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 | 1.1 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −44.8173 | −1.98066 | −0.990332 | − | 0.138716i | \(-0.955703\pi\) | ||||
−0.990332 | + | 0.138716i | \(0.955703\pi\) | |||||||
\(3\) | −222.555 | −1.58632 | −0.793162 | − | 0.609011i | \(-0.791566\pi\) | ||||
−0.793162 | + | 0.609011i | \(0.791566\pi\) | |||||||
\(4\) | 1496.59 | 2.92303 | ||||||||
\(5\) | 1221.65 | 0.874143 | 0.437072 | − | 0.899427i | \(-0.356016\pi\) | ||||
0.437072 | + | 0.899427i | \(0.356016\pi\) | |||||||
\(6\) | 9974.32 | 3.14197 | ||||||||
\(7\) | 2695.26 | 0.424287 | 0.212144 | − | 0.977239i | \(-0.431956\pi\) | ||||
0.212144 | + | 0.977239i | \(0.431956\pi\) | |||||||
\(8\) | −44126.8 | −3.80888 | ||||||||
\(9\) | 29847.7 | 1.51642 | ||||||||
\(10\) | −54751.2 | −1.73138 | ||||||||
\(11\) | −67291.8 | −1.38578 | −0.692891 | − | 0.721042i | \(-0.743663\pi\) | ||||
−0.692891 | + | 0.721042i | \(0.743663\pi\) | |||||||
\(12\) | −333074. | −4.63687 | ||||||||
\(13\) | 78776.4 | 0.764981 | 0.382491 | − | 0.923959i | \(-0.375066\pi\) | ||||
0.382491 | + | 0.923959i | \(0.375066\pi\) | |||||||
\(14\) | −120794. | −0.840370 | ||||||||
\(15\) | −271885. | −1.38667 | ||||||||
\(16\) | 1.21139e6 | 4.62108 | ||||||||
\(17\) | −456849. | −1.32664 | −0.663320 | − | 0.748336i | \(-0.730853\pi\) | ||||
−0.663320 | + | 0.748336i | \(0.730853\pi\) | |||||||
\(18\) | −1.33769e6 | −3.00352 | ||||||||
\(19\) | −1.02396e6 | −1.80256 | −0.901281 | − | 0.433234i | \(-0.857372\pi\) | ||||
−0.901281 | + | 0.433234i | \(0.857372\pi\) | |||||||
\(20\) | 1.82832e6 | 2.55515 | ||||||||
\(21\) | −599844. | −0.673056 | ||||||||
\(22\) | 3.01584e6 | 2.74477 | ||||||||
\(23\) | 1.05716e6 | 0.787711 | 0.393856 | − | 0.919172i | \(-0.371141\pi\) | ||||
0.393856 | + | 0.919172i | \(0.371141\pi\) | |||||||
\(24\) | 9.82064e6 | 6.04212 | ||||||||
\(25\) | −460690. | −0.235873 | ||||||||
\(26\) | −3.53055e6 | −1.51517 | ||||||||
\(27\) | −2.26221e6 | −0.819210 | ||||||||
\(28\) | 4.03371e6 | 1.24020 | ||||||||
\(29\) | 2.55701e6 | 0.671338 | 0.335669 | − | 0.941980i | \(-0.391038\pi\) | ||||
0.335669 | + | 0.941980i | \(0.391038\pi\) | |||||||
\(30\) | 1.21852e7 | 2.74654 | ||||||||
\(31\) | 6.29959e6 | 1.22514 | 0.612569 | − | 0.790417i | \(-0.290136\pi\) | ||||
0.612569 | + | 0.790417i | \(0.290136\pi\) | |||||||
\(32\) | −3.16983e7 | −5.34393 | ||||||||
\(33\) | 1.49761e7 | 2.19830 | ||||||||
\(34\) | 2.04748e7 | 2.62763 | ||||||||
\(35\) | 3.29267e6 | 0.370888 | ||||||||
\(36\) | 4.46699e7 | 4.43255 | ||||||||
\(37\) | −3.63397e6 | −0.318767 | −0.159383 | − | 0.987217i | \(-0.550951\pi\) | ||||
−0.159383 | + | 0.987217i | \(0.550951\pi\) | |||||||
\(38\) | 4.58910e7 | 3.57027 | ||||||||
\(39\) | −1.75321e7 | −1.21351 | ||||||||
\(40\) | −5.39076e7 | −3.32951 | ||||||||
\(41\) | −3.55107e7 | −1.96260 | −0.981300 | − | 0.192486i | \(-0.938345\pi\) | ||||
−0.981300 | + | 0.192486i | \(0.938345\pi\) | |||||||
\(42\) | 2.68834e7 | 1.33310 | ||||||||
\(43\) | 2.23251e7 | 0.995831 | 0.497915 | − | 0.867226i | \(-0.334099\pi\) | ||||
0.497915 | + | 0.867226i | \(0.334099\pi\) | |||||||
\(44\) | −1.00708e8 | −4.05069 | ||||||||
\(45\) | 3.64635e7 | 1.32557 | ||||||||
\(46\) | −4.73793e7 | −1.56019 | ||||||||
\(47\) | 3.40966e6 | 0.101923 | 0.0509613 | − | 0.998701i | \(-0.483771\pi\) | ||||
0.0509613 | + | 0.998701i | \(0.483771\pi\) | |||||||
\(48\) | −2.69601e8 | −7.33053 | ||||||||
\(49\) | −3.30892e7 | −0.819980 | ||||||||
\(50\) | 2.06469e7 | 0.467186 | ||||||||
\(51\) | 1.01674e8 | 2.10448 | ||||||||
\(52\) | 1.17896e8 | 2.23606 | ||||||||
\(53\) | −1.91404e7 | −0.333203 | −0.166602 | − | 0.986024i | \(-0.553279\pi\) | ||||
−0.166602 | + | 0.986024i | \(0.553279\pi\) | |||||||
\(54\) | 1.01386e8 | 1.62258 | ||||||||
\(55\) | −8.22072e7 | −1.21137 | ||||||||
\(56\) | −1.18933e8 | −1.61606 | ||||||||
\(57\) | 2.27887e8 | 2.85945 | ||||||||
\(58\) | −1.14598e8 | −1.32970 | ||||||||
\(59\) | −1.21878e8 | −1.30945 | −0.654727 | − | 0.755866i | \(-0.727216\pi\) | ||||
−0.654727 | + | 0.755866i | \(0.727216\pi\) | |||||||
\(60\) | −4.06901e8 | −4.05329 | ||||||||
\(61\) | −5.35936e7 | −0.495597 | −0.247799 | − | 0.968812i | \(-0.579707\pi\) | ||||
−0.247799 | + | 0.968812i | \(0.579707\pi\) | |||||||
\(62\) | −2.82331e8 | −2.42659 | ||||||||
\(63\) | 8.04474e7 | 0.643398 | ||||||||
\(64\) | 8.00402e8 | 5.96346 | ||||||||
\(65\) | 9.62373e7 | 0.668703 | ||||||||
\(66\) | −6.71190e8 | −4.35409 | ||||||||
\(67\) | 1.59987e8 | 0.969950 | 0.484975 | − | 0.874528i | \(-0.338829\pi\) | ||||
0.484975 | + | 0.874528i | \(0.338829\pi\) | |||||||
\(68\) | −6.83717e8 | −3.87781 | ||||||||
\(69\) | −2.35277e8 | −1.24956 | ||||||||
\(70\) | −1.47569e8 | −0.734604 | ||||||||
\(71\) | −6.15700e7 | −0.287545 | −0.143773 | − | 0.989611i | \(-0.545923\pi\) | ||||
−0.143773 | + | 0.989611i | \(0.545923\pi\) | |||||||
\(72\) | −1.31708e9 | −5.77587 | ||||||||
\(73\) | 1.80720e7 | 0.0744825 | 0.0372412 | − | 0.999306i | \(-0.488143\pi\) | ||||
0.0372412 | + | 0.999306i | \(0.488143\pi\) | |||||||
\(74\) | 1.62865e8 | 0.631370 | ||||||||
\(75\) | 1.02529e8 | 0.374171 | ||||||||
\(76\) | −1.53245e9 | −5.26895 | ||||||||
\(77\) | −1.81369e8 | −0.587970 | ||||||||
\(78\) | 7.85740e8 | 2.40355 | ||||||||
\(79\) | 3.43475e8 | 0.992140 | 0.496070 | − | 0.868282i | \(-0.334776\pi\) | ||||
0.496070 | + | 0.868282i | \(0.334776\pi\) | |||||||
\(80\) | 1.47990e9 | 4.03949 | ||||||||
\(81\) | −8.40272e7 | −0.216889 | ||||||||
\(82\) | 1.59149e9 | 3.88725 | ||||||||
\(83\) | 3.37643e8 | 0.780920 | 0.390460 | − | 0.920620i | \(-0.372316\pi\) | ||||
0.390460 | + | 0.920620i | \(0.372316\pi\) | |||||||
\(84\) | −8.97722e8 | −1.96737 | ||||||||
\(85\) | −5.58111e8 | −1.15967 | ||||||||
\(86\) | −1.00055e9 | −1.97241 | ||||||||
\(87\) | −5.69075e8 | −1.06496 | ||||||||
\(88\) | 2.96937e9 | 5.27828 | ||||||||
\(89\) | 9.24310e8 | 1.56157 | 0.780787 | − | 0.624797i | \(-0.214818\pi\) | ||||
0.780787 | + | 0.624797i | \(0.214818\pi\) | |||||||
\(90\) | −1.63420e9 | −2.62551 | ||||||||
\(91\) | 2.12323e8 | 0.324572 | ||||||||
\(92\) | 1.58214e9 | 2.30251 | ||||||||
\(93\) | −1.40201e9 | −1.94346 | ||||||||
\(94\) | −1.52812e8 | −0.201875 | ||||||||
\(95\) | −1.25092e9 | −1.57570 | ||||||||
\(96\) | 7.05461e9 | 8.47721 | ||||||||
\(97\) | 5.26076e8 | 0.603359 | 0.301680 | − | 0.953409i | \(-0.402453\pi\) | ||||
0.301680 | + | 0.953409i | \(0.402453\pi\) | |||||||
\(98\) | 1.48297e9 | 1.62411 | ||||||||
\(99\) | −2.00851e9 | −2.10143 | ||||||||
\(100\) | −6.89465e8 | −0.689465 | ||||||||
\(101\) | −1.20559e9 | −1.15280 | −0.576400 | − | 0.817167i | \(-0.695543\pi\) | ||||
−0.576400 | + | 0.817167i | \(0.695543\pi\) | |||||||
\(102\) | −4.55676e9 | −4.16827 | ||||||||
\(103\) | −1.48252e9 | −1.29787 | −0.648937 | − | 0.760842i | \(-0.724786\pi\) | ||||
−0.648937 | + | 0.760842i | \(0.724786\pi\) | |||||||
\(104\) | −3.47615e9 | −2.91372 | ||||||||
\(105\) | −7.32801e8 | −0.588348 | ||||||||
\(106\) | 8.57821e8 | 0.659964 | ||||||||
\(107\) | 1.39441e9 | 1.02841 | 0.514203 | − | 0.857668i | \(-0.328088\pi\) | ||||
0.514203 | + | 0.857668i | \(0.328088\pi\) | |||||||
\(108\) | −3.38560e9 | −2.39458 | ||||||||
\(109\) | −1.59761e9 | −1.08406 | −0.542028 | − | 0.840360i | \(-0.682343\pi\) | ||||
−0.542028 | + | 0.840360i | \(0.682343\pi\) | |||||||
\(110\) | 3.68431e9 | 2.39932 | ||||||||
\(111\) | 8.08757e8 | 0.505667 | ||||||||
