Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2,84,Mod(1,2)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 84, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2.1");
S:= CuspForms(chi, 84);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2 \) |
Weight: | \( k \) | \(=\) | \( 84 \) |
Character orbit: | \([\chi]\) | \(=\) | 2.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: | \(87.2544256533\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 287609867501924274375802127400x - 41230865304567060522794640394926417995512500 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{24}\cdot 3^{7}\cdot 5^{3}\cdot 7\cdot 11\cdot 17 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-4.40454e14\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.19902e12 | −0.707107 | ||||||||
\(3\) | −1.03294e20 | −1.63510 | −0.817550 | − | 0.575858i | \(-0.804668\pi\) | ||||
−0.817550 | + | 0.575858i | \(0.804668\pi\) | |||||||
\(4\) | 4.83570e24 | 0.500000 | ||||||||
\(5\) | −4.29409e28 | −0.422295 | −0.211147 | − | 0.977454i | \(-0.567720\pi\) | ||||
−0.211147 | + | 0.977454i | \(0.567720\pi\) | |||||||
\(6\) | 2.27146e32 | 1.15619 | ||||||||
\(7\) | −1.14250e35 | −0.968920 | −0.484460 | − | 0.874814i | \(-0.660984\pi\) | ||||
−0.484460 | + | 0.874814i | \(0.660984\pi\) | |||||||
\(8\) | −1.06338e37 | −0.353553 | ||||||||
\(9\) | 6.67886e39 | 1.67355 | ||||||||
\(10\) | 9.44280e40 | 0.298608 | ||||||||
\(11\) | 1.30069e43 | 0.787731 | 0.393866 | − | 0.919168i | \(-0.371138\pi\) | ||||
0.393866 | + | 0.919168i | \(0.371138\pi\) | |||||||
\(12\) | −4.99500e44 | −0.817550 | ||||||||
\(13\) | −2.19702e46 | −1.29773 | −0.648866 | − | 0.760903i | \(-0.724756\pi\) | ||||
−0.648866 | + | 0.760903i | \(0.724756\pi\) | |||||||
\(14\) | 2.51238e47 | 0.685130 | ||||||||
\(15\) | 4.43555e48 | 0.690494 | ||||||||
\(16\) | 2.33840e49 | 0.250000 | ||||||||
\(17\) | 1.57914e51 | 1.36392 | 0.681962 | − | 0.731388i | \(-0.261127\pi\) | ||||
0.681962 | + | 0.731388i | \(0.261127\pi\) | |||||||
\(18\) | −1.46870e52 | −1.18338 | ||||||||
\(19\) | −1.27500e53 | −1.08953 | −0.544763 | − | 0.838590i | \(-0.683380\pi\) | ||||
−0.544763 | + | 0.838590i | \(0.683380\pi\) | |||||||
\(20\) | −2.07649e53 | −0.211147 | ||||||||
\(21\) | 1.18014e55 | 1.58428 | ||||||||
\(22\) | −2.86025e55 | −0.557010 | ||||||||
\(23\) | 2.00354e56 | 0.616727 | 0.308364 | − | 0.951269i | \(-0.400219\pi\) | ||||
0.308364 | + | 0.951269i | \(0.400219\pi\) | |||||||
\(24\) | 1.09841e57 | 0.578095 | ||||||||
\(25\) | −8.49584e57 | −0.821667 | ||||||||
\(26\) | 4.83130e58 | 0.917635 | ||||||||
\(27\) | −2.77658e59 | −1.10132 | ||||||||
\(28\) | −5.52479e59 | −0.484460 | ||||||||
\(29\) | −5.73024e60 | −1.17127 | −0.585634 | − | 0.810576i | \(-0.699154\pi\) | ||||
−0.585634 | + | 0.810576i | \(0.699154\pi\) | |||||||
\(30\) | −9.75387e60 | −0.488253 | ||||||||
\(31\) | −1.28050e62 | −1.64387 | −0.821937 | − | 0.569579i | \(-0.807106\pi\) | ||||
−0.821937 | + | 0.569579i | \(0.807106\pi\) | |||||||
\(32\) | −5.14220e61 | −0.176777 | ||||||||
\(33\) | −1.34354e63 | −1.28802 | ||||||||
\(34\) | −3.47256e63 | −0.964440 | ||||||||
\(35\) | 4.90600e63 | 0.409170 | ||||||||
\(36\) | 3.22970e64 | 0.836775 | ||||||||
\(37\) | −1.04062e65 | −0.864811 | −0.432405 | − | 0.901679i | \(-0.642335\pi\) | ||||
−0.432405 | + | 0.901679i | \(0.642335\pi\) | |||||||
\(38\) | 2.80376e65 | 0.770411 | ||||||||
\(39\) | 2.26940e66 | 2.12192 | ||||||||
\(40\) | 4.56626e65 | 0.149304 | ||||||||
\(41\) | −9.99186e66 | −1.17251 | −0.586254 | − | 0.810127i | \(-0.699398\pi\) | ||||
−0.586254 | + | 0.810127i | \(0.699398\pi\) | |||||||
\(42\) | −2.59515e67 | −1.12025 | ||||||||
\(43\) | −9.84440e67 | −1.60047 | −0.800237 | − | 0.599685i | \(-0.795293\pi\) | ||||
−0.800237 | + | 0.599685i | \(0.795293\pi\) | |||||||
\(44\) | 6.28976e67 | 0.393866 | ||||||||
\(45\) | −2.86796e68 | −0.706731 | ||||||||
\(46\) | −4.40583e68 | −0.436092 | ||||||||
\(47\) | 1.51626e69 | 0.614768 | 0.307384 | − | 0.951586i | \(-0.400546\pi\) | ||||
0.307384 | + | 0.951586i | \(0.400546\pi\) | |||||||
\(48\) | −2.41544e69 | −0.408775 | ||||||||
\(49\) | −8.50850e68 | −0.0611950 | ||||||||
\(50\) | 1.86825e70 | 0.581006 | ||||||||
\(51\) | −1.63116e71 | −2.23015 | ||||||||
\(52\) | −1.06241e71 | −0.648866 | ||||||||
\(53\) | 6.81814e70 | 0.188894 | 0.0944468 | − | 0.995530i | \(-0.469892\pi\) | ||||
0.0944468 | + | 0.995530i | \(0.469892\pi\) | |||||||
\(54\) | 6.10576e71 | 0.778751 | ||||||||
\(55\) | −5.58529e71 | −0.332655 | ||||||||
\(56\) | 1.21491e72 | 0.342565 | ||||||||
\(57\) | 1.31701e73 | 1.78148 | ||||||||
\(58\) | 1.26009e73 | 0.828212 | ||||||||
\(59\) | −1.83347e73 | −0.592809 | −0.296404 | − | 0.955063i | \(-0.595788\pi\) | ||||
−0.296404 | + | 0.955063i | \(0.595788\pi\) | |||||||
\(60\) | 2.14490e73 | 0.345247 | ||||||||
\(61\) | −2.38826e74 | −1.93595 | −0.967973 | − | 0.251053i | \(-0.919223\pi\) | ||||
−0.967973 | + | 0.251053i | \(0.919223\pi\) | |||||||
\(62\) | 2.81584e74 | 1.16239 | ||||||||
\(63\) | −7.63061e74 | −1.62153 | ||||||||
\(64\) | 1.13078e74 | 0.125000 | ||||||||
\(65\) | 9.43420e74 | 0.548026 | ||||||||
\(66\) | 2.95448e75 | 0.910767 | ||||||||
\(67\) | −5.35438e75 | −0.884310 | −0.442155 | − | 0.896939i | \(-0.645786\pi\) | ||||
−0.442155 | + | 0.896939i | \(0.645786\pi\) | |||||||
\(68\) | 7.63625e75 | 0.681962 | ||||||||
\(69\) | −2.06954e76 | −1.00841 | ||||||||
\(70\) | −1.07884e76 | −0.289327 | ||||||||
\(71\) | 3.92598e76 | 0.584422 | 0.292211 | − | 0.956354i | \(-0.405609\pi\) | ||||
0.292211 | + | 0.956354i | \(0.405609\pi\) | |||||||
\(72\) | −7.10219e76 | −0.591689 | ||||||||
\(73\) | 2.57031e77 | 1.20806 | 0.604028 | − | 0.796963i | \(-0.293562\pi\) | ||||
0.604028 | + | 0.796963i | \(0.293562\pi\) | |||||||
\(74\) | 2.28835e77 | 0.611514 | ||||||||
\(75\) | 8.77571e77 | 1.34351 | ||||||||
\(76\) | −6.16554e77 | −0.544763 | ||||||||
\(77\) | −1.48604e78 | −0.763248 | ||||||||
\(78\) | −4.99045e78 | −1.50042 | ||||||||
\(79\) | 1.96704e78 | 0.348569 | 0.174284 | − | 0.984695i | \(-0.444239\pi\) | ||||
0.174284 | + | 0.984695i | \(0.444239\pi\) | |||||||
\(80\) | −1.00413e78 | −0.105574 | ||||||||
\(81\) | 2.02617e78 | 0.127218 | ||||||||
\(82\) | 2.19723e79 | 0.829089 | ||||||||
\(83\) | 4.85870e79 | 1.10861 | 0.554305 | − | 0.832314i | \(-0.312984\pi\) | ||||
0.554305 | + | 0.832314i | \(0.312984\pi\) | |||||||
\(84\) | 5.70679e79 | 0.792140 | ||||||||
\(85\) | −6.78096e79 | −0.575978 | ||||||||
\(86\) | 2.16481e80 | 1.13171 | ||||||||
\(87\) | 5.91901e80 | 1.91514 | ||||||||
\(88\) | −1.38313e80 | −0.278505 | ||||||||
\(89\) | −1.41759e81 | −1.78593 | −0.892967 | − | 0.450122i | \(-0.851381\pi\) | ||||
−0.892967 | + | 0.450122i | \(0.851381\pi\) | |||||||
\(90\) | 6.30672e80 | 0.499734 | ||||||||
\(91\) | 2.51010e81 | 1.25740 | ||||||||
\(92\) | 9.68853e80 | 0.308364 | ||||||||
\(93\) | 1.32268e82 | 2.68790 | ||||||||
\(94\) | −3.33428e81 | −0.434707 | ||||||||
\(95\) | 5.47498e81 | 0.460101 | ||||||||
\(96\) | 5.31160e81 | 0.289047 | ||||||||
\(97\) | 4.22235e82 | 1.49461 | 0.747303 | − | 0.664483i | \(-0.231348\pi\) | ||||
0.747303 | + | 0.664483i | \(0.231348\pi\) | |||||||
\(98\) | 1.87104e81 | 0.0432714 | ||||||||
\(99\) | 8.68714e82 | 1.31831 | ||||||||
\(100\) | −4.10834e82 | −0.410834 | ||||||||
\(101\) | 5.65742e82 | 0.374353 | 0.187176 | − | 0.982326i | \(-0.440066\pi\) | ||||
0.187176 | + | 0.982326i | \(0.440066\pi\) | |||||||
\(102\) | 3.58696e83 | 1.57696 | ||||||||
\(103\) | 1.09213e83 | 0.320280 | 0.160140 | − | 0.987094i | \(-0.448805\pi\) | ||||
0.160140 | + | 0.987094i | \(0.448805\pi\) | |||||||
\(104\) | 2.33627e83 | 0.458818 | ||||||||
