.47168 | ||||||||
\(29\) | −162161. | −0.0425750 | −0.0212875 | − | 0.999773i | \(-0.506777\pi\) | ||||
−0.0212875 | + | 0.999773i | \(0.506777\pi\) | |||||||
\(30\) | −1.61523e7 | −3.64073 | ||||||||
\(31\) | 6.06824e6 | 1.18015 | 0.590073 | − | 0.807350i | \(-0.299099\pi\) | ||||
0.590073 | + | 0.807350i | \(0.299099\pi\) | |||||||
\(32\) | 3.87769e6 | 0.653730 | ||||||||
\(33\) | 2.63455e6 | 0.386717 | ||||||||
\(34\) | 5.65364e6 | 0.725559 | ||||||||
\(35\) | 1.09035e7 | 1.22817 | ||||||||
\(36\) | 2.08360e7 | 2.06753 | ||||||||
\(37\) | 1.36648e7 | 1.19865 | 0.599327 | − | 0.800504i | \(-0.295435\pi\) | ||||
0.599327 | + | 0.800504i | \(0.295435\pi\) | |||||||
\(38\) | −1.63924e7 | −1.27532 | ||||||||
\(39\) | −2.22465e7 | −1.53982 | ||||||||
\(40\) | 3.12587e7 | 1.93064 | ||||||||
\(41\) | 1.98891e6 | 0.109923 | 0.0549615 | − | 0.998488i | \(-0.482496\pi\) | ||||
0.0549615 | + | 0.998488i | \(0.482496\pi\) | |||||||
\(42\) | −4.08782e7 | −2.02708 | ||||||||
\(43\) | −1.33138e7 | −0.593873 | −0.296936 | − | 0.954897i | \(-0.595965\pi\) | ||||
−0.296936 | + | 0.954897i | \(0.595965\pi\) | |||||||
\(44\) | −1.16377e7 | −0.468093 | ||||||||
\(45\) | −4.74631e7 | −1.72544 | ||||||||
\(46\) | −5.34524e7 | −1.76018 | ||||||||
\(47\) | −8.33704e6 | −0.249213 | −0.124607 | − | 0.992206i | \(-0.539767\pi\) | ||||
−0.124607 | + | 0.992206i | \(0.539767\pi\) | |||||||
\(48\) | −2.09576e7 | −0.569843 | ||||||||
\(49\) | −1.27590e7 | −0.316180 | ||||||||
\(50\) | −8.88505e7 | −2.01046 | ||||||||
\(51\) | 3.09132e7 | 0.639850 | ||||||||
\(52\) | 9.82709e7 | 1.86385 | ||||||||
\(53\) | 4.16397e7 | 0.724879 | 0.362440 | − | 0.932007i | \(-0.381944\pi\) | ||||
0.362440 | + | 0.932007i | \(0.381944\pi\) | |||||||
\(54\) | 2.47744e7 | 0.396489 | ||||||||
\(55\) | 2.65101e7 | 0.390643 | ||||||||
\(56\) | 7.91095e7 | 1.07494 | ||||||||
\(57\) | −8.96313e7 | −1.12466 | ||||||||
\(58\) | 6.11755e6 | 0.0709825 | ||||||||
\(59\) | −1.51523e8 | −1.62797 | −0.813983 | − | 0.580888i | \(-0.802705\pi\) | ||||
−0.813983 | + | 0.580888i | \(0.802705\pi\) | |||||||
\(60\) | 3.90134e8 | 3.88627 | ||||||||
\(61\) | 1.06168e6 | 0.00981770 | 0.00490885 | − | 0.999988i | \(-0.498437\pi\) | ||||
0.00490885 | + | 0.999988i | \(0.498437\pi\) | |||||||
\(62\) | −2.28926e8 | −1.96758 | ||||||||
\(63\) | −1.20120e8 | −0.960687 | ||||||||
\(64\) | −1.98306e8 | −1.47750 | ||||||||
\(65\) | −2.23856e8 | −1.55546 | ||||||||
\(66\) | −9.93889e7 | −0.644748 | ||||||||
\(67\) | −3.49032e7 | −0.211606 | −0.105803 | − | 0.994387i | \(-0.533741\pi\) | ||||
−0.105803 | + | 0.994387i | \(0.533741\pi\) | |||||||
\(68\) | −1.36555e8 | −0.774492 | ||||||||
\(69\) | −2.92269e8 | −1.55225 | ||||||||
\(70\) | −4.11338e8 | −2.04766 | ||||||||
\(71\) | −1.45435e8 | −0.679216 | −0.339608 | − | 0.940567i | \(-0.610294\pi\) | ||||
−0.339608 | + | 0.940567i | \(0.610294\pi\) | |||||||
\(72\) | −3.44365e8 | −1.51016 | ||||||||
\(73\) | 9.14830e7 | 0.377040 | 0.188520 | − | 0.982069i | \(-0.439631\pi\) | ||||
0.188520 | + | 0.982069i | \(0.439631\pi\) | |||||||
\(74\) | −5.15506e8 | −1.99844 | ||||||||
\(75\) | −4.85820e8 | −1.77296 | ||||||||
\(76\) | 3.95934e8 | 1.36132 | ||||||||
\(77\) | 6.70919e7 | 0.217501 | ||||||||
\(78\) | 8.39255e8 | 2.56725 | ||||||||
\(79\) | 1.99332e8 | 0.575778 | 0.287889 | − | 0.957664i | \(-0.407047\pi\) | ||||
0.287889 | + | 0.957664i | \(0.407047\pi\) | |||||||
\(80\) | −2.10886e8 | −0.575629 | ||||||||
\(81\) | −3.14621e8 | −0.812093 | ||||||||
\(82\) | −7.50323e7 | −0.183268 | ||||||||
\(83\) | 2.80259e7 | 0.0648199 | 0.0324100 | − | 0.999475i | \(-0.489682\pi\) | ||||
0.0324100 | + | 0.999475i | \(0.489682\pi\) | |||||||
\(84\) | 9.87350e8 | 2.16379 | ||||||||
\(85\) | 3.11064e8 | 0.646346 | ||||||||
\(86\) | 5.02266e8 | 0.990126 | ||||||||
\(87\) | 3.34498e7 | 0.0625974 | ||||||||
\(88\) | 1.92342e8 | 0.341903 | ||||||||
\(89\) | −7.74302e8 | −1.30814 | −0.654072 | − | 0.756432i | \(-0.726941\pi\) | ||||
−0.654072 | + | 0.756432i | \(0.726941\pi\) | |||||||
\(90\) | 1.79056e9 | 2.87672 | ||||||||
\(91\) | −5.66534e8 | −0.866043 | ||||||||
\(92\) | 1.29106e9 | 1.87889 | ||||||||
\(93\) | −1.25173e9 | −1.73515 | ||||||||
\(94\) | 3.14517e8 | 0.415498 | ||||||||
\(95\) | −9.01916e8 | −1.13608 | ||||||||
\(96\) | −7.99873e8 | −0.961171 | ||||||||
\(97\) | 4.57437e8 | 0.524637 | 0.262318 | − | 0.964981i | \(-0.415513\pi\) | ||||
0.262318 | + | 0.964981i | \(0.415513\pi\) | |||||||
\(98\) | 4.81337e8 | 0.527147 | ||||||||
\(99\) | −2.92052e8 | −0.305564 | ||||||||
\(100\) | 2.14605e9 | 2.14605 | ||||||||
\(101\) | 1.11363e9 | 1.06487 | 0.532435 | − | 0.846471i | \(-0.321277\pi\) | ||||
0.532435 | + | 0.846471i | \(0.321277\pi\) | |||||||
\(102\) | −1.16621e9 | −1.06678 | ||||||||
\(103\) | 1.98792e9 | 1.74033 | 0.870164 | − | 0.492762i | \(-0.164013\pi\) | ||||
0.870164 | + | 0.492762i | \(0.164013\pi\) | |||||||
\(104\) | −1.62417e9 | −1.36138 | ||||||||
\(105\) | −2.24913e9 | −1.80577 | ||||||||
\(106\) | −1.57087e9 | −1.20854 | ||||||||
\(107\) | −7.22563e8 | −0.532903 | −0.266452 | − | 0.963848i | \(-0.585851\pi\) | ||||
−0.266452 | + | 0.963848i | \(0.585851\pi\) | |||||||
\(108\) | −5.98387e8 | −0.423229 | ||||||||
\(109\) | 2.93596e8 | 0.199219 | 0.0996096 | − | 0.995027i | \(-0.468241\pi\) | ||||
0.0996096 | + | 0.995027i | \(0.468241\pi\) | |||||||
\(110\) | −1.00010e9 | −0.651294 | ||||||||
\(111\) | −2.81871e9 | −1.76237 | ||||||||
\(112\) | −5.33710e8 | −0.320497 | ||||||||
\(113\) | 5.00057e6 | 0.00288514 | 0.00144257 | − | 0.999999i | \(-0.499541\pi\) | ||||
0.00144257 | + | 0.999999i | \(0.499541\pi\) | |||||||
\(114\) | 3.38136e9 | 1.87508 | ||||||||
\(115\) | −2.94096e9 | −1.56801 | ||||||||
\(116\) | −1.47760e8 | −0.0757697 | ||||||||
\(117\) | 2.46613e9 | 1.21669 | ||||||||
\(118\) | 5.71626e9 | 2.71421 | ||||||||
\(119\) | 7.87241e8 | 0.359871 | ||||||||
\(120\) | −6.44791e9 | −2.83859 | ||||||||
\(121\) | −2.19482e9 | −0.930820 | ||||||||
\(122\) | −4.00522e7 | −0.0163684 | ||||||||
\(123\) | −4.10264e8 | −0.161618 | ||||||||
\(124\) | 5.52935e9 | 2.10028 | ||||||||
\(125\) | −8.34568e8 | −0.305750 | ||||||||
\(126\) | 4.53155e9 | 1.60169 | ||||||||
\(127\) | 3.36285e9 | 1.14707 | 0.573535 | − | 0.819181i | \(-0.305571\pi\) | ||||
0.573535 | + | 0.819181i | \(0.305571\pi\) | |||||||
\(128\) | 5.49577e9 | 1.80960 | ||||||||
\(129\) | 2.74631e9 | 0.873164 | ||||||||
\(130\) | 8.44501e9 | 2.59331 | ||||||||
\(131\) | 4.07101e9 | 1.20776 | 0.603881 | − | 0.797075i | \(-0.293620\pi\) | ||||
0.603881 | + | 0.797075i | \(0.293620\pi\) | |||||||
\(132\) | 2.40058e9 | 0.688231 | ||||||||
\(133\) | −2.28257e9 | −0.632545 | ||||||||
\(134\) | 1.31673e9 | 0.352797 | ||||||||
\(135\) | 1.36309e9 | 0.353202 | ||||||||
\(136\) | 2.25690e9 | 0.565702 | ||||||||
\(137\) | 2.88528e9 | 0.699754 | 0.349877 | − | 0.936796i | \(-0.386223\pi\) | ||||
0.349877 | + | 0.936796i | \(0.386223\pi\) | |||||||
\(138\) | 1.10259e10 | 2.58797 | ||||||||
\(139\) | −5.51965e9 | −1.25414 | −0.627068 | − | 0.778964i | \(-0.715745\pi\) | ||||
−0.627068 | + | 0.778964i | \(0.715745\pi\) | |||||||
\(140\) | 9.93522e9 | 2.18575 | ||||||||
\(141\) | 1.71973e9 | 0.366415 | ||||||||
\(142\) | 5.48659e9 | 1.13241 | ||||||||