\(112\) | 3.26501e9 | 1.96067 | ||||||||
\(113\) | −1.00787e8 | −0.0581503 | −0.0290752 | − | 0.999577i | \(-0.509256\pi\) | ||||
−0.0290752 | + | 0.999577i | \(0.509256\pi\) | |||||||
\(114\) | −1.02133e10 | −5.66360 | ||||||||
\(115\) | 1.29149e9 | 0.688573 | ||||||||
\(116\) | 3.82680e9 | 1.96234 | ||||||||
\(117\) | 2.35129e9 | 1.16003 | ||||||||
\(118\) | 5.46223e9 | 2.59359 | ||||||||
\(119\) | −1.23133e9 | −0.562876 | ||||||||
\(120\) | 1.19974e10 | 5.28168 | ||||||||
\(121\) | 2.17024e9 | 0.920393 | ||||||||
\(122\) | 2.40192e9 | 0.981611 | ||||||||
\(123\) | 7.90308e9 | 3.11332 | ||||||||
\(124\) | 9.42792e9 | 3.58111 | ||||||||
\(125\) | −2.94884e9 | −1.08033 | ||||||||
\(126\) | −3.60544e9 | −1.27436 | ||||||||
\(127\) | −1.65424e9 | −0.564265 | −0.282132 | − | 0.959375i | \(-0.591042\pi\) | ||||
−0.282132 | + | 0.959375i | \(0.591042\pi\) | |||||||
\(128\) | −1.96423e10 | −6.46767 | ||||||||
\(129\) | −4.96856e9 | −1.57971 | ||||||||
\(130\) | −4.31310e9 | −1.32448 | ||||||||
\(131\) | −1.98621e9 | −0.589257 | −0.294628 | − | 0.955612i | \(-0.595196\pi\) | ||||
−0.294628 | + | 0.955612i | \(0.595196\pi\) | |||||||
\(132\) | 2.24132e10 | 6.42570 | ||||||||
\(133\) | −2.75983e9 | −0.764804 | ||||||||
\(134\) | −7.17021e9 | −1.92115 | ||||||||
\(135\) | −2.76363e9 | −0.716107 | ||||||||
\(136\) | 2.01593e10 | 5.05301 | ||||||||
\(137\) | −6.89669e9 | −1.67262 | −0.836312 | − | 0.548254i | \(-0.815293\pi\) | ||||
−0.836312 | + | 0.548254i | \(0.815293\pi\) | |||||||
\(138\) | 1.05445e10 | 2.47497 | ||||||||
\(139\) | 4.02813e9 | 0.915243 | 0.457621 | − | 0.889147i | \(-0.348702\pi\) | ||||
0.457621 | + | 0.889147i | \(0.348702\pi\) | |||||||
\(140\) | 4.92779e9 | 1.08412 | ||||||||
\(141\) | −7.58837e8 | −0.161682 | ||||||||
\(142\) | 2.75940e9 | 0.569531 | ||||||||
\(143\) | −5.30100e9 | −1.06010 | ||||||||
\(144\) | 3.61572e10 | 7.00751 | ||||||||
\(145\) | 3.12378e9 | 0.586846 | ||||||||
\(146\) | −8.09940e8 | −0.147525 | ||||||||
\(147\) | 7.36416e9 | 1.30075 | ||||||||
\(148\) | −5.43857e9 | −0.931765 | ||||||||
\(149\) | −5.67750e9 | −0.943668 | −0.471834 | − | 0.881687i | \(-0.656408\pi\) | ||||
−0.471834 | + | 0.881687i | \(0.656408\pi\) | |||||||
\(150\) | −4.59507e9 | −0.741107 | ||||||||
\(151\) | −1.05118e10 | −1.64544 | −0.822720 | − | 0.568447i | \(-0.807544\pi\) | ||||
−0.822720 | + | 0.568447i | \(0.807544\pi\) | |||||||
\(152\) | 4.51839e10 | 6.86575 | ||||||||
\(153\) | −1.36359e10 | −2.01174 | ||||||||
\(154\) | 8.12847e9 | 1.16457 | ||||||||
\(155\) | 7.69591e9 | 1.07095 | ||||||||
\(156\) | −2.62384e10 | −3.54712 | ||||||||
\(157\) | 2.32592e9 | 0.305525 | 0.152762 | − | 0.988263i | \(-0.451183\pi\) | ||||
0.152762 | + | 0.988263i | \(0.451183\pi\) | |||||||
\(158\) | −1.53936e10 | −1.96510 | ||||||||
\(159\) | 4.25979e9 | 0.528568 | ||||||||
\(160\) | −3.87243e10 | −4.67137 | ||||||||
\(161\) | 2.84933e9 | 0.334216 | ||||||||
\(162\) | 3.76587e9 | 0.429584 | ||||||||
\(163\) | 9.30960e8 | 0.103297 | 0.0516484 | − | 0.998665i | \(-0.483552\pi\) | ||||
0.0516484 | + | 0.998665i | \(0.483552\pi\) | |||||||
\(164\) | −5.31450e10 | −5.73674 | ||||||||
\(165\) | 1.82956e10 | 1.92163 | ||||||||
\(166\) | −1.51323e10 | −1.54674 | ||||||||
\(167\) | 8.47247e9 | 0.842919 | 0.421459 | − | 0.906847i | \(-0.361518\pi\) | ||||
0.421459 | + | 0.906847i | \(0.361518\pi\) | |||||||
\(168\) | 2.64692e10 | 2.56359 | ||||||||
\(169\) | −4.39878e9 | −0.414804 | ||||||||
\(170\) | 2.50130e10 | 2.29692 | ||||||||
\(171\) | −3.05628e10 | −2.73344 | ||||||||
\(172\) | 3.34116e10 | 2.91084 | ||||||||
\(173\) | 3.24372e9 | 0.275319 | 0.137659 | − | 0.990480i | \(-0.456042\pi\) | ||||
0.137659 | + | 0.990480i | \(0.456042\pi\) | |||||||
\(174\) | 2.55044e10 | 2.10933 | ||||||||
\(175\) | −1.24168e9 | −0.100078 | ||||||||
\(176\) | −8.15166e10 | −6.40382 | ||||||||
\(177\) | 2.71245e10 | 2.07722 | ||||||||
\(178\) | −4.14251e10 | −3.09295 | ||||||||
\(179\) | −1.90933e9 | −0.139009 | −0.0695046 | − | 0.997582i | \(-0.522142\pi\) | ||||
−0.0695046 | + | 0.997582i | \(0.522142\pi\) | |||||||
\(180\) | 5.45710e10 | 3.87468 | ||||||||
\(181\) | −2.24205e10 | −1.55272 | −0.776359 | − | 0.630291i | \(-0.782935\pi\) | ||||
−0.776359 | + | 0.630291i | \(0.782935\pi\) | |||||||
\(182\) | −9.51575e9 | −0.642868 | ||||||||
\(183\) | 1.19275e10 | 0.786177 | ||||||||
\(184\) | −4.66493e10 | −3.00030 | ||||||||
\(185\) | −4.43944e9 | −0.278648 | ||||||||
\(186\) | 6.28341e10 | 3.84935 | ||||||||
\(187\) | 3.07422e10 | 1.83843 | ||||||||
\(188\) | 5.10287e9 | 0.297923 | ||||||||
\(189\) | −6.09724e9 | −0.347580 | ||||||||
\(190\) | 5.60629e10 | 3.12093 | ||||||||
\(191\) | 1.53199e10 | 0.832922 | 0.416461 | − | 0.909153i | \(-0.363270\pi\) | ||||
0.416461 | + | 0.909153i | \(0.363270\pi\) | |||||||
\(192\) | −1.78133e11 | −9.45997 | ||||||||
\(193\) | −6.62203e9 | −0.343545 | −0.171772 | − | 0.985137i | \(-0.554949\pi\) | ||||
−0.171772 | + | 0.985137i | \(0.554949\pi\) | |||||||
\(194\) | −2.35773e10 | −1.19505 | ||||||||
\(195\) | −2.14181e10 | −1.06078 | ||||||||
\(196\) | −4.95210e10 | −2.39683 | ||||||||
\(197\) | 1.50614e9 | 0.0712470 | ||||||||
\(198\) | 9.00159e10 | 4.16223 | ||||||||
\(199\) | 1.04676e10 | 0.473162 | 0.236581 | − | 0.971612i | \(-0.423973\pi\) | ||||
0.236581 | + | 0.971612i | \(0.423973\pi\) | |||||||
\(200\) | 2.03288e10 | 0.898413 | ||||||||
\(201\) | −3.56060e10 | −1.53865 | ||||||||
\(202\) | 5.40314e10 | 2.28331 | ||||||||
\(203\) | 6.89181e9 | 0.284840 | ||||||||
\(204\) | 1.52165e11 | 6.15146 | ||||||||
\(205\) | −4.33817e10 | −1.71559 | ||||||||
\(206\) | 6.64425e10 | 2.57065 | ||||||||
\(207\) | 3.15539e10 | 1.19450 | ||||||||
\(208\) | 9.54288e10 | 3.53504 | ||||||||
\(209\) | 6.89039e10 | 2.49796 | ||||||||
\(210\) | 3.28422e10 | 1.16532 | ||||||||
\(211\) | 3.16980e9 | 0.110093 | 0.0550466 | − | 0.998484i | \(-0.482469\pi\) | ||||
0.0550466 | + | 0.998484i | \(0.482469\pi\) | |||||||
\(212\) | −2.86453e10 | −0.973964 | ||||||||
\(213\) | 1.37027e10 | 0.456140 | ||||||||
\(214\) | −6.24939e10 | −2.03693 | ||||||||
\(215\) | 2.72735e10 | 0.870499 | ||||||||
\(216\) | 9.98239e10 | 3.12027 | ||||||||
\(217\) | 1.69790e10 | 0.519810 | ||||||||
\(218\) | 7.16006e10 | 2.14715 | ||||||||
\(219\) | −4.02202e9 | −0.118153 | ||||||||
\(220\) | −1.23031e11 | −3.54088 | ||||||||
\(221\) | −3.59889e10 | −1.01485 | ||||||||
\(222\) | −3.62463e10 | −1.00156 | ||||||||
\(223\) | 6.25531e10 | 1.69386 | 0.846929 | − | 0.531706i | \(-0.178449\pi\) | ||||
0.846929 | + | 0.531706i | \(0.178449\pi\) | |||||||
\(224\) | −8.54352e10 | −2.26736 | ||||||||
\(225\) | −1.37505e10 | −0.357683 | ||||||||
\(226\) | 4.51701e9 | 0.115176 | ||||||||
\(227\) | 5.40615e10 | 1.35136 | 0.675681 | − | 0.737194i | \(-0.263850\pi\) | ||||
0.675681 | + | 0.737194i | \(0.263850\pi\) | |||||||
\(228\) | 3.41053e11 | 8.35825 | ||||||||
\(229\) | −1.02334e10 | −0.245901 | −0.122950 | − | 0.992413i | \(-0.539236\pi\) | ||||
−0.122950 | + | 0.992413i | \(0.539236\pi\) | |||||||
\(230\) | −5.78810e10 | −1.36383 | ||||||||
\(231\) | 4.03646e10 | 0.932710 | ||||||||
\(232\) | −1.12833e11 | −2.55705 | ||||||||
\(233\) | −7.22261e10 | −1.60544 | −0.802718 | − | 0.596359i | \(-0.796613\pi\) | ||||
−0.802718 | + | 0.596359i | \(0.796613\pi\) | |||||||
\(234\) | −1.05379e11 | −2.29764 | ||||||||
\(235\) | 4.16542e9 | 0.0890950 | ||||||||
\(236\) | −1.82401e11 | −3.82757 | ||||||||
\(237\) | −7.64420e10 | −1.57385 | ||||||||