\(105\) | −5.06761e83 | −0.669033 | ||||||||
\(106\) | −1.49933e83 | −0.133568 | ||||||||
\(107\) | −1.45685e84 | −0.878996 | −0.439498 | − | 0.898244i | \(-0.644844\pi\) | ||||
−0.439498 | + | 0.898244i | \(0.644844\pi\) | |||||||
\(108\) | −1.34267e84 | −0.550660 | ||||||||
\(109\) | −5.32975e84 | −1.49110 | −0.745551 | − | 0.666449i | \(-0.767813\pi\) | ||||
−0.745551 | + | 0.666449i | \(0.767813\pi\) | |||||||
\(110\) | 1.22822e84 | 0.235222 | ||||||||
\(111\) | 1.07490e85 | 1.41405 | ||||||||
\(112\) | −2.67163e84 | −0.242230 | ||||||||
\(113\) | 5.29156e84 | 0.331763 | 0.165882 | − | 0.986146i | \(-0.446953\pi\) | ||||
0.165882 | + | 0.986146i | \(0.446953\pi\) | |||||||
\(114\) | −2.89613e85 | −1.25970 | ||||||||
\(115\) | −8.60338e84 | −0.260441 | ||||||||
\(116\) | −2.77098e85 | −0.585634 | ||||||||
\(117\) | −1.46736e86 | −2.17182 | ||||||||
\(118\) | 4.03184e85 | 0.419179 | ||||||||
\(119\) | −1.80417e86 | −1.32153 | ||||||||
\(120\) | −4.71668e85 | −0.244126 | ||||||||
\(121\) | −1.03462e86 | −0.379480 | ||||||||
\(122\) | 5.25184e86 | 1.36892 | ||||||||
\(123\) | 1.03210e87 | 1.91717 | ||||||||
\(124\) | −6.19211e86 | −0.821937 | ||||||||
\(125\) | 8.08817e86 | 0.769281 | ||||||||
\(126\) | 1.67799e87 | 1.14660 | ||||||||
\(127\) | −3.49676e87 | −1.72112 | −0.860561 | − | 0.509348i | \(-0.829887\pi\) | ||||
−0.860561 | + | 0.509348i | \(0.829887\pi\) | |||||||
\(128\) | −2.48662e86 | −0.0883883 | ||||||||
\(129\) | 1.01687e88 | 2.61693 | ||||||||
\(130\) | −2.07460e87 | −0.387513 | ||||||||
\(131\) | 1.58220e87 | 0.215032 | 0.107516 | − | 0.994203i | \(-0.465710\pi\) | ||||
0.107516 | + | 0.994203i | \(0.465710\pi\) | |||||||
\(132\) | −6.49696e87 | −0.644009 | ||||||||
\(133\) | 1.45669e88 | 1.05566 | ||||||||
\(134\) | 1.17744e88 | 0.625302 | ||||||||
\(135\) | 1.19229e88 | 0.465082 | ||||||||
\(136\) | −1.67923e88 | −0.482220 | ||||||||
\(137\) | −7.51570e88 | −1.59245 | −0.796225 | − | 0.605000i | \(-0.793173\pi\) | ||||
−0.796225 | + | 0.605000i | \(0.793173\pi\) | |||||||
\(138\) | 4.55097e88 | 0.713053 | ||||||||
\(139\) | −8.47750e87 | −0.0984359 | −0.0492180 | − | 0.998788i | \(-0.515673\pi\) | ||||
−0.0492180 | + | 0.998788i | \(0.515673\pi\) | |||||||
\(140\) | 2.37239e88 | 0.204585 | ||||||||
\(141\) | −1.56620e89 | −1.00521 | ||||||||
\(142\) | −8.63332e88 | −0.413249 | ||||||||
\(143\) | −2.85765e89 | −1.02226 | ||||||||
\(144\) | 1.56179e89 | 0.418387 | ||||||||
\(145\) | 2.46062e89 | 0.494620 | ||||||||
\(146\) | −5.65217e89 | −0.854224 | ||||||||
\(147\) | 8.78880e88 | 0.100060 | ||||||||
\(148\) | −5.03214e89 | −0.432405 | ||||||||
\(149\) | −1.32841e90 | −0.863179 | −0.431590 | − | 0.902070i | \(-0.642047\pi\) | ||||
−0.431590 | + | 0.902070i | \(0.642047\pi\) | |||||||
\(150\) | −1.92980e90 | −0.950003 | ||||||||
\(151\) | −4.33158e89 | −0.161847 | −0.0809233 | − | 0.996720i | \(-0.525787\pi\) | ||||
−0.0809233 | + | 0.996720i | \(0.525787\pi\) | |||||||
\(152\) | 1.35582e90 | 0.385205 | ||||||||
\(153\) | 1.05469e91 | 2.28259 | ||||||||
\(154\) | 3.26784e90 | 0.539698 | ||||||||
\(155\) | 5.49857e90 | 0.694199 | ||||||||
\(156\) | 1.09741e91 | 1.06096 | ||||||||
\(157\) | 5.67346e90 | 0.420738 | 0.210369 | − | 0.977622i | \(-0.432533\pi\) | ||||
0.210369 | + | 0.977622i | \(0.432533\pi\) | |||||||
\(158\) | −4.32557e90 | −0.246475 | ||||||||
\(159\) | −7.04275e90 | −0.308860 | ||||||||
\(160\) | 2.20811e90 | 0.0746519 | ||||||||
\(161\) | −2.28905e91 | −0.597559 | ||||||||
\(162\) | −4.45560e90 | −0.0899566 | ||||||||
\(163\) | −1.16681e91 | −0.182480 | −0.0912398 | − | 0.995829i | \(-0.529083\pi\) | ||||
−0.0912398 | + | 0.995829i | \(0.529083\pi\) | |||||||
\(164\) | −4.83177e91 | −0.586254 | ||||||||
\(165\) | 5.76928e91 | 0.543924 | ||||||||
\(166\) | −1.06844e92 | −0.783906 | ||||||||
\(167\) | 2.14296e92 | 1.22541 | 0.612704 | − | 0.790312i | \(-0.290082\pi\) | ||||
0.612704 | + | 0.790312i | \(0.290082\pi\) | |||||||
\(168\) | −1.25494e92 | −0.560127 | ||||||||
\(169\) | 1.96075e92 | 0.684108 | ||||||||
\(170\) | 1.49115e92 | 0.407278 | ||||||||
\(171\) | −8.51558e92 | −1.82337 | ||||||||
\(172\) | −4.76046e92 | −0.800237 | ||||||||
\(173\) | −7.99580e92 | −1.05669 | −0.528346 | − | 0.849029i | \(-0.677188\pi\) | ||||
−0.528346 | + | 0.849029i | \(0.677188\pi\) | |||||||
\(174\) | −1.30160e93 | −1.35421 | ||||||||
\(175\) | 9.70650e92 | 0.796129 | ||||||||
\(176\) | 3.04154e92 | 0.196933 | ||||||||
\(177\) | 1.89387e93 | 0.969301 | ||||||||
\(178\) | 3.11731e93 | 1.26285 | ||||||||
\(179\) | −5.47562e92 | −0.175806 | −0.0879028 | − | 0.996129i | \(-0.528016\pi\) | ||||
−0.0879028 | + | 0.996129i | \(0.528016\pi\) | |||||||
\(180\) | −1.38686e93 | −0.353366 | ||||||||
\(181\) | 3.75520e92 | 0.0760278 | 0.0380139 | − | 0.999277i | \(-0.487897\pi\) | ||||
0.0380139 | + | 0.999277i | \(0.487897\pi\) | |||||||
\(182\) | −5.51976e93 | −0.889115 | ||||||||
\(183\) | 2.46693e94 | 3.16546 | ||||||||
\(184\) | −2.13053e93 | −0.218046 | ||||||||
\(185\) | 4.46852e93 | 0.365205 | ||||||||
\(186\) | −2.90860e94 | −1.90063 | ||||||||
\(187\) | 2.05397e94 | 1.07441 | ||||||||
\(188\) | 7.33216e93 | 0.307384 | ||||||||
\(189\) | 3.17224e94 | 1.06709 | ||||||||
\(190\) | −1.20396e94 | −0.325340 | ||||||||
\(191\) | −1.48462e94 | −0.322648 | −0.161324 | − | 0.986901i | \(-0.551576\pi\) | ||||
−0.161324 | + | 0.986901i | \(0.551576\pi\) | |||||||
\(192\) | −1.16803e94 | −0.204387 | ||||||||
\(193\) | −2.82591e94 | −0.398593 | −0.199297 | − | 0.979939i | \(-0.563866\pi\) | ||||
−0.199297 | + | 0.979939i | \(0.563866\pi\) | |||||||
\(194\) | −9.28504e94 | −1.05685 | ||||||||
\(195\) | −9.74499e94 | −0.896076 | ||||||||
\(196\) | −4.11446e93 | −0.0305975 | ||||||||
\(197\) | −8.87059e93 | −0.0534077 | −0.0267039 | − | 0.999643i | \(-0.508501\pi\) | ||||
−0.0267039 | + | 0.999643i | \(0.508501\pi\) | |||||||
\(198\) | −1.91032e95 | −0.932184 | ||||||||
\(199\) | −1.43341e95 | −0.567501 | −0.283751 | − | 0.958898i | \(-0.591579\pi\) | ||||
−0.283751 | + | 0.958898i | \(0.591579\pi\) | |||||||
\(200\) | 9.03432e94 | 0.290503 | ||||||||
\(201\) | 5.53076e95 | 1.44593 | ||||||||
\(202\) | −1.24408e95 | −0.264707 | ||||||||
\(203\) | 6.54681e95 | 1.13486 | ||||||||
\(204\) | −7.88781e95 | −1.11508 | ||||||||
\(205\) | 4.29059e95 | 0.495145 | ||||||||
\(206\) | −2.40162e95 | −0.226472 | ||||||||
\(207\) | 1.33814e96 | 1.03212 | ||||||||
\(208\) | −5.13752e95 | −0.324433 | ||||||||
\(209\) | −1.65839e96 | −0.858253 | ||||||||
\(210\) | 1.11438e96 | 0.473078 | ||||||||
\(211\) | 2.58509e96 | 0.901062 | 0.450531 | − | 0.892761i | \(-0.351235\pi\) | ||||
0.450531 | + | 0.892761i | \(0.351235\pi\) | |||||||
\(212\) | 3.29705e95 | 0.0944468 | ||||||||
\(213\) | −4.05531e96 | −0.955588 | ||||||||
\(214\) | 3.20364e96 | 0.621544 | ||||||||
\(215\) | 4.22727e96 | 0.675872 | ||||||||
\(216\) | 2.95256e96 | 0.389375 | ||||||||
\(217\) | 1.46297e97 | 1.59278 | ||||||||
\(218\) | 1.17202e97 | 1.05437 | ||||||||
\(219\) | −2.65498e97 | −1.97529 | ||||||||
\(220\) | −2.70088e96 | −0.166327 | ||||||||
\(221\) | −3.46940e97 | −1.77001 | ||||||||
\(222\) | −2.36373e97 | −0.999885 | ||||||||
\(223\) | −1.00728e97 | −0.353589 | −0.176794 | − | 0.984248i | \(-0.556573\pi\) | ||||
−0.176794 | + | 0.984248i | \(0.556573\pi\) | |||||||
\(224\) | 5.87497e96 | 0.171282 | ||||||||
\(225\) | −5.67426e97 | −1.37510 | ||||||||
\(226\) | −1.16363e97 | −0.234592 | ||||||||
\(227\) | 1.41432e97 | 0.237396 | 0.118698 | − | 0.992930i | \(-0.462128\pi\) | ||||
0.118698 | + | 0.992930i | \(0.462128\pi\) | |||||||
\(228\) | 6.36865e97 | 0.890741 | ||||||||
\(229\) | 2.04340e97 | 0.238331 | 0.119165 | − | 0.992874i | \(-0.461978\pi\) | ||||
0.119165 | + | 0.992874i | \(0.461978\pi\) | |||||||