\(143\) | −1.37744e9 | −0.275461 | ||||||||
\(144\) | 2.32325e9 | 0.450261 | ||||||||
\(145\) | 3.36589e8 | 0.0632329 | ||||||||
\(146\) | −3.45122e9 | −0.628615 | ||||||||
\(147\) | 2.63187e9 | 0.464876 | ||||||||
\(148\) | 1.24513e10 | 2.13322 | ||||||||
\(149\) | 5.38947e9 | 0.895793 | 0.447897 | − | 0.894085i | \(-0.352173\pi\) | ||||
0.447897 | + | 0.894085i | \(0.352173\pi\) | |||||||
\(150\) | 1.83277e10 | 2.95595 | ||||||||
\(151\) | 7.90820e8 | 0.123789 | 0.0618944 | − | 0.998083i | \(-0.480286\pi\) | ||||
0.0618944 | + | 0.998083i | \(0.480286\pi\) | |||||||
\(152\) | −6.54378e9 | −0.994334 | ||||||||
\(153\) | −3.42687e9 | −0.505576 | ||||||||
\(154\) | −2.53106e9 | −0.362626 | ||||||||
\(155\) | −1.25956e10 | −1.75277 | ||||||||
\(156\) | −2.02709e10 | −2.74039 | ||||||||
\(157\) | 2.69380e9 | 0.353848 | 0.176924 | − | 0.984225i | \(-0.443385\pi\) | ||||
0.176924 | + | 0.984225i | \(0.443385\pi\) | |||||||
\(158\) | −7.51985e9 | −0.959958 | ||||||||
\(159\) | −8.58925e9 | −1.06578 | ||||||||
\(160\) | −8.04873e9 | −0.970929 | ||||||||
\(161\) | −7.44299e9 | −0.873034 | ||||||||
\(162\) | 1.18692e10 | 1.35395 | ||||||||
\(163\) | −1.45994e9 | −0.161991 | −0.0809955 | − | 0.996714i | \(-0.525810\pi\) | ||||
−0.0809955 | + | 0.996714i | \(0.525810\pi\) | |||||||
\(164\) | 1.81229e9 | 0.195627 | ||||||||
\(165\) | −5.46840e9 | −0.574358 | ||||||||
\(166\) | −1.05729e9 | −0.108070 | ||||||||
\(167\) | −1.00431e9 | −0.0999182 | −0.0499591 | − | 0.998751i | \(-0.515909\pi\) | ||||
−0.0499591 | + | 0.998751i | \(0.515909\pi\) | |||||||
\(168\) | −1.63184e10 | −1.58047 | ||||||||
\(169\) | 1.02678e9 | 0.0968249 | ||||||||
\(170\) | −1.17350e10 | −1.07761 | ||||||||
\(171\) | 9.93605e9 | 0.888651 | ||||||||
\(172\) | −1.21314e10 | −1.05690 | ||||||||
\(173\) | −1.72999e10 | −1.46838 | −0.734188 | − | 0.678946i | \(-0.762437\pi\) | ||||
−0.734188 | + | 0.678946i | \(0.762437\pi\) | |||||||
\(174\) | −1.26190e9 | −0.104365 | ||||||||
\(175\) | −1.23720e10 | −0.997169 | ||||||||
\(176\) | −1.29763e9 | −0.101940 | ||||||||
\(177\) | 3.12556e10 | 2.39358 | ||||||||
\(178\) | 2.92107e10 | 2.18098 | ||||||||
\(179\) | 3.55457e9 | 0.258790 | 0.129395 | − | 0.991593i | \(-0.458696\pi\) | ||||
0.129395 | + | 0.991593i | \(0.458696\pi\) | |||||||
\(180\) | −4.32482e10 | −3.07073 | ||||||||
\(181\) | −9.12520e9 | −0.631959 | −0.315980 | − | 0.948766i | \(-0.602333\pi\) | ||||
−0.315980 | + | 0.948766i | \(0.602333\pi\) | |||||||
\(182\) | 2.13726e10 | 1.44390 | ||||||||
\(183\) | −2.18999e8 | −0.0144348 | ||||||||
\(184\) | −2.13379e10 | −1.37237 | ||||||||
\(185\) | −2.83633e10 | −1.78026 | ||||||||
\(186\) | 4.72219e10 | 2.89291 | ||||||||
\(187\) | 1.91405e9 | 0.114463 | ||||||||
\(188\) | −7.59666e9 | −0.443519 | ||||||||
\(189\) | 3.44971e9 | 0.196655 | ||||||||
\(190\) | 3.40250e10 | 1.89412 | ||||||||
\(191\) | −1.75219e10 | −0.952643 | −0.476322 | − | 0.879271i | \(-0.658030\pi\) | ||||
−0.476322 | + | 0.879271i | \(0.658030\pi\) | |||||||
\(192\) | 4.09057e10 | 2.17234 | ||||||||
\(193\) | 2.96074e10 | 1.53600 | 0.768002 | − | 0.640447i | \(-0.221251\pi\) | ||||
0.768002 | + | 0.640447i | \(0.221251\pi\) | |||||||
\(194\) | −1.72569e10 | −0.874693 | ||||||||
\(195\) | 4.61760e10 | 2.28697 | ||||||||
\(196\) | −1.16259e10 | −0.562698 | ||||||||
\(197\) | 1.50614e9 | 0.0712470 | ||||||||
\(198\) | 1.10177e10 | 0.509447 | ||||||||
\(199\) | 3.92021e10 | 1.77203 | 0.886014 | − | 0.463658i | \(-0.153464\pi\) | ||||
0.886014 | + | 0.463658i | \(0.153464\pi\) | |||||||
\(200\) | −3.54686e10 | −1.56751 | ||||||||
\(201\) | 7.19967e9 | 0.311122 | ||||||||
\(202\) | −4.20121e10 | −1.77539 | ||||||||
\(203\) | 8.51838e8 | 0.0352067 | ||||||||
\(204\) | 2.81679e10 | 1.13873 | ||||||||
\(205\) | −4.12829e9 | −0.163259 | ||||||||
\(206\) | −7.49947e10 | −2.90154 | ||||||||
\(207\) | 3.23994e10 | 1.22651 | ||||||||
\(208\) | 1.09574e10 | 0.405903 | ||||||||
\(209\) | −5.54970e9 | −0.201192 | ||||||||
\(210\) | 8.48489e10 | 3.01064 | ||||||||
\(211\) | 2.37581e9 | 0.0825164 | 0.0412582 | − | 0.999149i | \(-0.486863\pi\) | ||||
0.0412582 | + | 0.999149i | \(0.486863\pi\) | |||||||
\(212\) | 3.79418e10 | 1.29005 | ||||||||
\(213\) | 2.99998e10 | 0.998642 | ||||||||
\(214\) | 2.72589e10 | 0.888476 | ||||||||
\(215\) | 2.76348e10 | 0.882029 | ||||||||
\(216\) | 9.88981e9 | 0.309133 | ||||||||
\(217\) | −3.18768e10 | −0.975902 | ||||||||
\(218\) | −1.10760e10 | −0.332145 | ||||||||
\(219\) | −1.88707e10 | −0.554358 | ||||||||
\(220\) | 2.41559e10 | 0.695218 | ||||||||
\(221\) | −1.61625e10 | −0.455769 | ||||||||
\(222\) | 1.06336e11 | 2.93828 | ||||||||
\(223\) | 1.31894e9 | 0.0357151 | 0.0178576 | − | 0.999841i | \(-0.494315\pi\) | ||||
0.0178576 | + | 0.999841i | \(0.494315\pi\) | |||||||
\(224\) | −2.03697e10 | −0.540592 | ||||||||
\(225\) | 5.38555e10 | 1.40091 | ||||||||
\(226\) | −1.88648e8 | −0.00481020 | ||||||||
\(227\) | −6.43494e10 | −1.60853 | −0.804263 | − | 0.594273i | \(-0.797440\pi\) | ||||
−0.804263 | + | 0.594273i | \(0.797440\pi\) | |||||||
\(228\) | −8.16715e10 | −2.00154 | ||||||||
\(229\) | 6.63740e10 | 1.59492 | 0.797459 | − | 0.603373i | \(-0.206177\pi\) | ||||
0.797459 | + | 0.603373i | \(0.206177\pi\) | |||||||
\(230\) | 1.10949e11 | 2.61425 | ||||||||
\(231\) | −1.38394e10 | −0.319789 | ||||||||
\(232\) | 2.44209e9 | 0.0553434 | ||||||||
\(233\) | −3.44486e10 | −0.765721 | −0.382860 | − | 0.923806i | \(-0.625061\pi\) | ||||
−0.382860 | + | 0.923806i | \(0.625061\pi\) | |||||||
\(234\) | −9.30354e10 | −2.02851 | ||||||||
\(235\) | 1.73048e10 | 0.370135 | ||||||||
\(236\) | −1.38067e11 | −2.89725 | ||||||||
\(237\) | −4.11173e10 | −0.846559 | ||||||||
\(238\) | −2.96989e10 | −0.599990 | ||||||||
\(239\) | 1.96234e9 | 0.0389030 | 0.0194515 | − | 0.999811i | \(-0.493808\pi\) | ||||
0.0194515 | + | 0.999811i | \(0.493808\pi\) | |||||||
\(240\) | 4.35006e10 | 0.846340 | ||||||||
\(241\) | −3.35622e10 | −0.640876 | −0.320438 | − | 0.947269i | \(-0.603830\pi\) | ||||
−0.320438 | + | 0.947269i | \(0.603830\pi\) | |||||||
\(242\) | 8.28003e10 | 1.55190 | ||||||||
\(243\) | 7.78247e10 | 1.43182 | ||||||||
\(244\) | 9.67398e8 | 0.0174723 | ||||||||
\(245\) | 2.64832e10 | 0.469595 | ||||||||
\(246\) | 1.54773e10 | 0.269456 | ||||||||
\(247\) | 4.68625e10 | 0.801104 | ||||||||
\(248\) | −9.13860e10 | −1.53408 | ||||||||
\(249\) | −5.78107e9 | −0.0953039 | ||||||||
\(250\) | 3.14843e10 | 0.509758 | ||||||||
\(251\) | 6.31282e10 | 1.00390 | 0.501952 | − | 0.864896i | \(-0.332616\pi\) | ||||
0.501952 | + | 0.864896i | \(0.332616\pi\) | |||||||
\(252\) | −1.09452e11 | −1.70971 | ||||||||
\(253\) | −1.80964e10 | −0.277684 | ||||||||
\(254\) | −1.26864e11 | −1.91244 | ||||||||
\(255\) | −6.41650e10 | −0.950314 | ||||||||
\(256\) | −1.05796e11 | −1.53954 | ||||||||
\(257\) | 1.10368e11 | 1.57814 | 0.789070 | − | 0.614303i | \(-0.210563\pi\) | ||||
0.789070 | + | 0.614303i | \(0.210563\pi\) | |||||||
\(258\) | −1.03605e11 | −1.45577 | ||||||||
\(259\) | −7.17817e10 | −0.991209 | ||||||||
\(260\) | −2.03976e11 | −2.76821 | ||||||||
\(261\) | −3.70807e9 | −0.0494613 | ||||||||
\(262\) | −1.53580e11 | −2.01362 | ||||||||
\(263\) | 2.94937e10 | 0.380127 | 0.190063 | − | 0.981772i | \(-0.439131\pi\) | ||||