\(238\) | 5.51849e10 | 1.11487 | ||||||||
\(239\) | 7.08890e10 | 1.40536 | 0.702681 | − | 0.711505i | \(-0.251986\pi\) | ||||
0.702681 | + | 0.711505i | \(0.251986\pi\) | |||||||
\(240\) | −3.29358e11 | −6.40794 | ||||||||
\(241\) | 4.67626e10 | 0.892940 | 0.446470 | − | 0.894799i | \(-0.352681\pi\) | ||||
0.446470 | + | 0.894799i | \(0.352681\pi\) | |||||||
\(242\) | −9.72643e10 | −1.82299 | ||||||||
\(243\) | 6.32277e10 | 1.16327 | ||||||||
\(244\) | −8.02078e10 | −1.44865 | ||||||||
\(245\) | −4.04235e10 | −0.716781 | ||||||||
\(246\) | −3.54195e11 | −6.16644 | ||||||||
\(247\) | −8.06636e10 | −1.37893 | ||||||||
\(248\) | −2.77981e11 | −4.66640 | ||||||||
\(249\) | −7.51442e10 | −1.23879 | ||||||||
\(250\) | 1.32159e11 | 2.13977 | ||||||||
\(251\) | 4.40203e10 | 0.700037 | 0.350019 | − | 0.936743i | \(-0.386175\pi\) | ||||
0.350019 | + | 0.936743i | \(0.386175\pi\) | |||||||
\(252\) | 1.20397e11 | 1.88067 | ||||||||
\(253\) | −7.11385e10 | −1.09160 | ||||||||
\(254\) | 7.41388e10 | 1.11762 | ||||||||
\(255\) | 1.24210e11 | 1.83962 | ||||||||
\(256\) | 4.70511e11 | 6.84684 | ||||||||
\(257\) | 8.86934e9 | 0.126821 | 0.0634106 | − | 0.997988i | \(-0.479802\pi\) | ||||
0.0634106 | + | 0.997988i | \(0.479802\pi\) | |||||||
\(258\) | 2.22678e11 | 3.12887 | ||||||||
\(259\) | −9.79449e9 | −0.135249 | ||||||||
\(260\) | 1.44028e11 | 1.95464 | ||||||||
\(261\) | 7.63209e10 | 1.01803 | ||||||||
\(262\) | 8.90166e10 | 1.16712 | ||||||||
\(263\) | −9.73763e10 | −1.25503 | −0.627513 | − | 0.778606i | \(-0.715927\pi\) | ||||
−0.627513 | + | 0.778606i | \(0.715927\pi\) | |||||||
\(264\) | −6.60848e11 | −8.37306 | ||||||||
\(265\) | −2.33829e10 | −0.291267 | ||||||||
\(266\) | 1.23688e11 | 1.51482 | ||||||||
\(267\) | −2.05710e11 | −2.47716 | ||||||||
\(268\) | 2.39436e11 | 2.83519 | ||||||||
\(269\) | −5.05560e10 | −0.588691 | −0.294345 | − | 0.955699i | \(-0.595102\pi\) | ||||
−0.294345 | + | 0.955699i | \(0.595102\pi\) | |||||||
\(270\) | 1.23859e11 | 1.41837 | ||||||||
\(271\) | −1.51161e10 | −0.170247 | −0.0851233 | − | 0.996370i | \(-0.527128\pi\) | ||||
−0.0851233 | + | 0.996370i | \(0.527128\pi\) | |||||||
\(272\) | −5.53422e11 | −6.13051 | ||||||||
\(273\) | −4.72535e10 | −0.514876 | ||||||||
\(274\) | 3.09091e11 | 3.31291 | ||||||||
\(275\) | 3.10006e10 | 0.326869 | ||||||||
\(276\) | −3.52114e11 | −3.65252 | ||||||||
\(277\) | −7.29515e10 | −0.744518 | −0.372259 | − | 0.928129i | \(-0.621417\pi\) | ||||
−0.372259 | + | 0.928129i | \(0.621417\pi\) | |||||||
\(278\) | −1.80530e11 | −1.81279 | ||||||||
\(279\) | 1.88028e11 | 1.85782 | ||||||||
\(280\) | −1.45295e11 | −1.41267 | ||||||||
\(281\) | −1.82658e10 | −0.174767 | −0.0873835 | − | 0.996175i | \(-0.527851\pi\) | ||||
−0.0873835 | + | 0.996175i | \(0.527851\pi\) | |||||||
\(282\) | 3.40090e10 | 0.320238 | ||||||||
\(283\) | 5.96501e10 | 0.552805 | 0.276402 | − | 0.961042i | \(-0.410858\pi\) | ||||
0.276402 | + | 0.961042i | \(0.410858\pi\) | |||||||
\(284\) | −9.21452e10 | −0.840505 | ||||||||
\(285\) | 2.78398e11 | 2.49957 | ||||||||
\(286\) | 2.37577e11 | 2.09970 | ||||||||
\(287\) | −9.57106e10 | −0.832706 | ||||||||
\(288\) | −9.46122e11 | −8.10365 | ||||||||
\(289\) | 9.01234e10 | 0.759972 | ||||||||
\(290\) | −1.39999e11 | −1.16234 | ||||||||
\(291\) | −1.17081e11 | −0.957122 | ||||||||
\(292\) | 2.70465e10 | 0.217715 | ||||||||
\(293\) | −7.96661e10 | −0.631494 | −0.315747 | − | 0.948843i | \(-0.602255\pi\) | ||||
−0.315747 | + | 0.948843i | \(0.602255\pi\) | |||||||
\(294\) | −3.30042e11 | −2.57636 | ||||||||
\(295\) | −1.48892e11 | −1.14465 | ||||||||
\(296\) | 1.60355e11 | 1.21414 | ||||||||
\(297\) | 1.52228e11 | 1.13525 | ||||||||
\(298\) | 2.54450e11 | 1.86909 | ||||||||
\(299\) | 8.32795e10 | 0.602585 | ||||||||
\(300\) | 1.53444e11 | 1.09371 | ||||||||
\(301\) | 6.01720e10 | 0.422518 | ||||||||
\(302\) | 4.71112e11 | 3.25906 | ||||||||
\(303\) | 2.68311e11 | 1.82871 | ||||||||
\(304\) | −1.24041e12 | −8.32979 | ||||||||
\(305\) | −6.54728e10 | −0.433223 | ||||||||
\(306\) | 6.11125e11 | 3.98459 | ||||||||
\(307\) | −1.04450e11 | −0.671099 | −0.335549 | − | 0.942023i | \(-0.608922\pi\) | ||||
−0.335549 | + | 0.942023i | \(0.608922\pi\) | |||||||
\(308\) | −2.71435e11 | −1.71865 | ||||||||
\(309\) | 3.29942e11 | 2.05885 | ||||||||
\(310\) | −3.44910e11 | −2.12118 | ||||||||
\(311\) | −1.32059e11 | −0.800472 | −0.400236 | − | 0.916412i | \(-0.631072\pi\) | ||||
−0.400236 | + | 0.916412i | \(0.631072\pi\) | |||||||
\(312\) | 7.73634e11 | 4.62211 | ||||||||
\(313\) | −7.55896e10 | −0.445156 | −0.222578 | − | 0.974915i | \(-0.571447\pi\) | ||||
−0.222578 | + | 0.974915i | \(0.571447\pi\) | |||||||
\(314\) | −1.04241e11 | −0.605142 | ||||||||
\(315\) | 9.82788e10 | 0.562422 | ||||||||
\(316\) | 5.14042e11 | 2.90006 | ||||||||
\(317\) | 3.22598e11 | 1.79430 | 0.897149 | − | 0.441727i | \(-0.145634\pi\) | ||||
0.897149 | + | 0.441727i | \(0.145634\pi\) | |||||||
\(318\) | −1.90912e11 | −1.04692 | ||||||||
\(319\) | −1.72066e11 | −0.930329 | ||||||||
\(320\) | 9.77813e11 | 5.21292 | ||||||||
\(321\) | −3.10334e11 | −1.63138 | ||||||||
\(322\) | −1.27700e11 | −0.661969 | ||||||||
\(323\) | 4.67794e11 | 2.39135 | ||||||||
\(324\) | −1.25754e11 | −0.633973 | ||||||||
\(325\) | −3.62915e10 | −0.180439 | ||||||||
\(326\) | −4.17232e10 | −0.204596 | ||||||||
\(327\) | 3.55556e11 | 1.71966 | ||||||||
\(328\) | 1.56697e12 | 7.47531 | ||||||||
\(329\) | 9.18993e9 | 0.0432445 | ||||||||
\(330\) | −8.19961e11 | −3.80610 | ||||||||
\(331\) | 6.11091e10 | 0.279821 | 0.139910 | − | 0.990164i | \(-0.455319\pi\) | ||||
0.139910 | + | 0.990164i | \(0.455319\pi\) | |||||||
\(332\) | 5.05314e11 | 2.28265 | ||||||||
\(333\) | −1.08466e11 | −0.483385 | ||||||||
\(334\) | −3.79713e11 | −1.66954 | ||||||||
\(335\) | 1.95449e11 | 0.847876 | ||||||||
\(336\) | −7.26644e11 | −3.11025 | ||||||||
\(337\) | 1.02396e11 | 0.432463 | 0.216231 | − | 0.976342i | \(-0.430623\pi\) | ||||
0.216231 | + | 0.976342i | \(0.430623\pi\) | |||||||
\(338\) | 1.97142e11 | 0.821587 | ||||||||
\(339\) | 2.24307e10 | 0.0922452 | ||||||||
\(340\) | −8.35265e11 | −3.38976 | ||||||||
\(341\) | −4.23911e11 | −1.69777 | ||||||||
\(342\) | 1.36974e12 | 5.41403 | ||||||||
\(343\) | −1.97948e11 | −0.772194 | ||||||||
\(344\) | −9.85135e11 | −3.79300 | ||||||||
\(345\) | −2.87427e11 | −1.09230 | ||||||||
\(346\) | −1.45375e11 | −0.545314 | ||||||||
\(347\) | −2.15746e11 | −0.798842 | −0.399421 | − | 0.916768i | \(-0.630789\pi\) | ||||
−0.399421 | + | 0.916768i | \(0.630789\pi\) | |||||||
\(348\) | −8.51673e11 | −3.11291 | ||||||||
\(349\) | 5.15468e11 | 1.85989 | 0.929945 | − | 0.367699i | \(-0.119854\pi\) | ||||
0.929945 | + | 0.367699i | \(0.119854\pi\) | |||||||
\(350\) | 5.56488e10 | 0.198221 | ||||||||
\(351\) | −1.78208e11 | −0.626680 | ||||||||
\(352\) | 2.13304e12 | 7.40553 | ||||||||
\(353\) | 6.74884e10 | 0.231336 | 0.115668 | − | 0.993288i | \(-0.463099\pi\) | ||||
0.115668 | + | 0.993288i | \(0.463099\pi\) | |||||||
\(354\) | −1.21565e12 | −4.11427 | ||||||||
\(355\) | −7.52171e10 | −0.251356 | ||||||||
\(356\) | 1.38331e12 | 4.56453 | ||||||||
\(357\) | 2.74038e11 | 0.892903 | ||||||||
\(358\) | 8.55713e10 | 0.275331 | ||||||||
\(359\) | −2.26879e11 | −0.720892 | −0.360446 | − | 0.932780i | \(-0.617375\pi\) | ||||
−0.360446 | + | 0.932780i | \(0.617375\pi\) | |||||||
\(360\) | −1.60902e12 | −5.04894 | ||||||||
\(361\) | 7.25800e11 | 2.24923 | ||||||||