\(230\) | 1.89190e97 | 0.184159 | ||||||||
\(231\) | 1.53499e98 | 1.24799 | ||||||||
\(232\) | 6.09344e97 | 0.414106 | ||||||||
\(233\) | −3.00584e98 | −1.70882 | −0.854408 | − | 0.519602i | \(-0.826080\pi\) | ||||
−0.854408 | + | 0.519602i | \(0.826080\pi\) | |||||||
\(234\) | 3.22676e98 | 1.53571 | ||||||||
\(235\) | −6.51093e97 | −0.259613 | ||||||||
\(236\) | −8.86610e97 | −0.296404 | ||||||||
\(237\) | −2.03184e98 | −0.569945 | ||||||||
\(238\) | 3.96741e98 | 0.934465 | ||||||||
\(239\) | 7.25519e98 | 1.43594 | 0.717970 | − | 0.696075i | \(-0.245072\pi\) | ||||
0.717970 | + | 0.696075i | \(0.245072\pi\) | |||||||
\(240\) | 1.03721e98 | 0.172623 | ||||||||
\(241\) | −5.92738e98 | −0.830148 | −0.415074 | − | 0.909788i | \(-0.636244\pi\) | ||||
−0.415074 | + | 0.909788i | \(0.636244\pi\) | |||||||
\(242\) | 2.27516e98 | 0.268333 | ||||||||
\(243\) | 8.98795e98 | 0.893306 | ||||||||
\(244\) | −1.15489e99 | −0.967973 | ||||||||
\(245\) | 3.65363e97 | 0.0258423 | ||||||||
\(246\) | −2.26962e99 | −1.35564 | ||||||||
\(247\) | 2.80121e99 | 1.41391 | ||||||||
\(248\) | 1.36166e99 | 0.581197 | ||||||||
\(249\) | −5.01875e99 | −1.81269 | ||||||||
\(250\) | −1.77861e99 | −0.543964 | ||||||||
\(251\) | −4.82400e99 | −1.25011 | −0.625055 | − | 0.780581i | \(-0.714923\pi\) | ||||
−0.625055 | + | 0.780581i | \(0.714923\pi\) | |||||||
\(252\) | −3.68993e99 | −0.810767 | ||||||||
\(253\) | 2.60599e99 | 0.485815 | ||||||||
\(254\) | 7.68946e99 | 1.21702 | ||||||||
\(255\) | 7.00435e99 | 0.941781 | ||||||||
\(256\) | 5.46813e98 | 0.0625000 | ||||||||
\(257\) | 3.56965e99 | 0.347057 | 0.173528 | − | 0.984829i | \(-0.444483\pi\) | ||||
0.173528 | + | 0.984829i | \(0.444483\pi\) | |||||||
\(258\) | −2.23612e100 | −1.85045 | ||||||||
\(259\) | 1.18891e100 | 0.837932 | ||||||||
\(260\) | 4.56210e99 | 0.274013 | ||||||||
\(261\) | −3.82715e100 | −1.96017 | ||||||||
\(262\) | −3.47929e99 | −0.152050 | ||||||||
\(263\) | 4.92723e100 | 1.83840 | 0.919198 | − | 0.393795i | \(-0.128838\pi\) | ||||
0.919198 | + | 0.393795i | \(0.128838\pi\) | |||||||
\(264\) | 1.42870e100 | 0.455383 | ||||||||
\(265\) | −2.92777e99 | −0.0797688 | ||||||||
\(266\) | −3.20330e100 | −0.746466 | ||||||||
\(267\) | 1.46429e101 | 2.92018 | ||||||||
\(268\) | −2.58922e100 | −0.442155 | ||||||||
\(269\) | 7.28865e100 | 1.06642 | 0.533209 | − | 0.845984i | \(-0.320986\pi\) | ||||
0.533209 | + | 0.845984i | \(0.320986\pi\) | |||||||
\(270\) | −2.62187e100 | −0.328862 | ||||||||
\(271\) | −6.10148e98 | −0.00656462 | −0.00328231 | − | 0.999995i | \(-0.501045\pi\) | ||||
−0.00328231 | + | 0.999995i | \(0.501045\pi\) | |||||||
\(272\) | 3.69266e100 | 0.340981 | ||||||||
\(273\) | −2.59279e101 | −2.05597 | ||||||||
\(274\) | 1.65272e101 | 1.12603 | ||||||||
\(275\) | −1.10505e101 | −0.647253 | ||||||||
\(276\) | −1.00077e101 | −0.504205 | ||||||||
\(277\) | −9.74468e100 | −0.422530 | −0.211265 | − | 0.977429i | \(-0.567758\pi\) | ||||
−0.211265 | + | 0.977429i | \(0.567758\pi\) | |||||||
\(278\) | 1.86422e100 | 0.0696047 | ||||||||
\(279\) | −8.55227e101 | −2.75110 | ||||||||
\(280\) | −5.21695e100 | −0.144663 | ||||||||
\(281\) | −1.63743e101 | −0.391608 | −0.195804 | − | 0.980643i | \(-0.562732\pi\) | ||||
−0.195804 | + | 0.980643i | \(0.562732\pi\) | |||||||
\(282\) | 3.44412e101 | 0.710788 | ||||||||
\(283\) | 8.27407e101 | 1.47429 | 0.737144 | − | 0.675736i | \(-0.236174\pi\) | ||||
0.737144 | + | 0.675736i | \(0.236174\pi\) | |||||||
\(284\) | 1.89849e101 | 0.292211 | ||||||||
\(285\) | −5.65534e101 | −0.752311 | ||||||||
\(286\) | 6.28403e101 | 0.722850 | ||||||||
\(287\) | 1.14157e102 | 1.13607 | ||||||||
\(288\) | −3.43441e101 | −0.295845 | ||||||||
\(289\) | 1.15320e102 | 0.860289 | ||||||||
\(290\) | −5.41096e101 | −0.349749 | ||||||||
\(291\) | −4.36144e102 | −2.44383 | ||||||||
\(292\) | 1.24293e102 | 0.604028 | ||||||||
\(293\) | 4.00055e102 | 1.68699 | 0.843496 | − | 0.537136i | \(-0.180494\pi\) | ||||
0.843496 | + | 0.537136i | \(0.180494\pi\) | |||||||
\(294\) | −1.93268e101 | −0.0707530 | ||||||||
\(295\) | 7.87307e101 | 0.250340 | ||||||||
\(296\) | 1.10658e102 | 0.305757 | ||||||||
\(297\) | −3.61147e102 | −0.867544 | ||||||||
\(298\) | 2.92120e102 | 0.610360 | ||||||||
\(299\) | −4.40182e102 | −0.800346 | ||||||||
\(300\) | 4.24367e102 | 0.671754 | ||||||||
\(301\) | 1.12472e103 | 1.55073 | ||||||||
\(302\) | 9.52525e101 | 0.114443 | ||||||||
\(303\) | −5.84379e102 | −0.612104 | ||||||||
\(304\) | −2.98147e102 | −0.272381 | ||||||||
\(305\) | 1.02554e103 | 0.817540 | ||||||||
\(306\) | −2.31928e103 | −1.61404 | ||||||||
\(307\) | −2.83956e103 | −1.72587 | −0.862935 | − | 0.505315i | \(-0.831376\pi\) | ||||
−0.862935 | + | 0.505315i | \(0.831376\pi\) | |||||||
\(308\) | −7.18605e102 | −0.381624 | ||||||||
\(309\) | −1.12811e103 | −0.523689 | ||||||||
\(310\) | −1.20915e103 | −0.490873 | ||||||||
\(311\) | 4.46634e103 | 1.58634 | 0.793168 | − | 0.609003i | \(-0.208430\pi\) | ||||
0.793168 | + | 0.609003i | \(0.208430\pi\) | |||||||
\(312\) | −2.41324e103 | −0.750212 | ||||||||
\(313\) | 2.11903e103 | 0.576828 | 0.288414 | − | 0.957506i | \(-0.406872\pi\) | ||||
0.288414 | + | 0.957506i | \(0.406872\pi\) | |||||||
\(314\) | −1.24761e103 | −0.297507 | ||||||||
\(315\) | 3.27665e103 | 0.684766 | ||||||||
\(316\) | 9.51202e102 | 0.174284 | ||||||||
\(317\) | 5.56458e102 | 0.0894280 | 0.0447140 | − | 0.999000i | \(-0.485762\pi\) | ||||
0.0447140 | + | 0.999000i | \(0.485762\pi\) | |||||||
\(318\) | 1.54872e103 | 0.218397 | ||||||||
\(319\) | −7.45328e103 | −0.922644 | ||||||||
\(320\) | −4.85568e102 | −0.0527869 | ||||||||
\(321\) | 1.50484e104 | 1.43724 | ||||||||
\(322\) | 5.03367e103 | 0.422538 | ||||||||
\(323\) | −2.01341e104 | −1.48603 | ||||||||
\(324\) | 9.79797e102 | 0.0636089 | ||||||||
\(325\) | 1.86655e104 | 1.06630 | ||||||||
\(326\) | 2.56584e103 | 0.129033 | ||||||||
\(327\) | 5.50532e104 | 2.43810 | ||||||||
\(328\) | 1.06252e104 | 0.414545 | ||||||||
\(329\) | −1.73232e104 | −0.595661 | ||||||||
\(330\) | −1.26868e104 | −0.384612 | ||||||||
\(331\) | −3.54907e104 | −0.948970 | −0.474485 | − | 0.880264i | \(-0.657366\pi\) | ||||
−0.474485 | + | 0.880264i | \(0.657366\pi\) | |||||||
\(332\) | 2.34952e104 | 0.554305 | ||||||||
\(333\) | −6.95017e104 | −1.44730 | ||||||||
\(334\) | −4.71242e104 | −0.866494 | ||||||||
\(335\) | 2.29922e104 | 0.373440 | ||||||||
\(336\) | 2.75964e104 | 0.396070 | ||||||||
\(337\) | −1.01616e105 | −1.28920 | −0.644598 | − | 0.764521i | \(-0.722975\pi\) | ||||
−0.644598 | + | 0.764521i | \(0.722975\pi\) | |||||||
\(338\) | −4.31174e104 | −0.483738 | ||||||||
\(339\) | −5.46587e104 | −0.542466 | ||||||||
\(340\) | −3.27907e104 | −0.287989 | ||||||||
\(341\) | −1.66553e105 | −1.29493 | ||||||||
\(342\) | 1.87260e105 | 1.28932 | ||||||||
\(343\) | 1.68573e105 | 1.02821 | ||||||||
\(344\) | 1.04684e105 | 0.565853 | ||||||||
\(345\) | 8.88680e104 | 0.425846 | ||||||||
\(346\) | 1.75829e105 | 0.747194 | ||||||||
\(347\) | −6.72752e104 | −0.253619 | −0.126809 | − | 0.991927i | \(-0.540474\pi\) | ||||
−0.126809 | + | 0.991927i | \(0.540474\pi\) | |||||||
\(348\) | 2.86226e105 | 0.957570 | ||||||||
\(349\) | −4.68889e105 | −1.39256 | −0.696282 | − | 0.717769i | \(-0.745163\pi\) | ||||
−0.696282 | + | 0.717769i | \(0.745163\pi\) | |||||||
\(350\) | −2.13448e105 | −0.562948 | ||||||||
\(351\) | 6.10020e105 | 1.42922 | ||||||||
\(352\) | −6.68842e104 | −0.139253 | ||||||||
\(353\) | −1.13177e105 | −0.209463 | −0.104731 | − | 0.994501i | \(-0.533398\pi\) | ||||
−0.104731 | + | 0.994501i | \(0.533398\pi\) | |||||||
\(354\) | −4.16465e105 | −0.685399 | ||||||||
\(355\) | −1.68585e105 | −0.246798 | ||||||||