0.190063 | + | 0.981772i | \(0.439131\pi\) | |||||||
\(264\) | −3.96755e10 | −0.502695 | ||||||||
\(265\) | −8.64294e10 | −1.07660 | ||||||||
\(266\) | 8.61104e10 | 1.05460 | ||||||||
\(267\) | 1.59720e11 | 1.92335 | ||||||||
\(268\) | −3.18036e10 | −0.376591 | ||||||||
\(269\) | −1.38102e11 | −1.60811 | −0.804054 | − | 0.594556i | \(-0.797328\pi\) | ||||
−0.804054 | + | 0.594556i | \(0.797328\pi\) | |||||||
\(270\) | −5.14230e10 | −0.588871 | ||||||||
\(271\) | −3.76108e10 | −0.423595 | −0.211797 | − | 0.977314i | \(-0.567932\pi\) | ||||
−0.211797 | + | 0.977314i | \(0.567932\pi\) | |||||||
\(272\) | −1.52261e10 | −0.168667 | ||||||||
\(273\) | 1.16862e11 | 1.27333 | ||||||||
\(274\) | −1.08848e11 | −1.16666 | ||||||||
\(275\) | −3.00805e10 | −0.317167 | ||||||||
\(276\) | −2.66314e11 | −2.76251 | ||||||||
\(277\) | −4.03699e10 | −0.412001 | −0.206000 | − | 0.978552i | \(-0.566045\pi\) | ||||
−0.206000 | + | 0.978552i | \(0.566045\pi\) | |||||||
\(278\) | 2.08230e11 | 2.09094 | ||||||||
\(279\) | 1.38760e11 | 1.37103 | ||||||||
\(280\) | −1.64204e11 | −1.59651 | ||||||||
\(281\) | −1.61017e11 | −1.54061 | −0.770307 | − | 0.637673i | \(-0.779897\pi\) | ||||
−0.770307 | + | 0.637673i | \(0.779897\pi\) | |||||||
\(282\) | −6.48771e10 | −0.610901 | ||||||||
\(283\) | −2.06961e11 | −1.91801 | −0.959004 | − | 0.283394i | \(-0.908540\pi\) | ||||
−0.959004 | + | 0.283394i | \(0.908540\pi\) | |||||||
\(284\) | −1.32520e11 | −1.20878 | ||||||||
\(285\) | 1.86043e11 | 1.67037 | ||||||||
\(286\) | 5.19641e10 | 0.459258 | ||||||||
\(287\) | −1.04479e10 | −0.0908991 | ||||||||
\(288\) | 8.86698e10 | 0.759468 | ||||||||
\(289\) | −9.61288e10 | −0.810612 | ||||||||
\(290\) | −1.26979e10 | −0.105424 | ||||||||
\(291\) | −9.43581e10 | −0.771367 | ||||||||
\(292\) | 8.33588e10 | 0.671010 | ||||||||
\(293\) | −2.23194e11 | −1.76921 | −0.884603 | − | 0.466345i | \(-0.845570\pi\) | ||||
−0.884603 | + | 0.466345i | \(0.845570\pi\) | |||||||
\(294\) | −9.92880e10 | −0.775058 | ||||||||
\(295\) | 3.14510e11 | 2.41788 | ||||||||
\(296\) | −2.05787e11 | −1.55814 | ||||||||
\(297\) | 8.38743e9 | 0.0625497 | ||||||||
\(298\) | −2.03319e11 | −1.49350 | ||||||||
\(299\) | 1.52809e11 | 1.10568 | ||||||||
\(300\) | −4.42677e11 | −3.15530 | ||||||||
\(301\) | 6.99381e10 | 0.491094 | ||||||||
\(302\) | −2.98339e10 | −0.206385 | ||||||||
\(303\) | −2.29716e11 | −1.56566 | ||||||||
\(304\) | 4.41474e10 | 0.296465 | ||||||||
\(305\) | −2.20368e9 | −0.0145814 | ||||||||
\(306\) | 1.29280e11 | 0.842915 | ||||||||
\(307\) | 2.70294e11 | 1.73666 | 0.868329 | − | 0.495989i | \(-0.165195\pi\) | ||||
0.868329 | + | 0.495989i | \(0.165195\pi\) | |||||||
\(308\) | 6.11338e10 | 0.387082 | ||||||||
\(309\) | −4.10059e11 | −2.55878 | ||||||||
\(310\) | 4.75170e11 | 2.92228 | ||||||||
\(311\) | −1.91974e10 | −0.116365 | −0.0581823 | − | 0.998306i | \(-0.518530\pi\) | ||||
−0.0581823 | + | 0.998306i | \(0.518530\pi\) | |||||||
\(312\) | 3.35026e11 | 2.00162 | ||||||||
\(313\) | −3.44294e10 | −0.202759 | −0.101379 | − | 0.994848i | \(-0.532326\pi\) | ||||
−0.101379 | + | 0.994848i | \(0.532326\pi\) | |||||||
\(314\) | −1.01624e11 | −0.589948 | ||||||||
\(315\) | 2.49327e11 | 1.42683 | ||||||||
\(316\) | 1.81630e11 | 1.02470 | ||||||||
\(317\) | 1.25656e11 | 0.698901 | 0.349450 | − | 0.936955i | \(-0.386368\pi\) | ||||
0.349450 | + | 0.936955i | \(0.386368\pi\) | |||||||
\(318\) | 3.24031e11 | 1.77691 | ||||||||
\(319\) | 2.07111e9 | 0.0111981 | ||||||||
\(320\) | 4.11614e11 | 2.19440 | ||||||||
\(321\) | 1.49047e11 | 0.783521 | ||||||||
\(322\) | 2.80789e11 | 1.45555 | ||||||||
\(323\) | −6.51190e10 | −0.332886 | ||||||||
\(324\) | −2.86681e11 | −1.44526 | ||||||||
\(325\) | 2.54005e11 | 1.26289 | ||||||||
\(326\) | 5.50766e10 | 0.270077 | ||||||||
\(327\) | −6.05617e10 | −0.292909 | ||||||||
\(328\) | −2.99525e10 | −0.142890 | ||||||||
\(329\) | 4.37949e10 | 0.206083 | ||||||||
\(330\) | 2.06297e11 | 0.957590 | ||||||||
\(331\) | −3.60390e10 | −0.165024 | −0.0825119 | − | 0.996590i | \(-0.526294\pi\) | ||||
−0.0825119 | + | 0.996590i | \(0.526294\pi\) | |||||||
\(332\) | 2.55371e10 | 0.115359 | ||||||||
\(333\) | 3.12467e11 | 1.39253 | ||||||||
\(334\) | 3.78879e10 | 0.166587 | ||||||||
\(335\) | 7.24468e10 | 0.314281 | ||||||||
\(336\) | 1.10091e11 | 0.471223 | ||||||||
\(337\) | −3.32706e11 | −1.40516 | −0.702580 | − | 0.711604i | \(-0.747969\pi\) | ||||
−0.702580 | + | 0.711604i | \(0.747969\pi\) | |||||||
\(338\) | −3.87355e10 | −0.161430 | ||||||||
\(339\) | −1.03150e9 | −0.00424198 | ||||||||
\(340\) | 2.83440e11 | 1.15029 | ||||||||
\(341\) | −7.75034e10 | −0.310403 | ||||||||
\(342\) | −3.74840e11 | −1.48159 | ||||||||
\(343\) | 2.79004e11 | 1.08839 | ||||||||
\(344\) | 2.00502e11 | 0.771979 | ||||||||
\(345\) | 6.06649e11 | 2.30543 | ||||||||
\(346\) | 6.52645e11 | 2.44813 | ||||||||
\(347\) | 2.61204e11 | 0.967157 | 0.483578 | − | 0.875301i | \(-0.339337\pi\) | ||||
0.483578 | + | 0.875301i | \(0.339337\pi\) | |||||||
\(348\) | 3.04792e10 | 0.111403 | ||||||||
\(349\) | −1.42093e11 | −0.512695 | −0.256347 | − | 0.966585i | \(-0.582519\pi\) | ||||
−0.256347 | + | 0.966585i | \(0.582519\pi\) | |||||||
\(350\) | 4.66737e11 | 1.66252 | ||||||||
\(351\) | −7.08247e10 | −0.249059 | ||||||||
\(352\) | −4.95258e10 | −0.171945 | ||||||||
\(353\) | −4.00093e11 | −1.37143 | −0.685716 | − | 0.727869i | \(-0.740511\pi\) | ||||
−0.685716 | + | 0.727869i | \(0.740511\pi\) | |||||||
\(354\) | −1.17912e12 | −3.99066 | ||||||||
\(355\) | 3.01873e11 | 1.00878 | ||||||||
\(356\) | −7.05540e11 | −2.32807 | ||||||||
\(357\) | −1.62389e11 | −0.529113 | ||||||||
\(358\) | −1.34097e11 | −0.431465 | ||||||||
\(359\) | 4.36609e10 | 0.138729 | 0.0693645 | − | 0.997591i | \(-0.477903\pi\) | ||||
0.0693645 | + | 0.997591i | \(0.477903\pi\) | |||||||
\(360\) | 7.14781e11 | 2.24291 | ||||||||
\(361\) | −1.33878e11 | −0.414885 | ||||||||
\(362\) | 3.44251e11 | 1.05363 | ||||||||
\(363\) | 4.52739e11 | 1.36857 | ||||||||
\(364\) | −5.16222e11 | −1.54128 | ||||||||
\(365\) | −1.89887e11 | −0.559986 | ||||||||
\(366\) | 8.26179e9 | 0.0240663 | ||||||||
\(367\) | 2.27984e11 | 0.656006 | 0.328003 | − | 0.944677i | \(-0.393624\pi\) | ||||
0.328003 | + | 0.944677i | \(0.393624\pi\) | |||||||
\(368\) | 1.43956e11 | 0.409179 | ||||||||
\(369\) | 4.54798e10 | 0.127703 | ||||||||
\(370\) | 1.07001e12 | 2.96811 | ||||||||
\(371\) | −2.18735e11 | −0.599427 | ||||||||
\(372\) | −1.14057e12 | −3.08801 | ||||||||
\(373\) | 2.72543e11 | 0.729030 | 0.364515 | − | 0.931198i | \(-0.381235\pi\) | ||||
0.364515 | + | 0.931198i | \(0.381235\pi\) | |||||||
\(374\) | −7.22081e10 | −0.190837 | ||||||||
\(375\) | 1.72151e11 | 0.449541 | ||||||||
\(376\) | 1.25553e11 | 0.323954 | ||||||||
\(377\) | −1.74888e10 | −0.0445885 | ||||||||
\(378\) | −1.30141e11 | −0.327870 | ||||||||
\(379\) | −1.97263e11 | −0.491099 | −0.245549 | − | 0.969384i | \(-0.578968\pi\) | ||||
−0.245549 | + | 0.969384i | \(0.578968\pi\) | |||||||
\(380\) | −8.21821e11 | −2.02186 | ||||||||
\(381\) | −6.93673e11 | −1.68652 | ||||||||
\(382\) | 6.61017e11 | 1.58828 | ||||||||
\(383\) | 3.57275e11 | 0.848415 | 0.424208 | − | 0.905565i | \(-0.360553\pi\) | ||||