\(362\) | 1.00483e12 | 3.07541 | ||||||||
\(363\) | −4.82997e11 | −1.46004 | ||||||||
\(364\) | 3.17761e11 | 0.948733 | ||||||||
\(365\) | 2.20777e10 | 0.0651084 | ||||||||
\(366\) | −5.34560e11 | −1.55715 | ||||||||
\(367\) | 4.09124e11 | 1.17722 | 0.588611 | − | 0.808417i | \(-0.299675\pi\) | ||||
0.588611 | + | 0.808417i | \(0.299675\pi\) | |||||||
\(368\) | 1.28064e12 | 3.64008 | ||||||||
\(369\) | −1.05991e12 | −2.97613 | ||||||||
\(370\) | 1.98964e11 | 0.551908 | ||||||||
\(371\) | −5.15883e10 | −0.141374 | ||||||||
\(372\) | −2.09823e12 | −5.68080 | ||||||||
\(373\) | 1.37033e11 | 0.366552 | 0.183276 | − | 0.983062i | \(-0.441330\pi\) | ||||
0.183276 | + | 0.983062i | \(0.441330\pi\) | |||||||
\(374\) | −1.37778e12 | −3.64132 | ||||||||
\(375\) | 6.56280e11 | 1.71375 | ||||||||
\(376\) | −1.50457e11 | −0.388211 | ||||||||
\(377\) | 2.01432e11 | 0.513561 | ||||||||
\(378\) | 2.73262e11 | 0.688440 | ||||||||
\(379\) | 4.52490e11 | 1.12650 | 0.563251 | − | 0.826286i | \(-0.309550\pi\) | ||||
0.563251 | + | 0.826286i | \(0.309550\pi\) | |||||||
\(380\) | −1.87212e12 | −4.60582 | ||||||||
\(381\) | 3.68160e11 | 0.895106 | ||||||||
\(382\) | −6.86595e11 | −1.64974 | ||||||||
\(383\) | 3.36445e11 | 0.798950 | 0.399475 | − | 0.916744i | \(-0.369192\pi\) | ||||
0.399475 | + | 0.916744i | \(0.369192\pi\) | |||||||
\(384\) | 4.37150e12 | 10.2598 | ||||||||
\(385\) | −2.21570e11 | −0.513970 | ||||||||
\(386\) | 2.96782e11 | 0.680447 | ||||||||
\(387\) | 6.66353e11 | 1.51010 | ||||||||
\(388\) | 7.87322e11 | 1.76364 | ||||||||
\(389\) | 4.52622e11 | 1.00222 | 0.501109 | − | 0.865384i | \(-0.332926\pi\) | ||||
0.501109 | + | 0.865384i | \(0.332926\pi\) | |||||||
\(390\) | 9.59902e11 | 2.10105 | ||||||||
\(391\) | −4.82965e11 | −1.04501 | ||||||||
\(392\) | 1.46012e12 | 3.12321 | ||||||||
\(393\) | 4.42041e11 | 0.934751 | ||||||||
\(394\) | −6.75011e10 | −0.141117 | ||||||||
\(395\) | 4.19607e11 | 0.867273 | ||||||||
\(396\) | −3.00591e12 | −6.14254 | ||||||||
\(397\) | 1.78064e11 | 0.359766 | 0.179883 | − | 0.983688i | \(-0.442428\pi\) | ||||
0.179883 | + | 0.983688i | \(0.442428\pi\) | |||||||
\(398\) | −4.69131e11 | −0.937175 | ||||||||
\(399\) | 6.14214e11 | 1.21323 | ||||||||
\(400\) | −5.58075e11 | −1.08999 | ||||||||
\(401\) | 1.71522e11 | 0.331261 | 0.165630 | − | 0.986188i | \(-0.447034\pi\) | ||||
0.165630 | + | 0.986188i | \(0.447034\pi\) | |||||||
\(402\) | 1.59577e12 | 3.04756 | ||||||||
\(403\) | 4.96259e11 | 0.937207 | ||||||||
\(404\) | −1.80428e12 | −3.36967 | ||||||||
\(405\) | −1.02652e11 | −0.189592 | ||||||||
\(406\) | −3.08872e11 | −0.564173 | ||||||||
\(407\) | 2.44536e11 | 0.441741 | ||||||||
\(408\) | −4.48655e12 | −8.01571 | ||||||||
\(409\) | 8.48987e11 | 1.50019 | 0.750094 | − | 0.661331i | \(-0.230008\pi\) | ||||
0.750094 | + | 0.661331i | \(0.230008\pi\) | |||||||
\(410\) | 1.94425e12 | 3.39801 | ||||||||
\(411\) | 1.53489e12 | 2.65332 | ||||||||
\(412\) | −2.21873e12 | −3.79373 | ||||||||
\(413\) | −3.28492e11 | −0.555584 | ||||||||
\(414\) | −1.41416e12 | −2.36591 | ||||||||
\(415\) | 4.12483e11 | 0.682636 | ||||||||
\(416\) | −2.49708e12 | −4.08801 | ||||||||
\(417\) | −8.96479e11 | −1.45187 | ||||||||
\(418\) | −3.08809e12 | −4.94762 | ||||||||
\(419\) | −7.15732e11 | −1.13445 | −0.567227 | − | 0.823561i | \(-0.691984\pi\) | ||||
−0.567227 | + | 0.823561i | \(0.691984\pi\) | |||||||
\(420\) | −1.09670e12 | −1.71976 | ||||||||
\(421\) | 8.23979e11 | 1.27834 | 0.639170 | − | 0.769065i | \(-0.279278\pi\) | ||||
0.639170 | + | 0.769065i | \(0.279278\pi\) | |||||||
\(422\) | −1.42062e11 | −0.218058 | ||||||||
\(423\) | 1.01771e11 | 0.154558 | ||||||||
\(424\) | 8.44604e11 | 1.26913 | ||||||||
\(425\) | 2.10466e11 | 0.312919 | ||||||||
\(426\) | −6.14119e11 | −0.903460 | ||||||||
\(427\) | −1.44449e11 | −0.210275 | ||||||||
\(428\) | 2.08687e12 | 3.00606 | ||||||||
\(429\) | 1.17976e12 | 1.68166 | ||||||||
\(430\) | −1.22233e12 | −1.72417 | ||||||||
\(431\) | −8.64097e11 | −1.20619 | −0.603094 | − | 0.797670i | \(-0.706066\pi\) | ||||
−0.603094 | + | 0.797670i | \(0.706066\pi\) | |||||||
\(432\) | −2.74041e12 | −3.78564 | ||||||||
\(433\) | 1.09124e12 | 1.49184 | 0.745921 | − | 0.666034i | \(-0.232010\pi\) | ||||
0.745921 | + | 0.666034i | \(0.232010\pi\) | |||||||
\(434\) | −7.60955e11 | −1.02957 | ||||||||
\(435\) | −6.95212e11 | −0.930927 | ||||||||
\(436\) | −2.39097e12 | −3.16873 | ||||||||
\(437\) | −1.08249e12 | −1.41990 | ||||||||
\(438\) | 1.80256e11 | 0.234022 | ||||||||
\(439\) | −1.39581e12 | −1.79364 | −0.896821 | − | 0.442393i | \(-0.854130\pi\) | ||||
−0.896821 | + | 0.442393i | \(0.854130\pi\) | |||||||
\(440\) | 3.62754e12 | 4.61397 | ||||||||
\(441\) | −9.87636e11 | −1.24344 | ||||||||
\(442\) | 1.61293e12 | 2.01009 | ||||||||
\(443\) | −7.88480e11 | −0.972688 | −0.486344 | − | 0.873767i | \(-0.661670\pi\) | ||||
−0.486344 | + | 0.873767i | \(0.661670\pi\) | |||||||
\(444\) | 1.21038e12 | 1.47808 | ||||||||
\(445\) | 1.12919e12 | 1.36504 | ||||||||
\(446\) | −2.80346e12 | −3.35496 | ||||||||
\(447\) | 1.26356e12 | 1.49696 | ||||||||
\(448\) | 2.15729e12 | 2.53022 | ||||||||
\(449\) | 2.71552e11 | 0.315315 | 0.157658 | − | 0.987494i | \(-0.449606\pi\) | ||||
0.157658 | + | 0.987494i | \(0.449606\pi\) | |||||||
\(450\) | 6.16262e11 | 0.708450 | ||||||||
\(451\) | 2.38958e12 | 2.71974 | ||||||||
\(452\) | −1.50837e11 | −0.169975 | ||||||||
\(453\) | 2.33946e12 | 2.61020 | ||||||||
\(454\) | −2.42289e12 | −2.67660 | ||||||||
\(455\) | 2.59385e11 | 0.283722 | ||||||||
\(456\) | −1.00559e13 | −10.8913 | ||||||||
\(457\) | −1.08795e12 | −1.16678 | −0.583388 | − | 0.812193i | \(-0.698273\pi\) | ||||
−0.583388 | + | 0.812193i | \(0.698273\pi\) | |||||||
\(458\) | 4.58633e11 | 0.487047 | ||||||||
\(459\) | 1.03349e12 | 1.08680 | ||||||||
\(460\) | 1.93283e12 | 2.01272 | ||||||||
\(461\) | 9.84892e11 | 1.01563 | 0.507814 | − | 0.861467i | \(-0.330454\pi\) | ||||
0.507814 | + | 0.861467i | \(0.330454\pi\) | |||||||
\(462\) | −1.80903e12 | −1.84738 | ||||||||
\(463\) | 9.87306e11 | 0.998475 | 0.499238 | − | 0.866465i | \(-0.333614\pi\) | ||||
0.499238 | + | 0.866465i | \(0.333614\pi\) | |||||||
\(464\) | 3.09753e12 | 3.10231 | ||||||||
\(465\) | −1.71276e12 | −1.69887 | ||||||||
\(466\) | 3.23698e12 | 3.17983 | ||||||||
\(467\) | −1.47391e12 | −1.43399 | −0.716994 | − | 0.697079i | \(-0.754483\pi\) | ||||
−0.716994 | + | 0.697079i | \(0.754483\pi\) | |||||||
\(468\) | 3.51893e12 | 3.39081 | ||||||||
\(469\) | 4.31208e11 | 0.411537 | ||||||||
\(470\) | −1.86683e11 | −0.176467 | ||||||||
\(471\) | −5.17645e11 | −0.484661 | ||||||||
\(472\) | 5.37807e12 | 4.98755 | ||||||||
\(473\) | −1.50230e12 | −1.38000 | ||||||||
\(474\) | 3.42593e12 | 3.11728 | ||||||||
\(475\) | 4.71726e11 | 0.425176 | ||||||||
\(476\) | −1.84280e12 | −1.64530 | ||||||||
\(477\) | −5.71297e11 | −0.505276 | ||||||||
\(478\) | −3.17705e12 | −2.78355 | ||||||||
\(479\) | 2.90657e11 | 0.252273 | 0.126136 | − | 0.992013i | \(-0.459742\pi\) | ||||
0.126136 | + | 0.992013i | \(0.459742\pi\) | |||||||
\(480\) | 8.61829e12 | 7.41029 | ||||||||
\(481\) | −2.86271e11 | −0.243851 | ||||||||
\(482\) | −2.09578e12 | −1.76861 | ||||||||
\(483\) | −6.34133e11 | −0.530174 | ||||||||
\(484\) | 3.24796e12 | 2.69034 | ||||||||
\(485\) | 6.42682e11 | 0.527422 | ||||||||
\(486\) | −2.83370e12 | −2.30404 | ||||||||
\(487\) | 1.52538e11 | 0.122885 | 0.0614425 | − | 0.998111i | \(-0.480430\pi\) | ||||
0.0614425 | + | 0.998111i | \(0.480430\pi\) | |||||||
\(488\) | 2.36491e12 | 1.88767 | ||||||||
\(489\) | −2.07190e11 | −0.163862 | ||||||||
\(490\) | 1.81167e12 | 1.41970 | ||||||||
\(491\) | −8.75599e11 | −0.679890 | −0.339945 | − | 0.940445i | \(-0.610408\pi\) | ||||
−0.339945 | + | 0.940445i | \(0.610408\pi\) | |||||||
\(492\) | 1.18277e13 | 9.10032 | ||||||||
\(493\) | −1.16817e12 | −0.890623 | ||||||||
\(494\) | 3.61513e12 | 2.73119 | ||||||||
\(495\) | −2.45370e12 | −1.83695 | ||||||||
\(496\) | 7.63126e12 | 5.66146 | ||||||||
\(497\) | −1.65947e11 | −0.122002 | ||||||||
\(498\) | 3.36776e12 | 2.45363 | ||||||||
\(499\) | 2.97579e11 | 0.214857 | 0.107428 | − | 0.994213i | \(-0.465738\pi\) | ||||
0.107428 | + | 0.994213i | \(0.465738\pi\) | |||||||
\(500\) | −4.41322e12 | −3.15784 | ||||||||
\(501\) | −1.88559e12 | −1.33714 | ||||||||
\(502\) | −1.97287e12 | −1.38654 | ||||||||
\(503\) | 1.70664e11 | 0.118873 | 0.0594367 | − | 0.998232i | \(-0.481070\pi\) | ||||
0.0594367 | + | 0.998232i | \(0.481070\pi\) | |||||||
\(504\) | −3.54989e12 | −2.45063 | ||||||||
\(505\) | −1.47281e12 | −1.00771 | ||||||||
\(506\) | 3.18824e12 | 2.16209 | ||||||||
\(507\) | 9.78971e11 | 0.658012 | ||||||||
\(508\) | −2.47573e12 | −1.64936 | ||||||||
\(509\) | 1.12422e12 | 0.742372 | 0.371186 | − | 0.928558i | \(-0.378951\pi\) | ||||
0.371186 | + | 0.928558i | \(0.378951\pi\) | |||||||
\(510\) | −5.56678e12 | −3.64366 | ||||||||
\(511\) | 4.87089e10 | 0.0316020 | ||||||||
\(512\) | −1.10302e13 | −7.09361 | ||||||||
\(513\) | 2.31640e12 | 1.47668 | ||||||||
\(514\) | −3.97500e11 | −0.251190 | ||||||||
\(515\) | −1.81112e12 | −1.13453 | ||||||||
\(516\) | −7.43591e12 | −4.61754 | ||||||||
\(517\) | −2.29442e11 | −0.141243 | ||||||||
\(518\) | 4.38963e11 | 0.267882 | ||||||||
\(519\) | −7.21906e11 | −0.436745 | ||||||||
\(520\) | −4.24665e12 | −2.54701 | ||||||||
\(521\) | −2.17786e12 | −1.29497 | −0.647486 | − | 0.762078i | \(-0.724179\pi\) | ||||
−0.647486 | + | 0.762078i | \(0.724179\pi\) | |||||||
\(522\) | −3.42050e12 | −2.01638 | ||||||||
\(523\) | 3.09707e12 | 1.81006 | 0.905030 | − | 0.425348i | \(-0.139848\pi\) | ||||
0.905030 | + | 0.425348i | \(0.139848\pi\) | |||||||
\(524\) | −2.97255e12 | −1.72242 | ||||||||
\(525\) | 2.76342e11 | 0.158756 | ||||||||
\(526\) | 4.36415e12 | 2.48578 | ||||||||
\(527\) | −2.87796e12 | −1.62531 | ||||||||
\(528\) | 1.81419e13 | 10.1585 | ||||||||
\(529\) | −6.83557e11 | −0.379511 | ||||||||
\(530\) | 1.04796e12 | 0.576903 | ||||||||
\(531\) | −3.63777e12 | −1.98568 | ||||||||
\(532\) | −4.13034e12 | −2.23555 | ||||||||
\(533\) | −2.79740e12 | −1.50135 | ||||||||
\(534\) | 9.21936e12 | 4.90642 | ||||||||
\(535\) | 1.70349e12 | 0.898975 | ||||||||
\(536\) | −7.05973e12 | −3.69442 | ||||||||
\(537\) | 4.24932e11 | 0.220513 | ||||||||
\(538\) | 2.26578e12 | 1.16600 | ||||||||
\(539\) | 2.22663e12 | 1.13631 | ||||||||
\(540\) | −4.13603e12 | −2.09320 | ||||||||
\(541\) | 1.45425e12 | 0.729882 | 0.364941 | − | 0.931031i | \(-0.381089\pi\) | ||||
0.364941 | + | 0.931031i | \(0.381089\pi\) | |||||||
\(542\) | 6.77464e11 | 0.337201 | ||||||||
\(543\) | 4.98980e12 | 2.46311 | ||||||||
\(544\) | 1.44813e13 | 7.08947 | ||||||||
\(545\) | −1.95173e12 | −0.947620 | ||||||||
\(546\) | 2.11778e12 | 1.01980 | ||||||||
\(547\) | −1.55288e12 | −0.741645 | −0.370822 | − | 0.928704i | \(-0.620924\pi\) | ||||
−0.370822 | + | 0.928704i | \(0.620924\pi\) | |||||||
\(548\) | −1.03215e13 | −4.88913 | ||||||||
\(549\) | −1.59965e12 | −0.751534 | ||||||||
\(550\) | −1.38937e12 | −0.647418 | ||||||||
\(551\) | −2.61827e12 | −1.21013 | ||||||||
\(552\) | 1.03820e13 | 4.75944 | ||||||||
\(553\) | 9.25755e11 | 0.420952 | ||||||||
\(554\) | 3.26949e12 | 1.47464 | ||||||||
\(555\) | 9.88020e11 | 0.442026 | ||||||||
\(556\) | 6.02846e12 | 2.67528 | ||||||||
\(557\) | 3.78885e12 | 1.66786 | 0.833929 | − | 0.551872i | \(-0.186086\pi\) | ||||
0.833929 | + | 0.551872i | \(0.186086\pi\) | |||||||
\(558\) | −8.42693e12 | −3.67972 | ||||||||
\(559\) | 1.75869e12 | 0.761792 | ||||||||
\(560\) | 3.98871e12 | 1.71390 | ||||||||
\(561\) | −6.84183e12 | −2.91635 | ||||||||
\(562\) | 8.18623e11 | 0.346155 | ||||||||
\(563\) | 5.74431e11 | 0.240963 | 0.120481 | − | 0.992716i | \(-0.461556\pi\) | ||||
0.120481 | + | 0.992716i | \(0.461556\pi\) | |||||||
\(564\) | −1.13567e12 | −0.472602 | ||||||||
\(565\) | −1.23127e11 | −0.0508317 | ||||||||
\(566\) | −2.67336e12 | −1.09492 | ||||||||
\(567\) | −2.26475e11 | −0.0920231 | ||||||||
\(568\) | 2.71689e12 | 1.09523 | ||||||||
\(569\) | 1.18683e12 | 0.474659 | 0.237330 | − | 0.971429i | \(-0.423728\pi\) | ||||
0.237330 | + | 0.971429i | \(0.423728\pi\) | |||||||
\(570\) | −1.24771e13 | −4.95080 | ||||||||
\(571\) | −3.85781e12 | −1.51872 | −0.759362 | − | 0.650669i | \(-0.774489\pi\) | ||||
−0.759362 | + | 0.650669i | \(0.774489\pi\) | |||||||
\(572\) | −7.93344e12 | −3.09870 | ||||||||
\(573\) | −3.40951e12 | −1.32128 | ||||||||
\(574\) | 4.28949e12 | 1.64931 | ||||||||
\(575\) | −4.87025e11 | −0.185800 | ||||||||
\(576\) | 2.38902e13 | 9.04311 | ||||||||
\(577\) | 1.08972e12 | 0.409285 | 0.204642 | − | 0.978837i | \(-0.434397\pi\) | ||||
0.204642 | + | 0.978837i | \(0.434397\pi\) | |||||||
\(578\) | −4.03909e12 | −1.50525 | ||||||||
\(579\) | 1.47377e12 | 0.544973 | ||||||||
\(580\) | 4.67502e12 | 1.71537 | ||||||||
\(581\) | 9.10037e11 | 0.331334 | ||||||||
\(582\) | 5.24725e12 | 1.89574 | ||||||||
\(583\) | 1.28799e12 | 0.461747 | ||||||||
\(584\) | −7.97461e11 | −0.283695 | ||||||||
\(585\) | 2.87246e12 | 1.01404 | ||||||||
\(586\) | 3.57042e12 | 1.25078 | ||||||||
\(587\) | 4.09283e12 | 1.42283 | 0.711415 | − | 0.702773i | \(-0.248055\pi\) | ||||
0.711415 | + | 0.702773i | \(0.248055\pi\) | |||||||
\(588\) | 1.10211e13 | 3.80215 | ||||||||
\(589\) | −6.45051e12 | −2.20839 | ||||||||
\(590\) | 6.67295e12 | 2.26717 | ||||||||
\(591\) | −3.35199e11 | −0.113021 | ||||||||
\(592\) | −4.40215e12 | −1.47305 | ||||||||
\(593\) | 5.77011e10 | 0.0191619 | 0.00958094 | − | 0.999954i | \(-0.496950\pi\) | ||||
0.00958094 | + | 0.999954i | \(0.496950\pi\) | |||||||
\(594\) | −6.82245e12 | −2.24854 | ||||||||
\(595\) | −1.50426e12 | −0.492034 | ||||||||
\(596\) | −8.49691e12 | −2.75837 | ||||||||
\(597\) | −2.32962e12 | −0.750588 | ||||||||
\(598\) | −3.73237e12 | −1.19352 | ||||||||
\(599\) | 2.66229e12 | 0.844959 | 0.422479 | − | 0.906373i | \(-0.361160\pi\) | ||||
0.422479 | + | 0.906373i | \(0.361160\pi\) | |||||||
\(600\) | −4.52427e12 | −1.42517 | ||||||||
\(601\) | 1.09906e12 | 0.343628 | 0.171814 | − | 0.985129i | \(-0.445037\pi\) | ||||
0.171814 | + | 0.985129i | \(0.445037\pi\) | |||||||
\(602\) | −2.69675e12 | −0.836867 | ||||||||
\(603\) | 4.77526e12 | 1.47085 | ||||||||
\(604\) | −1.57319e13 | −4.80967 | ||||||||
\(605\) | 2.65128e12 | 0.804555 | ||||||||
\(606\) | −1.20250e13 | −3.62207 | ||||||||
\(607\) | −3.35207e12 | −1.00222 | −0.501111 | − | 0.865383i | \(-0.667075\pi\) | ||||
−0.501111 | + | 0.865383i | \(0.667075\pi\) | |||||||
\(608\) | 3.24577e13 | 9.63278 | ||||||||
\(609\) | −1.53381e12 | −0.451848 | ||||||||
\(610\) | 2.93431e12 | 0.858069 | ||||||||
\(611\) | 2.68601e11 | 0.0779689 | ||||||||
\(612\) | −2.04074e13 | −5.88039 | ||||||||
\(613\) | 1.83381e12 | 0.524543 | 0.262272 | − | 0.964994i | \(-0.415528\pi\) | ||||
0.262272 | + | 0.964994i | \(0.415528\pi\) | |||||||
\(614\) | 4.68117e12 | 1.32922 | ||||||||
\(615\) | 9.65482e12 | 2.72149 | ||||||||
\(616\) | 8.00323e12 | 2.23951 | ||||||||
\(617\) | −3.83331e11 | −0.106486 | −0.0532428 | − | 0.998582i | \(-0.516956\pi\) | ||||
−0.0532428 | + | 0.998582i | \(0.516956\pi\) | |||||||
\(618\) | −1.47871e13 | −4.07789 | ||||||||
\(619\) | −3.21657e12 | −0.880614 | −0.440307 | − | 0.897847i | \(-0.645130\pi\) | ||||
−0.440307 | + | 0.897847i | \(0.645130\pi\) | |||||||
\(620\) | 1.15176e13 | 3.13041 | ||||||||
\(621\) | −2.39152e12 | −0.645301 | ||||||||
\(622\) | 5.91853e12 | 1.58547 | ||||||||
\(623\) | 2.49126e12 | 0.662556 | ||||||||
\(624\) | −2.12382e13 | −5.60772 | ||||||||
\(625\) | −2.70268e12 | −0.708491 | ||||||||
\(626\) | 3.38772e12 | 0.881705 | ||||||||
\(627\) | −1.53349e13 | −3.96257 | ||||||||
\(628\) | 3.48095e12 | 0.893058 | ||||||||
\(629\) | 1.66017e12 | 0.422889 | ||||||||
\(630\) | −4.40459e12 | −1.11397 | ||||||||
\(631\) | −1.73641e12 | −0.436033 | −0.218017 | − | 0.975945i | \(-0.569959\pi\) | ||||
−0.218017 | + | 0.975945i | \(0.569959\pi\) | |||||||
\(632\) | −1.51564e13 | −3.77894 | ||||||||
\(633\) | −7.05455e11 | −0.174643 | ||||||||
\(634\) | −1.44580e13 | −3.55390 | ||||||||
\(635\) | −2.02091e12 | −0.493248 | ||||||||
\(636\) | 6.37516e12 | 1.54502 | ||||||||
\(637\) | −2.60664e12 | −0.627270 | ||||||||
\(638\) | 7.71153e12 | 1.84267 | ||||||||
\(639\) | −1.83772e12 | −0.436040 | ||||||||
\(640\) | −2.39961e13 | −5.65368 | ||||||||
\(641\) | 3.58482e12 | 0.838699 | 0.419349 | − | 0.907825i | \(-0.362258\pi\) | ||||
0.419349 | + | 0.907825i | \(0.362258\pi\) | |||||||
\(642\) | 1.39083e13 | 3.23123 | ||||||||
\(643\) | 5.75914e12 | 1.32864 | 0.664322 | − | 0.747447i | \(-0.268720\pi\) | ||||
0.664322 | + | 0.747447i | \(0.268720\pi\) | |||||||
\(644\) | 4.26429e12 | 0.976923 | ||||||||
\(645\) | −6.06986e12 | −1.38089 | ||||||||
\(646\) | −2.09653e13 | −4.73646 | ||||||||
\(647\) | −6.62154e12 | −1.48556 | −0.742779 | − | 0.669537i | \(-0.766493\pi\) | ||||
−0.742779 | + | 0.669537i | \(0.766493\pi\) | |||||||
\(648\) | 3.70785e12 | 0.826104 | ||||||||
\(649\) | 8.20137e12 | 1.81462 | ||||||||
\(650\) | 1.62649e12 | 0.357388 | ||||||||
\(651\) | −3.77877e12 | −0.824586 | ||||||||
\(652\) | 1.39327e12 | 0.301940 | ||||||||
\(653\) | 6.05429e12 | 1.30303 | 0.651515 | − | 0.758636i | \(-0.274134\pi\) | ||||
0.651515 | + | 0.758636i | \(0.274134\pi\) | |||||||
\(654\) | −1.59351e13 | −3.40608 | ||||||||
\(655\) | −2.42646e12 | −0.515095 | ||||||||
\(656\) | −4.30173e13 | −9.06933 | ||||||||
\(657\) | 5.39409e11 | 0.112947 | ||||||||
\(658\) | −4.11868e11 | −0.0856528 | ||||||||
\(659\) | −1.17210e12 | −0.242092 | −0.121046 | − | 0.992647i | \(-0.538625\pi\) | ||||
−0.121046 | + | 0.992647i | \(0.538625\pi\) | |||||||
\(660\) | 2.73811e13 | 5.61698 | ||||||||
\(661\) | 5.80806e12 | 1.18338 | 0.591691 | − | 0.806165i | \(-0.298461\pi\) | ||||
0.591691 | + | 0.806165i | \(0.298461\pi\) | |||||||
\(662\) | −2.73875e12 | −0.554231 | ||||||||
\(663\) | 8.00951e12 | 1.60989 | ||||||||
\(664\) | −1.48991e13 | −2.97443 | ||||||||
\(665\) | −3.37156e12 | −0.668548 | ||||||||
\(666\) | 4.86114e12 | 0.957423 | ||||||||
\(667\) | 2.70318e12 | 0.528821 | ||||||||
\(668\) | 1.26798e13 | 2.46388 | ||||||||
\(669\) | −1.39215e13 | −2.68701 | ||||||||
\(670\) | −8.75951e12 | −1.67936 | ||||||||
\(671\) | 3.60641e12 | 0.686790 | ||||||||
\(672\) | 1.90140e13 | 3.59677 | ||||||||
\(673\) | −5.92596e11 | −0.111350 | −0.0556751 | − | 0.998449i | \(-0.517731\pi\) | ||||
−0.0556751 | + | 0.998449i | \(0.517731\pi\) | |||||||
\(674\) | −4.58911e12 | −0.856563 | ||||||||
\(675\) | 1.04218e12 | 0.193230 | ||||||||
\(676\) | −6.58319e12 | −1.21248 | ||||||||
\(677\) | −3.03014e12 | −0.554388 | −0.277194 | − | 0.960814i | \(-0.589404\pi\) | ||||
−0.277194 | + | 0.960814i | \(0.589404\pi\) | |||||||
\(678\) | −1.00528e12 | −0.182707 | ||||||||
\(679\) | 1.41791e12 | 0.255997 | ||||||||
\(680\) | 2.46277e13 | 4.41706 | ||||||||
\(681\) | −1.20317e13 | −2.14370 | ||||||||
\(682\) | 1.89985e13 | 3.36272 | ||||||||
\(683\) | 2.26695e12 | 0.398611 | 0.199306 | − | 0.979937i | \(-0.436131\pi\) | ||||
0.199306 | + | 0.979937i | \(0.436131\pi\) | |||||||
\(684\) | −4.57400e13 | −7.98994 | ||||||||
\(685\) | −8.42536e12 | −1.46211 | ||||||||
\(686\) | 8.87148e12 | 1.52946 | ||||||||
\(687\) | 2.27749e12 | 0.390078 | ||||||||
\(688\) | 2.70444e13 | 4.60182 | ||||||||
\(689\) | −1.50781e12 | −0.254894 | ||||||||
\(690\) | 1.28817e13 | 2.16348 | ||||||||
\(691\) | 1.93380e12 | 0.322671 | 0.161335 | − | 0.986900i | \(-0.448420\pi\) | ||||
0.161335 | + | 0.986900i | \(0.448420\pi\) | |||||||
\(692\) | 4.85453e12 | 0.804766 | ||||||||
\(693\) | −5.41345e12 | −0.891609 | ||||||||
\(694\) | 9.66918e12 | 1.58224 | ||||||||
\(695\) | 4.92097e12 | 0.800054 | ||||||||
\(696\) | 2.51115e13 | 4.05630 | ||||||||
\(697\) | 1.62230e13 | 2.60366 | ||||||||
\(698\) | −2.31019e13 | −3.68382 | ||||||||
\(699\) | 1.60743e13 | 2.54674 | ||||||||
\(700\) | −1.85829e12 | −0.292531 | ||||||||
\(701\) | −5.12984e12 | −0.802366 | −0.401183 | − | 0.915998i | \(-0.631401\pi\) | ||||
−0.401183 | + | 0.915998i | \(0.631401\pi\) | |||||||
\(702\) | 7.98682e12 | 1.24124 | ||||||||
\(703\) | 3.72102e12 | 0.574597 | ||||||||
\(704\) | −5.38605e13 | −8.26405 | ||||||||
\(705\) | −9.27035e11 | −0.141333 | ||||||||
\(706\) | −3.02465e12 | −0.458198 | ||||||||
\(707\) | −3.24939e12 | −0.489118 | ||||||||
\(708\) | 4.05943e13 | 6.07177 | ||||||||
\(709\) | 2.22190e12 | 0.330229 | 0.165115 | − | 0.986274i | \(-0.447201\pi\) | ||||
0.165115 | + | 0.986274i | \(0.447201\pi\) | |||||||
\(710\) | 3.37103e12 | 0.497852 | ||||||||
\(711\) | 1.02519e13 | 1.50450 | ||||||||
\(712\) | −4.07868e13 | −5.94785 | ||||||||
\(713\) | 6.65970e12 | 0.965054 | ||||||||
\(714\) | −1.22817e13 | −1.76854 | ||||||||
\(715\) | −6.47598e12 | −0.926677 | ||||||||
\(716\) | −2.85750e12 | −0.406328 | ||||||||
\(717\) | −1.57767e13 | −2.22936 | ||||||||
\(718\) | 1.01681e13 | 1.42784 | ||||||||
\(719\) | 9.71447e12 | 1.35562 | 0.677812 | − | 0.735235i | \(-0.262928\pi\) | ||||
0.677812 | + | 0.735235i | \(0.262928\pi\) | |||||||
\(720\) | 4.41715e13 | 6.12557 | ||||||||
\(721\) | −3.99578e12 | −0.550671 | ||||||||
\(722\) | −3.25284e13 | −4.45497 | ||||||||
\(723\) | −1.04073e13 | −1.41649 | ||||||||
\(724\) | −3.35544e13 | −4.53864 | ||||||||
\(725\) | −1.17799e12 | −0.158351 | ||||||||
\(726\) | 2.16466e13 | 2.89185 | ||||||||
\(727\) | 1.33708e13 | 1.77522 | 0.887611 | − | 0.460594i | \(-0.152364\pi\) | ||||
0.887611 | + | 0.460594i | \(0.152364\pi\) | |||||||
\(728\) | −9.36913e12 | −1.23625 | ||||||||
\(729\) | −1.24177e13 | −1.62843 | ||||||||
\(730\) | −9.89465e11 | −0.128958 | ||||||||
\(731\) | −1.01992e13 | −1.32111 | ||||||||
\(732\) | 1.78506e13 | 2.29802 | ||||||||
\(733\) | 3.68952e12 | 0.472065 | 0.236032 | − | 0.971745i | \(-0.424153\pi\) | ||||
0.236032 | + | 0.971745i | \(0.424153\pi\) | |||||||
\(734\) | −1.83359e13 | −2.33168 | ||||||||
\(735\) | 8.99644e12 | 1.13705 | ||||||||
\(736\) | −3.35103e13 | −4.20948 | ||||||||
\(737\) | −1.07658e13 | −1.34414 | ||||||||
\(738\) | 4.75024e13 | 5.89471 | ||||||||
\(739\) | 8.68235e12 | 1.07087 | 0.535436 | − | 0.844576i | \(-0.320147\pi\) | ||||
0.535436 | + | 0.844576i | \(0.320147\pi\) | |||||||
\(740\) | −6.64404e12 | −0.814497 | ||||||||
\(741\) | 1.79521e13 | 2.18742 | ||||||||
\(742\) | 2.31205e12 | 0.280014 | ||||||||
\(743\) | 1.16035e13 | 1.39682 | 0.698409 | − | 0.715699i | \(-0.253892\pi\) | ||||
0.698409 | + | 0.715699i | \(0.253892\pi\) | |||||||
\(744\) | 6.18660e13 | 7.40242 | ||||||||
\(745\) | −6.93594e12 | −0.824901 | ||||||||
\(746\) | −6.14145e12 | −0.726016 | ||||||||
\(747\) | 1.00779e13 | 1.18420 | ||||||||
\(748\) | 4.60086e13 | 5.37380 | ||||||||
\(749\) | 3.75831e12 | 0.436339 | ||||||||
\(750\) | −2.94127e13 | −3.39437 | ||||||||
\(751\) | 1.32142e12 | 0.151587 | 0.0757935 | − | 0.997124i | \(-0.475851\pi\) | ||||
0.0757935 | + | 0.997124i | \(0.475851\pi\) | |||||||
\(752\) | 4.13043e12 | 0.470993 | ||||||||
\(753\) | −9.79693e12 | −1.11048 | ||||||||
\(754\) | −9.02764e12 | −1.01719 | ||||||||
\(755\) | −1.28418e13 | −1.43835 | ||||||||
\(756\) | −9.12508e12 | −1.01599 | ||||||||
\(757\) | −2.71976e12 | −0.301022 | −0.150511 | − | 0.988608i | \(-0.548092\pi\) | ||||
−0.150511 | + | 0.988608i | \(0.548092\pi\) | |||||||
\(758\) | −2.02794e13 | −2.23122 | ||||||||
\(759\) | 1.58322e13 | 1.73162 | ||||||||
\(760\) | 5.51991e13 | 6.00165 | ||||||||
\(761\) | 4.08482e12 | 0.441512 | 0.220756 | − | 0.975329i | \(-0.429148\pi\) | ||||
0.220756 | + | 0.975329i | \(0.429148\pi\) | |||||||
\(762\) | −1.65000e13 | −1.77290 | ||||||||
\(763\) | −4.30598e12 | −0.459951 | ||||||||
\(764\) | 2.29276e13 | 2.43466 | ||||||||
\(765\) | −1.66583e13 | −1.75855 | ||||||||
\(766\) | −1.50786e13 | −1.58245 | ||||||||
\(767\) | −9.60108e12 | −1.00171 | ||||||||
\(768\) | −1.04715e14 | −10.8613 | ||||||||
\(769\) | 6.25441e12 | 0.644938 | 0.322469 | − | 0.946580i | \(-0.395487\pi\) | ||||
0.322469 | + | 0.946580i | \(0.395487\pi\) | |||||||
\(770\) | 9.93017e12 | 1.01800 | ||||||||
\(771\) | −1.97392e12 | −0.201180 | ||||||||
\(772\) | −9.91048e12 | −1.00419 | ||||||||
\(773\) | 9.39092e12 | 0.946020 | 0.473010 | − | 0.881057i | \(-0.343167\pi\) | ||||
0.473010 | + | 0.881057i | \(0.343167\pi\) | |||||||
\(774\) | −2.98642e13 | −2.99100 | ||||||||
\(775\) | −2.90216e12 | −0.288977 | ||||||||
\(776\) | −2.32141e13 | −2.29812 | ||||||||
\(777\) | 2.17981e12 | 0.214548 | ||||||||
\(778\) | −2.02853e13 | −1.98506 | ||||||||
\(779\) | 3.63614e13 | 3.53771 | ||||||||
\(780\) | −3.20542e13 | −3.10069 | ||||||||
\(781\) | 4.14316e12 | 0.398475 | ||||||||
\(782\) | 2.16452e13 | 2.06981 | ||||||||
\(783\) | −5.78448e12 | −0.549967 | ||||||||
\(784\) | −4.00839e13 | −3.78920 | ||||||||
\(785\) | 2.84147e12 | 0.267072 | ||||||||
\(786\) | −1.98111e13 | −1.85143 | ||||||||
\(787\) | −4.53235e12 | −0.421151 | −0.210575 | − | 0.977578i | \(-0.567534\pi\) | ||||
−0.210575 | + | 0.977578i | \(0.567534\pi\) | |||||||
\(788\) | 2.25408e12 | 0.208257 | ||||||||
\(789\) | 2.16716e13 | 1.99088 | ||||||||
\(790\) | −1.88057e13 | −1.71778 | ||||||||
\(791\) | −2.71648e11 | −0.0246724 | ||||||||
\(792\) | 8.86289e13 | 8.00409 | ||||||||
\(793\) | −4.22191e12 | −0.379122 | ||||||||
\(794\) | −7.98037e12 | −0.712575 | ||||||||
\(795\) | 5.20398e12 | 0.462044 | ||||||||
\(796\) | 1.56658e13 | 1.38307 | ||||||||
\(797\) | 8.62990e12 | 0.757606 | 0.378803 | − | 0.925477i | \(-0.376336\pi\) | ||||
0.378803 | + | 0.925477i | \(0.376336\pi\) | |||||||
\(798\) | −2.75274e13 | −2.40299 | ||||||||
\(799\) | −1.55770e12 | −0.135215 | ||||||||
\(800\) | 1.46031e13 | 1.26049 | ||||||||
\(801\) | 2.75885e13 | 2.36800 | ||||||||
\(802\) | −7.68715e12 | −0.656116 | ||||||||
\(803\) | −1.21610e12 | −0.103216 | ||||||||
\(804\) | −5.32877e13 | −4.49754 | ||||||||
\(805\) | 3.48090e12 | 0.292153 | ||||||||
\(806\) | −2.22410e13 | −1.85629 | ||||||||
\(807\) | 1.12515e13 | 0.933854 | ||||||||
\(808\) | 5.31989e13 | 4.39088 | ||||||||
\(809\) | 1.97247e13 | 1.61898 | 0.809492 | − | 0.587131i | \(-0.199743\pi\) | ||||
0.809492 | + | 0.587131i | \(0.199743\pi\) | |||||||
\(810\) | 4.60059e12 | 0.375518 | ||||||||
\(811\) | −1.75013e12 | −0.142062 | −0.0710308 | − | 0.997474i | \(-0.522629\pi\) | ||||
−0.0710308 | + | 0.997474i | \(0.522629\pi\) | |||||||
\(812\) | 1.03142e13 | 0.832597 | ||||||||
\(813\) | 3.36417e12 | 0.270066 | ||||||||
\(814\) | −1.09595e13 | −0.874942 | ||||||||
\(815\) | 1.13731e12 | 0.0902962 | ||||||||
\(816\) | 1.23167e14 | 9.72497 | ||||||||
\(817\) | −2.28599e13 | −1.79505 | ||||||||
\(818\) | −3.80493e13 | −2.97137 | ||||||||
\(819\) | 6.33735e12 | 0.492187 | ||||||||
\(820\) | −6.49247e13 | −5.01473 | ||||||||
\(821\) | 2.78743e12 | 0.214121 | 0.107060 | − | 0.994253i | \(-0.465856\pi\) | ||||
0.107060 | + | 0.994253i | \(0.465856\pi\) | |||||||
\(822\) | −6.87898e13 | −5.25534 | ||||||||
\(823\) | −1.19850e13 | −0.910620 | −0.455310 | − | 0.890333i | \(-0.650472\pi\) | ||||
−0.455310 | + | 0.890333i | \(0.650472\pi\) | |||||||
\(824\) | 6.54188e13 | 4.94345 | ||||||||
\(825\) | −6.89935e12 | −0.518520 | ||||||||
\(826\) | 1.47221e13 | 1.10043 | ||||||||
\(827\) | 1.38928e13 | 1.03279 | 0.516397 | − | 0.856349i | \(-0.327273\pi\) | ||||
0.516397 | + | 0.856349i | \(0.327273\pi\) | |||||||
\(828\) | 4.72234e13 | 3.49157 | ||||||||
\(829\) | −2.18676e13 | −1.60808 | −0.804038 | − | 0.594578i | \(-0.797319\pi\) | ||||
−0.804038 | + | 0.594578i | \(0.797319\pi\) | |||||||
\(830\) | −1.84864e13 | −1.35207 | ||||||||
\(831\) | 1.62357e13 | 1.18105 | ||||||||
\(832\) | 6.30527e13 | 4.56193 | ||||||||
\(833\) | 1.51168e13 | 1.08782 | ||||||||
\(834\) | 4.01778e13 | 2.87567 | ||||||||
\(835\) | 1.03504e13 | 0.736832 | ||||||||
\(836\) | 1.03121e14 | 7.30162 | ||||||||
\(837\) | −1.42510e13 | −1.00364 | ||||||||
\(838\) | 3.20772e13 | 2.24697 | ||||||||
\(839\) | −1.67339e13 | −1.16592 | −0.582960 | − | 0.812501i | \(-0.698105\pi\) | ||||
−0.582960 | + | 0.812501i | \(0.698105\pi\) | |||||||
\(840\) | 3.23362e13 | 2.24095 | ||||||||
\(841\) | −7.96885e12 | −0.549305 | ||||||||
\(842\) | −3.69285e13 | −2.53196 | ||||||||
\(843\) | 4.06514e12 | 0.277237 | ||||||||
\(844\) | 4.74390e12 | 0.321806 | ||||||||
\(845\) | −5.37379e12 | −0.362598 | ||||||||
\(846\) | −4.56108e12 | −0.306127 | ||||||||
\(847\) | 5.84936e12 | 0.390511 | ||||||||
\(848\) | −2.31865e13 | −1.53976 | ||||||||
\(849\) | −1.32754e13 | −0.876927 | ||||||||
\(850\) | −9.43252e12 | −0.619787 | ||||||||
\(851\) | −3.84170e12 | −0.251096 | ||||||||
\(852\) | 2.05074e13 | 1.33331 | ||||||||
\(853\) | −2.38228e13 | −1.54072 | −0.770358 | − | 0.637612i | \(-0.779923\pi\) | ||||
−0.770358 | + | 0.637612i | \(0.779923\pi\) | |||||||
\(854\) | 6.47381e12 | 0.416485 | ||||||||
\(855\) | −3.73371e13 | −2.38942 | ||||||||
\(856\) | −6.15310e13 | −3.91708 | ||||||||
\(857\) | 1.50682e13 | 0.954218 | 0.477109 | − | 0.878844i | \(-0.341685\pi\) | ||||
0.477109 | + | 0.878844i | \(0.341685\pi\) | |||||||
\(858\) | −5.28739e13 | −3.33080 | ||||||||
\(859\) | 2.51544e13 | 1.57632 | 0.788161 | − | 0.615470i | \(-0.211034\pi\) | ||||
0.788161 | + | 0.615470i | \(0.211034\pi\) | |||||||
\(860\) | 4.08173e13 | 2.54450 | ||||||||
\(861\) | 2.13009e13 | 1.32094 | ||||||||
\(862\) | 3.87265e13 | 2.38905 | ||||||||
\(863\) | −4.61597e12 | −0.283279 | −0.141639 | − | 0.989918i | \(-0.545237\pi\) | ||||
−0.141639 | + | 0.989918i | \(0.545237\pi\) | |||||||
\(864\) | 7.17081e13 | 4.37781 | ||||||||
\(865\) | 3.96270e12 | 0.240668 | ||||||||
\(866\) | −4.89062e13 | −2.95484 | ||||||||
\(867\) | −2.00574e13 | −1.20556 | ||||||||
\(868\) | 2.54107e13 | 1.51942 | ||||||||
\(869\) | −2.31130e13 | −1.37489 | ||||||||
\(870\) | 3.11575e13 | 1.84385 | ||||||||
\(871\) | 1.26032e13 | 0.741994 | ||||||||
\(872\) | 7.04974e13 | 4.12904 | ||||||||