\(356\) | −6.85505e105 | −0.892967 | ||||||||
\(357\) | 1.86360e106 | 2.16084 | ||||||||
\(358\) | 1.20410e105 | 0.124313 | ||||||||
\(359\) | 2.87765e105 | 0.264618 | 0.132309 | − | 0.991209i | \(-0.457761\pi\) | ||||
0.132309 | + | 0.991209i | \(0.457761\pi\) | |||||||
\(360\) | 3.04974e105 | 0.249867 | ||||||||
\(361\) | 2.56178e105 | 0.187065 | ||||||||
\(362\) | −8.25777e104 | −0.0537597 | ||||||||
\(363\) | 1.06870e106 | 0.620487 | ||||||||
\(364\) | 1.21381e106 | 0.628699 | ||||||||
\(365\) | −1.10371e106 | −0.510156 | ||||||||
\(366\) | −5.42485e106 | −2.23832 | ||||||||
\(367\) | 1.27588e105 | 0.0470075 | 0.0235038 | − | 0.999724i | \(-0.492518\pi\) | ||||
0.0235038 | + | 0.999724i | \(0.492518\pi\) | |||||||
\(368\) | 4.68509e105 | 0.154182 | ||||||||
\(369\) | −6.67343e106 | −1.96225 | ||||||||
\(370\) | −9.82638e105 | −0.258239 | ||||||||
\(371\) | −7.78973e105 | −0.183023 | ||||||||
\(372\) | 6.39609e106 | 1.34395 | ||||||||
\(373\) | 2.10282e106 | 0.395262 | 0.197631 | − | 0.980277i | \(-0.436675\pi\) | ||||
0.197631 | + | 0.980277i | \(0.436675\pi\) | |||||||
\(374\) | −4.51674e106 | −0.759719 | ||||||||
\(375\) | −8.35462e106 | −1.25785 | ||||||||
\(376\) | −1.61236e106 | −0.217353 | ||||||||
\(377\) | 1.25895e107 | 1.51999 | ||||||||
\(378\) | −6.97583e106 | −0.754547 | ||||||||
\(379\) | 7.47993e105 | 0.0725054 | 0.0362527 | − | 0.999343i | \(-0.488458\pi\) | ||||
0.0362527 | + | 0.999343i | \(0.488458\pi\) | |||||||
\(380\) | 2.64754e106 | 0.230050 | ||||||||
\(381\) | 3.61195e107 | 2.81420 | ||||||||
\(382\) | 3.26470e106 | 0.228147 | ||||||||
\(383\) | 3.35164e106 | 0.210140 | 0.105070 | − | 0.994465i | \(-0.466493\pi\) | ||||
0.105070 | + | 0.994465i | \(0.466493\pi\) | |||||||
\(384\) | 2.56853e106 | 0.144524 | ||||||||
\(385\) | 6.38119e106 | 0.322316 | ||||||||
\(386\) | 6.21424e106 | 0.281848 | ||||||||
\(387\) | −6.57494e107 | −2.67847 | ||||||||
\(388\) | 2.04180e107 | 0.747303 | ||||||||
\(389\) | −1.56169e107 | −0.513672 | −0.256836 | − | 0.966455i | \(-0.582680\pi\) | ||||
−0.256836 | + | 0.966455i | \(0.582680\pi\) | |||||||
\(390\) | 2.14295e107 | 0.633621 | ||||||||
\(391\) | 3.16387e107 | 0.841169 | ||||||||
\(392\) | 9.04779e105 | 0.0216357 | ||||||||
\(393\) | −1.63432e107 | −0.351598 | ||||||||
\(394\) | 1.95066e106 | 0.0377650 | ||||||||
\(395\) | −8.44664e106 | −0.147199 | ||||||||
\(396\) | 4.20085e107 | 0.659153 | ||||||||
\(397\) | −5.50364e107 | −0.777757 | −0.388879 | − | 0.921289i | \(-0.627137\pi\) | ||||
−0.388879 | + | 0.921289i | \(0.627137\pi\) | |||||||
\(398\) | 3.15210e107 | 0.401284 | ||||||||
\(399\) | −1.50468e108 | −1.72611 | ||||||||
\(400\) | −1.98667e107 | −0.205417 | ||||||||
\(401\) | −1.60678e108 | −1.49784 | −0.748918 | − | 0.662663i | \(-0.769426\pi\) | ||||
−0.748918 | + | 0.662663i | \(0.769426\pi\) | |||||||
\(402\) | −1.21623e108 | −1.02243 | ||||||||
\(403\) | 2.81328e108 | 2.13331 | ||||||||
\(404\) | 2.73576e107 | 0.187176 | ||||||||
\(405\) | −8.70056e106 | −0.0537234 | ||||||||
\(406\) | −1.43966e108 | −0.802470 | ||||||||
\(407\) | −1.35353e108 | −0.681238 | ||||||||
\(408\) | 1.73455e108 | 0.788478 | ||||||||
\(409\) | 7.03093e107 | 0.288733 | 0.144366 | − | 0.989524i | \(-0.453886\pi\) | ||||
0.144366 | + | 0.989524i | \(0.453886\pi\) | |||||||
\(410\) | −9.43511e107 | −0.350120 | ||||||||
\(411\) | 7.76329e108 | 2.60381 | ||||||||
\(412\) | 5.28122e107 | 0.160140 | ||||||||
\(413\) | 2.09474e108 | 0.574384 | ||||||||
\(414\) | −2.94260e108 | −0.729821 | ||||||||
\(415\) | −2.08637e108 | −0.468160 | ||||||||
\(416\) | 1.12975e108 | 0.229409 | ||||||||
\(417\) | 8.75677e107 | 0.160953 | ||||||||
\(418\) | 3.64683e108 | 0.606876 | ||||||||
\(419\) | −4.79455e108 | −0.722546 | −0.361273 | − | 0.932460i | \(-0.617658\pi\) | ||||
−0.361273 | + | 0.932460i | \(0.617658\pi\) | |||||||
\(420\) | −2.45055e108 | −0.334517 | ||||||||
\(421\) | −2.55619e108 | −0.316144 | −0.158072 | − | 0.987428i | \(-0.550528\pi\) | ||||
−0.158072 | + | 0.987428i | \(0.550528\pi\) | |||||||
\(422\) | −5.68468e108 | −0.637147 | ||||||||
\(423\) | 1.01269e109 | 1.02884 | ||||||||
\(424\) | −7.25029e107 | −0.0667840 | ||||||||
\(425\) | −1.34161e109 | −1.12069 | ||||||||
\(426\) | 8.91773e108 | 0.675703 | ||||||||
\(427\) | 2.72859e109 | 1.87578 | ||||||||
\(428\) | −7.04487e108 | −0.439498 | ||||||||
\(429\) | 2.95179e109 | 1.67150 | ||||||||
\(430\) | −9.29587e108 | −0.477913 | ||||||||
\(431\) | −1.60739e109 | −0.750439 | −0.375219 | − | 0.926936i | \(-0.622433\pi\) | ||||
−0.375219 | + | 0.926936i | \(0.622433\pi\) | |||||||
\(432\) | −6.49275e108 | −0.275330 | ||||||||
\(433\) | −3.88996e109 | −1.49864 | −0.749320 | − | 0.662208i | \(-0.769619\pi\) | ||||
−0.749320 | + | 0.662208i | \(0.769619\pi\) | |||||||
\(434\) | −3.21710e109 | −1.12627 | ||||||||
\(435\) | −2.54168e109 | −0.808753 | ||||||||
\(436\) | −2.57731e109 | −0.745551 | ||||||||
\(437\) | −2.55452e109 | −0.671940 | ||||||||
\(438\) | 5.83837e109 | 1.39674 | ||||||||
\(439\) | −1.08744e109 | −0.236662 | −0.118331 | − | 0.992974i | \(-0.537754\pi\) | ||||
−0.118331 | + | 0.992974i | \(0.537754\pi\) | |||||||
\(440\) | 5.93929e108 | 0.117611 | ||||||||
\(441\) | −5.68272e108 | −0.102413 | ||||||||
\(442\) | 7.62929e109 | 1.25158 | ||||||||
\(443\) | −9.18366e109 | −1.37171 | −0.685853 | − | 0.727740i | \(-0.740571\pi\) | ||||
−0.685853 | + | 0.727740i | \(0.740571\pi\) | |||||||
\(444\) | 5.19791e109 | 0.707026 | ||||||||
\(445\) | 6.08726e109 | 0.754191 | ||||||||
\(446\) | 2.21503e109 | 0.250025 | ||||||||
\(447\) | 1.37217e110 | 1.41138 | ||||||||
\(448\) | −1.29192e109 | −0.121115 | ||||||||
\(449\) | 1.27943e110 | 1.09344 | 0.546719 | − | 0.837316i | \(-0.315876\pi\) | ||||
0.546719 | + | 0.837316i | \(0.315876\pi\) | |||||||
\(450\) | 1.24778e110 | 0.972343 | ||||||||
\(451\) | −1.29963e110 | −0.923622 | ||||||||
\(452\) | 2.55884e109 | 0.165882 | ||||||||
\(453\) | 4.47428e109 | 0.264635 | ||||||||
\(454\) | −3.11012e109 | −0.167865 | ||||||||
\(455\) | −1.07786e110 | −0.530993 | ||||||||
\(456\) | −1.40048e110 | −0.629849 | ||||||||
\(457\) | −4.23892e109 | −0.174074 | −0.0870368 | − | 0.996205i | \(-0.527740\pi\) | ||||
−0.0870368 | + | 0.996205i | \(0.527740\pi\) | |||||||
\(458\) | −4.49348e109 | −0.168525 | ||||||||
\(459\) | −4.38460e110 | −1.50212 | ||||||||
\(460\) | −4.16034e109 | −0.130220 | ||||||||
\(461\) | 4.70364e110 | 1.34538 | 0.672691 | − | 0.739924i | \(-0.265138\pi\) | ||||
0.672691 | + | 0.739924i | \(0.265138\pi\) | |||||||
\(462\) | −3.37549e110 | −0.882460 | ||||||||
\(463\) | 4.36920e110 | 1.04422 | 0.522108 | − | 0.852879i | \(-0.325146\pi\) | ||||
0.522108 | + | 0.852879i | \(0.325146\pi\) | |||||||
\(464\) | −1.33996e110 | −0.292817 | ||||||||
\(465\) | −5.67971e110 | −1.13508 | ||||||||
\(466\) | 6.60992e110 | 1.20832 | ||||||||
\(467\) | −3.41274e110 | −0.570759 | −0.285379 | − | 0.958415i | \(-0.592120\pi\) | ||||
−0.285379 | + | 0.958415i | \(0.592120\pi\) | |||||||
\(468\) | −7.09572e110 | −1.08591 | ||||||||
\(469\) | 6.11738e110 | 0.856825 | ||||||||
\(470\) | 1.43177e110 | 0.183574 | ||||||||
\(471\) | −5.86036e110 | −0.687949 | ||||||||
\(472\) | 1.94968e110 | 0.209589 | ||||||||
\(473\) | −1.28045e111 | −1.26074 | ||||||||
\(474\) | 4.46806e110 | 0.403012 | ||||||||
\(475\) | 1.08322e111 | 0.895227 | ||||||||
\(476\) | −8.72442e110 | −0.660766 | ||||||||
\(477\) | 4.55374e110 | 0.316123 | ||||||||
\(478\) | −1.59543e111 | −1.01536 | ||||||||
\(479\) | 2.76718e111 | 1.61478 | 0.807390 | − | 0.590019i | \(-0.200880\pi\) | ||||
0.807390 | + | 0.590019i | \(0.200880\pi\) | |||||||
\(480\) | −2.28085e110 | −0.122063 | ||||||||
\(481\) | 2.28627e111 | 1.12229 | ||||||||
\(482\) | 1.30344e111 | 0.587003 | ||||||||