0.424208 | + | 0.905565i | \(0.360553\pi\) | |||||||
\(384\) | −1.13364e12 | −2.66064 | ||||||||
\(385\) | −1.39259e11 | −0.323036 | ||||||||
\(386\) | −1.11695e12 | −2.56088 | ||||||||
\(387\) | −3.04441e11 | −0.689929 | ||||||||
\(388\) | 4.16814e11 | 0.933684 | ||||||||
\(389\) | 7.13622e11 | 1.58014 | 0.790069 | − | 0.613018i | \(-0.210045\pi\) | ||||
0.790069 | + | 0.613018i | \(0.210045\pi\) | |||||||
\(390\) | −1.74200e12 | −3.81292 | ||||||||
\(391\) | −2.12340e11 | −0.459447 | ||||||||
\(392\) | 1.92147e11 | 0.411004 | ||||||||
\(393\) | −8.39750e11 | −1.77576 | ||||||||
\(394\) | −5.68195e10 | −0.118786 | ||||||||
\(395\) | −4.13743e11 | −0.855154 | ||||||||
\(396\) | −2.66116e11 | −0.543805 | ||||||||
\(397\) | 5.92892e11 | 1.19789 | 0.598947 | − | 0.800789i | \(-0.295586\pi\) | ||||
0.598947 | + | 0.800789i | \(0.295586\pi\) | |||||||
\(398\) | −1.47891e12 | −2.95439 | ||||||||
\(399\) | 4.70838e11 | 0.930023 | ||||||||
\(400\) | 2.39288e11 | 0.467360 | ||||||||
\(401\) | 1.93675e11 | 0.374045 | 0.187023 | − | 0.982356i | \(-0.440116\pi\) | ||||
0.187023 | + | 0.982356i | \(0.440116\pi\) | |||||||
\(402\) | −2.71610e11 | −0.518714 | ||||||||
\(403\) | 6.54450e11 | 1.23596 | ||||||||
\(404\) | 1.01474e12 | 1.89512 | ||||||||
\(405\) | 6.53044e11 | 1.20613 | ||||||||
\(406\) | −3.21358e10 | −0.0586979 | ||||||||
\(407\) | −1.74526e11 | −0.315272 | ||||||||
\(408\) | −4.65544e11 | −0.831744 | ||||||||
\(409\) | 7.57275e11 | 1.33813 | 0.669065 | − | 0.743204i | \(-0.266695\pi\) | ||||
0.669065 | + | 0.743204i | \(0.266695\pi\) | |||||||
\(410\) | 1.55741e11 | 0.272192 | ||||||||
\(411\) | −5.95163e11 | −1.02884 | ||||||||
\(412\) | 1.81138e12 | 3.09722 | ||||||||
\(413\) | 7.95961e11 | 1.34622 | ||||||||
\(414\) | −1.22228e12 | −2.04488 | ||||||||
\(415\) | −5.81720e10 | −0.0962715 | ||||||||
\(416\) | 4.18203e11 | 0.684648 | ||||||||
\(417\) | 1.13857e12 | 1.84394 | ||||||||
\(418\) | 2.09364e11 | 0.335435 | ||||||||
\(419\) | 6.09257e11 | 0.965689 | 0.482844 | − | 0.875706i | \(-0.339604\pi\) | ||||
0.482844 | + | 0.875706i | \(0.339604\pi\) | |||||||
\(420\) | −2.04939e12 | −3.21369 | ||||||||
\(421\) | 1.21601e12 | 1.88655 | 0.943273 | − | 0.332019i | \(-0.107730\pi\) | ||||
0.943273 | + | 0.332019i | \(0.107730\pi\) | |||||||
\(422\) | −8.96279e10 | −0.137574 | ||||||||
\(423\) | −1.90640e11 | −0.289522 | ||||||||
\(424\) | −6.27081e11 | −0.942275 | ||||||||
\(425\) | −3.52959e11 | −0.524775 | ||||||||
\(426\) | −1.13175e12 | −1.66497 | ||||||||
\(427\) | −5.57707e9 | −0.00811859 | ||||||||
\(428\) | −6.58395e11 | −0.948396 | ||||||||
\(429\) | 2.84132e11 | 0.405006 | ||||||||
\(430\) | −1.04253e12 | −1.47055 | ||||||||
\(431\) | −1.35749e12 | −1.89492 | −0.947458 | − | 0.319880i | \(-0.896357\pi\) | ||||
−0.947458 | + | 0.319880i | \(0.896357\pi\) | |||||||
\(432\) | −6.67213e10 | −0.0921695 | ||||||||
\(433\) | −1.07630e12 | −1.47142 | −0.735712 | − | 0.677295i | \(-0.763152\pi\) | ||||
−0.735712 | + | 0.677295i | \(0.763152\pi\) | |||||||
\(434\) | 1.20256e12 | 1.62706 | ||||||||
\(435\) | −6.94300e10 | −0.0929706 | ||||||||
\(436\) | 2.67523e11 | 0.354546 | ||||||||
\(437\) | 6.15669e11 | 0.807571 | ||||||||
\(438\) | 7.11903e11 | 0.924245 | ||||||||
\(439\) | 1.41075e12 | 1.81283 | 0.906417 | − | 0.422383i | \(-0.138806\pi\) | ||||
0.906417 | + | 0.422383i | \(0.138806\pi\) | |||||||
\(440\) | −3.99235e11 | −0.507799 | ||||||||
\(441\) | −2.91756e11 | −0.367321 | ||||||||
\(442\) | 6.09736e11 | 0.759874 | ||||||||
\(443\) | −1.32083e12 | −1.62941 | −0.814706 | − | 0.579874i | \(-0.803102\pi\) | ||||
−0.814706 | + | 0.579874i | \(0.803102\pi\) | |||||||
\(444\) | −2.56839e12 | −3.13644 | ||||||||
\(445\) | 1.60718e12 | 1.94287 | ||||||||
\(446\) | −4.97572e10 | −0.0595456 | ||||||||
\(447\) | −1.11172e12 | −1.31707 | ||||||||
\(448\) | 1.04171e12 | 1.22179 | ||||||||
\(449\) | −5.52487e11 | −0.641524 | −0.320762 | − | 0.947160i | \(-0.603939\pi\) | ||||
−0.320762 | + | 0.947160i | \(0.603939\pi\) | |||||||
\(450\) | −2.03171e12 | −2.33564 | ||||||||
\(451\) | −2.54023e10 | −0.0289121 | ||||||||
\(452\) | 4.55649e9 | 0.00513461 | ||||||||
\(453\) | −1.63127e11 | −0.182005 | ||||||||
\(454\) | 2.42760e12 | 2.68179 | ||||||||
\(455\) | 1.17593e12 | 1.28626 | ||||||||
\(456\) | 1.34982e12 | 1.46196 | ||||||||
\(457\) | 5.84967e11 | 0.627348 | 0.313674 | − | 0.949531i | \(-0.398440\pi\) | ||||
0.313674 | + | 0.949531i | \(0.398440\pi\) | |||||||
\(458\) | −2.50398e12 | −2.65911 | ||||||||
\(459\) | 9.84163e10 | 0.103493 | ||||||||
\(460\) | −2.67979e12 | −2.79055 | ||||||||
\(461\) | 5.24862e11 | 0.541242 | 0.270621 | − | 0.962686i | \(-0.412771\pi\) | ||||
0.270621 | + | 0.962686i | \(0.412771\pi\) | |||||||
\(462\) | 5.22096e11 | 0.533164 | ||||||||
\(463\) | 5.08969e11 | 0.514727 | 0.257363 | − | 0.966315i | \(-0.417146\pi\) | ||||
0.257363 | + | 0.966315i | \(0.417146\pi\) | |||||||
\(464\) | −1.64755e10 | −0.0165009 | ||||||||
\(465\) | 2.59816e12 | 2.57707 | ||||||||
\(466\) | 1.29958e12 | 1.27664 | ||||||||
\(467\) | 9.74520e10 | 0.0948123 | 0.0474062 | − | 0.998876i | \(-0.484904\pi\) | ||||
0.0474062 | + | 0.998876i | \(0.484904\pi\) | |||||||
\(468\) | 2.24712e12 | 2.16531 | ||||||||
\(469\) | 1.83348e11 | 0.174984 | ||||||||
\(470\) | −6.52827e11 | −0.617103 | ||||||||
\(471\) | −5.55665e11 | −0.520259 | ||||||||
\(472\) | 2.28190e12 | 2.11620 | ||||||||
\(473\) | 1.70043e11 | 0.156201 | ||||||||
\(474\) | 1.55116e12 | 1.41141 | ||||||||
\(475\) | 1.02339e12 | 0.922398 | ||||||||
\(476\) | 7.17330e11 | 0.640454 | ||||||||
\(477\) | 9.52159e11 | 0.842125 | ||||||||
\(478\) | −7.40297e10 | −0.0648605 | ||||||||
\(479\) | −9.32524e11 | −0.809376 | −0.404688 | − | 0.914455i | \(-0.632620\pi\) | ||||
−0.404688 | + | 0.914455i | \(0.632620\pi\) | |||||||
\(480\) | 1.66026e12 | 1.42755 | ||||||||
\(481\) | 1.47372e12 | 1.25534 | ||||||||
\(482\) | 1.26614e12 | 1.06849 | ||||||||
\(483\) | 1.53531e12 | 1.28361 | ||||||||
\(484\) | −1.99991e12 | −1.65656 | ||||||||
\(485\) | −9.49480e11 | −0.779198 | ||||||||
\(486\) | −2.93596e12 | −2.38719 | ||||||||
\(487\) | −2.38809e12 | −1.92384 | −0.961922 | − | 0.273323i | \(-0.911877\pi\) | ||||
−0.961922 | + | 0.273323i | \(0.911877\pi\) | |||||||
\(488\) | −1.59886e10 | −0.0127621 | ||||||||
\(489\) | 3.01150e11 | 0.238173 | ||||||||
\(490\) | −9.99087e11 | −0.782926 | ||||||||
\(491\) | −4.08754e11 | −0.317392 | −0.158696 | − | 0.987328i | \(-0.550729\pi\) | ||||
−0.158696 | + | 0.987328i | \(0.550729\pi\) | |||||||
\(492\) | −3.73831e11 | −0.287629 | ||||||||
\(493\) | 2.43019e10 | 0.0185281 | ||||||||
\(494\) | −1.76790e12 | −1.33563 | ||||||||
\(495\) | 6.06198e11 | 0.453828 | ||||||||
\(496\) | 6.16533e11 | 0.457392 | ||||||||
\(497\) | 7.63981e11 | 0.561667 | ||||||||
\(498\) | 2.18092e11 | 0.158894 | ||||||||
\(499\) | −1.26604e12 | −0.914103 | −0.457052 | − | 0.889440i | \(-0.651095\pi\) | ||||
−0.457052 | + | 0.889440i | \(0.651095\pi\) | |||||||
\(500\) | −7.60454e11 | −0.544136 | ||||||||
\(501\) | 2.07165e11 | 0.146908 | ||||||||
\(502\) | −2.38153e12 | −1.67374 | ||||||||
\(503\) | 1.10610e12 | 0.770440 | 0.385220 | − | 0.922825i | \(-0.374126\pi\) | ||||