\(873\) | 1.57022e13 | 0.914946 | ||||||||
\(874\) | 4.85143e13 | 2.81234 | ||||||||
\(875\) | −7.94791e12 | −0.458370 | ||||||||
\(876\) | −6.01932e12 | −0.345366 | ||||||||
\(877\) | 2.51807e13 | 1.43738 | 0.718688 | − | 0.695333i | \(-0.244743\pi\) | ||||
0.718688 | + | 0.695333i | \(0.244743\pi\) | |||||||
\(878\) | 6.25565e13 | 3.55260 | ||||||||
\(879\) | 1.77301e13 | 1.00175 | ||||||||
\(880\) | −9.95849e13 | −5.59785 | ||||||||
\(881\) | −1.18325e13 | −0.661736 | −0.330868 | − | 0.943677i | \(-0.607342\pi\) | ||||
−0.330868 | + | 0.943677i | \(0.607342\pi\) | |||||||
\(882\) | 4.42632e13 | 2.46283 | ||||||||
\(883\) | −1.66652e13 | −0.922544 | −0.461272 | − | 0.887259i | \(-0.652607\pi\) | ||||
−0.461272 | + | 0.887259i | \(0.652607\pi\) | |||||||
\(884\) | −5.38608e13 | −2.96645 | ||||||||
\(885\) | 3.31367e13 | 1.81579 | ||||||||
\(886\) | 3.53375e13 | 1.92657 | ||||||||
\(887\) | 3.54685e11 | 0.0192392 | 0.00961958 | − | 0.999954i | \(-0.496938\pi\) | ||||
0.00961958 | + | 0.999954i | \(0.496938\pi\) | |||||||
\(888\) | −3.56879e13 | −1.92603 | ||||||||
\(889\) | −4.45862e12 | −0.239410 | ||||||||
\(890\) | −5.06071e13 | −2.70369 | ||||||||
\(891\) | 5.65434e12 | 0.300561 | ||||||||
\(892\) | 9.36165e13 | 4.95120 | ||||||||
\(893\) | −3.49134e12 | −0.183722 | ||||||||
\(894\) | −5.66292e13 | −2.96498 | ||||||||
\(895\) | −2.33254e12 | −0.121514 | ||||||||
\(896\) | −5.29412e13 | −2.74415 | ||||||||
\(897\) | −1.85343e13 | −0.955894 | ||||||||
\(898\) | −1.21703e13 | −0.624534 | ||||||||
\(899\) | 1.61081e13 | 0.822481 | ||||||||
\(900\) | −2.05789e13 | −1.04552 | ||||||||
\(901\) | 8.74427e12 | 0.442040 | ||||||||
\(902\) | −1.07094e14 | −5.38688 | ||||||||
\(903\) | −1.33916e13 | −0.670250 | ||||||||
\(904\) | 4.44741e12 | 0.221488 | ||||||||
\(905\) | −2.73901e13 | −1.35730 | ||||||||
\(906\) | −1.04848e14 | −5.16993 | ||||||||
\(907\) | 3.20467e13 | 1.57236 | 0.786178 | − | 0.618001i | \(-0.212057\pi\) | ||||
0.786178 | + | 0.618001i | \(0.212057\pi\) | |||||||
\(908\) | 8.09080e13 | 3.95007 | ||||||||
\(909\) | −3.59842e13 | −1.74813 | ||||||||
\(910\) | −1.16249e13 | −0.561959 | ||||||||
\(911\) | 3.62046e12 | 0.174153 | 0.0870764 | − | 0.996202i | \(-0.472248\pi\) | ||||
0.0870764 | + | 0.996202i | \(0.472248\pi\) | |||||||
\(912\) | 2.76059e14 | 13.2137 | ||||||||
\(913\) | −2.27206e13 | −1.08219 | ||||||||
\(914\) | 4.87592e13 | 2.31099 | ||||||||
\(915\) | 1.45713e13 | 0.687231 | ||||||||
\(916\) | −1.53152e13 | −0.718776 | ||||||||
\(917\) | −5.35336e12 | −0.250014 | ||||||||
\(918\) | −4.63181e13 | −2.15258 | ||||||||
\(919\) | 5.46114e12 | 0.252559 | 0.126280 | − | 0.991995i | \(-0.459696\pi\) | ||||
0.126280 | + | 0.991995i | \(0.459696\pi\) | |||||||
\(920\) | −5.69892e13 | −2.62269 | ||||||||
\(921\) | 2.32459e13 | 1.06458 | ||||||||
\(922\) | −4.41402e13 | −2.01162 | ||||||||
\(923\) | −4.85026e12 | −0.219967 | ||||||||
\(924\) | 6.04093e13 | 2.72634 | ||||||||
\(925\) | 1.67413e12 | 0.0751885 | ||||||||
\(926\) | −4.42484e13 | −1.97764 | ||||||||
\(927\) | −4.42498e13 | −1.96812 | ||||||||
\(928\) | −8.10528e13 | −3.58759 | ||||||||
\(929\) | 2.23394e13 | 0.984013 | 0.492006 | − | 0.870592i | \(-0.336264\pi\) | ||||
0.492006 | + | 0.870592i | \(0.336264\pi\) | |||||||
\(930\) | 7.67615e13 | 3.36488 | ||||||||
\(931\) | 3.38819e13 | 1.47807 | ||||||||
\(932\) | −1.08093e14 | −4.69274 | ||||||||
\(933\) | 2.93904e13 | 1.26981 | ||||||||
\(934\) | 6.60568e13 | 2.84025 | ||||||||
\(935\) | 3.75563e13 | 1.60705 | ||||||||
\(936\) | −1.03755e14 | −4.41843 | ||||||||
\(937\) | −3.42060e13 | −1.44969 | −0.724844 | − | 0.688913i | \(-0.758088\pi\) | ||||
−0.724844 | + | 0.688913i | \(0.758088\pi\) | |||||||
\(938\) | −1.93256e13 | −0.815117 | ||||||||
\(939\) | 1.68228e13 | 0.706161 | ||||||||
\(940\) | 6.23394e12 | 0.260428 | ||||||||
\(941\) | −3.53611e13 | −1.47019 | −0.735094 | − | 0.677965i | \(-0.762862\pi\) | ||||
−0.735094 | + | 0.677965i | \(0.762862\pi\) | |||||||
\(942\) | 2.31995e13 | 0.959950 | ||||||||
\(943\) | −3.75406e13 | −1.54596 | ||||||||
\(944\) | −1.47641e14 | −6.05109 | ||||||||
\(945\) | −7.44871e12 | −0.303835 | ||||||||
\(946\) | 6.73289e13 | 2.73333 | ||||||||
\(947\) | 4.68361e13 | 1.89237 | 0.946185 | − | 0.323627i | \(-0.104902\pi\) | ||||
0.946185 | + | 0.323627i | \(0.104902\pi\) | |||||||
\(948\) | −1.14403e14 | −4.60043 | ||||||||
\(949\) | 1.42365e12 | 0.0569777 | ||||||||
\(950\) | −2.11415e13 | −0.842131 | ||||||||
\(951\) | −7.17957e13 | −2.84634 | ||||||||
\(952\) | 5.43346e13 | 2.14393 | ||||||||
\(953\) | 3.94090e13 | 1.54767 | 0.773833 | − | 0.633390i | \(-0.218337\pi\) | ||||
0.773833 | + | 0.633390i | \(0.218337\pi\) | |||||||
\(954\) | 2.56040e13 | 1.00078 | ||||||||
\(955\) | 1.87155e13 | 0.728094 | ||||||||
\(956\) | 1.06092e14 | 4.10792 | ||||||||
\(957\) | 3.82941e13 | 1.47580 | ||||||||
\(958\) | −1.30264e13 | −0.499668 | ||||||||
\(959\) | −1.85884e13 | −0.709673 | ||||||||
\(960\) | −2.17617e14 | −8.26937 | ||||||||
\(961\) | 1.32452e13 | 0.500961 | ||||||||
\(962\) | 1.28299e13 | 0.482986 | ||||||||
\(963\) | 4.16201e13 | 1.55950 | ||||||||
\(964\) | 6.99846e13 | 2.61009 | ||||||||
\(965\) | −8.08982e12 | −0.300307 | ||||||||
\(966\) | 2.84202e13 | 1.05010 | ||||||||
\(967\) | −2.58756e13 | −0.951637 | −0.475819 | − | 0.879543i | \(-0.657848\pi\) | ||||
−0.475819 | + | 0.879543i | \(0.657848\pi\) | |||||||
\(968\) | −9.57656e13 | −3.50567 | ||||||||
\(969\) | −1.04110e14 | −3.79345 | ||||||||
\(970\) | −2.88033e13 | −1.04465 | ||||||||
\(971\) | 8.30034e12 | 0.299646 | 0.149823 | − | 0.988713i | \(-0.452130\pi\) | ||||
0.149823 | + | 0.988713i | \(0.452130\pi\) | |||||||
\(972\) | 9.46261e13 | 3.40026 | ||||||||
\(973\) | 1.08569e13 | 0.388326 | ||||||||
\(974\) | −6.83636e12 | −0.243394 | ||||||||
\(975\) | 8.07685e12 | 0.286234 | ||||||||
\(976\) | −6.49227e13 | −2.29020 | ||||||||
\(977\) | −2.36004e13 | −0.828694 | −0.414347 | − | 0.910119i | \(-0.635990\pi\) | ||||
−0.414347 | + | 0.910119i | \(0.635990\pi\) | |||||||
\(978\) | 9.28569e12 | 0.324556 | ||||||||
\(979\) | −6.21985e13 | −2.16400 | ||||||||
\(980\) | −6.04975e13 | −2.09517 | ||||||||
\(981\) | −4.76850e13 | −1.64388 | ||||||||
\(982\) | 3.92420e13 | 1.34663 | ||||||||
\(983\) | −4.25392e12 | −0.145311 | −0.0726555 | − | 0.997357i | \(-0.523147\pi\) | ||||
−0.0726555 | + | 0.997357i | \(0.523147\pi\) | |||||||
\(984\) | −3.48737e14 | −11.8583 | ||||||||
\(985\) | 1.83998e12 | 0.0622801 | ||||||||
\(986\) | 5.23542e13 | 1.76403 | ||||||||
\(987\) | −2.04526e12 | −0.0685997 | ||||||||
\(988\) | −1.20720e14 | −4.03065 | ||||||||
\(989\) | 2.36013e13 | 0.784427 | ||||||||
\(990\) | 1.09968e14 | 3.63838 | ||||||||
\(991\) | −4.80502e13 | −1.58257 | −0.791287 | − | 0.611445i | \(-0.790589\pi\) | ||||
−0.791287 | + | 0.611445i | \(0.790589\pi\) | |||||||
\(992\) | −1.99686e14 | −6.54705 | ||||||||
\(993\) | −1.36001e13 | −0.443886 | ||||||||
\(994\) | 7.43731e12 | 0.241645 | ||||||||
\(995\) | 1.27878e13 | 0.413611 | ||||||||
\(996\) | −1.12460e14 | −3.62103 | ||||||||
\(997\) | 8.87826e12 | 0.284577 | 0.142288 | − | 0.989825i | \(-0.454554\pi\) | ||||
0.142288 | + | 0.989825i | \(0.454554\pi\) | |||||||
\(998\) | −1.33367e13 | −0.425559 | ||||||||
\(999\) | 8.22078e12 | 0.261137 |
(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.1.1 | ✓ | 76 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
197.10.a.b.1.1 | ✓ | 76 | 1.1 | even | 1 | trivial |