\(483\) | 2.36445e111 | 0.977068 | ||||||||
\(484\) | −5.00312e110 | −0.189740 | ||||||||
\(485\) | −1.81311e111 | −0.631165 | ||||||||
\(486\) | −1.97647e111 | −0.631663 | ||||||||
\(487\) | −2.44275e111 | −0.716848 | −0.358424 | − | 0.933559i | \(-0.616686\pi\) | ||||
−0.358424 | + | 0.933559i | \(0.616686\pi\) | |||||||
\(488\) | 2.53963e111 | 0.684460 | ||||||||
\(489\) | 1.20525e111 | 0.298372 | ||||||||
\(490\) | −8.03441e109 | −0.0182733 | ||||||||
\(491\) | 5.89465e111 | 1.23190 | 0.615951 | − | 0.787784i | \(-0.288772\pi\) | ||||
0.615951 | + | 0.787784i | \(0.288772\pi\) | |||||||
\(492\) | 4.99094e111 | 0.958584 | ||||||||
\(493\) | −9.04886e111 | −1.59752 | ||||||||
\(494\) | −6.15993e111 | −0.999786 | ||||||||
\(495\) | −3.73034e111 | −0.556714 | ||||||||
\(496\) | −2.99432e111 | −0.410968 | ||||||||
\(497\) | −4.48543e111 | −0.566258 | ||||||||
\(498\) | 1.10364e112 | 1.28176 | ||||||||
\(499\) | −2.73792e110 | −0.0292582 | −0.0146291 | − | 0.999893i | \(-0.504657\pi\) | ||||
−0.0146291 | + | 0.999893i | \(0.504657\pi\) | |||||||
\(500\) | 3.91120e111 | 0.384640 | ||||||||
\(501\) | −2.21356e112 | −2.00366 | ||||||||
\(502\) | 1.06081e112 | 0.883961 | ||||||||
\(503\) | 1.90695e111 | 0.146308 | 0.0731541 | − | 0.997321i | \(-0.476694\pi\) | ||||
0.0731541 | + | 0.997321i | \(0.476694\pi\) | |||||||
\(504\) | 8.11425e111 | 0.573299 | ||||||||
\(505\) | −2.42934e111 | −0.158087 | ||||||||
\(506\) | −5.73063e111 | −0.343523 | ||||||||
\(507\) | −2.02535e112 | −1.11858 | ||||||||
\(508\) | −1.69093e112 | −0.860561 | ||||||||
\(509\) | 3.53459e112 | 1.65787 | 0.828937 | − | 0.559343i | \(-0.188946\pi\) | ||||
0.828937 | + | 0.559343i | \(0.188946\pi\) | |||||||
\(510\) | −1.54027e112 | −0.665940 | ||||||||
\(511\) | −2.93658e112 | −1.17051 | ||||||||
\(512\) | −1.20245e111 | −0.0441942 | ||||||||
\(513\) | 3.54015e112 | 1.19992 | ||||||||
\(514\) | −7.84973e111 | −0.245406 | ||||||||
\(515\) | −4.68970e111 | −0.135253 | ||||||||
\(516\) | 4.91728e112 | 1.30847 | ||||||||
\(517\) | 1.97218e112 | 0.484272 | ||||||||
\(518\) | −2.61444e112 | −0.592507 | ||||||||
\(519\) | 8.25920e112 | 1.72780 | ||||||||
\(520\) | −1.00322e112 | −0.193756 | ||||||||
\(521\) | 7.36394e112 | 1.31324 | 0.656621 | − | 0.754221i | \(-0.271985\pi\) | ||||
0.656621 | + | 0.754221i | \(0.271985\pi\) | |||||||
\(522\) | 8.41600e112 | 1.38605 | ||||||||
\(523\) | 7.79465e112 | 1.18571 | 0.592853 | − | 0.805311i | \(-0.298002\pi\) | ||||
0.592853 | + | 0.805311i | \(0.298002\pi\) | |||||||
\(524\) | 7.65104e111 | 0.107516 | ||||||||
\(525\) | −1.00263e113 | −1.30175 | ||||||||
\(526\) | −1.08351e113 | −1.29994 | ||||||||
\(527\) | −2.02208e113 | −2.24212 | ||||||||
\(528\) | −3.14174e112 | −0.322005 | ||||||||
\(529\) | −6.53966e112 | −0.619648 | ||||||||
\(530\) | 6.43824e111 | 0.0564051 | ||||||||
\(531\) | −1.22455e113 | −0.992094 | ||||||||
\(532\) | 7.04414e112 | 0.527831 | ||||||||
\(533\) | 2.19523e113 | 1.52160 | ||||||||
\(534\) | −3.22001e113 | −2.06488 | ||||||||
\(535\) | 6.25582e112 | 0.371195 | ||||||||
\(536\) | 5.69375e112 | 0.312651 | ||||||||
\(537\) | 5.65600e112 | 0.287460 | ||||||||
\(538\) | −1.60279e113 | −0.754071 | ||||||||
\(539\) | −1.10669e112 | −0.0482052 | ||||||||
\(540\) | 5.76554e112 | 0.232541 | ||||||||
\(541\) | 2.42827e113 | 0.907007 | 0.453504 | − | 0.891254i | \(-0.350174\pi\) | ||||
0.453504 | + | 0.891254i | \(0.350174\pi\) | |||||||
\(542\) | 1.34173e111 | 0.00464189 | ||||||||
\(543\) | −3.87891e112 | −0.124313 | ||||||||
\(544\) | −8.12025e112 | −0.241110 | ||||||||
\(545\) | 2.28864e113 | 0.629684 | ||||||||
\(546\) | 5.70160e113 | 1.45379 | ||||||||
\(547\) | 1.47490e113 | 0.348570 | 0.174285 | − | 0.984695i | \(-0.444239\pi\) | ||||
0.174285 | + | 0.984695i | \(0.444239\pi\) | |||||||
\(548\) | −3.63437e113 | −0.796225 | ||||||||
\(549\) | −1.59509e114 | −3.23990 | ||||||||
\(550\) | 2.43002e113 | 0.457677 | ||||||||
\(551\) | 7.30609e113 | 1.27613 | ||||||||
\(552\) | 2.20072e113 | 0.356527 | ||||||||
\(553\) | −2.24734e113 | −0.337735 | ||||||||
\(554\) | 2.14288e113 | 0.298774 | ||||||||
\(555\) | −4.61572e113 | −0.597147 | ||||||||
\(556\) | −4.09947e112 | −0.0492180 | ||||||||
\(557\) | 5.37828e113 | 0.599312 | 0.299656 | − | 0.954047i | \(-0.403128\pi\) | ||||
0.299656 | + | 0.954047i | \(0.403128\pi\) | |||||||
\(558\) | 1.88066e114 | 1.94532 | ||||||||
\(559\) | 2.16284e114 | 2.07699 | ||||||||
\(560\) | 1.14722e113 | 0.102292 | ||||||||
\(561\) | −2.12164e114 | −1.75676 | ||||||||
\(562\) | 3.60075e113 | 0.276908 | ||||||||
\(563\) | −6.68778e113 | −0.477731 | −0.238865 | − | 0.971053i | \(-0.576775\pi\) | ||||
−0.238865 | + | 0.971053i | \(0.576775\pi\) | |||||||
\(564\) | −7.57370e113 | −0.502603 | ||||||||
\(565\) | −2.27224e113 | −0.140102 | ||||||||
\(566\) | −1.81949e114 | −1.04248 | ||||||||
\(567\) | −2.31490e113 | −0.123264 | ||||||||
\(568\) | −4.17482e113 | −0.206624 | ||||||||
\(569\) | 1.42170e114 | 0.654109 | 0.327055 | − | 0.945005i | \(-0.393944\pi\) | ||||
0.327055 | + | 0.945005i | \(0.393944\pi\) | |||||||
\(570\) | 1.24362e114 | 0.531964 | ||||||||
\(571\) | −3.32521e114 | −1.32258 | −0.661288 | − | 0.750132i | \(-0.729990\pi\) | ||||
−0.661288 | + | 0.750132i | \(0.729990\pi\) | |||||||
\(572\) | −1.38187e114 | −0.511132 | ||||||||
\(573\) | 1.53352e114 | 0.527562 | ||||||||
\(574\) | −2.51034e114 | −0.803321 | ||||||||
\(575\) | −1.70218e114 | −0.506744 | ||||||||
\(576\) | 7.55234e113 | 0.209194 | ||||||||
\(577\) | −2.94311e113 | −0.0758596 | −0.0379298 | − | 0.999280i | \(-0.512076\pi\) | ||||
−0.0379298 | + | 0.999280i | \(0.512076\pi\) | |||||||
\(578\) | −2.53592e114 | −0.608316 | ||||||||
\(579\) | 2.91900e114 | 0.651740 | ||||||||
\(580\) | 1.18988e114 | 0.247310 | ||||||||
\(581\) | −5.55106e114 | −1.07415 | ||||||||
\(582\) | 9.59091e114 | 1.72805 | ||||||||
\(583\) | 8.86830e113 | 0.148797 | ||||||||
\(584\) | −2.73322e114 | −0.427112 | ||||||||
\(585\) | 6.30097e114 | 0.917148 | ||||||||
\(586\) | −8.79729e114 | −1.19288 | ||||||||
\(587\) | 4.24230e114 | 0.535945 | 0.267972 | − | 0.963427i | \(-0.413646\pi\) | ||||
0.267972 | + | 0.963427i | \(0.413646\pi\) | |||||||
\(588\) | 4.25000e113 | 0.0500299 | ||||||||
\(589\) | 1.63264e115 | 1.79104 | ||||||||
\(590\) | −1.73131e114 | −0.177017 | ||||||||
\(591\) | 9.16281e113 | 0.0873269 | ||||||||
\(592\) | −2.43339e114 | −0.216203 | ||||||||
\(593\) | −1.50009e115 | −1.24265 | −0.621325 | − | 0.783553i | \(-0.713405\pi\) | ||||
−0.621325 | + | 0.783553i | \(0.713405\pi\) | |||||||
\(594\) | 7.94171e114 | 0.613446 | ||||||||
\(595\) | 7.74725e114 | 0.558076 | ||||||||
\(596\) | −6.42378e114 | −0.431590 | ||||||||
\(597\) | 1.48063e115 | 0.927921 | ||||||||
\(598\) | 9.67971e114 | 0.565930 | ||||||||
\(599\) | 1.81515e115 | 0.990148 | 0.495074 | − | 0.868851i | \(-0.335141\pi\) | ||||
0.495074 | + | 0.868851i | \(0.335141\pi\) | |||||||
\(600\) | −9.33194e114 | −0.475001 | ||||||||
\(601\) | 1.94124e115 | 0.922124 | 0.461062 | − | 0.887368i | \(-0.347469\pi\) | ||||
0.461062 | + | 0.887368i | \(0.347469\pi\) | |||||||
\(602\) | −2.47329e115 | −1.09653 | ||||||||
\(603\) | −3.57612e115 | −1.47994 | ||||||||
\(604\) | −2.09463e114 | −0.0809233 | ||||||||
\(605\) | 4.44276e114 | 0.160252 | ||||||||
\(606\) | 1.28506e115 | 0.432823 | ||||||||
\(607\) | −6.13296e115 | −1.92903 | −0.964515 | − | 0.264026i | \(-0.914949\pi\) | ||||
−0.964515 | + | 0.264026i | \(0.914949\pi\) | |||||||
\(608\) | 6.55633e114 | 0.192603 | ||||||||
\(609\) | −6.76248e115 | −1.85562 | ||||||||
\(610\) | −2.25519e115 | −0.578088 | ||||||||
\(611\) | −3.33124e115 | −0.797804 | ||||||||
\(612\) | 5.10015e115 | 1.14130 | ||||||||