0.385220 | + | 0.922825i | \(0.374126\pi\) | |||||||
\(504\) | 1.80897e12 | 1.24880 | ||||||||
\(505\) | −2.31151e12 | −1.58156 | ||||||||
\(506\) | 6.82693e11 | 0.462965 | ||||||||
\(507\) | −2.11800e11 | −0.142360 | ||||||||
\(508\) | 3.06421e12 | 2.04142 | ||||||||
\(509\) | −4.72966e11 | −0.312320 | −0.156160 | − | 0.987732i | \(-0.549912\pi\) | ||||
−0.156160 | + | 0.987732i | \(0.549912\pi\) | |||||||
\(510\) | 2.42064e12 | 1.58440 | ||||||||
\(511\) | −4.80566e11 | −0.311787 | ||||||||
\(512\) | 1.17737e12 | 0.757176 | ||||||||
\(513\) | −2.85353e11 | −0.181909 | ||||||||
\(514\) | −4.16368e12 | −2.63113 | ||||||||
\(515\) | −4.12622e12 | −2.58476 | ||||||||
\(516\) | 2.50242e12 | 1.55395 | ||||||||
\(517\) | 1.06480e11 | 0.0655484 | ||||||||
\(518\) | 2.70798e12 | 1.65258 | ||||||||
\(519\) | 3.56856e12 | 2.15894 | ||||||||
\(520\) | 3.37120e12 | 2.02195 | ||||||||
\(521\) | −2.21607e12 | −1.31769 | −0.658845 | − | 0.752278i | \(-0.728955\pi\) | ||||
−0.658845 | + | 0.752278i | \(0.728955\pi\) | |||||||
\(522\) | 1.39888e11 | 0.0824636 | ||||||||
\(523\) | −2.30683e12 | −1.34821 | −0.674107 | − | 0.738634i | \(-0.735471\pi\) | ||||
−0.674107 | + | 0.738634i | \(0.735471\pi\) | |||||||
\(524\) | 3.70948e12 | 2.14942 | ||||||||
\(525\) | 2.55204e12 | 1.46612 | ||||||||
\(526\) | −1.11266e12 | −0.633761 | ||||||||
\(527\) | −9.09408e11 | −0.513584 | ||||||||
\(528\) | 2.67670e11 | 0.149881 | ||||||||
\(529\) | 2.06417e11 | 0.114603 | ||||||||
\(530\) | 3.26057e12 | 1.79495 | ||||||||
\(531\) | −3.46483e12 | −1.89128 | ||||||||
\(532\) | −2.07986e12 | −1.12573 | ||||||||
\(533\) | 2.14501e11 | 0.115122 | ||||||||
\(534\) | −6.02546e12 | −3.20667 | ||||||||
\(535\) | 1.49979e12 | 0.791476 | ||||||||
\(536\) | 5.25632e11 | 0.275068 | ||||||||
\(537\) | −7.33220e11 | −0.380496 | ||||||||
\(538\) | 5.20994e12 | 2.68110 | ||||||||
\(539\) | 1.62958e11 | 0.0831621 | ||||||||
\(540\) | 1.24204e12 | 0.628586 | ||||||||
\(541\) | −9.20712e11 | −0.462100 | −0.231050 | − | 0.972942i | \(-0.574216\pi\) | ||||
−0.231050 | + | 0.972942i | \(0.574216\pi\) | |||||||
\(542\) | 1.41888e12 | 0.706233 | ||||||||
\(543\) | 1.88231e12 | 0.929161 | ||||||||
\(544\) | −5.81125e11 | −0.284495 | ||||||||
\(545\) | −6.09403e11 | −0.295883 | ||||||||
\(546\) | −4.40865e12 | −2.12295 | ||||||||
\(547\) | −1.99861e11 | −0.0954519 | −0.0477259 | − | 0.998860i | \(-0.515197\pi\) | ||||
−0.0477259 | + | 0.998860i | \(0.515197\pi\) | |||||||
\(548\) | 2.62905e12 | 1.24534 | ||||||||
\(549\) | 2.42771e10 | 0.0114057 | ||||||||
\(550\) | 1.13480e12 | 0.528793 | ||||||||
\(551\) | −7.04623e10 | −0.0325668 | ||||||||
\(552\) | 4.40149e12 | 2.01778 | ||||||||
\(553\) | −1.04710e12 | −0.476130 | ||||||||
\(554\) | 1.52296e12 | 0.686903 | ||||||||
\(555\) | 5.85065e12 | 2.61749 | ||||||||
\(556\) | −5.02947e12 | −2.23196 | ||||||||
\(557\) | −1.16526e12 | −0.512947 | −0.256474 | − | 0.966551i | \(-0.582561\pi\) | ||||
−0.256474 | + | 0.966551i | \(0.582561\pi\) | |||||||
\(558\) | −5.23477e12 | −2.28583 | ||||||||
\(559\) | −1.43587e12 | −0.621960 | ||||||||
\(560\) | 1.10780e12 | 0.476007 | ||||||||
\(561\) | −3.94822e11 | −0.168294 | ||||||||
\(562\) | 6.07442e12 | 2.56857 | ||||||||
\(563\) | 3.38943e12 | 1.42180 | 0.710900 | − | 0.703293i | \(-0.248288\pi\) | ||||
0.710900 | + | 0.703293i | \(0.248288\pi\) | |||||||
\(564\) | 1.56701e12 | 0.652101 | ||||||||
\(565\) | −1.03794e10 | −0.00428505 | ||||||||
\(566\) | 7.80767e12 | 3.19777 | ||||||||
\(567\) | 1.65272e12 | 0.671547 | ||||||||
\(568\) | 2.19022e12 | 0.882916 | ||||||||
\(569\) | 5.58181e11 | 0.223239 | 0.111619 | − | 0.993751i | \(-0.464396\pi\) | ||||
0.111619 | + | 0.993751i | \(0.464396\pi\) | |||||||
\(570\) | −7.01853e12 | −2.78490 | ||||||||
\(571\) | 3.83146e11 | 0.150835 | 0.0754174 | − | 0.997152i | \(-0.475971\pi\) | ||||
0.0754174 | + | 0.997152i | \(0.475971\pi\) | |||||||
\(572\) | −1.25511e12 | −0.490231 | ||||||||
\(573\) | 3.61434e12 | 1.40066 | ||||||||
\(574\) | 3.94149e11 | 0.151550 | ||||||||
\(575\) | 3.33705e12 | 1.27309 | ||||||||
\(576\) | −4.53459e12 | −1.71647 | ||||||||
\(577\) | −4.27490e12 | −1.60559 | −0.802795 | − | 0.596255i | \(-0.796655\pi\) | ||||
−0.802795 | + | 0.596255i | \(0.796655\pi\) | |||||||
\(578\) | 3.62648e12 | 1.35148 | ||||||||
\(579\) | −6.10729e12 | −2.25837 | ||||||||
\(580\) | 3.06698e11 | 0.112534 | ||||||||
\(581\) | −1.47222e11 | −0.0536018 | ||||||||
\(582\) | 3.55968e12 | 1.28605 | ||||||||
\(583\) | −5.31820e11 | −0.190659 | ||||||||
\(584\) | −1.37771e12 | −0.490117 | ||||||||
\(585\) | −5.11882e12 | −1.80704 | ||||||||
\(586\) | 8.42005e12 | 2.94968 | ||||||||
\(587\) | 6.39907e11 | 0.222457 | 0.111228 | − | 0.993795i | \(-0.464521\pi\) | ||||
0.111228 | + | 0.993795i | \(0.464521\pi\) | |||||||
\(588\) | 2.39815e12 | 0.827328 | ||||||||
\(589\) | 2.63678e12 | 0.902726 | ||||||||
\(590\) | −1.18650e13 | −4.03118 | ||||||||
\(591\) | −3.10680e11 | −0.104754 | ||||||||
\(592\) | 1.38834e12 | 0.464566 | ||||||||
\(593\) | 3.15740e12 | 1.04854 | 0.524269 | − | 0.851553i | \(-0.324339\pi\) | ||||
0.524269 | + | 0.851553i | \(0.324339\pi\) | |||||||
\(594\) | −3.16418e11 | −0.104285 | ||||||||
\(595\) | −1.63404e12 | −0.534485 | ||||||||
\(596\) | 4.91086e12 | 1.59422 | ||||||||
\(597\) | −8.08644e12 | −2.60539 | ||||||||
\(598\) | −5.76476e12 | −1.84343 | ||||||||
\(599\) | −3.82726e12 | −1.21470 | −0.607348 | − | 0.794436i | \(-0.707767\pi\) | ||||
−0.607348 | + | 0.794436i | \(0.707767\pi\) | |||||||
\(600\) | 7.31632e12 | 2.30469 | ||||||||
\(601\) | −3.13182e12 | −0.979178 | −0.489589 | − | 0.871953i | \(-0.662853\pi\) | ||||
−0.489589 | + | 0.871953i | \(0.662853\pi\) | |||||||
\(602\) | −2.63843e12 | −0.818769 | ||||||||
\(603\) | −7.98118e11 | −0.245832 | ||||||||
\(604\) | 7.20591e11 | 0.220304 | ||||||||
\(605\) | 4.55569e12 | 1.38247 | ||||||||
\(606\) | 8.66608e12 | 2.61033 | ||||||||
\(607\) | 2.48901e12 | 0.744178 | 0.372089 | − | 0.928197i | \(-0.378642\pi\) | ||||
0.372089 | + | 0.928197i | \(0.378642\pi\) | |||||||
\(608\) | 1.68494e12 | 0.500056 | ||||||||
\(609\) | −1.75714e11 | −0.0517639 | ||||||||
\(610\) | 8.31344e10 | 0.0243106 | ||||||||
\(611\) | −8.99136e11 | −0.261000 | ||||||||
\(612\) | −3.12255e12 | −0.899762 | ||||||||
\(613\) | 5.51889e12 | 1.57863 | 0.789313 | − | 0.613991i | \(-0.210437\pi\) | ||||
0.789313 | + | 0.613991i | \(0.210437\pi\) | |||||||
\(614\) | −1.01969e13 | −2.89542 | ||||||||
\(615\) | 8.51566e11 | 0.240038 | ||||||||
\(616\) | −1.01038e12 | −0.282731 | ||||||||
\(617\) | 2.13114e12 | 0.592010 | 0.296005 | − | 0.955186i | \(-0.404345\pi\) | ||||
0.296005 | + | 0.955186i | \(0.404345\pi\) | |||||||
\(618\) | 1.54696e13 | 4.26610 | ||||||||
\(619\) | 2.15468e12 | 0.589896 | 0.294948 | − | 0.955513i | \(-0.404698\pi\) | ||||
0.294948 | + | 0.955513i | \(0.404698\pi\) | |||||||
\(620\) | −1.14770e13 | −3.11936 | ||||||||
\(621\) | −9.30479e11 | −0.251070 | ||||||||
\(622\) | 7.24227e11 | 0.194007 | ||||||||
\(623\) | 4.06745e12 | 1.08175 | ||||||||
\(624\) | −2.26024e12 | −0.596794 | ||||||||
\(625\) | −2.86773e12 | −0.751758 | ||||||||
\(626\) | 1.29886e12 | 0.338047 | ||||||||
\(627\) | 1.14477e12 | 0.295810 | ||||||||
\(628\) | 2.45458e12 | 0.629735 | ||||||||
\(629\) | −2.04785e12 | −0.521639 | ||||||||
\(630\) | −9.40591e12 | −2.37886 | ||||||||
\(631\) | −5.88766e12 | −1.47846 | −0.739231 | − | 0.673452i | \(-0.764811\pi\) | ||||
−0.739231 | + | 0.673452i | \(0.764811\pi\) | |||||||
\(632\) | −3.00188e12 | −0.748457 | ||||||||
\(633\) | −4.90071e11 | −0.121323 | ||||||||
\(634\) | −4.74039e12 | −1.16523 | ||||||||
\(635\) | −6.98009e12 | −1.70365 | ||||||||
\(636\) | −7.82647e12 | −1.89675 | ||||||||
\(637\) | −1.37604e12 | −0.331134 | ||||||||
\(638\) | −7.81331e10 | −0.0186699 | ||||||||
\(639\) | −3.32562e12 | −0.789076 | ||||||||
\(640\) | −1.14073e13 | −2.68765 | ||||||||
\(641\) | −4.94911e12 | −1.15789 | −0.578944 | − | 0.815367i | \(-0.696535\pi\) | ||||
−0.578944 | + | 0.815367i | \(0.696535\pi\) | |||||||
\(642\) | −5.62284e12 | −1.30632 | ||||||||
\(643\) | 1.63185e12 | 0.376471 | 0.188235 | − | 0.982124i | \(-0.439723\pi\) | ||||
0.188235 | + | 0.982124i | \(0.439723\pi\) | |||||||
\(644\) | −6.78201e12 | −1.55372 | ||||||||
\(645\) | −5.70038e12 | −1.29684 | ||||||||
\(646\) | 2.45663e12 | 0.555000 | ||||||||
\(647\) | 1.18883e12 | 0.266718 | 0.133359 | − | 0.991068i | \(-0.457424\pi\) | ||||
0.133359 | + | 0.991068i | \(0.457424\pi\) | |||||||
\(648\) | 4.73811e12 | 1.05564 | ||||||||
\(649\) | 1.93525e12 | 0.428190 | ||||||||
\(650\) | −9.58239e12 | −2.10554 | ||||||||
\(651\) | 6.57541e12 | 1.43486 | ||||||||
\(652\) | −1.33029e12 | −0.288292 | ||||||||
\(653\) | 2.46630e12 | 0.530807 | 0.265404 | − | 0.964137i | \(-0.414495\pi\) | ||||
0.265404 | + | 0.964137i | \(0.414495\pi\) | |||||||
\(654\) | 2.28471e12 | 0.488349 | ||||||||
\(655\) | −8.44999e12 | −1.79378 | ||||||||
\(656\) | 2.02073e11 | 0.0426032 | ||||||||
\(657\) | 2.09191e12 | 0.438025 | ||||||||
\(658\) | −1.65217e12 | −0.343589 | ||||||||
\(659\) | −8.71065e12 | −1.79914 | −0.899572 | − | 0.436772i | \(-0.856122\pi\) | ||||
−0.899572 | + | 0.436772i | \(0.856122\pi\) | |||||||
\(660\) | −4.98277e12 | −1.02217 | ||||||||
\(661\) | 8.35219e10 | 0.0170174 | 0.00850871 | − | 0.999964i | \(-0.497292\pi\) | ||||
0.00850871 | + | 0.999964i | \(0.497292\pi\) | |||||||
\(662\) | 1.35958e12 | 0.275134 | ||||||||
\(663\) | 3.33394e12 | 0.670111 | ||||||||
\(664\) | −4.22062e11 | −0.0842598 | ||||||||
\(665\) | 4.73781e12 | 0.939465 | ||||||||
\(666\) | −1.17879e13 | −2.32168 | ||||||||
\(667\) | −2.29763e11 | −0.0449484 | ||||||||
\(668\) | −9.15124e11 | −0.177822 | ||||||||
\(669\) | −2.72065e11 | −0.0525115 | ||||||||
\(670\) | −2.73307e12 | −0.523980 | ||||||||
\(671\) | −1.35598e10 | −0.00258226 | ||||||||
\(672\) | 4.20178e12 | 0.794825 | ||||||||
\(673\) | −3.26734e12 | −0.613941 | −0.306970 | − | 0.951719i | \(-0.599315\pi\) | ||||
−0.306970 | + | 0.951719i | \(0.599315\pi\) | |||||||
\(674\) | 1.25514e13 | 2.34273 | ||||||||
\(675\) | −1.54667e12 | −0.286769 | ||||||||
\(676\) | 9.35596e11 | 0.172317 | ||||||||
\(677\) | 6.31103e12 | 1.15465 | 0.577327 | − | 0.816513i | \(-0.304096\pi\) | ||||
0.577327 | + | 0.816513i | \(0.304096\pi\) | |||||||
\(678\) | 3.89134e10 | 0.00707238 | ||||||||
\(679\) | −2.40294e12 | −0.433840 | ||||||||
\(680\) | −4.68454e12 | −0.840188 | ||||||||
\(681\) | 1.32737e13 | 2.36500 | ||||||||
\(682\) | 2.92384e12 | 0.517516 | ||||||||
\(683\) | 4.01246e12 | 0.705533 | 0.352766 | − | 0.935711i | \(-0.385241\pi\) | ||||
0.352766 | + | 0.935711i | \(0.385241\pi\) | |||||||
\(684\) | 9.05368e12 | 1.58151 | ||||||||
\(685\) | −5.98883e12 | −1.03929 | ||||||||
\(686\) | −1.05255e13 | −1.81461 | ||||||||
\(687\) | −1.36913e13 | −2.34499 | ||||||||
\(688\) | −1.35268e12 | −0.230169 | ||||||||
\(689\) | 4.49077e12 | 0.759162 | ||||||||
\(690\) | −2.28860e13 | −3.84369 | ||||||||
\(691\) | 8.60086e12 | 1.43513 | 0.717564 | − | 0.696492i | \(-0.245257\pi\) | ||||
0.717564 | + | 0.696492i | \(0.245257\pi\) | |||||||
\(692\) | −1.57636e13 | −2.61324 | ||||||||
\(693\) | 1.53417e12 | 0.252681 | ||||||||
\(694\) | −9.85398e12 | −1.61248 | ||||||||
\(695\) | 1.14569e13 | 1.86266 | ||||||||
\(696\) | −5.03744e11 | −0.0813707 | ||||||||
\(697\) | −2.98066e11 | −0.0478370 | ||||||||
\(698\) | 5.36050e12 | 0.854783 | ||||||||
\(699\) | 7.10592e12 | 1.12583 | ||||||||
\(700\) | −1.12733e13 | −1.77464 | ||||||||
\(701\) | −8.66222e12 | −1.35487 | −0.677436 | − | 0.735582i | \(-0.736909\pi\) | ||||
−0.677436 | + | 0.735582i | \(0.736909\pi\) | |||||||
\(702\) | 2.67188e12 | 0.415241 | ||||||||
\(703\) | 5.93764e12 | 0.916885 | ||||||||
\(704\) | 2.53276e12 | 0.388613 | ||||||||
\(705\) | −3.56955e12 | −0.544205 | ||||||||
\(706\) | 1.50936e13 | 2.28650 | ||||||||
\(707\) | −5.84998e12 | −0.880577 | ||||||||
\(708\) | 2.84799e13 | 4.25980 | ||||||||
\(709\) | −3.10340e12 | −0.461244 | −0.230622 | − | 0.973043i | \(-0.574076\pi\) | ||||
−0.230622 | + | 0.973043i | \(0.574076\pi\) | |||||||
\(710\) | −1.13882e13 | −1.68188 | ||||||||
\(711\) | 4.55805e12 | 0.668907 | ||||||||
\(712\) | 1.16608e13 | 1.70046 | ||||||||
\(713\) | 8.59802e12 | 1.24594 | ||||||||
\(714\) | 6.12615e12 | 0.882157 | ||||||||
\(715\) | 2.85908e12 | 0.409118 | ||||||||
\(716\) | 3.23890e12 | 0.460563 | ||||||||
\(717\) | −4.04782e11 | −0.0571986 | ||||||||
\(718\) | −1.64712e12 | −0.231294 | ||||||||
\(719\) | 7.46663e12 | 1.04194 | 0.520972 | − | 0.853574i | \(-0.325570\pi\) | ||||
0.520972 | + | 0.853574i | \(0.325570\pi\) | |||||||
\(720\) | −4.82225e12 | −0.668734 | ||||||||
\(721\) | −1.04426e13 | −1.43914 | ||||||||
\(722\) | 5.05060e12 | 0.691712 | ||||||||
\(723\) | 6.92307e12 | 0.942272 | ||||||||
\(724\) | −8.31484e12 | −1.12468 | ||||||||
\(725\) | −3.81921e11 | −0.0513395 | ||||||||
\(726\) | −1.70797e13 | −2.28173 | ||||||||
\(727\) | −2.77617e12 | −0.368587 | −0.184294 | − | 0.982871i | \(-0.559000\pi\) | ||||
−0.184294 | + | 0.982871i | \(0.559000\pi\) | |||||||
\(728\) | 8.53184e12 | 1.12577 | ||||||||
\(729\) | −9.86064e12 | −1.29310 | ||||||||
\(730\) | 7.16353e12 | 0.933629 | ||||||||
\(731\) | 1.99525e12 | 0.258446 | ||||||||
\(732\) | −1.99551e11 | −0.0256894 | ||||||||
\(733\) | −7.50272e12 | −0.959955 | −0.479977 | − | 0.877281i | \(-0.659355\pi\) | ||||
−0.479977 | + | 0.877281i | \(0.659355\pi\) | |||||||
\(734\) | −8.60077e12 | −1.09372 | ||||||||
\(735\) | −5.46285e12 | −0.690440 | ||||||||
\(736\) | 5.49425e12 | 0.690174 | ||||||||
\(737\) | 4.45782e11 | 0.0556569 | ||||||||
\(738\) | −1.71574e12 | −0.212910 | ||||||||
\(739\) | 1.01345e13 | 1.24997 | 0.624986 | − | 0.780636i | \(-0.285105\pi\) | ||||
0.624986 | + | 0.780636i | \(0.285105\pi\) | |||||||
\(740\) | −2.58445e13 | −3.16829 | ||||||||
\(741\) | −9.66659e12 | −1.17785 | ||||||||
\(742\) | 8.25185e12 | 0.999387 | ||||||||
\(743\) | 8.50223e11 | 0.102349 | 0.0511745 | − | 0.998690i | \(-0.483704\pi\) | ||||
0.0511745 | + | 0.998690i | \(0.483704\pi\) | |||||||
\(744\) | 1.88507e13 | 2.25553 | ||||||||
\(745\) | −1.11867e13 | −1.33045 | ||||||||
\(746\) | −1.02818e13 | −1.21546 | ||||||||
\(747\) | 6.40859e11 | 0.0753043 | ||||||||
\(748\) | 1.74407e12 | 0.203708 | ||||||||
\(749\) | 3.79566e12 | 0.440676 | ||||||||
\(750\) | −6.49444e12 | −0.749490 | ||||||||
\(751\) | 1.24461e13 | 1.42775 | 0.713877 | − | 0.700271i | \(-0.246937\pi\) | ||||