\(613\) | 1.77170e115 | 0.370494 | 0.185247 | − | 0.982692i | \(-0.440691\pi\) | ||||
0.185247 | + | 0.982692i | \(0.440691\pi\) | |||||||
\(614\) | 6.24425e115 | 1.22037 | ||||||||
\(615\) | −4.43193e115 | −0.809610 | ||||||||
\(616\) | 1.58023e115 | 0.269849 | ||||||||
\(617\) | 8.94061e114 | 0.142736 | 0.0713679 | − | 0.997450i | \(-0.477264\pi\) | ||||
0.0713679 | + | 0.997450i | \(0.477264\pi\) | |||||||
\(618\) | 2.48073e115 | 0.370304 | ||||||||
\(619\) | 6.13479e115 | 0.856324 | 0.428162 | − | 0.903702i | \(-0.359161\pi\) | ||||
0.428162 | + | 0.903702i | \(0.359161\pi\) | |||||||
\(620\) | 2.65894e115 | 0.347100 | ||||||||
\(621\) | −5.56298e115 | −0.679214 | ||||||||
\(622\) | −9.82158e115 | −1.12171 | ||||||||
\(623\) | 1.61960e116 | 1.73043 | ||||||||
\(624\) | 5.30676e115 | 0.530480 | ||||||||
\(625\) | 5.31136e115 | 0.496804 | ||||||||
\(626\) | −4.65979e115 | −0.407879 | ||||||||
\(627\) | 1.71302e116 | 1.40333 | ||||||||
\(628\) | 2.74352e115 | 0.210369 | ||||||||
\(629\) | −1.64329e116 | −1.17954 | ||||||||
\(630\) | −7.20543e115 | −0.484202 | ||||||||
\(631\) | −9.48977e114 | −0.0597087 | −0.0298543 | − | 0.999554i | \(-0.509504\pi\) | ||||
−0.0298543 | + | 0.999554i | \(0.509504\pi\) | |||||||
\(632\) | −2.09171e115 | −0.123238 | ||||||||
\(633\) | −2.67025e116 | −1.47333 | ||||||||
\(634\) | −1.22367e115 | −0.0632351 | ||||||||
\(635\) | 1.50154e116 | 0.726821 | ||||||||
\(636\) | −3.40566e115 | −0.154430 | ||||||||
\(637\) | 1.86934e115 | 0.0794147 | ||||||||
\(638\) | 1.63899e116 | 0.652408 | ||||||||
\(639\) | 2.62211e116 | 0.978059 | ||||||||
\(640\) | 1.06777e115 | 0.0373259 | ||||||||
\(641\) | 3.38116e116 | 1.10779 | 0.553895 | − | 0.832587i | \(-0.313141\pi\) | ||||
0.553895 | + | 0.832587i | \(0.313141\pi\) | |||||||
\(642\) | −3.30917e116 | −1.01629 | ||||||||
\(643\) | −1.04336e116 | −0.300386 | −0.150193 | − | 0.988657i | \(-0.547989\pi\) | ||||
−0.150193 | + | 0.988657i | \(0.547989\pi\) | |||||||
\(644\) | −1.10691e116 | −0.298779 | ||||||||
\(645\) | −4.36653e116 | −1.10512 | ||||||||
\(646\) | 4.42753e116 | 1.05078 | ||||||||
\(647\) | 5.39355e116 | 1.20046 | 0.600229 | − | 0.799828i | \(-0.295076\pi\) | ||||
0.600229 | + | 0.799828i | \(0.295076\pi\) | |||||||
\(648\) | −2.15460e115 | −0.0449783 | ||||||||
\(649\) | −2.38477e116 | −0.466974 | ||||||||
\(650\) | −4.10459e116 | −0.753991 | ||||||||
\(651\) | −1.51116e117 | −2.60436 | ||||||||
\(652\) | −5.64234e115 | −0.0912398 | ||||||||
\(653\) | −1.35184e116 | −0.205129 | −0.102565 | − | 0.994726i | \(-0.532705\pi\) | ||||
−0.102565 | + | 0.994726i | \(0.532705\pi\) | |||||||
\(654\) | −1.21063e117 | −1.72400 | ||||||||
\(655\) | −6.79410e115 | −0.0908067 | ||||||||
\(656\) | −2.33650e116 | −0.293127 | ||||||||
\(657\) | 1.71668e117 | 2.02174 | ||||||||
\(658\) | 3.80942e116 | 0.421196 | ||||||||
\(659\) | −1.65504e115 | −0.0171816 | −0.00859078 | − | 0.999963i | \(-0.502735\pi\) | ||||
−0.00859078 | + | 0.999963i | \(0.502735\pi\) | |||||||
\(660\) | 2.78985e116 | 0.271962 | ||||||||
\(661\) | −1.24490e116 | −0.113966 | −0.0569828 | − | 0.998375i | \(-0.518148\pi\) | ||||
−0.0569828 | + | 0.998375i | \(0.518148\pi\) | |||||||
\(662\) | 7.80448e116 | 0.671023 | ||||||||
\(663\) | 3.58369e117 | 2.89414 | ||||||||
\(664\) | −5.16665e116 | −0.391953 | ||||||||
\(665\) | −6.25517e116 | −0.445801 | ||||||||
\(666\) | 1.52836e117 | 1.02340 | ||||||||
\(667\) | −1.14808e117 | −0.722353 | ||||||||
\(668\) | 1.03627e117 | 0.612704 | ||||||||
\(669\) | 1.04046e117 | 0.578153 | ||||||||
\(670\) | −5.05603e116 | −0.264062 | ||||||||
\(671\) | −3.10639e117 | −1.52501 | ||||||||
\(672\) | −6.06850e116 | −0.280064 | ||||||||
\(673\) | −9.57675e116 | −0.415521 | −0.207760 | − | 0.978180i | \(-0.566617\pi\) | ||||
−0.207760 | + | 0.978180i | \(0.566617\pi\) | |||||||
\(674\) | 2.23455e117 | 0.911600 | ||||||||
\(675\) | 2.35893e117 | 0.904918 | ||||||||
\(676\) | 9.48162e116 | 0.342054 | ||||||||
\(677\) | −3.00293e117 | −1.01886 | −0.509430 | − | 0.860512i | \(-0.670144\pi\) | ||||
−0.509430 | + | 0.860512i | \(0.670144\pi\) | |||||||
\(678\) | 1.20196e117 | 0.383581 | ||||||||
\(679\) | −4.82403e117 | −1.44815 | ||||||||
\(680\) | 7.21076e116 | 0.203639 | ||||||||
\(681\) | −1.46091e117 | −0.388167 | ||||||||
\(682\) | 3.66255e117 | 0.915654 | ||||||||
\(683\) | −1.21635e117 | −0.286154 | −0.143077 | − | 0.989712i | \(-0.545700\pi\) | ||||
−0.143077 | + | 0.989712i | \(0.545700\pi\) | |||||||
\(684\) | −4.11788e117 | −0.911687 | ||||||||
\(685\) | 3.22731e117 | 0.672484 | ||||||||
\(686\) | −3.70697e117 | −0.727056 | ||||||||
\(687\) | −2.11071e117 | −0.389695 | ||||||||
\(688\) | −2.30202e117 | −0.400118 | ||||||||
\(689\) | −1.49796e117 | −0.245133 | ||||||||
\(690\) | −1.95423e117 | −0.301119 | ||||||||
\(691\) | 1.25037e118 | 1.81427 | 0.907133 | − | 0.420844i | \(-0.138266\pi\) | ||||
0.907133 | + | 0.420844i | \(0.138266\pi\) | |||||||
\(692\) | −3.86653e117 | −0.528346 | ||||||||
\(693\) | −9.92507e117 | −1.27733 | ||||||||
\(694\) | 1.47940e117 | 0.179336 | ||||||||
\(695\) | 3.64031e116 | 0.0415690 | ||||||||
\(696\) | −6.29417e117 | −0.677104 | ||||||||
\(697\) | −1.57785e118 | −1.59921 | ||||||||
\(698\) | 1.03110e118 | 0.984691 | ||||||||
\(699\) | 3.10486e118 | 2.79408 | ||||||||
\(700\) | 4.69377e117 | 0.398065 | ||||||||
\(701\) | −5.96129e116 | −0.0476478 | −0.0238239 | − | 0.999716i | \(-0.507584\pi\) | ||||
−0.0238239 | + | 0.999716i | \(0.507584\pi\) | |||||||
\(702\) | −1.34145e118 | −1.01061 | ||||||||
\(703\) | 1.32680e118 | 0.942233 | ||||||||
\(704\) | 1.47080e117 | 0.0984664 | ||||||||
\(705\) | 6.72542e117 | 0.424494 | ||||||||
\(706\) | 2.48878e117 | 0.148113 | ||||||||
\(707\) | −6.46360e117 | −0.362718 | ||||||||
\(708\) | 9.15817e117 | 0.484650 | ||||||||
\(709\) | 1.74484e118 | 0.870835 | 0.435418 | − | 0.900229i | \(-0.356601\pi\) | ||||
0.435418 | + | 0.900229i | \(0.356601\pi\) | |||||||
\(710\) | 3.70722e117 | 0.174513 | ||||||||
\(711\) | 1.31376e118 | 0.583347 | ||||||||
\(712\) | 1.50744e118 | 0.631423 | ||||||||
\(713\) | −2.56553e118 | −1.01382 | ||||||||
\(714\) | −4.09810e118 | −1.52794 | ||||||||
\(715\) | 1.22710e118 | 0.431697 | ||||||||
\(716\) | −2.64785e117 | −0.0879028 | ||||||||
\(717\) | −7.49420e118 | −2.34790 | ||||||||
\(718\) | −6.32802e117 | −0.187113 | ||||||||
\(719\) | 4.18565e118 | 1.16819 | 0.584096 | − | 0.811685i | \(-0.301449\pi\) | ||||
0.584096 | + | 0.811685i | \(0.301449\pi\) | |||||||
\(720\) | −6.70645e117 | −0.176683 | ||||||||
\(721\) | −1.24776e118 | −0.310325 | ||||||||
\(722\) | −5.63341e117 | −0.132275 | ||||||||
\(723\) | 6.12264e118 | 1.35737 | ||||||||
\(724\) | 1.81590e117 | 0.0380139 | ||||||||
\(725\) | 4.86832e118 | 0.962392 | ||||||||
\(726\) | −2.35011e118 | −0.438751 | ||||||||
\(727\) | −6.43388e117 | −0.113448 | −0.0567238 | − | 0.998390i | \(-0.518065\pi\) | ||||
−0.0567238 | + | 0.998390i | \(0.518065\pi\) | |||||||
\(728\) | −2.66919e118 | −0.444557 | ||||||||
\(729\) | −1.00926e119 | −1.58786 | ||||||||
\(730\) | 2.42709e118 | 0.360735 | ||||||||
\(731\) | −1.55457e119 | −2.18292 | ||||||||
\(732\) | 1.19294e119 | 1.58273 | ||||||||
\(733\) | 7.11810e118 | 0.892379 | 0.446190 | − | 0.894938i | \(-0.352781\pi\) | ||||
0.446190 | + | 0.894938i | \(0.352781\pi\) | |||||||
\(734\) | −2.80569e117 | −0.0332394 | ||||||||
\(735\) | −3.77399e117 | −0.0422548 | ||||||||
\(736\) | −1.03026e118 | −0.109023 | ||||||||
\(737\) | −6.96439e118 | −0.696599 | ||||||||
\(738\) | 1.46750e119 | 1.38752 | ||||||||
\(739\) | −1.72404e118 | −0.154100 | −0.0770501 | − | 0.997027i | \(-0.524550\pi\) | ||||
−0.0770501 | + | 0.997027i | \(0.524550\pi\) | |||||||
\(740\) | 2.16084e118 | 0.182603 | ||||||||
\(741\) | −2.89349e119 | −2.31189 | ||||||||
\(742\) | 1.71298e118 | 0.129417 | ||||||||
\(743\) | 5.38470e118 | 0.384703 | 0.192352 | − | 0.981326i | \(-0.438389\pi\) | ||||
0.192352 | + | 0.981326i | \(0.438389\pi\) | |||||||
\(744\) | −1.40651e119 | −0.950315 | ||||||||
\(745\) | 5.70430e118 | 0.364516 | ||||||||
\(746\) | −4.62414e118 | −0.279492 | ||||||||
\(747\) | 3.24506e119 | 1.85531 | ||||||||
\(748\) | 9.93241e118 | 0.537203 | ||||||||
\(749\) | 1.66445e119 | 0.851676 | ||||||||
\(750\) | 1.83720e119 | 0.889434 | ||||||||
\(751\) | 1.80640e119 | 0.827477 | 0.413738 | − | 0.910396i | \(-0.364223\pi\) | ||||
0.413738 | + | 0.910396i | \(0.364223\pi\) | |||||||
\(752\) | 3.54562e118 | 0.153692 | ||||||||
\(753\) | 4.98292e119 | 2.04405 | ||||||||
\(754\) | −2.76845e119 | −1.07480 | ||||||||
\(755\) | 1.86002e118 | 0.0683470 | ||||||||
\(756\) | 1.53400e119 | 0.533545 | ||||||||
\(757\) | −4.76923e119 | −1.57025 | −0.785126 | − | 0.619336i | \(-0.787402\pi\) | ||||
−0.785126 | + | 0.619336i | \(0.787402\pi\) | |||||||
\(758\) | −1.64485e118 | −0.0512691 | ||||||||
\(759\) | −2.69184e119 | −0.794356 | ||||||||
\(760\) | −5.82200e118 | −0.162670 | ||||||||
\(761\) | −3.92999e119 | −1.03975 | −0.519874 | − | 0.854243i | \(-0.674021\pi\) | ||||
−0.519874 | + | 0.854243i | \(0.674021\pi\) | |||||||
\(762\) | −7.94277e119 | −1.98994 | ||||||||
\(763\) | 6.08924e119 | 1.44476 | ||||||||
\(764\) | −7.17916e118 | −0.161324 | ||||||||
\(765\) | −4.52891e119 | −0.963928 | ||||||||
\(766\) | −7.37033e118 | −0.148591 | ||||||||
\(767\) | 4.02816e119 | 0.769307 | ||||||||
\(768\) | −5.64826e118 | −0.102194 | ||||||||
\(769\) | −8.76719e119 | −1.50286 | −0.751428 | − | 0.659816i | \(-0.770634\pi\) | ||||
−0.751428 | + | 0.659816i | \(0.770634\pi\) | |||||||
\(770\) | −1.40324e119 | −0.227912 | ||||||||
\(771\) | −3.68724e119 | −0.567472 | ||||||||
\(772\) | −1.36653e119 | −0.199297 | ||||||||
\(773\) | 1.45033e119 | 0.200455 | 0.100228 | − | 0.994965i | \(-0.468043\pi\) | ||||
0.100228 | + | 0.994965i | \(0.468043\pi\) | |||||||
\(774\) | 1.44584e120 | 1.89396 | ||||||||
\(775\) | 1.08789e120 | 1.35072 | ||||||||
\(776\) | −4.48997e119 | −0.528423 | ||||||||
\(777\) | −1.22808e120 | −1.37010 | ||||||||
\(778\) | 3.43419e119 | 0.363221 | ||||||||
\(779\) | 1.27397e120 | 1.27748 | ||||||||
\(780\) | −4.71239e119 | −0.448038 | ||||||||
\(781\) | 5.10649e119 | 0.460367 | ||||||||
\(782\) | −6.95742e119 | −0.594796 | ||||||||
\(783\) | 1.59105e120 | 1.28994 | ||||||||
\(784\) | −1.98963e118 | −0.0152987 | ||||||||
\(785\) | −2.43623e119 | −0.177676 | ||||||||
\(786\) | 3.59391e119 | 0.248617 | ||||||||
\(787\) | 1.84189e120 | 1.20868 | 0.604342 | − | 0.796725i | \(-0.293436\pi\) | ||||
0.604342 | + | 0.796725i | \(0.293436\pi\) | |||||||
\(788\) | −4.28955e118 | −0.0267039 | ||||||||
\(789\) | −5.08955e120 | −3.00596 | ||||||||
\(790\) | 1.85744e119 | 0.104085 | ||||||||
\(791\) | −6.04561e119 | −0.321452 | ||||||||
\(792\) | −9.23776e119 | −0.466092 | ||||||||
\(793\) | 5.24706e120 | 2.51234 | ||||||||
\(794\) | 1.21026e120 | 0.549957 | ||||||||
\(795\) | 3.02422e119 | 0.130430 | ||||||||
\(796\) | −6.93153e119 | −0.283751 | ||||||||
\(797\) | −1.39642e120 | −0.542619 | −0.271309 | − | 0.962492i | \(-0.587457\pi\) | ||||
−0.271309 | + | 0.962492i | \(0.587457\pi\) | |||||||
\(798\) | 3.30883e120 | 1.22055 | ||||||||
\(799\) | 2.39438e120 | 0.838497 | ||||||||
\(800\) | 4.36873e119 | 0.145252 | ||||||||
\(801\) | −9.46789e120 | −2.98885 | ||||||||
\(802\) | 3.53334e120 | 1.05913 | ||||||||
\(803\) | 3.34318e120 | 0.951623 | ||||||||
\(804\) | 2.67451e120 | 0.722967 | ||||||||
\(805\) | 9.82937e119 | 0.252346 | ||||||||
\(806\) | −6.18647e120 | −1.50848 | ||||||||
\(807\) | −7.52876e120 | −1.74370 | ||||||||
\(808\) | −6.01600e119 | −0.132354 | ||||||||
\(809\) | −5.03160e120 | −1.05158 | −0.525790 | − | 0.850614i | \(-0.676230\pi\) | ||||
−0.525790 | + | 0.850614i | \(0.676230\pi\) | |||||||
\(810\) | 1.91327e119 | 0.0379882 | ||||||||
\(811\) | −8.02832e120 | −1.51446 | −0.757232 | − | 0.653146i | \(-0.773449\pi\) | ||||
−0.757232 | + | 0.653146i | \(0.773449\pi\) | |||||||
\(812\) | 3.16584e120 | 0.567432 | ||||||||
\(813\) | 6.30248e118 | 0.0107338 | ||||||||
\(814\) | 2.97644e120 | 0.481708 | ||||||||
\(815\) | 5.01038e119 | 0.0770602 | ||||||||
\(816\) | −3.81431e120 | −0.557538 | ||||||||
\(817\) | 1.25517e121 | 1.74376 | ||||||||
\(818\) | −1.54612e120 | −0.204165 | ||||||||
\(819\) | 1.67646e121 | 2.10432 | ||||||||
\(820\) | 2.07480e120 | 0.247572 | ||||||||
\(821\) | −1.39011e121 | −1.57692 | −0.788458 | − | 0.615088i | \(-0.789120\pi\) | ||||
−0.788458 | + | 0.615088i | \(0.789120\pi\) | |||||||
\(822\) | −1.70716e121 | −1.84117 | ||||||||
\(823\) | 1.60136e121 | 1.64209 | 0.821045 | − | 0.570863i | \(-0.193391\pi\) | ||||
0.821045 | + | 0.570863i | \(0.193391\pi\) | |||||||
\(824\) | −1.16135e120 | −0.113236 | ||||||||
\(825\) | 1.14145e121 | 1.05832 | ||||||||
\(826\) | −4.60637e120 | −0.406151 | ||||||||
\(827\) | −2.18012e121 | −1.82810 | −0.914052 | − | 0.405597i | \(-0.867064\pi\) | ||||
−0.914052 | + | 0.405597i | \(0.867064\pi\) | |||||||
\(828\) | 6.47084e120 | 0.516062 | ||||||||
\(829\) | 9.78667e120 | 0.742373 | 0.371186 | − | 0.928558i | \(-0.378951\pi\) | ||||
0.371186 | + | 0.928558i | \(0.378951\pi\) | |||||||
\(830\) | 4.58797e120 | 0.331039 | ||||||||
\(831\) | 1.00657e121 | 0.690878 | ||||||||
\(832\) | −2.48435e120 | −0.162216 | ||||||||
\(833\) | −1.34361e120 | −0.0834653 | ||||||||
\(834\) | −1.92563e120 | −0.113811 | ||||||||
\(835\) | −9.20207e120 | −0.517484 | ||||||||
\(836\) | −8.01947e120 | −0.429126 | ||||||||
\(837\) | 3.55540e121 | 1.81043 | ||||||||
\(838\) | 1.05433e121 | 0.510917 | ||||||||
\(839\) | −1.48371e121 | −0.684272 | −0.342136 | − | 0.939650i | \(-0.611150\pi\) | ||||
−0.342136 | + | 0.939650i | \(0.611150\pi\) | |||||||
\(840\) | 5.38881e120 | 0.236539 | ||||||||
\(841\) | 8.90068e120 | 0.371869 | ||||||||
\(842\) | 5.62111e120 | 0.223548 | ||||||||
\(843\) | 1.69137e121 | 0.640317 | ||||||||
\(844\) | 1.25007e121 | 0.450531 | ||||||||
\(845\) | −8.41965e120 | −0.288895 | ||||||||
\(846\) | −2.22692e121 | −0.727503 | ||||||||
\(847\) | 1.18206e121 | 0.367685 | ||||||||
\(848\) | 1.59436e120 | 0.0472234 | ||||||||
\(849\) | −8.54664e121 | −2.41061 | ||||||||
\(850\) | 2.95023e121 | 0.792449 | ||||||||
\(851\) | −2.08493e121 | −0.533352 | ||||||||
\(852\) | −1.96103e121 | −0.477794 | ||||||||
\(853\) | −1.85049e120 | −0.0429440 | −0.0214720 | − | 0.999769i | \(-0.506835\pi\) | ||||
−0.0214720 | + | 0.999769i | \(0.506835\pi\) | |||||||
\(854\) | −6.00023e121 | −1.32637 | ||||||||
\(855\) | 3.65667e121 | 0.770001 | ||||||||
\(856\) | 1.54918e121 | 0.310772 | ||||||||
\(857\) | −7.15910e121 | −1.36822 | −0.684108 | − | 0.729381i | \(-0.739808\pi\) | ||||
−0.684108 | + | 0.729381i | \(0.739808\pi\) | |||||||
\(858\) | −6.49104e121 | −1.18193 | ||||||||
\(859\) | 5.29467e121 | 0.918592 | 0.459296 | − | 0.888283i | \(-0.348102\pi\) | ||||
0.459296 | + | 0.888283i | \(0.348102\pi\) | |||||||
\(860\) | 2.04418e121 | 0.337936 | ||||||||
\(861\) | −1.17918e122 | −1.85758 | ||||||||
\(862\) | 3.53469e121 | 0.530640 | ||||||||
\(863\) | 5.72396e121 | 0.818933 | 0.409467 | − | 0.912325i | \(-0.365715\pi\) | ||||
0.409467 | + | 0.912325i | \(0.365715\pi\) | |||||||
\(864\) | 1.42777e121 | 0.194688 | ||||||||
\(865\) | 3.43347e121 | 0.446236 | ||||||||
\(866\) | 8.55411e121 | 1.05970 | ||||||||
\(867\) | −1.19119e122 | −1.40666 | ||||||||
\(868\) | 7.07448e121 | 0.796391 | ||||||||
\(869\) | 2.55851e121 | 0.274579 | ||||||||
\(870\) | 5.58921e121 | 0.571875 | ||||||||