0.713877 | + | 0.700271i | \(0.246937\pi\) | |||||||
\(752\) | −8.47042e11 | −0.0965883 | ||||||||
\(753\) | −1.30218e13 | −1.47603 | ||||||||
\(754\) | 6.59768e11 | 0.0743396 | ||||||||
\(755\) | −1.64147e12 | −0.183853 | ||||||||
\(756\) | 3.14336e12 | 0.349982 | ||||||||
\(757\) | 3.37433e12 | 0.373470 | 0.186735 | − | 0.982410i | \(-0.440209\pi\) | ||||
0.186735 | + | 0.982410i | \(0.440209\pi\) | |||||||
\(758\) | 7.44179e12 | 0.818777 | ||||||||
\(759\) | 3.73286e12 | 0.408275 | ||||||||
\(760\) | 1.35826e13 | 1.47680 | ||||||||
\(761\) | −9.72420e12 | −1.05105 | −0.525524 | − | 0.850779i | \(-0.676131\pi\) | ||||
−0.525524 | + | 0.850779i | \(0.676131\pi\) | |||||||
\(762\) | 2.61690e13 | 2.81183 | ||||||||
\(763\) | −1.54228e12 | −0.164741 | ||||||||
\(764\) | −1.59658e13 | −1.69540 | ||||||||
\(765\) | 7.11299e12 | 0.750889 | ||||||||
\(766\) | −1.34783e13 | −1.41451 | ||||||||
\(767\) | −1.63416e13 | −1.70496 | ||||||||
\(768\) | 2.18232e13 | 2.26357 | ||||||||
\(769\) | 2.91544e11 | 0.0300632 | 0.0150316 | − | 0.999887i | \(-0.495215\pi\) | ||||
0.0150316 | + | 0.999887i | \(0.495215\pi\) | |||||||
\(770\) | 5.25359e12 | 0.538577 | ||||||||
\(771\) | −2.27663e13 | −2.32032 | ||||||||
\(772\) | 2.69781e13 | 2.73359 | ||||||||
\(773\) | 6.57221e11 | 0.0662069 | 0.0331035 | − | 0.999452i | \(-0.489461\pi\) | ||||
0.0331035 | + | 0.999452i | \(0.489461\pi\) | |||||||
\(774\) | 1.14851e13 | 1.15027 | ||||||||
\(775\) | 1.42919e13 | 1.42309 | ||||||||
\(776\) | −6.88887e12 | −0.681978 | ||||||||
\(777\) | 1.48068e13 | 1.45736 | ||||||||
\(778\) | −2.69216e13 | −2.63446 | ||||||||
\(779\) | 8.64227e11 | 0.0840832 | ||||||||
\(780\) | 4.20753e13 | 4.07006 | ||||||||
\(781\) | 1.85750e12 | 0.178648 | ||||||||
\(782\) | 8.01057e12 | 0.766007 | ||||||||
\(783\) | 1.06492e11 | 0.0101248 | ||||||||
\(784\) | −1.29631e12 | −0.122543 | ||||||||
\(785\) | −5.59139e12 | −0.525540 | ||||||||
\(786\) | 3.16798e13 | 2.96061 | ||||||||
\(787\) | −1.43680e13 | −1.33509 | −0.667544 | − | 0.744570i | \(-0.732655\pi\) | ||||
−0.667544 | + | 0.744570i | \(0.732655\pi\) | |||||||
\(788\) | 1.37239e12 | 0.126797 | ||||||||
\(789\) | −6.08383e12 | −0.558896 | ||||||||
\(790\) | 1.56086e13 | 1.42574 | ||||||||
\(791\) | −2.62683e10 | −0.00238582 | ||||||||
\(792\) | 4.39822e12 | 0.397204 | ||||||||
\(793\) | 1.14501e11 | 0.0102820 | ||||||||
\(794\) | −2.23670e13 | −1.99717 | ||||||||
\(795\) | 1.78283e13 | 1.58291 | ||||||||
\(796\) | 3.57207e13 | 3.15364 | ||||||||
\(797\) | −1.41338e11 | −0.0124079 | −0.00620393 | − | 0.999981i | \(-0.501975\pi\) | ||||
−0.00620393 | + | 0.999981i | \(0.501975\pi\) | |||||||
\(798\) | −1.77625e13 | −1.55057 | ||||||||
\(799\) | 1.24942e12 | 0.108454 | ||||||||
\(800\) | 9.13274e12 | 0.788309 | ||||||||
\(801\) | −1.77057e13 | −1.51973 | ||||||||
\(802\) | −7.30644e12 | −0.623622 | ||||||||
\(803\) | −1.16842e12 | −0.0991696 | ||||||||
\(804\) | 6.56030e12 | 0.553696 | ||||||||
\(805\) | 1.54490e13 | 1.29664 | ||||||||
\(806\) | −2.46893e13 | −2.06064 | ||||||||
\(807\) | 2.84871e13 | 2.36438 | ||||||||
\(808\) | −1.67710e13 | −1.38423 | ||||||||
\(809\) | 1.19441e13 | 0.980361 | 0.490180 | − | 0.871621i | \(-0.336931\pi\) | ||||
0.490180 | + | 0.871621i | \(0.336931\pi\) | |||||||
\(810\) | −2.46363e13 | −2.01091 | ||||||||
\(811\) | −4.81505e12 | −0.390847 | −0.195424 | − | 0.980719i | \(-0.562608\pi\) | ||||
−0.195424 | + | 0.980719i | \(0.562608\pi\) | |||||||
\(812\) | 7.76191e11 | 0.0626565 | ||||||||
\(813\) | 7.75819e12 | 0.622806 | ||||||||
\(814\) | 6.58403e12 | 0.525632 | ||||||||
\(815\) | 3.03033e12 | 0.240591 | ||||||||
\(816\) | 3.14078e12 | 0.247988 | ||||||||
\(817\) | −5.78513e12 | −0.454270 | ||||||||
\(818\) | −2.85684e13 | −2.23098 | ||||||||
\(819\) | −1.29547e13 | −1.00612 | ||||||||
\(820\) | −3.76168e12 | −0.290549 | ||||||||
\(821\) | 1.00327e13 | 0.770679 | 0.385340 | − | 0.922775i | \(-0.374084\pi\) | ||||
0.385340 | + | 0.922775i | \(0.374084\pi\) | |||||||
\(822\) | 2.24527e13 | 1.71532 | ||||||||
\(823\) | 1.10769e13 | 0.841624 | 0.420812 | − | 0.907148i | \(-0.361745\pi\) | ||||
0.420812 | + | 0.907148i | \(0.361745\pi\) | |||||||
\(824\) | −2.99375e13 | −2.26226 | ||||||||
\(825\) | 6.20488e12 | 0.466327 | ||||||||
\(826\) | −3.00278e13 | −2.24447 | ||||||||
\(827\) | 1.69072e13 | 1.25689 | 0.628444 | − | 0.777855i | \(-0.283692\pi\) | ||||
0.628444 | + | 0.777855i | \(0.283692\pi\) | |||||||
\(828\) | 2.95222e13 | 2.18279 | ||||||||
\(829\) | −1.41723e13 | −1.04219 | −0.521094 | − | 0.853499i | \(-0.674476\pi\) | ||||
−0.521094 | + | 0.853499i | \(0.674476\pi\) | |||||||
\(830\) | 2.19455e12 | 0.160507 | ||||||||
\(831\) | 8.32732e12 | 0.605760 | ||||||||
\(832\) | −2.13870e13 | −1.54737 | ||||||||
\(833\) | 1.91211e12 | 0.137597 | ||||||||
\(834\) | −4.29528e13 | −3.07428 | ||||||||
\(835\) | 2.08460e12 | 0.148400 | ||||||||
\(836\) | −5.05686e12 | −0.358057 | ||||||||
\(837\) | −3.98505e12 | −0.280653 | ||||||||
\(838\) | −2.29844e13 | −1.61003 | ||||||||
\(839\) | −4.27646e12 | −0.297959 | −0.148979 | − | 0.988840i | \(-0.547599\pi\) | ||||
−0.148979 | + | 0.988840i | \(0.547599\pi\) | |||||||
\(840\) | 3.38712e13 | 2.34733 | ||||||||
\(841\) | −1.44808e13 | −0.998187 | ||||||||
\(842\) | −4.58742e13 | −3.14532 | ||||||||
\(843\) | 3.32139e13 | 2.26515 | ||||||||
\(844\) | 2.16482e12 | 0.146853 | ||||||||
\(845\) | −2.13124e12 | −0.143806 | ||||||||
\(846\) | 7.19194e12 | 0.482702 | ||||||||
\(847\) | 1.15295e13 | 0.769727 | ||||||||
\(848\) | 4.23058e12 | 0.280944 | ||||||||
\(849\) | 4.26911e13 | 2.82002 | ||||||||
\(850\) | 1.33154e13 | 0.874925 | ||||||||
\(851\) | 1.93614e13 | 1.26548 | ||||||||
\(852\) | 2.73356e13 | 1.77726 | ||||||||
\(853\) | 4.74625e12 | 0.306959 | 0.153479 | − | 0.988152i | \(-0.450952\pi\) | ||||
0.153479 | + | 0.988152i | \(0.450952\pi\) | |||||||
\(854\) | 2.10396e11 | 0.0135356 | ||||||||
\(855\) | −2.06238e13 | −1.31984 | ||||||||
\(856\) | 1.08816e13 | 0.692724 | ||||||||
\(857\) | 7.59340e12 | 0.480864 | 0.240432 | − | 0.970666i | \(-0.422711\pi\) | ||||
0.240432 | + | 0.970666i | \(0.422711\pi\) | |||||||
\(858\) | −1.07189e13 | −0.675241 | ||||||||
\(859\) | 9.14456e12 | 0.573052 | 0.286526 | − | 0.958073i | \(-0.407500\pi\) | ||||
0.286526 | + | 0.958073i | \(0.407500\pi\) | |||||||
\(860\) | 2.51806e13 | 1.56973 | ||||||||
\(861\) | 2.15514e12 | 0.133648 | ||||||||
\(862\) | 5.12118e13 | 3.15927 | ||||||||
\(863\) | 1.27626e13 | 0.783232 | 0.391616 | − | 0.920129i | \(-0.371916\pi\) | ||||
0.391616 | + | 0.920129i | \(0.371916\pi\) | |||||||
\(864\) | −2.54650e12 | −0.155465 | ||||||||
\(865\) | 3.59086e13 | 2.18085 | ||||||||
\(866\) | 4.06037e13 | 2.45321 | ||||||||
\(867\) | 1.98290e13 | 1.19183 | ||||||||
\(868\) | −2.90460e13 | −1.73679 | ||||||||
\(869\) | −2.54586e12 | −0.151442 | ||||||||
\(870\) | 2.61927e12 | 0.155004 | ||||||||
\(871\) | −3.76425e12 | −0.221614 | ||||||||
\(872\) | −4.42147e12 | −0.258966 | ||||||||
\(873\) | 1.04600e13 | 0.609494 | ||||||||
\(874\) | −2.32263e13 | −1.34641 | ||||||||
\(875\) | 4.38403e12 | 0.252835 | ||||||||
\(876\) | −1.71949e13 | −0.986577 | ||||||||
\(877\) | 2.34914e13 | 1.34094 | 0.670472 | − | 0.741935i | \(-0.266092\pi\) | ||||
0.670472 | + | 0.741935i | \(0.266092\pi\) | |||||||
\(878\) | −5.32207e13 | −3.02242 | ||||||||
\(879\) | 4.60395e13 | 2.60124 | ||||||||
\(880\) | 2.69343e12 | 0.151403 | ||||||||
\(881\) | 1.89053e13 | 1.05728 | 0.528641 | − | 0.848845i | \(-0.322702\pi\) | ||||
0.528641 | + | 0.848845i | \(0.322702\pi\) | |||||||
\(882\) | 1.10066e13 | 0.612410 | ||||||||
\(883\) | 1.68521e13 | 0.932892 | 0.466446 | − | 0.884550i | \(-0.345534\pi\) | ||||
0.466446 | + | 0.884550i | \(0.345534\pi\) | |||||||
\(884\) | −1.47272e13 | −0.811121 | ||||||||
\(885\) | −6.48757e13 | −3.55498 | ||||||||
\(886\) | 4.98288e13 | 2.71662 | ||||||||
\(887\) | 2.06874e13 | 1.12215 | 0.561073 | − | 0.827767i | \(-0.310389\pi\) | ||||
0.561073 | + | 0.827767i | \(0.310389\pi\) | |||||||
\(888\) | 4.24489e13 | 2.29091 | ||||||||
\(889\) | −1.76652e13 | −0.948552 | ||||||||
\(890\) | −6.06313e13 | −3.23923 | ||||||||
\(891\) | 4.01834e12 | 0.213598 | ||||||||
\(892\) | 1.20181e12 | 0.0635614 | ||||||||
\(893\) | −3.62262e12 | −0.190630 | ||||||||
\(894\) | 4.19398e13 | 2.19587 | ||||||||
\(895\) | −7.37804e12 | −0.384359 | ||||||||
\(896\) | −2.88696e13 | −1.49642 | ||||||||
\(897\) | −3.15208e13 | −1.62566 | ||||||||
\(898\) | 2.08427e13 | 1.06957 | ||||||||
\(899\) | −9.84030e11 | −0.0502446 | ||||||||
\(900\) | 4.90728e13 | 2.49316 | ||||||||
\(901\) | −6.24026e12 | −0.315458 | ||||||||
\(902\) | 9.58310e11 | 0.0482033 | ||||||||
\(903\) | −1.44265e13 | −0.722049 | ||||||||
\(904\) | −7.53071e10 | −0.00375040 | ||||||||
\(905\) | 1.89407e13 | 0.938595 | ||||||||
\(906\) | 6.15400e12 | 0.303446 | ||||||||
\(907\) | 1.83836e13 | 0.901980 | 0.450990 | − | 0.892529i | \(-0.351071\pi\) | ||||
0.450990 | + | 0.892529i | \(0.351071\pi\) | |||||||
\(908\) | −5.86348e13 | −2.86266 | ||||||||
\(909\) | 2.54651e13 | 1.23711 | ||||||||
\(910\) | −4.43621e13 | −2.14450 | ||||||||
\(911\) | −3.49240e13 | −1.67993 | −0.839964 | − | 0.542642i | \(-0.817424\pi\) | ||||
−0.839964 | + | 0.542642i | \(0.817424\pi\) | |||||||
\(912\) | −9.10653e12 | −0.435889 | ||||||||
\(913\) | −3.57946e11 | −0.0170490 | ||||||||
\(914\) | −2.20680e13 | −1.04594 | ||||||||
\(915\) | 4.54565e11 | 0.0214388 | ||||||||
\(916\) | 6.04796e13 | 2.83844 | ||||||||
\(917\) | −2.13852e13 | −0.998739 | ||||||||
\(918\) | −3.71278e12 | −0.172547 | ||||||||
\(919\) | 1.01770e13 | 0.470650 | 0.235325 | − | 0.971917i | \(-0.424384\pi\) | ||||
0.235325 | + | 0.971917i | \(0.424384\pi\) | |||||||
\(920\) | 4.42901e13 | 2.03827 | ||||||||
\(921\) | −5.57551e13 | −2.55339 | ||||||||
\(922\) | −1.98006e13 | −0.902378 | ||||||||
\(923\) | −1.56850e13 | −0.711339 | ||||||||
\(924\) | −1.26104e13 | −0.569122 | ||||||||
\(925\) | 3.21832e13 | 1.44541 | ||||||||
\(926\) | −1.92010e13 | −0.858171 | ||||||||
\(927\) | 4.54570e13 | 2.02182 | ||||||||
\(928\) | −6.28809e11 | −0.0278325 | ||||||||
\(929\) | 1.16393e13 | 0.512690 | 0.256345 | − | 0.966585i | \(-0.417482\pi\) | ||||
0.256345 | + | 0.966585i | \(0.417482\pi\) | |||||||
\(930\) | −9.80161e13 | −4.29659 | ||||||||
\(931\) | −5.54407e12 | −0.241855 | ||||||||
\(932\) | −3.13894e13 | −1.36274 | ||||||||
\(933\) | 3.95996e12 | 0.171089 | ||||||||
\(934\) | −3.67640e12 | −0.158075 | ||||||||
\(935\) | −3.97290e12 | −0.170003 | ||||||||
\(936\) | −3.71392e13 | −1.58158 | ||||||||
\(937\) | −4.07911e13 | −1.72877 | −0.864384 | − | 0.502832i | \(-0.832291\pi\) | ||||
−0.864384 | + | 0.502832i | \(0.832291\pi\) | |||||||
\(938\) | −6.91686e12 | −0.291740 | ||||||||
\(939\) | 7.10194e12 | 0.298114 | ||||||||
\(940\) | 1.57680e13 | 0.658721 | ||||||||
\(941\) | 8.56043e12 | 0.355912 | 0.177956 | − | 0.984038i | \(-0.443052\pi\) | ||||
0.177956 | + | 0.984038i | \(0.443052\pi\) | |||||||
\(942\) | 2.09626e13 | 0.867394 | ||||||||
\(943\) | 2.81807e12 | 0.116051 | ||||||||
\(944\) | −1.53948e13 | −0.630956 | ||||||||
\(945\) | −7.16040e12 | −0.292075 | ||||||||
\(946\) | −6.41492e12 | −0.260424 | ||||||||
\(947\) | −1.43826e12 | −0.0581117 | −0.0290558 | − | 0.999578i | \(-0.509250\pi\) | ||||
−0.0290558 | + | 0.999578i | \(0.509250\pi\) | |||||||
\(948\) | −3.74659e13 | −1.50660 | ||||||||
\(949\) | 9.86630e12 | 0.394872 | ||||||||
\(950\) | −3.86075e13 | −1.53786 | ||||||||
\(951\) | −2.59197e13 | −1.02759 | ||||||||
\(952\) | −1.18556e13 | −0.467798 | ||||||||
\(953\) | −1.77380e13 | −0.696605 | −0.348303 | − | 0.937382i | \(-0.613242\pi\) | ||||
−0.348303 | + | 0.937382i | \(0.613242\pi\) | |||||||
\(954\) | −3.59204e13 | −1.40402 | ||||||||
\(955\) | 3.63693e13 | 1.41488 | ||||||||
\(956\) | 1.78807e12 | 0.0692348 | ||||||||
\(957\) | −4.27219e11 | −0.0164645 | ||||||||
\(958\) | 3.51797e13 | 1.34942 | ||||||||
\(959\) | −1.51565e13 | −0.578650 | ||||||||
\(960\) | −8.49060e13 | −3.22640 | ||||||||
\(961\) | 1.03840e13 | 0.392742 | ||||||||
\(962\) | −5.55965e13 | −2.09296 | ||||||||
\(963\) | −1.65226e13 | −0.619098 | ||||||||
\(964\) | −3.05817e13 | −1.14055 | ||||||||
\(965\) | −6.14546e13 | −2.28130 | ||||||||
\(966\) | −5.79199e13 | −2.14008 | ||||||||
\(967\) | −4.73857e12 | −0.174272 | −0.0871361 | − | 0.996196i | \(-0.527771\pi\) | ||||
−0.0871361 | + | 0.996196i | \(0.527771\pi\) | |||||||
\(968\) | 3.30534e13 | 1.20998 | ||||||||
\(969\) | 1.34325e13 | 0.489439 | ||||||||
\(970\) | 3.58194e13 | 1.29911 | ||||||||
\(971\) | 1.29945e13 | 0.469107 | 0.234554 | − | 0.972103i | \(-0.424637\pi\) | ||||
0.234554 | + | 0.972103i | \(0.424637\pi\) | |||||||
\(972\) | 7.09134e13 | 2.54818 | ||||||||
\(973\) | 2.89950e13 | 1.03709 | ||||||||
\(974\) | 9.00912e13 | 3.20750 | ||||||||
\(975\) | −5.23950e13 | −1.85682 | ||||||||
\(976\) | 1.07867e11 | 0.00380507 | ||||||||
\(977\) | 3.68324e13 | 1.29331 | 0.646657 | − | 0.762780i | \(-0.276166\pi\) | ||||
0.646657 | + | 0.762780i | \(0.276166\pi\) | |||||||
\(978\) | −1.13610e13 | −0.397091 | ||||||||
\(979\) | 9.88937e12 | 0.344070 | ||||||||
\(980\) | 2.41314e13 | 0.835728 | ||||||||
\(981\) | 6.71356e12 | 0.231442 | ||||||||
\(982\) | 1.54204e13 | 0.529167 | ||||||||
\(983\) | −3.14481e13 | −1.07424 | −0.537122 | − | 0.843504i | \(-0.680489\pi\) | ||||
−0.537122 | + | 0.843504i | \(0.680489\pi\) | |||||||
\(984\) | 6.17847e12 | 0.210089 | ||||||||
\(985\) | −3.12622e12 | −0.105817 | ||||||||
\(986\) | −9.16797e11 | −0.0308906 | ||||||||
\(987\) | −9.03382e12 | −0.303001 | ||||||||
\(988\) | 4.27008e13 | 1.42571 | ||||||||
\(989\) | −1.88641e13 | −0.626980 | ||||||||
\(990\) | −2.28690e13 | −0.756638 | ||||||||
\(991\) | 2.75782e13 | 0.908309 | 0.454155 | − | 0.890923i | \(-0.349941\pi\) | ||||
0.454155 | + | 0.890923i | \(0.349941\pi\) | |||||||
\(992\) | 2.35308e13 | 0.771496 | ||||||||
\(993\) | 7.43397e12 | 0.242633 | ||||||||
\(994\) | −2.88214e13 | −0.936431 | ||||||||
\(995\) | −8.13699e13 | −2.63184 | ||||||||
\(996\) | −5.26768e12 | −0.169610 | ||||||||
\(997\) | 3.87369e13 | 1.24164 | 0.620821 | − | 0.783953i | \(-0.286800\pi\) | ||||
0.620821 | + | 0.783953i | \(0.286800\pi\) | |||||||
\(998\) | 4.77617e13 | 1.52403 | ||||||||
\(999\) | −8.97373e12 | −0.285055 |
(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 | 197.10.a.b.1.9 | ✓ | 76 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
197.10.a.b.1.9 | ✓ | 76 | 1.1 | even | 1 | trivial |