\(871\) | 1.17637e122 | 1.14760 | ||||||||
\(872\) | 5.66756e121 | 0.527184 | ||||||||
\(873\) | 2.82005e122 | 2.50130 | ||||||||
\(874\) | 5.61746e121 | 0.475133 | ||||||||
\(875\) | −9.24074e121 | −0.745371 | ||||||||
\(876\) | −1.28387e122 | −0.987645 | ||||||||
\(877\) | 3.36192e121 | 0.246663 | 0.123332 | − | 0.992366i | \(-0.460642\pi\) | ||||
0.123332 | + | 0.992366i | \(0.460642\pi\) | |||||||
\(878\) | 2.39131e121 | 0.167345 | ||||||||
\(879\) | −4.13233e122 | −2.75840 | ||||||||
\(880\) | −1.30606e121 | −0.0831637 | ||||||||
\(881\) | 1.10886e122 | 0.673558 | 0.336779 | − | 0.941584i | \(-0.390662\pi\) | ||||
0.336779 | + | 0.941584i | \(0.390662\pi\) | |||||||
\(882\) | 1.24964e121 | 0.0724168 | ||||||||
\(883\) | 7.23485e121 | 0.400000 | 0.200000 | − | 0.979796i | \(-0.435906\pi\) | ||||
0.200000 | + | 0.979796i | \(0.435906\pi\) | |||||||
\(884\) | −1.67770e122 | −0.885004 | ||||||||
\(885\) | −8.13243e121 | −0.409331 | ||||||||
\(886\) | 2.01951e122 | 0.969943 | ||||||||
\(887\) | −2.13789e122 | −0.979842 | −0.489921 | − | 0.871767i | \(-0.662974\pi\) | ||||
−0.489921 | + | 0.871767i | \(0.662974\pi\) | |||||||
\(888\) | −1.14303e122 | −0.499943 | ||||||||
\(889\) | 3.99505e122 | 1.66763 | ||||||||
\(890\) | −1.33860e122 | −0.533294 | ||||||||
\(891\) | 2.63543e121 | 0.100213 | ||||||||
\(892\) | −4.87091e121 | −0.176794 | ||||||||
\(893\) | −1.93323e122 | −0.669805 | ||||||||
\(894\) | −3.01743e122 | −0.997999 | ||||||||
\(895\) | 2.35128e121 | 0.0742418 | ||||||||
\(896\) | 2.84096e121 | 0.0856412 | ||||||||
\(897\) | 4.54683e122 | 1.30865 | ||||||||
\(898\) | −2.81350e122 | −0.773178 | ||||||||
\(899\) | 7.33756e122 | 1.92542 | ||||||||
\(900\) | −2.74390e122 | −0.687550 | ||||||||
\(901\) | 1.07668e122 | 0.257637 | ||||||||
\(902\) | 2.85792e122 | 0.653099 | ||||||||
\(903\) | −1.16177e123 | −2.53560 | ||||||||
\(904\) | −5.62695e121 | −0.117296 | ||||||||
\(905\) | −1.61252e121 | −0.0321061 | ||||||||
\(906\) | −9.83904e121 | −0.187125 | ||||||||
\(907\) | −4.89353e122 | −0.889037 | −0.444518 | − | 0.895770i | \(-0.646625\pi\) | ||||
−0.444518 | + | 0.895770i | \(0.646625\pi\) | |||||||
\(908\) | 6.83923e121 | 0.118698 | ||||||||
\(909\) | 3.77851e122 | 0.626498 | ||||||||
\(910\) | 2.37023e122 | 0.375468 | ||||||||
\(911\) | −6.97388e122 | −1.05551 | −0.527754 | − | 0.849397i | \(-0.676966\pi\) | ||||
−0.527754 | + | 0.849397i | \(0.676966\pi\) | |||||||
\(912\) | 3.07969e122 | 0.445370 | ||||||||
\(913\) | 6.31967e122 | 0.873287 | ||||||||
\(914\) | 9.32148e121 | 0.123089 | ||||||||
\(915\) | −1.05932e123 | −1.33676 | ||||||||
\(916\) | 9.88126e121 | 0.119165 | ||||||||
\(917\) | −1.80766e122 | −0.208348 | ||||||||
\(918\) | 9.64184e122 | 1.06216 | ||||||||
\(919\) | 1.31449e123 | 1.38408 | 0.692042 | − | 0.721858i | \(-0.256711\pi\) | ||||
0.692042 | + | 0.721858i | \(0.256711\pi\) | |||||||
\(920\) | 9.14868e121 | 0.0920797 | ||||||||
\(921\) | 2.93310e123 | 2.82197 | ||||||||
\(922\) | −1.03434e123 | −0.951328 | ||||||||
\(923\) | −8.62546e122 | −0.758423 | ||||||||
\(924\) | 7.42278e122 | 0.623993 | ||||||||
\(925\) | 8.84095e122 | 0.710587 | ||||||||
\(926\) | −9.60796e122 | −0.738372 | ||||||||
\(927\) | 7.29419e122 | 0.536004 | ||||||||
\(928\) | 2.94661e122 | 0.207053 | ||||||||
\(929\) | −2.01957e123 | −1.35708 | −0.678542 | − | 0.734561i | \(-0.737388\pi\) | ||||
−0.678542 | + | 0.734561i | \(0.737388\pi\) | |||||||
\(930\) | 1.24898e123 | 0.802626 | ||||||||
\(931\) | 1.08484e122 | 0.0666735 | ||||||||
\(932\) | −1.45354e123 | −0.854408 | ||||||||
\(933\) | −4.61347e123 | −2.59382 | ||||||||
\(934\) | 7.50469e122 | 0.403587 | ||||||||
\(935\) | −8.81994e122 | −0.453716 | ||||||||
\(936\) | 1.56037e123 | 0.767854 | ||||||||
\(937\) | 2.92262e123 | 1.37588 | 0.687939 | − | 0.725768i | \(-0.258516\pi\) | ||||
0.687939 | + | 0.725768i | \(0.258516\pi\) | |||||||
\(938\) | −1.34523e123 | −0.605867 | ||||||||
\(939\) | −2.18883e123 | −0.943171 | ||||||||
\(940\) | −3.14849e122 | −0.129807 | ||||||||
\(941\) | 1.19629e123 | 0.471919 | 0.235960 | − | 0.971763i | \(-0.424177\pi\) | ||||
0.235960 | + | 0.971763i | \(0.424177\pi\) | |||||||
\(942\) | 1.28871e123 | 0.486454 | ||||||||
\(943\) | −2.00191e123 | −0.723118 | ||||||||
\(944\) | −4.28738e122 | −0.148202 | ||||||||
\(945\) | −1.36219e123 | −0.450627 | ||||||||
\(946\) | 2.81575e123 | 0.891480 | ||||||||
\(947\) | 1.81217e123 | 0.549131 | 0.274565 | − | 0.961568i | \(-0.411466\pi\) | ||||
0.274565 | + | 0.961568i | \(0.411466\pi\) | |||||||
\(948\) | −9.82537e122 | −0.284972 | ||||||||
\(949\) | −5.64703e123 | −1.56773 | ||||||||
\(950\) | −2.38203e123 | −0.633021 | ||||||||
\(951\) | −5.74790e122 | −0.146224 | ||||||||
\(952\) | 1.91852e123 | 0.467232 | ||||||||
\(953\) | −3.82422e123 | −0.891636 | −0.445818 | − | 0.895124i | \(-0.647087\pi\) | ||||
−0.445818 | + | 0.895124i | \(0.647087\pi\) | |||||||
\(954\) | −1.00138e123 | −0.223533 | ||||||||
\(955\) | 6.37507e122 | 0.136253 | ||||||||
\(956\) | 3.50840e123 | 0.717970 | ||||||||
\(957\) | 7.69881e123 | 1.50861 | ||||||||
\(958\) | −6.08509e123 | −1.14182 | ||||||||
\(959\) | 8.58669e123 | 1.54296 | ||||||||
\(960\) | 5.01564e122 | 0.0863117 | ||||||||
\(961\) | 1.03291e124 | 1.70232 | ||||||||
\(962\) | −5.02755e123 | −0.793581 | ||||||||
\(963\) | −9.73007e123 | −1.47104 | ||||||||
\(964\) | −2.86630e123 | −0.415074 | ||||||||
\(965\) | 1.21347e123 | 0.168324 | ||||||||
\(966\) | −5.19949e123 | −0.690891 | ||||||||
\(967\) | 6.70761e123 | 0.853826 | 0.426913 | − | 0.904293i | \(-0.359601\pi\) | ||||
0.426913 | + | 0.904293i | \(0.359601\pi\) | |||||||
\(968\) | 1.10020e123 | 0.134166 | ||||||||
\(969\) | 2.07974e124 | 2.42981 | ||||||||
\(970\) | 3.98708e123 | 0.446301 | ||||||||
\(971\) | 1.45055e124 | 1.55573 | 0.777867 | − | 0.628429i | \(-0.216302\pi\) | ||||
0.777867 | + | 0.628429i | \(0.216302\pi\) | |||||||
\(972\) | 4.34631e123 | 0.446653 | ||||||||
\(973\) | 9.68555e122 | 0.0953765 | ||||||||
\(974\) | 5.37167e123 | 0.506888 | ||||||||
\(975\) | −1.92804e124 | −1.74351 | ||||||||
\(976\) | −5.58471e123 | −0.483987 | ||||||||
\(977\) | 3.08503e123 | 0.256233 | 0.128117 | − | 0.991759i | \(-0.459107\pi\) | ||||
0.128117 | + | 0.991759i | \(0.459107\pi\) | |||||||
\(978\) | −2.65037e123 | −0.210981 | ||||||||
\(979\) | −1.84385e124 | −1.40684 | ||||||||
\(980\) | 1.76679e122 | 0.0129212 | ||||||||
\(981\) | −3.55967e124 | −2.49543 | ||||||||
\(982\) | −1.29625e124 | −0.871086 | ||||||||
\(983\) | −1.23536e124 | −0.795836 | −0.397918 | − | 0.917421i | \(-0.630267\pi\) | ||||
−0.397918 | + | 0.917421i | \(0.630267\pi\) | |||||||
\(984\) | −1.09752e124 | −0.677821 | ||||||||
\(985\) | 3.80911e122 | 0.0225538 | ||||||||
\(986\) | 1.98986e124 | 1.12962 | ||||||||
\(987\) | 1.78939e124 | 0.973964 | ||||||||
\(988\) | 1.35458e124 | 0.706956 | ||||||||
\(989\) | −1.97237e124 | −0.987055 | ||||||||
\(990\) | 8.20310e123 | 0.393656 | ||||||||
\(991\) | −1.22699e124 | −0.564658 | −0.282329 | − | 0.959318i | \(-0.591107\pi\) | ||||
−0.282329 | + | 0.959318i | \(0.591107\pi\) | |||||||
\(992\) | 6.58458e123 | 0.290599 | ||||||||
\(993\) | 3.66598e124 | 1.55166 | ||||||||
\(994\) | 9.86357e123 | 0.400405 | ||||||||
\(995\) | 6.15518e123 | 0.239653 | ||||||||
\(996\) | −2.42692e124 | −0.906344 | ||||||||
\(997\) | −3.62789e124 | −1.29959 | −0.649794 | − | 0.760111i | \(-0.725145\pi\) | ||||
−0.649794 | + | 0.760111i | \(0.725145\pi\) | |||||||
\(998\) | 6.02074e122 | 0.0206887 | ||||||||
\(999\) | 2.88936e124 | 0.952433 |
(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 | 2.84.a.a.1.1 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.84.a.a.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial |