Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,34,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 34, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 34);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 34 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(68.9828288810\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3937184160 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(62747.5\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 65536.0 | 0.707107 | ||||||||
\(3\) | −7.12076e7 | −0.955049 | −0.477524 | − | 0.878619i | \(-0.658466\pi\) | ||||
−0.477524 | + | 0.878619i | \(0.658466\pi\) | |||||||
\(4\) | 4.29497e9 | 0.500000 | ||||||||
\(5\) | 1.52588e11 | 0.447214 | ||||||||
\(6\) | −4.66666e12 | −0.675321 | ||||||||
\(7\) | −7.62676e13 | −0.867406 | −0.433703 | − | 0.901056i | \(-0.642793\pi\) | ||||
−0.433703 | + | 0.901056i | \(0.642793\pi\) | |||||||
\(8\) | 2.81475e14 | 0.353553 | ||||||||
\(9\) | −4.88541e14 | −0.0878820 | ||||||||
\(10\) | 1.00000e16 | 0.316228 | ||||||||
\(11\) | 1.14348e17 | 0.750323 | 0.375161 | − | 0.926959i | \(-0.377587\pi\) | ||||
0.375161 | + | 0.926959i | \(0.377587\pi\) | |||||||
\(12\) | −3.05834e17 | −0.477524 | ||||||||
\(13\) | 3.91852e18 | 1.63326 | 0.816632 | − | 0.577159i | \(-0.195839\pi\) | ||||
0.816632 | + | 0.577159i | \(0.195839\pi\) | |||||||
\(14\) | −4.99828e18 | −0.613349 | ||||||||
\(15\) | −1.08654e19 | −0.427111 | ||||||||
\(16\) | 1.84467e19 | 0.250000 | ||||||||
\(17\) | −1.94707e20 | −0.970453 | −0.485227 | − | 0.874388i | \(-0.661263\pi\) | ||||
−0.485227 | + | 0.874388i | \(0.661263\pi\) | |||||||
\(18\) | −3.20170e19 | −0.0621420 | ||||||||
\(19\) | −1.21873e21 | −0.969330 | −0.484665 | − | 0.874700i | \(-0.661058\pi\) | ||||
−0.484665 | + | 0.874700i | \(0.661058\pi\) | |||||||
\(20\) | 6.55360e20 | 0.223607 | ||||||||
\(21\) | 5.43083e21 | 0.828415 | ||||||||
\(22\) | 7.49389e21 | 0.530558 | ||||||||
\(23\) | −4.03724e21 | −0.137270 | −0.0686350 | − | 0.997642i | \(-0.521864\pi\) | ||||
−0.0686350 | + | 0.997642i | \(0.521864\pi\) | |||||||
\(24\) | −2.00432e22 | −0.337661 | ||||||||
\(25\) | 2.32831e22 | 0.200000 | ||||||||
\(26\) | 2.56804e23 | 1.15489 | ||||||||
\(27\) | 4.30635e23 | 1.03898 | ||||||||
\(28\) | −3.27567e23 | −0.433703 | ||||||||
\(29\) | 1.32420e23 | 0.0982621 | 0.0491310 | − | 0.998792i | \(-0.484355\pi\) | ||||
0.0491310 | + | 0.998792i | \(0.484355\pi\) | |||||||
\(30\) | −7.12076e23 | −0.302013 | ||||||||
\(31\) | 4.55893e24 | 1.12563 | 0.562814 | − | 0.826583i | \(-0.309719\pi\) | ||||
0.562814 | + | 0.826583i | \(0.309719\pi\) | |||||||
\(32\) | 1.20893e24 | 0.176777 | ||||||||
\(33\) | −8.14242e24 | −0.716595 | ||||||||
\(34\) | −1.27603e25 | −0.686214 | ||||||||
\(35\) | −1.16375e25 | −0.387916 | ||||||||
\(36\) | −2.09827e24 | −0.0439410 | ||||||||
\(37\) | −4.62500e25 | −0.616288 | −0.308144 | − | 0.951340i | \(-0.599708\pi\) | ||||
−0.308144 | + | 0.951340i | \(0.599708\pi\) | |||||||
\(38\) | −7.98704e25 | −0.685420 | ||||||||
\(39\) | −2.79028e26 | −1.55985 | ||||||||
\(40\) | 4.29497e25 | 0.158114 | ||||||||
\(41\) | −4.25054e26 | −1.04114 | −0.520571 | − | 0.853818i | \(-0.674281\pi\) | ||||
−0.520571 | + | 0.853818i | \(0.674281\pi\) | |||||||
\(42\) | 3.55915e26 | 0.585778 | ||||||||
\(43\) | 5.95880e26 | 0.665165 | 0.332582 | − | 0.943074i | \(-0.392080\pi\) | ||||
0.332582 | + | 0.943074i | \(0.392080\pi\) | |||||||
\(44\) | 4.91120e26 | 0.375161 | ||||||||
\(45\) | −7.45455e25 | −0.0393020 | ||||||||
\(46\) | −2.64585e26 | −0.0970645 | ||||||||
\(47\) | −3.08054e27 | −0.792524 | −0.396262 | − | 0.918138i | \(-0.629693\pi\) | ||||
−0.396262 | + | 0.918138i | \(0.629693\pi\) | |||||||
\(48\) | −1.31355e27 | −0.238762 | ||||||||
\(49\) | −1.91424e27 | −0.247606 | ||||||||
\(50\) | 1.52588e27 | 0.141421 | ||||||||
\(51\) | 1.38646e28 | 0.926830 | ||||||||
\(52\) | 1.68299e28 | 0.816632 | ||||||||
\(53\) | −5.55613e28 | −1.96889 | −0.984443 | − | 0.175706i | \(-0.943779\pi\) | ||||
−0.984443 | + | 0.175706i | \(0.943779\pi\) | |||||||
\(54\) | 2.82221e28 | 0.734670 | ||||||||
\(55\) | 1.74481e28 | 0.335555 | ||||||||
\(56\) | −2.14674e28 | −0.306674 | ||||||||
\(57\) | 8.67825e28 | 0.925757 | ||||||||
\(58\) | 8.67826e27 | 0.0694818 | ||||||||
\(59\) | −1.85966e29 | −1.12299 | −0.561494 | − | 0.827481i | \(-0.689773\pi\) | ||||
−0.561494 | + | 0.827481i | \(0.689773\pi\) | |||||||
\(60\) | −4.66666e28 | −0.213555 | ||||||||
\(61\) | −1.55295e29 | −0.541023 | −0.270511 | − | 0.962717i | \(-0.587193\pi\) | ||||
−0.270511 | + | 0.962717i | \(0.587193\pi\) | |||||||
\(62\) | 2.98774e29 | 0.795940 | ||||||||
\(63\) | 3.72599e28 | 0.0762294 | ||||||||
\(64\) | 7.92282e28 | 0.125000 | ||||||||
\(65\) | 5.97918e29 | 0.730418 | ||||||||
\(66\) | −5.33622e29 | −0.506709 | ||||||||
\(67\) | −2.16431e30 | −1.60356 | −0.801778 | − | 0.597622i | \(-0.796112\pi\) | ||||
−0.801778 | + | 0.597622i | \(0.796112\pi\) | |||||||
\(68\) | −8.36261e29 | −0.485227 | ||||||||
\(69\) | 2.87482e29 | 0.131099 | ||||||||
\(70\) | −7.62676e29 | −0.274298 | ||||||||
\(71\) | −3.10911e30 | −0.884856 | −0.442428 | − | 0.896804i | \(-0.645883\pi\) | ||||
−0.442428 | + | 0.896804i | \(0.645883\pi\) | |||||||
\(72\) | −1.37512e29 | −0.0310710 | ||||||||
\(73\) | −7.37969e30 | −1.32804 | −0.664020 | − | 0.747715i | \(-0.731151\pi\) | ||||
−0.664020 | + | 0.747715i | \(0.731151\pi\) | |||||||
\(74\) | −3.03104e30 | −0.435781 | ||||||||
\(75\) | −1.65793e30 | −0.191010 | ||||||||
\(76\) | −5.23439e30 | −0.484665 | ||||||||
\(77\) | −8.72103e30 | −0.650835 | ||||||||
\(78\) | −1.82864e31 | −1.10298 | ||||||||
\(79\) | 6.89383e30 | 0.336988 | 0.168494 | − | 0.985703i | \(-0.446110\pi\) | ||||
0.168494 | + | 0.985703i | \(0.446110\pi\) | |||||||
\(80\) | 2.81475e30 | 0.111803 | ||||||||
\(81\) | −2.79487e31 | −0.904395 | ||||||||
\(82\) | −2.78563e31 | −0.736199 | ||||||||
\(83\) | 5.09132e31 | 1.10165 | 0.550823 | − | 0.834622i | \(-0.314314\pi\) | ||||
0.550823 | + | 0.834622i | \(0.314314\pi\) | |||||||
\(84\) | 2.33253e31 | 0.414208 | ||||||||
\(85\) | −2.97099e31 | −0.434000 | ||||||||
\(86\) | 3.90516e31 | 0.470342 | ||||||||
\(87\) | −9.42929e30 | −0.0938450 | ||||||||
\(88\) | 3.21860e31 | 0.265279 | ||||||||
\(89\) | −2.16513e32 | −1.48098 | −0.740489 | − | 0.672069i | \(-0.765406\pi\) | ||||
−0.740489 | + | 0.672069i | \(0.765406\pi\) | |||||||
\(90\) | −4.88541e30 | −0.0277907 | ||||||||
\(91\) | −2.98856e32 | −1.41670 | ||||||||
\(92\) | −1.73398e31 | −0.0686350 | ||||||||
\(93\) | −3.24631e32 | −1.07503 | ||||||||
\(94\) | −2.01886e32 | −0.560399 | ||||||||
\(95\) | −1.85963e32 | −0.433498 | ||||||||
\(96\) | −8.60847e31 | −0.168830 | ||||||||
\(97\) | 1.46729e32 | 0.242539 | 0.121270 | − | 0.992620i | \(-0.461303\pi\) | ||||
0.121270 | + | 0.992620i | \(0.461303\pi\) | |||||||
\(98\) | −1.25452e32 | −0.175084 | ||||||||
\(99\) | −5.58636e31 | −0.0659399 | ||||||||
\(100\) | 1.00000e32 | 0.100000 | ||||||||
\(101\) | 1.73454e32 | 0.147191 | 0.0735957 | − | 0.997288i | \(-0.476553\pi\) | ||||
0.0735957 | + | 0.997288i | \(0.476553\pi\) | |||||||
\(102\) | 9.08632e32 | 0.655368 | ||||||||
\(103\) | 2.04881e33 | 1.25802 | 0.629010 | − | 0.777397i | \(-0.283460\pi\) | ||||
0.629010 | + | 0.777397i | \(0.283460\pi\) | |||||||
\(104\) | 1.10296e33 | 0.577446 | ||||||||
\(105\) | 8.28679e32 | 0.370479 | ||||||||
\(106\) | −3.64126e33 | −1.39221 | ||||||||
\(107\) | 2.99134e33 | 0.979564 | 0.489782 | − | 0.871845i | \(-0.337076\pi\) | ||||
0.489782 | + | 0.871845i | \(0.337076\pi\) | |||||||
\(108\) | 1.84956e33 | 0.519490 | ||||||||
\(109\) | 1.01197e33 | 0.244136 | 0.122068 | − | 0.992522i | \(-0.461047\pi\) | ||||
0.122068 | + | 0.992522i | \(0.461047\pi\) | |||||||
\(110\) | 1.14348e33 | 0.237273 | ||||||||
\(111\) | 3.29335e33 | 0.588585 | ||||||||
\(112\) | −1.40689e33 | −0.216852 | ||||||||
\(113\) | 1.11805e34 | 1.48822 | 0.744112 | − | 0.668055i | \(-0.232873\pi\) | ||||
0.744112 | + | 0.668055i | \(0.232873\pi\) | |||||||
\(114\) | 5.68738e33 | 0.654609 | ||||||||
\(115\) | −6.16034e32 | −0.0613890 | ||||||||
\(116\) | 5.68739e32 | 0.0491310 | ||||||||
\(117\) | −1.91436e33 | −0.143535 | ||||||||
\(118\) | −1.21875e34 | −0.794073 | ||||||||
\(119\) | 1.48498e34 | 0.841777 | ||||||||
\(120\) | −3.05834e33 | −0.151006 | ||||||||
\(121\) | −1.01498e34 | −0.437015 | ||||||||
\(122\) | −1.01774e34 | −0.382561 | ||||||||
\(123\) | 3.02670e34 | 0.994342 | ||||||||
\(124\) | 1.95805e34 | 0.562814 | ||||||||
\(125\) | 3.55271e33 | 0.0894427 | ||||||||
\(126\) | 2.44186e33 | 0.0539023 | ||||||||
\(127\) | −3.93900e33 | −0.0763176 | −0.0381588 | − | 0.999272i | \(-0.512149\pi\) | ||||
−0.0381588 | + | 0.999272i | \(0.512149\pi\) | |||||||
\(128\) | 5.19230e33 | 0.0883883 | ||||||||
\(129\) | −4.24312e34 | −0.635265 | ||||||||
\(130\) | 3.91852e34 | 0.516484 | ||||||||
\(131\) | −1.47962e35 | −1.71860 | −0.859298 | − | 0.511475i | \(-0.829099\pi\) | ||||
−0.859298 | + | 0.511475i | \(0.829099\pi\) | |||||||
\(132\) | −3.49714e34 | −0.358297 | ||||||||
\(133\) | 9.29493e34 | 0.840803 | ||||||||
\(134\) | −1.41840e35 | −1.13389 | ||||||||
\(135\) | 6.57097e34 | 0.464646 | ||||||||
\(136\) | −5.48052e34 | −0.343107 | ||||||||
\(137\) | −1.94112e35 | −1.07687 | −0.538433 | − | 0.842668i | \(-0.680984\pi\) | ||||
−0.538433 | + | 0.842668i | \(0.680984\pi\) | |||||||
\(138\) | 1.88404e34 | 0.0927013 | ||||||||
\(139\) | −2.46485e35 | −1.07658 | −0.538290 | − | 0.842760i | \(-0.680929\pi\) | ||||
−0.538290 | + | 0.842760i | \(0.680929\pi\) | |||||||
\(140\) | −4.99828e34 | −0.193958 | ||||||||
\(141\) | 2.19358e35 | 0.756899 | ||||||||
\(142\) | −2.03758e35 | −0.625688 | ||||||||
\(143\) | 4.48074e35 | 1.22548 | ||||||||
\(144\) | −9.01200e33 | −0.0219705 | ||||||||
\(145\) | 2.02057e34 | 0.0439441 | ||||||||
\(146\) | −4.83636e35 | −0.939066 | ||||||||
\(147\) | 1.36309e35 | 0.236476 | ||||||||
\(148\) | −1.98642e35 | −0.308144 | ||||||||
\(149\) | 3.11387e35 | 0.432243 | 0.216121 | − | 0.976367i | \(-0.430659\pi\) | ||||
0.216121 | + | 0.976367i | \(0.430659\pi\) | |||||||
\(150\) | −1.08654e35 | −0.135064 | ||||||||
\(151\) | 9.07358e34 | 0.101079 | 0.0505393 | − | 0.998722i | \(-0.483906\pi\) | ||||
0.0505393 | + | 0.998722i | \(0.483906\pi\) | |||||||
\(152\) | −3.43041e35 | −0.342710 | ||||||||
\(153\) | 9.51225e34 | 0.0852854 | ||||||||
\(154\) | −5.71541e35 | −0.460210 | ||||||||
\(155\) | 6.95638e35 | 0.503397 | ||||||||
\(156\) | −1.19842e36 | −0.779923 | ||||||||
\(157\) | −1.67723e36 | −0.982311 | −0.491156 | − | 0.871072i | \(-0.663425\pi\) | ||||
−0.491156 | + | 0.871072i | \(0.663425\pi\) | |||||||
\(158\) | 4.51794e35 | 0.238286 | ||||||||
\(159\) | 3.95638e36 | 1.88038 | ||||||||
\(160\) | 1.84467e35 | 0.0790569 | ||||||||
\(161\) | 3.07911e35 | 0.119069 | ||||||||
\(162\) | −1.83164e36 | −0.639504 | ||||||||
\(163\) | 1.61172e36 | 0.508386 | 0.254193 | − | 0.967154i | \(-0.418190\pi\) | ||||
0.254193 | + | 0.967154i | \(0.418190\pi\) | |||||||
\(164\) | −1.82559e36 | −0.520571 | ||||||||
\(165\) | −1.24244e36 | −0.320471 | ||||||||
\(166\) | 3.33665e36 | 0.778981 | ||||||||
\(167\) | 4.78201e36 | 1.01109 | 0.505544 | − | 0.862801i | \(-0.331292\pi\) | ||||
0.505544 | + | 0.862801i | \(0.331292\pi\) | |||||||
\(168\) | 1.52864e36 | 0.292889 | ||||||||
\(169\) | 9.59865e36 | 1.66755 | ||||||||
\(170\) | −1.94707e36 | −0.306884 | ||||||||
\(171\) | 5.95398e35 | 0.0851867 | ||||||||
\(172\) | 2.55928e36 | 0.332582 | ||||||||
\(173\) | 3.21818e36 | 0.380057 | 0.190029 | − | 0.981779i | \(-0.439142\pi\) | ||||
0.190029 | + | 0.981779i | \(0.439142\pi\) | |||||||
\(174\) | −6.17958e35 | −0.0663585 | ||||||||
\(175\) | −1.77574e36 | −0.173481 | ||||||||
\(176\) | 2.10934e36 | 0.187581 | ||||||||
\(177\) | 1.32422e37 | 1.07251 | ||||||||
\(178\) | −1.41894e37 | −1.04721 | ||||||||
\(179\) | 7.43648e35 | 0.0500372 | 0.0250186 | − | 0.999687i | \(-0.492036\pi\) | ||||
0.0250186 | + | 0.999687i | \(0.492036\pi\) | |||||||
\(180\) | −3.20170e35 | −0.0196510 | ||||||||
\(181\) | 1.48729e37 | 0.833103 | 0.416551 | − | 0.909112i | \(-0.363239\pi\) | ||||
0.416551 | + | 0.909112i | \(0.363239\pi\) | |||||||
\(182\) | −1.95858e37 | −1.00176 | ||||||||
\(183\) | 1.10582e37 | 0.516703 | ||||||||
\(184\) | −1.13638e36 | −0.0485323 | ||||||||
\(185\) | −7.05719e36 | −0.275612 | ||||||||
\(186\) | −2.12750e37 | −0.760161 | ||||||||
\(187\) | −2.22643e37 | −0.728153 | ||||||||
\(188\) | −1.32308e37 | −0.396262 | ||||||||
\(189\) | −3.28435e37 | −0.901218 | ||||||||
\(190\) | −1.21873e37 | −0.306529 | ||||||||
\(191\) | −4.87779e36 | −0.112505 | −0.0562526 | − | 0.998417i | \(-0.517915\pi\) | ||||
−0.0562526 | + | 0.998417i | \(0.517915\pi\) | |||||||
\(192\) | −5.64165e36 | −0.119381 | ||||||||
\(193\) | −7.11316e37 | −1.38155 | −0.690776 | − | 0.723069i | \(-0.742731\pi\) | ||||
−0.690776 | + | 0.723069i | \(0.742731\pi\) | |||||||
\(194\) | 9.61602e36 | 0.171501 | ||||||||
\(195\) | −4.25763e37 | −0.697585 | ||||||||
\(196\) | −8.22161e36 | −0.123803 | ||||||||
\(197\) | −1.21522e38 | −1.68252 | −0.841261 | − | 0.540630i | \(-0.818186\pi\) | ||||
−0.841261 | + | 0.540630i | \(0.818186\pi\) | |||||||
\(198\) | −3.66108e36 | −0.0466265 | ||||||||
\(199\) | 1.59347e38 | 1.86754 | 0.933768 | − | 0.357878i | \(-0.116500\pi\) | ||||
0.933768 | + | 0.357878i | \(0.116500\pi\) | |||||||
\(200\) | 6.55360e36 | 0.0707107 | ||||||||
\(201\) | 1.54115e38 | 1.53147 | ||||||||
\(202\) | 1.13675e37 | 0.104080 | ||||||||
\(203\) | −1.00993e37 | −0.0852331 | ||||||||
\(204\) | 5.95481e37 | 0.463415 | ||||||||
\(205\) | −6.48580e37 | −0.465613 | ||||||||
\(206\) | 1.34271e38 | 0.889555 | ||||||||
\(207\) | 1.97236e36 | 0.0120636 | ||||||||
\(208\) | 7.22839e37 | 0.408316 | ||||||||
\(209\) | −1.39359e38 | −0.727311 | ||||||||
\(210\) | 5.43083e37 | 0.261968 | ||||||||
\(211\) | −1.86059e38 | −0.829832 | −0.414916 | − | 0.909860i | \(-0.636189\pi\) | ||||
−0.414916 | + | 0.909860i | \(0.636189\pi\) | |||||||
\(212\) | −2.38634e38 | −0.984443 | ||||||||
\(213\) | 2.21392e38 | 0.845081 | ||||||||
\(214\) | 1.96040e38 | 0.692656 | ||||||||
\(215\) | 9.09241e37 | 0.297471 | ||||||||
\(216\) | 1.21213e38 | 0.367335 | ||||||||
\(217\) | −3.47699e38 | −0.976378 | ||||||||
\(218\) | 6.63207e37 | 0.172630 | ||||||||
\(219\) | 5.25490e38 | 1.26834 | ||||||||
\(220\) | 7.49389e37 | 0.167777 | ||||||||
\(221\) | −7.62963e38 | −1.58501 | ||||||||
\(222\) | 2.15833e38 | 0.416192 | ||||||||
\(223\) | 2.35939e38 | 0.422444 | 0.211222 | − | 0.977438i | \(-0.432256\pi\) | ||||
0.211222 | + | 0.977438i | \(0.432256\pi\) | |||||||
\(224\) | −9.22019e37 | −0.153337 | ||||||||
\(225\) | −1.13747e37 | −0.0175764 | ||||||||
\(226\) | 7.32727e38 | 1.05233 | ||||||||
\(227\) | 3.89426e38 | 0.519994 | 0.259997 | − | 0.965609i | \(-0.416278\pi\) | ||||
0.259997 | + | 0.965609i | \(0.416278\pi\) | |||||||
\(228\) | 3.72728e38 | 0.462879 | ||||||||
\(229\) | −6.42546e38 | −0.742368 | −0.371184 | − | 0.928559i | \(-0.621048\pi\) | ||||
−0.371184 | + | 0.928559i | \(0.621048\pi\) | |||||||
\(230\) | −4.03724e37 | −0.0434086 | ||||||||
\(231\) | 6.21003e38 | 0.621579 | ||||||||
\(232\) | 3.72728e37 | 0.0347409 | ||||||||
\(233\) | 9.96582e38 | 0.865248 | 0.432624 | − | 0.901574i | \(-0.357588\pi\) | ||||
0.432624 | + | 0.901574i | \(0.357588\pi\) | |||||||
\(234\) | −1.25459e38 | −0.101494 | ||||||||
\(235\) | −4.70053e38 | −0.354427 | ||||||||
\(236\) | −7.98718e38 | −0.561494 | ||||||||
\(237\) | −4.90893e38 | −0.321839 | ||||||||
\(238\) | 9.73200e38 | 0.595226 | ||||||||
\(239\) | 2.06735e39 | 1.17991 | 0.589956 | − | 0.807435i | \(-0.299145\pi\) | ||||
0.589956 | + | 0.807435i | \(0.299145\pi\) | |||||||
\(240\) | −2.00432e38 | −0.106778 | ||||||||
\(241\) | −2.94996e39 | −1.46735 | −0.733677 | − | 0.679498i | \(-0.762197\pi\) | ||||
−0.733677 | + | 0.679498i | \(0.762197\pi\) | |||||||
\(242\) | −6.65174e38 | −0.309017 | ||||||||
\(243\) | −4.03771e38 | −0.175239 | ||||||||
\(244\) | −6.66987e38 | −0.270511 | ||||||||
\(245\) | −2.92090e38 | −0.110733 | ||||||||
\(246\) | 1.98358e39 | 0.703106 | ||||||||
\(247\) | −4.77560e39 | −1.58317 | ||||||||
\(248\) | 1.28323e39 | 0.397970 | ||||||||
\(249\) | −3.62541e39 | −1.05213 | ||||||||
\(250\) | 2.32831e38 | 0.0632456 | ||||||||
\(251\) | −5.46260e39 | −1.38926 | −0.694630 | − | 0.719368i | \(-0.744432\pi\) | ||||
−0.694630 | + | 0.719368i | \(0.744432\pi\) | |||||||
\(252\) | 1.60030e38 | 0.0381147 | ||||||||
\(253\) | −4.61649e38 | −0.102997 | ||||||||
\(254\) | −2.58146e38 | −0.0539647 | ||||||||
\(255\) | 2.11557e39 | 0.414491 | ||||||||
\(256\) | 3.40282e38 | 0.0625000 | ||||||||
\(257\) | 1.10808e40 | 1.90843 | 0.954213 | − | 0.299129i | \(-0.0966960\pi\) | ||||
0.954213 | + | 0.299129i | \(0.0966960\pi\) | |||||||
\(258\) | −2.78077e39 | −0.449200 | ||||||||
\(259\) | 3.52738e39 | 0.534572 | ||||||||
\(260\) | 2.56804e39 | 0.365209 | ||||||||
\(261\) | −6.46925e37 | −0.00863547 | ||||||||
\(262\) | −9.69684e39 | −1.21523 | ||||||||
\(263\) | −1.40170e40 | −1.64963 | −0.824815 | − | 0.565403i | \(-0.808721\pi\) | ||||
−0.824815 | + | 0.565403i | \(0.808721\pi\) | |||||||
\(264\) | −2.29189e39 | −0.253355 | ||||||||
\(265\) | −8.47798e39 | −0.880512 | ||||||||
\(266\) | 6.09153e39 | 0.594538 | ||||||||
\(267\) | 1.54174e40 | 1.41441 | ||||||||
\(268\) | −9.29562e39 | −0.801778 | ||||||||
\(269\) | −6.31508e39 | −0.512232 | −0.256116 | − | 0.966646i | \(-0.582443\pi\) | ||||
−0.256116 | + | 0.966646i | \(0.582443\pi\) | |||||||
\(270\) | 4.30635e39 | 0.328554 | ||||||||
\(271\) | 1.08648e40 | 0.779879 | 0.389939 | − | 0.920841i | \(-0.372496\pi\) | ||||
0.389939 | + | 0.920841i | \(0.372496\pi\) | |||||||
\(272\) | −3.59171e39 | −0.242613 | ||||||||
\(273\) | 2.12808e40 | 1.35302 | ||||||||
\(274\) | −1.27213e40 | −0.761460 | ||||||||
\(275\) | 2.66237e39 | 0.150065 | ||||||||
\(276\) | 1.23473e39 | 0.0655497 | ||||||||
\(277\) | 2.33494e40 | 1.16778 | 0.583889 | − | 0.811834i | \(-0.301530\pi\) | ||||
0.583889 | + | 0.811834i | \(0.301530\pi\) | |||||||
\(278\) | −1.61536e40 | −0.761257 | ||||||||
\(279\) | −2.22723e39 | −0.0989225 | ||||||||
\(280\) | −3.27567e39 | −0.137149 | ||||||||
\(281\) | 3.50713e40 | 1.38451 | 0.692257 | − | 0.721652i | \(-0.256617\pi\) | ||||
0.692257 | + | 0.721652i | \(0.256617\pi\) | |||||||
\(282\) | 1.43758e40 | 0.535208 | ||||||||
\(283\) | 2.34001e40 | 0.821753 | 0.410876 | − | 0.911691i | \(-0.365223\pi\) | ||||
0.410876 | + | 0.911691i | \(0.365223\pi\) | |||||||
\(284\) | −1.33535e40 | −0.442428 | ||||||||
\(285\) | 1.32420e40 | 0.414011 | ||||||||
\(286\) | 2.93649e40 | 0.866542 | ||||||||
\(287\) | 3.24178e40 | 0.903093 | ||||||||
\(288\) | −5.90610e38 | −0.0155355 | ||||||||
\(289\) | −2.34364e39 | −0.0582205 | ||||||||
\(290\) | 1.32420e39 | 0.0310732 | ||||||||
\(291\) | −1.04482e40 | −0.231637 | ||||||||
\(292\) | −3.16955e40 | −0.664020 | ||||||||
\(293\) | −3.11041e40 | −0.615889 | −0.307944 | − | 0.951404i | \(-0.599641\pi\) | ||||
−0.307944 | + | 0.951404i | \(0.599641\pi\) | |||||||
\(294\) | 8.93312e39 | 0.167214 | ||||||||
\(295\) | −2.83762e40 | −0.502216 | ||||||||
\(296\) | −1.30182e40 | −0.217891 | ||||||||
\(297\) | 4.92421e40 | 0.779571 | ||||||||
\(298\) | 2.04071e40 | 0.305642 | ||||||||
\(299\) | −1.58200e40 | −0.224198 | ||||||||
\(300\) | −7.12076e39 | −0.0955049 | ||||||||
\(301\) | −4.54463e40 | −0.576968 | ||||||||
\(302\) | 5.94646e39 | 0.0714733 | ||||||||
\(303\) | −1.23513e40 | −0.140575 | ||||||||
\(304\) | −2.24815e40 | −0.242333 | ||||||||
\(305\) | −2.36962e40 | −0.241953 | ||||||||
\(306\) | 6.23395e39 | 0.0603059 | ||||||||
\(307\) | −1.56830e41 | −1.43762 | −0.718811 | − | 0.695206i | \(-0.755313\pi\) | ||||
−0.718811 | + | 0.695206i | \(0.755313\pi\) | |||||||
\(308\) | −3.74565e40 | −0.325417 | ||||||||
\(309\) | −1.45891e41 | −1.20147 | ||||||||
\(310\) | 4.55893e40 | 0.355955 | ||||||||
\(311\) | −1.90389e41 | −1.40960 | −0.704798 | − | 0.709408i | \(-0.748963\pi\) | ||||
−0.704798 | + | 0.709408i | \(0.748963\pi\) | |||||||
\(312\) | −7.85394e40 | −0.551489 | ||||||||
\(313\) | 3.43316e40 | 0.228671 | 0.114336 | − | 0.993442i | \(-0.463526\pi\) | ||||
0.114336 | + | 0.993442i | \(0.463526\pi\) | |||||||
\(314\) | −1.09919e41 | −0.694599 | ||||||||
\(315\) | 5.68541e39 | 0.0340908 | ||||||||
\(316\) | 2.96088e40 | 0.168494 | ||||||||
\(317\) | 2.69572e41 | 1.45612 | 0.728060 | − | 0.685514i | \(-0.240422\pi\) | ||||
0.728060 | + | 0.685514i | \(0.240422\pi\) | |||||||
\(318\) | 2.59286e41 | 1.32963 | ||||||||
\(319\) | 1.51419e40 | 0.0737283 | ||||||||
\(320\) | 1.20893e40 | 0.0559017 | ||||||||
\(321\) | −2.13006e41 | −0.935531 | ||||||||
\(322\) | 2.01792e40 | 0.0841944 | ||||||||
\(323\) | 2.37295e41 | 0.940689 | ||||||||
\(324\) | −1.20039e41 | −0.452197 | ||||||||
\(325\) | 9.12351e40 | 0.326653 | ||||||||
\(326\) | 1.05626e41 | 0.359483 | ||||||||
\(327\) | −7.20602e40 | −0.233162 | ||||||||
\(328\) | −1.19642e41 | −0.368099 | ||||||||
\(329\) | 2.34946e41 | 0.687440 | ||||||||
\(330\) | −8.14242e40 | −0.226607 | ||||||||
\(331\) | 1.12474e41 | 0.297777 | 0.148888 | − | 0.988854i | \(-0.452430\pi\) | ||||
0.148888 | + | 0.988854i | \(0.452430\pi\) | |||||||
\(332\) | 2.18671e41 | 0.550823 | ||||||||
\(333\) | 2.25950e40 | 0.0541606 | ||||||||
\(334\) | 3.13394e41 | 0.714947 | ||||||||
\(335\) | −3.30247e41 | −0.717132 | ||||||||
\(336\) | 1.00181e41 | 0.207104 | ||||||||
\(337\) | −8.06548e41 | −1.58759 | −0.793793 | − | 0.608188i | \(-0.791897\pi\) | ||||
−0.793793 | + | 0.608188i | \(0.791897\pi\) | |||||||
\(338\) | 6.29057e41 | 1.17914 | ||||||||
\(339\) | −7.96139e41 | −1.42133 | ||||||||
\(340\) | −1.27603e41 | −0.217000 | ||||||||
\(341\) | 5.21304e41 | 0.844585 | ||||||||
\(342\) | 3.90200e40 | 0.0602361 | ||||||||
\(343\) | 7.35619e41 | 1.08218 | ||||||||
\(344\) | 1.67725e41 | 0.235171 | ||||||||
\(345\) | 4.38663e40 | 0.0586295 | ||||||||
\(346\) | 2.10906e41 | 0.268741 | ||||||||
\(347\) | −6.20227e41 | −0.753553 | −0.376777 | − | 0.926304i | \(-0.622968\pi\) | ||||
−0.376777 | + | 0.926304i | \(0.622968\pi\) | |||||||
\(348\) | −4.04985e40 | −0.0469225 | ||||||||
\(349\) | −8.80550e41 | −0.973048 | −0.486524 | − | 0.873667i | \(-0.661735\pi\) | ||||
−0.486524 | + | 0.873667i | \(0.661735\pi\) | |||||||
\(350\) | −1.16375e41 | −0.122670 | ||||||||
\(351\) | 1.68745e42 | 1.69693 | ||||||||
\(352\) | 1.38238e41 | 0.132640 | ||||||||
\(353\) | 1.63312e42 | 1.49533 | 0.747663 | − | 0.664078i | \(-0.231176\pi\) | ||||
0.747663 | + | 0.664078i | \(0.231176\pi\) | |||||||
\(354\) | 8.67840e41 | 0.758378 | ||||||||
\(355\) | −4.74412e41 | −0.395720 | ||||||||
\(356\) | −9.29915e41 | −0.740489 | ||||||||
\(357\) | −1.05742e42 | −0.803938 | ||||||||
\(358\) | 4.87357e40 | 0.0353816 | ||||||||
\(359\) | −4.69226e41 | −0.325330 | −0.162665 | − | 0.986681i | \(-0.552009\pi\) | ||||
−0.162665 | + | 0.986681i | \(0.552009\pi\) | |||||||
\(360\) | −2.09827e40 | −0.0138954 | ||||||||
\(361\) | −9.54774e40 | −0.0603993 | ||||||||
\(362\) | 9.74709e41 | 0.589092 | ||||||||
\(363\) | 7.22739e41 | 0.417371 | ||||||||
\(364\) | −1.28358e42 | −0.708352 | ||||||||
\(365\) | −1.12605e42 | −0.593918 | ||||||||
\(366\) | 7.24709e41 | 0.365364 | ||||||||
\(367\) | 2.12758e42 | 1.02541 | 0.512704 | − | 0.858565i | \(-0.328644\pi\) | ||||
0.512704 | + | 0.858565i | \(0.328644\pi\) | |||||||
\(368\) | −7.44740e40 | −0.0343175 | ||||||||
\(369\) | 2.07656e41 | 0.0914977 | ||||||||
\(370\) | −4.62500e41 | −0.194887 | ||||||||
\(371\) | 4.23753e42 | 1.70782 | ||||||||
\(372\) | −1.39428e42 | −0.537515 | ||||||||
\(373\) | −3.78223e42 | −1.39493 | −0.697465 | − | 0.716619i | \(-0.745689\pi\) | ||||
−0.697465 | + | 0.716619i | \(0.745689\pi\) | |||||||
\(374\) | −1.45911e42 | −0.514882 | ||||||||
\(375\) | −2.52980e41 | −0.0854222 | ||||||||
\(376\) | −8.67095e41 | −0.280199 | ||||||||
\(377\) | 5.18889e41 | 0.160488 | ||||||||
\(378\) | −2.15243e42 | −0.637257 | ||||||||
\(379\) | −6.08338e42 | −1.72424 | −0.862121 | − | 0.506702i | \(-0.830864\pi\) | ||||
−0.862121 | + | 0.506702i | \(0.830864\pi\) | |||||||
\(380\) | −7.98704e41 | −0.216749 | ||||||||
\(381\) | 2.80487e41 | 0.0728870 | ||||||||
\(382\) | −3.19671e41 | −0.0795532 | ||||||||
\(383\) | 8.15229e41 | 0.194312 | 0.0971560 | − | 0.995269i | \(-0.469025\pi\) | ||||
0.0971560 | + | 0.995269i | \(0.469025\pi\) | |||||||
\(384\) | −3.69731e41 | −0.0844152 | ||||||||
\(385\) | −1.33072e42 | −0.291062 | ||||||||
\(386\) | −4.66168e42 | −0.976905 | ||||||||
\(387\) | −2.91112e41 | −0.0584560 | ||||||||
\(388\) | 6.30195e41 | 0.121270 | ||||||||
\(389\) | −2.71183e42 | −0.500143 | −0.250071 | − | 0.968227i | \(-0.580454\pi\) | ||||
−0.250071 | + | 0.968227i | \(0.580454\pi\) | |||||||
\(390\) | −2.79028e42 | −0.493267 | ||||||||
\(391\) | 7.86080e41 | 0.133214 | ||||||||
\(392\) | −5.38811e41 | −0.0875420 | ||||||||
\(393\) | 1.05360e43 | 1.64134 | ||||||||
\(394\) | −7.96404e42 | −1.18972 | ||||||||
\(395\) | 1.05192e42 | 0.150705 | ||||||||
\(396\) | −2.39932e41 | −0.0329699 | ||||||||
\(397\) | 3.40205e42 | 0.448432 | 0.224216 | − | 0.974539i | \(-0.428018\pi\) | ||||
0.224216 | + | 0.974539i | \(0.428018\pi\) | |||||||
\(398\) | 1.04430e43 | 1.32055 | ||||||||
\(399\) | −6.61870e42 | −0.803008 | ||||||||
\(400\) | 4.29497e41 | 0.0500000 | ||||||||
\(401\) | 5.96117e42 | 0.665961 | 0.332981 | − | 0.942934i | \(-0.391946\pi\) | ||||
0.332981 | + | 0.942934i | \(0.391946\pi\) | |||||||
\(402\) | 1.01001e43 | 1.08292 | ||||||||
\(403\) | 1.78643e43 | 1.83845 | ||||||||
\(404\) | 7.44981e41 | 0.0735957 | ||||||||
\(405\) | −4.26463e42 | −0.404458 | ||||||||
\(406\) | −6.61870e41 | −0.0602689 | ||||||||
\(407\) | −5.28858e42 | −0.462415 | ||||||||
\(408\) | 3.90254e42 | 0.327684 | ||||||||
\(409\) | −2.07282e43 | −1.67158 | −0.835788 | − | 0.549052i | \(-0.814989\pi\) | ||||
−0.835788 | + | 0.549052i | \(0.814989\pi\) | |||||||
\(410\) | −4.25054e42 | −0.329238 | ||||||||
\(411\) | 1.38222e43 | 1.02846 | ||||||||
\(412\) | 8.79958e42 | 0.629010 | ||||||||
\(413\) | 1.41832e43 | 0.974087 | ||||||||
\(414\) | 1.29261e41 | 0.00853022 | ||||||||
\(415\) | 7.76874e42 | 0.492671 | ||||||||
\(416\) | 4.73720e42 | 0.288723 | ||||||||
\(417\) | 1.75516e43 | 1.02819 | ||||||||
\(418\) | −9.13300e42 | −0.514286 | ||||||||
\(419\) | −7.96843e42 | −0.431362 | −0.215681 | − | 0.976464i | \(-0.569197\pi\) | ||||
−0.215681 | + | 0.976464i | \(0.569197\pi\) | |||||||
\(420\) | 3.55915e42 | 0.185239 | ||||||||
\(421\) | −1.40035e43 | −0.700779 | −0.350390 | − | 0.936604i | \(-0.613951\pi\) | ||||
−0.350390 | + | 0.936604i | \(0.613951\pi\) | |||||||
\(422\) | −1.21936e43 | −0.586780 | ||||||||
\(423\) | 1.50497e42 | 0.0696486 | ||||||||
\(424\) | −1.56391e43 | −0.696106 | ||||||||
\(425\) | −4.53338e42 | −0.194091 | ||||||||
\(426\) | 1.45091e43 | 0.597562 | ||||||||
\(427\) | 1.18440e43 | 0.469287 | ||||||||
\(428\) | 1.28477e43 | 0.489782 | ||||||||
\(429\) | −3.19062e43 | −1.17039 | ||||||||
\(430\) | 5.95880e42 | 0.210344 | ||||||||
\(431\) | −2.19278e42 | −0.0744937 | −0.0372468 | − | 0.999306i | \(-0.511859\pi\) | ||||
−0.0372468 | + | 0.999306i | \(0.511859\pi\) | |||||||
\(432\) | 7.94382e42 | 0.259745 | ||||||||
\(433\) | 4.94849e43 | 1.55748 | 0.778739 | − | 0.627348i | \(-0.215859\pi\) | ||||
0.778739 | + | 0.627348i | \(0.215859\pi\) | |||||||
\(434\) | −2.27868e43 | −0.690403 | ||||||||
\(435\) | −1.43880e42 | −0.0419688 | ||||||||
\(436\) | 4.34639e42 | 0.122068 | ||||||||
\(437\) | 4.92029e42 | 0.133060 | ||||||||
\(438\) | 3.44385e43 | 0.896854 | ||||||||
\(439\) | −5.29628e43 | −1.32833 | −0.664165 | − | 0.747586i | \(-0.731213\pi\) | ||||
−0.664165 | + | 0.747586i | \(0.731213\pi\) | |||||||
\(440\) | 4.91120e42 | 0.118636 | ||||||||
\(441\) | 9.35187e41 | 0.0217601 | ||||||||
\(442\) | −5.00016e43 | −1.12077 | ||||||||
\(443\) | −6.57483e43 | −1.41979 | −0.709893 | − | 0.704309i | \(-0.751257\pi\) | ||||
−0.709893 | + | 0.704309i | \(0.751257\pi\) | |||||||
\(444\) | 1.41448e43 | 0.294292 | ||||||||
\(445\) | −3.30372e43 | −0.662313 | ||||||||
\(446\) | 1.54625e43 | 0.298713 | ||||||||
\(447\) | −2.21731e43 | −0.412813 | ||||||||
\(448\) | −6.04254e42 | −0.108426 | ||||||||
\(449\) | −7.00108e43 | −1.21088 | −0.605439 | − | 0.795892i | \(-0.707002\pi\) | ||||
−0.605439 | + | 0.795892i | \(0.707002\pi\) | |||||||
\(450\) | −7.45455e41 | −0.0124284 | ||||||||
\(451\) | −4.86039e43 | −0.781193 | ||||||||
\(452\) | 4.80200e43 | 0.744112 | ||||||||
\(453\) | −6.46108e42 | −0.0965349 | ||||||||
\(454\) | 2.55214e43 | 0.367692 | ||||||||
\(455\) | −4.56018e43 | −0.633569 | ||||||||
\(456\) | 2.44271e43 | 0.327305 | ||||||||
\(457\) | −4.08696e42 | −0.0528181 | −0.0264091 | − | 0.999651i | \(-0.508407\pi\) | ||||
−0.0264091 | + | 0.999651i | \(0.508407\pi\) | |||||||
\(458\) | −4.21099e43 | −0.524933 | ||||||||
\(459\) | −8.38477e43 | −1.00828 | ||||||||
\(460\) | −2.64585e42 | −0.0306945 | ||||||||
\(461\) | 5.94001e43 | 0.664848 | 0.332424 | − | 0.943130i | \(-0.392134\pi\) | ||||
0.332424 | + | 0.943130i | \(0.392134\pi\) | |||||||
\(462\) | 4.06981e43 | 0.439523 | ||||||||
\(463\) | 1.30594e44 | 1.36093 | 0.680466 | − | 0.732780i | \(-0.261777\pi\) | ||||
0.680466 | + | 0.732780i | \(0.261777\pi\) | |||||||
\(464\) | 2.44271e42 | 0.0245655 | ||||||||
\(465\) | −4.95347e43 | −0.480768 | ||||||||
\(466\) | 6.53120e43 | 0.611823 | ||||||||
\(467\) | −3.66775e43 | −0.331643 | −0.165822 | − | 0.986156i | \(-0.553028\pi\) | ||||
−0.165822 | + | 0.986156i | \(0.553028\pi\) | |||||||
\(468\) | −8.22210e42 | −0.0717673 | ||||||||
\(469\) | 1.65066e44 | 1.39093 | ||||||||
\(470\) | −3.08054e43 | −0.250618 | ||||||||
\(471\) | 1.19432e44 | 0.938155 | ||||||||
\(472\) | −5.23448e43 | −0.397036 | ||||||||
\(473\) | 6.81375e43 | 0.499088 | ||||||||
\(474\) | −3.21712e43 | −0.227575 | ||||||||
\(475\) | −2.83757e43 | −0.193866 | ||||||||
\(476\) | 6.37796e43 | 0.420889 | ||||||||
\(477\) | 2.71440e43 | 0.173030 | ||||||||
\(478\) | 1.35486e44 | 0.834324 | ||||||||
\(479\) | 1.79143e44 | 1.06577 | 0.532885 | − | 0.846188i | \(-0.321108\pi\) | ||||
0.532885 | + | 0.846188i | \(0.321108\pi\) | |||||||
\(480\) | −1.31355e43 | −0.0755032 | ||||||||
\(481\) | −1.81231e44 | −1.00656 | ||||||||
\(482\) | −1.93329e44 | −1.03758 | ||||||||
\(483\) | −2.19256e43 | −0.113717 | ||||||||
\(484\) | −4.35928e43 | −0.218508 | ||||||||
\(485\) | 2.23890e43 | 0.108467 | ||||||||
\(486\) | −2.64615e43 | −0.123913 | ||||||||
\(487\) | 2.85315e44 | 1.29151 | 0.645753 | − | 0.763546i | \(-0.276543\pi\) | ||||
0.645753 | + | 0.763546i | \(0.276543\pi\) | |||||||
\(488\) | −4.37117e43 | −0.191280 | ||||||||
\(489\) | −1.14767e44 | −0.485533 | ||||||||
\(490\) | −1.91424e43 | −0.0783000 | ||||||||
\(491\) | 1.91812e44 | 0.758631 | 0.379316 | − | 0.925267i | \(-0.376159\pi\) | ||||
0.379316 | + | 0.925267i | \(0.376159\pi\) | |||||||
\(492\) | 1.29996e44 | 0.497171 | ||||||||
\(493\) | −2.57831e43 | −0.0953587 | ||||||||
\(494\) | −3.12974e44 | −1.11947 | ||||||||
\(495\) | −8.52411e42 | −0.0294892 | ||||||||
\(496\) | 8.40975e43 | 0.281407 | ||||||||
\(497\) | 2.37124e44 | 0.767530 | ||||||||
\(498\) | −2.37595e44 | −0.743965 | ||||||||
\(499\) | 2.99230e44 | 0.906456 | 0.453228 | − | 0.891395i | \(-0.350272\pi\) | ||||
0.453228 | + | 0.891395i | \(0.350272\pi\) | |||||||
\(500\) | 1.52588e43 | 0.0447214 | ||||||||
\(501\) | −3.40515e44 | −0.965638 | ||||||||
\(502\) | −3.57997e44 | −0.982355 | ||||||||
\(503\) | 2.22024e44 | 0.589559 | 0.294780 | − | 0.955565i | \(-0.404754\pi\) | ||||
0.294780 | + | 0.955565i | \(0.404754\pi\) | |||||||
\(504\) | 1.04877e43 | 0.0269512 | ||||||||
\(505\) | 2.64670e43 | 0.0658260 | ||||||||
\(506\) | −3.02547e43 | −0.0728297 | ||||||||
\(507\) | −6.83496e44 | −1.59259 | ||||||||
\(508\) | −1.69179e43 | −0.0381588 | ||||||||
\(509\) | 7.25178e44 | 1.58344 | 0.791720 | − | 0.610885i | \(-0.209186\pi\) | ||||
0.791720 | + | 0.610885i | \(0.209186\pi\) | |||||||
\(510\) | 1.38646e44 | 0.293089 | ||||||||
\(511\) | 5.62832e44 | 1.15195 | ||||||||
\(512\) | 2.23007e43 | 0.0441942 | ||||||||
\(513\) | −5.24826e44 | −1.00711 | ||||||||
\(514\) | 7.26192e44 | 1.34946 | ||||||||
\(515\) | 3.12624e44 | 0.562604 | ||||||||
\(516\) | −1.82240e44 | −0.317632 | ||||||||
\(517\) | −3.52253e44 | −0.594649 | ||||||||
\(518\) | 2.31170e44 | 0.377999 | ||||||||
\(519\) | −2.29158e44 | −0.362973 | ||||||||
\(520\) | 1.68299e44 | 0.258242 | ||||||||
\(521\) | −1.11989e45 | −1.66476 | −0.832382 | − | 0.554202i | \(-0.813023\pi\) | ||||
−0.832382 | + | 0.554202i | \(0.813023\pi\) | |||||||
\(522\) | −4.23969e42 | −0.00610620 | ||||||||
\(523\) | 1.32139e45 | 1.84396 | 0.921981 | − | 0.387234i | \(-0.126569\pi\) | ||||
0.921981 | + | 0.387234i | \(0.126569\pi\) | |||||||
\(524\) | −6.35492e44 | −0.859298 | ||||||||
\(525\) | 1.26446e44 | 0.165683 | ||||||||
\(526\) | −9.18621e44 | −1.16646 | ||||||||
\(527\) | −8.87657e44 | −1.09237 | ||||||||
\(528\) | −1.50201e44 | −0.179149 | ||||||||
\(529\) | −8.48706e44 | −0.981157 | ||||||||
\(530\) | −5.55613e44 | −0.622616 | ||||||||
\(531\) | 9.08521e43 | 0.0986905 | ||||||||
\(532\) | 3.99214e44 | 0.420401 | ||||||||
\(533\) | −1.66558e45 | −1.70046 | ||||||||
\(534\) | 1.01039e45 | 1.00014 | ||||||||
\(535\) | 4.56442e44 | 0.438074 | ||||||||
\(536\) | −6.09198e44 | −0.566943 | ||||||||
\(537\) | −5.29534e43 | −0.0477879 | ||||||||
\(538\) | −4.13865e44 | −0.362203 | ||||||||
\(539\) | −2.18889e44 | −0.185785 | ||||||||
\(540\) | 2.82221e44 | 0.232323 | ||||||||
\(541\) | 7.54315e42 | 0.00602279 | 0.00301140 | − | 0.999995i | \(-0.499041\pi\) | ||||
0.00301140 | + | 0.999995i | \(0.499041\pi\) | |||||||
\(542\) | 7.12033e44 | 0.551458 | ||||||||
\(543\) | −1.05906e45 | −0.795654 | ||||||||
\(544\) | −2.35386e44 | −0.171554 | ||||||||
\(545\) | 1.54415e44 | 0.109181 | ||||||||
\(546\) | 1.39466e45 | 0.956730 | ||||||||
\(547\) | 1.65387e45 | 1.10080 | 0.550402 | − | 0.834900i | \(-0.314475\pi\) | ||||
0.550402 | + | 0.834900i | \(0.314475\pi\) | |||||||
\(548\) | −8.33703e44 | −0.538433 | ||||||||
\(549\) | 7.58681e43 | 0.0475462 | ||||||||
\(550\) | 1.74481e44 | 0.106112 | ||||||||
\(551\) | −1.61383e44 | −0.0952484 | ||||||||
\(552\) | 8.09191e43 | 0.0463507 | ||||||||
\(553\) | −5.25776e44 | −0.292305 | ||||||||
\(554\) | 1.53023e45 | 0.825744 | ||||||||
\(555\) | 5.02526e44 | 0.263223 | ||||||||
\(556\) | −1.05864e45 | −0.538290 | ||||||||
\(557\) | 8.23792e44 | 0.406637 | 0.203318 | − | 0.979113i | \(-0.434827\pi\) | ||||
0.203318 | + | 0.979113i | \(0.434827\pi\) | |||||||
\(558\) | −1.45964e44 | −0.0699488 | ||||||||
\(559\) | 2.33497e45 | 1.08639 | ||||||||
\(560\) | −2.14674e44 | −0.0969790 | ||||||||
\(561\) | 1.58539e45 | 0.695422 | ||||||||
\(562\) | 2.29843e45 | 0.978999 | ||||||||
\(563\) | −2.90289e45 | −1.20072 | −0.600360 | − | 0.799730i | \(-0.704976\pi\) | ||||
−0.600360 | + | 0.799730i | \(0.704976\pi\) | |||||||
\(564\) | 9.42135e44 | 0.378449 | ||||||||
\(565\) | 1.70601e45 | 0.665554 | ||||||||
\(566\) | 1.53355e45 | 0.581067 | ||||||||
\(567\) | 2.13158e45 | 0.784478 | ||||||||
\(568\) | −8.75135e44 | −0.312844 | ||||||||
\(569\) | 3.12951e45 | 1.08674 | 0.543369 | − | 0.839494i | \(-0.317149\pi\) | ||||
0.543369 | + | 0.839494i | \(0.317149\pi\) | |||||||
\(570\) | 8.67825e44 | 0.292750 | ||||||||
\(571\) | −3.84526e45 | −1.26017 | −0.630086 | − | 0.776525i | \(-0.716980\pi\) | ||||
−0.630086 | + | 0.776525i | \(0.716980\pi\) | |||||||
\(572\) | 1.92446e45 | 0.612738 | ||||||||
\(573\) | 3.47336e44 | 0.107448 | ||||||||
\(574\) | 2.12454e45 | 0.638583 | ||||||||
\(575\) | −9.39994e43 | −0.0274540 | ||||||||
\(576\) | −3.87062e43 | −0.0109853 | ||||||||
\(577\) | −2.53135e45 | −0.698154 | −0.349077 | − | 0.937094i | \(-0.613505\pi\) | ||||
−0.349077 | + | 0.937094i | \(0.613505\pi\) | |||||||
\(578\) | −1.53593e44 | −0.0411681 | ||||||||
\(579\) | 5.06511e45 | 1.31945 | ||||||||
\(580\) | 8.67826e43 | 0.0219721 | ||||||||
\(581\) | −3.88303e45 | −0.955575 | ||||||||
\(582\) | −6.84733e44 | −0.163792 | ||||||||
\(583\) | −6.35331e45 | −1.47730 | ||||||||
\(584\) | −2.07720e45 | −0.469533 | ||||||||
\(585\) | −2.92108e44 | −0.0641906 | ||||||||
\(586\) | −2.03844e45 | −0.435499 | ||||||||
\(587\) | −1.89473e45 | −0.393568 | −0.196784 | − | 0.980447i | \(-0.563050\pi\) | ||||
−0.196784 | + | 0.980447i | \(0.563050\pi\) | |||||||
\(588\) | 5.85441e44 | 0.118238 | ||||||||
\(589\) | −5.55609e45 | −1.09111 | ||||||||
\(590\) | −1.85966e45 | −0.355120 | ||||||||
\(591\) | 8.65326e45 | 1.60689 | ||||||||
\(592\) | −8.53162e44 | −0.154072 | ||||||||
\(593\) | −9.96728e45 | −1.75055 | −0.875275 | − | 0.483626i | \(-0.839320\pi\) | ||||
−0.875275 | + | 0.483626i | \(0.839320\pi\) | |||||||
\(594\) | 3.22713e45 | 0.551240 | ||||||||
\(595\) | 2.26591e45 | 0.376454 | ||||||||
\(596\) | 1.33740e45 | 0.216121 | ||||||||
\(597\) | −1.13467e46 | −1.78359 | ||||||||
\(598\) | −1.03678e45 | −0.158532 | ||||||||
\(599\) | 5.94982e45 | 0.885037 | 0.442518 | − | 0.896759i | \(-0.354085\pi\) | ||||
0.442518 | + | 0.896759i | \(0.354085\pi\) | |||||||
\(600\) | −4.66666e44 | −0.0675321 | ||||||||
\(601\) | 1.42873e45 | 0.201150 | 0.100575 | − | 0.994929i | \(-0.467932\pi\) | ||||
0.100575 | + | 0.994929i | \(0.467932\pi\) | |||||||
\(602\) | −2.97837e45 | −0.407978 | ||||||||
\(603\) | 1.05735e45 | 0.140924 | ||||||||
\(604\) | 3.89707e44 | 0.0505393 | ||||||||
\(605\) | −1.54873e45 | −0.195439 | ||||||||
\(606\) | −8.09452e44 | −0.0994015 | ||||||||
\(607\) | 5.41904e45 | 0.647603 | 0.323801 | − | 0.946125i | \(-0.395039\pi\) | ||||
0.323801 | + | 0.946125i | \(0.395039\pi\) | |||||||
\(608\) | −1.47335e45 | −0.171355 | ||||||||
\(609\) | 7.19150e44 | 0.0814018 | ||||||||
\(610\) | −1.55295e45 | −0.171086 | ||||||||
\(611\) | −1.20712e46 | −1.29440 | ||||||||
\(612\) | 4.08548e44 | 0.0426427 | ||||||||
\(613\) | 1.66868e46 | 1.69541 | 0.847705 | − | 0.530467i | \(-0.177984\pi\) | ||||
0.847705 | + | 0.530467i | \(0.177984\pi\) | |||||||
\(614\) | −1.02780e46 | −1.01655 | ||||||||
\(615\) | 4.61838e45 | 0.444683 | ||||||||
\(616\) | −2.45475e45 | −0.230105 | ||||||||
\(617\) | −5.91960e45 | −0.540240 | −0.270120 | − | 0.962827i | \(-0.587063\pi\) | ||||
−0.270120 | + | 0.962827i | \(0.587063\pi\) | |||||||
\(618\) | −9.56111e45 | −0.849568 | ||||||||
\(619\) | 8.04200e45 | 0.695774 | 0.347887 | − | 0.937536i | \(-0.386899\pi\) | ||||
0.347887 | + | 0.937536i | \(0.386899\pi\) | |||||||
\(620\) | 2.98774e45 | 0.251698 | ||||||||
\(621\) | −1.73858e45 | −0.142621 | ||||||||
\(622\) | −1.24773e46 | −0.996736 | ||||||||
\(623\) | 1.65129e46 | 1.28461 | ||||||||
\(624\) | −5.14716e45 | −0.389962 | ||||||||
\(625\) | 5.42101e44 | 0.0400000 | ||||||||
\(626\) | 2.24995e45 | 0.161695 | ||||||||
\(627\) | 9.92339e45 | 0.694617 | ||||||||
\(628\) | −7.20366e45 | −0.491156 | ||||||||
\(629\) | 9.00521e45 | 0.598078 | ||||||||
\(630\) | 3.72599e44 | 0.0241059 | ||||||||
\(631\) | −1.17738e46 | −0.742050 | −0.371025 | − | 0.928623i | \(-0.620994\pi\) | ||||
−0.371025 | + | 0.928623i | \(0.620994\pi\) | |||||||
\(632\) | 1.94044e45 | 0.119143 | ||||||||
\(633\) | 1.32488e46 | 0.792530 | ||||||||
\(634\) | 1.76667e46 | 1.02963 | ||||||||
\(635\) | −6.01044e44 | −0.0341303 | ||||||||
\(636\) | 1.69925e46 | 0.940191 | ||||||||
\(637\) | −7.50099e45 | −0.404406 | ||||||||
\(638\) | 9.92339e44 | 0.0521338 | ||||||||
\(639\) | 1.51893e45 | 0.0777629 | ||||||||
\(640\) | 7.92282e44 | 0.0395285 | ||||||||
\(641\) | −1.99312e46 | −0.969116 | −0.484558 | − | 0.874759i | \(-0.661019\pi\) | ||||
−0.484558 | + | 0.874759i | \(0.661019\pi\) | |||||||
\(642\) | −1.39595e46 | −0.661520 | ||||||||
\(643\) | 3.26909e46 | 1.50989 | 0.754946 | − | 0.655787i | \(-0.227663\pi\) | ||||
0.754946 | + | 0.655787i | \(0.227663\pi\) | |||||||
\(644\) | 1.32247e45 | 0.0595344 | ||||||||
\(645\) | −6.47448e45 | −0.284099 | ||||||||
\(646\) | 1.55513e46 | 0.665168 | ||||||||
\(647\) | 1.84958e46 | 0.771174 | 0.385587 | − | 0.922672i | \(-0.373999\pi\) | ||||
0.385587 | + | 0.922672i | \(0.373999\pi\) | |||||||
\(648\) | −7.86685e45 | −0.319752 | ||||||||
\(649\) | −2.12648e46 | −0.842604 | ||||||||
\(650\) | 5.97918e45 | 0.230978 | ||||||||
\(651\) | 2.47588e46 | 0.932488 | ||||||||
\(652\) | 6.92228e45 | 0.254193 | ||||||||
\(653\) | −2.33266e46 | −0.835189 | −0.417594 | − | 0.908634i | \(-0.637127\pi\) | ||||
−0.417594 | + | 0.908634i | \(0.637127\pi\) | |||||||
\(654\) | −4.72254e45 | −0.164870 | ||||||||
\(655\) | −2.25772e46 | −0.768580 | ||||||||
\(656\) | −7.84086e45 | −0.260286 | ||||||||
\(657\) | 3.60529e45 | 0.116711 | ||||||||
\(658\) | 1.53974e46 | 0.486094 | ||||||||
\(659\) | 1.31702e46 | 0.405493 | 0.202747 | − | 0.979231i | \(-0.435013\pi\) | ||||
0.202747 | + | 0.979231i | \(0.435013\pi\) | |||||||
\(660\) | −5.33622e45 | −0.160236 | ||||||||
\(661\) | −8.17736e45 | −0.239491 | −0.119746 | − | 0.992805i | \(-0.538208\pi\) | ||||
−0.119746 | + | 0.992805i | \(0.538208\pi\) | |||||||
\(662\) | 7.37111e45 | 0.210560 | ||||||||
\(663\) | 5.43288e46 | 1.51376 | ||||||||
\(664\) | 1.43308e46 | 0.389491 | ||||||||
\(665\) | 1.41829e46 | 0.376019 | ||||||||
\(666\) | 1.48079e45 | 0.0382973 | ||||||||
\(667\) | −5.34611e44 | −0.0134884 | ||||||||
\(668\) | 2.05386e46 | 0.505544 | ||||||||
\(669\) | −1.68006e46 | −0.403455 | ||||||||
\(670\) | −2.16431e46 | −0.507089 | ||||||||
\(671\) | −1.77576e46 | −0.405942 | ||||||||
\(672\) | 6.56547e45 | 0.146445 | ||||||||
\(673\) | −4.48159e46 | −0.975401 | −0.487701 | − | 0.873011i | \(-0.662164\pi\) | ||||
−0.487701 | + | 0.873011i | \(0.662164\pi\) | |||||||
\(674\) | −5.28580e46 | −1.12259 | ||||||||
\(675\) | 1.00265e46 | 0.207796 | ||||||||
\(676\) | 4.12259e46 | 0.833776 | ||||||||
\(677\) | −5.83822e46 | −1.15231 | −0.576153 | − | 0.817342i | \(-0.695447\pi\) | ||||
−0.576153 | + | 0.817342i | \(0.695447\pi\) | |||||||
\(678\) | −5.21757e46 | −1.00503 | ||||||||
\(679\) | −1.11907e46 | −0.210380 | ||||||||
\(680\) | −8.36261e45 | −0.153442 | ||||||||
\(681\) | −2.77301e46 | −0.496620 | ||||||||
\(682\) | 3.41642e46 | 0.597212 | ||||||||
\(683\) | 2.10568e46 | 0.359295 | 0.179647 | − | 0.983731i | \(-0.442504\pi\) | ||||
0.179647 | + | 0.983731i | \(0.442504\pi\) | |||||||
\(684\) | 2.55722e45 | 0.0425933 | ||||||||
\(685\) | −2.96191e46 | −0.481589 | ||||||||
\(686\) | 4.82095e46 | 0.765218 | ||||||||
\(687\) | 4.57542e46 | 0.708997 | ||||||||
\(688\) | 1.09920e46 | 0.166291 | ||||||||
\(689\) | −2.17718e47 | −3.21571 | ||||||||
\(690\) | 2.87482e45 | 0.0414573 | ||||||||
\(691\) | 8.94914e46 | 1.26007 | 0.630033 | − | 0.776568i | \(-0.283041\pi\) | ||||
0.630033 | + | 0.776568i | \(0.283041\pi\) | |||||||
\(692\) | 1.38220e46 | 0.190029 | ||||||||
\(693\) | 4.26058e45 | 0.0571967 | ||||||||
\(694\) | −4.06472e46 | −0.532843 | ||||||||
\(695\) | −3.76106e46 | −0.481461 | ||||||||
\(696\) | −2.65411e45 | −0.0331792 | ||||||||
\(697\) | 8.27610e46 | 1.01038 | ||||||||
\(698\) | −5.77077e46 | −0.688049 | ||||||||
\(699\) | −7.09642e46 | −0.826354 | ||||||||
\(700\) | −7.62676e45 | −0.0867406 | ||||||||
\(701\) | −6.16333e45 | −0.0684650 | −0.0342325 | − | 0.999414i | \(-0.510899\pi\) | ||||
−0.0342325 | + | 0.999414i | \(0.510899\pi\) | |||||||
\(702\) | 1.10589e47 | 1.19991 | ||||||||
\(703\) | 5.63661e46 | 0.597386 | ||||||||
\(704\) | 9.05956e45 | 0.0937904 | ||||||||
\(705\) | 3.34714e46 | 0.338495 | ||||||||
\(706\) | 1.07028e47 | 1.05736 | ||||||||
\(707\) | −1.32290e46 | −0.127675 | ||||||||
\(708\) | 5.68748e46 | 0.536254 | ||||||||
\(709\) | −4.95391e46 | −0.456336 | −0.228168 | − | 0.973622i | \(-0.573274\pi\) | ||||
−0.228168 | + | 0.973622i | \(0.573274\pi\) | |||||||
\(710\) | −3.10911e46 | −0.279816 | ||||||||
\(711\) | −3.36792e45 | −0.0296151 | ||||||||
\(712\) | −6.09429e46 | −0.523605 | ||||||||
\(713\) | −1.84055e46 | −0.154515 | ||||||||
\(714\) | −6.92992e46 | −0.568470 | ||||||||
\(715\) | 6.83706e46 | 0.548049 | ||||||||
\(716\) | 3.19395e45 | 0.0250186 | ||||||||
\(717\) | −1.47211e47 | −1.12687 | ||||||||
\(718\) | −3.07512e46 | −0.230043 | ||||||||
\(719\) | −2.13187e47 | −1.55860 | −0.779300 | − | 0.626651i | \(-0.784425\pi\) | ||||
−0.779300 | + | 0.626651i | \(0.784425\pi\) | |||||||
\(720\) | −1.37512e45 | −0.00982551 | ||||||||
\(721\) | −1.56258e47 | −1.09122 | ||||||||
\(722\) | −6.25721e45 | −0.0427088 | ||||||||
\(723\) | 2.10060e47 | 1.40139 | ||||||||
\(724\) | 6.38785e46 | 0.416551 | ||||||||
\(725\) | 3.08314e45 | 0.0196524 | ||||||||
\(726\) | 4.73654e46 | 0.295126 | ||||||||
\(727\) | 1.31060e47 | 0.798273 | 0.399137 | − | 0.916891i | \(-0.369310\pi\) | ||||
0.399137 | + | 0.916891i | \(0.369310\pi\) | |||||||
\(728\) | −8.41205e46 | −0.500880 | ||||||||
\(729\) | 1.84120e47 | 1.07176 | ||||||||
\(730\) | −7.37969e46 | −0.419963 | ||||||||
\(731\) | −1.16022e47 | −0.645511 | ||||||||
\(732\) | 4.74946e46 | 0.258352 | ||||||||
\(733\) | 3.54336e47 | 1.88451 | 0.942257 | − | 0.334892i | \(-0.108700\pi\) | ||||
0.942257 | + | 0.334892i | \(0.108700\pi\) | |||||||
\(734\) | 1.39433e47 | 0.725073 | ||||||||
\(735\) | 2.07990e46 | 0.105755 | ||||||||
\(736\) | −4.88073e45 | −0.0242661 | ||||||||
\(737\) | −2.47483e47 | −1.20319 | ||||||||
\(738\) | 1.36090e46 | 0.0646986 | ||||||||
\(739\) | 2.64104e47 | 1.22784 | 0.613919 | − | 0.789369i | \(-0.289592\pi\) | ||||
0.613919 | + | 0.789369i | \(0.289592\pi\) | |||||||
\(740\) | −3.03104e46 | −0.137806 | ||||||||
\(741\) | 3.40059e47 | 1.51201 | ||||||||
\(742\) | 2.77711e47 | 1.20761 | ||||||||
\(743\) | 1.68076e47 | 0.714809 | 0.357404 | − | 0.933950i | \(-0.383662\pi\) | ||||
0.357404 | + | 0.933950i | \(0.383662\pi\) | |||||||
\(744\) | −9.13754e46 | −0.380081 | ||||||||
\(745\) | 4.75139e46 | 0.193305 | ||||||||
\(746\) | −2.47872e47 | −0.986364 | ||||||||
\(747\) | −2.48732e46 | −0.0968149 | ||||||||
\(748\) | −9.56245e46 | −0.364077 | ||||||||
\(749\) | −2.28142e47 | −0.849680 | ||||||||
\(750\) | −1.65793e46 | −0.0604026 | ||||||||
\(751\) | 4.23831e47 | 1.51055 | 0.755273 | − | 0.655410i | \(-0.227504\pi\) | ||||
0.755273 | + | 0.655410i | \(0.227504\pi\) | |||||||
\(752\) | −5.68259e46 | −0.198131 | ||||||||
\(753\) | 3.88979e47 | 1.32681 | ||||||||
\(754\) | 3.40059e46 | 0.113482 | ||||||||
\(755\) | 1.38452e46 | 0.0452037 | ||||||||
\(756\) | −1.41062e47 | −0.450609 | ||||||||
\(757\) | 4.49973e47 | 1.40639 | 0.703193 | − | 0.710999i | \(-0.251757\pi\) | ||||
0.703193 | + | 0.710999i | \(0.251757\pi\) | |||||||
\(758\) | −3.98681e47 | −1.21922 | ||||||||
\(759\) | 3.28729e46 | 0.0983670 | ||||||||
\(760\) | −5.23439e46 | −0.153265 | ||||||||
\(761\) | −3.43548e47 | −0.984329 | −0.492164 | − | 0.870502i | \(-0.663794\pi\) | ||||
−0.492164 | + | 0.870502i | \(0.663794\pi\) | |||||||
\(762\) | 1.83820e46 | 0.0515389 | ||||||||
\(763\) | −7.71808e46 | −0.211765 | ||||||||
\(764\) | −2.09499e46 | −0.0562526 | ||||||||
\(765\) | 1.45145e46 | 0.0381408 | ||||||||
\(766\) | 5.34268e46 | 0.137399 | ||||||||
\(767\) | −7.28711e47 | −1.83414 | ||||||||
\(768\) | −2.42307e46 | −0.0596905 | ||||||||
\(769\) | −7.98461e47 | −1.92517 | −0.962585 | − | 0.270981i | \(-0.912652\pi\) | ||||
−0.962585 | + | 0.270981i | \(0.912652\pi\) | |||||||
\(770\) | −8.72103e46 | −0.205812 | ||||||||
\(771\) | −7.89038e47 | −1.82264 | ||||||||
\(772\) | −3.05508e47 | −0.690776 | ||||||||
\(773\) | 4.85460e47 | 1.07446 | 0.537232 | − | 0.843435i | \(-0.319470\pi\) | ||||
0.537232 | + | 0.843435i | \(0.319470\pi\) | |||||||
\(774\) | −1.90783e46 | −0.0413346 | ||||||||
\(775\) | 1.06146e47 | 0.225126 | ||||||||
\(776\) | 4.13005e46 | 0.0857505 | ||||||||
\(777\) | −2.51176e47 | −0.510542 | ||||||||
\(778\) | −1.77723e47 | −0.353654 | ||||||||
\(779\) | 5.18024e47 | 1.00921 | ||||||||
\(780\) | −1.82864e47 | −0.348792 | ||||||||
\(781\) | −3.55519e47 | −0.663928 | ||||||||
\(782\) | 5.15165e46 | 0.0941966 | ||||||||
\(783\) | 5.70246e46 | 0.102092 | ||||||||
\(784\) | −3.53115e46 | −0.0619016 | ||||||||
\(785\) | −2.55925e47 | −0.439303 | ||||||||
\(786\) | 6.90489e47 | 1.16061 | ||||||||
\(787\) | −4.81834e47 | −0.793075 | −0.396538 | − | 0.918018i | \(-0.629788\pi\) | ||||
−0.396538 | + | 0.918018i | \(0.629788\pi\) | |||||||
\(788\) | −5.21931e47 | −0.841261 | ||||||||
\(789\) | 9.98120e47 | 1.57548 | ||||||||
\(790\) | 6.89383e46 | 0.106565 | ||||||||
\(791\) | −8.52713e47 | −1.29089 | ||||||||
\(792\) | −1.57242e46 | −0.0233133 | ||||||||
\(793\) | −6.08527e47 | −0.883633 | ||||||||
\(794\) | 2.22956e47 | 0.317089 | ||||||||
\(795\) | 6.03696e47 | 0.840932 | ||||||||
\(796\) | 6.84392e47 | 0.933768 | ||||||||
\(797\) | −2.06006e47 | −0.275307 | −0.137654 | − | 0.990480i | \(-0.543956\pi\) | ||||
−0.137654 | + | 0.990480i | \(0.543956\pi\) | |||||||
\(798\) | −4.33763e47 | −0.567812 | ||||||||
\(799\) | 5.99803e47 | 0.769107 | ||||||||
\(800\) | 2.81475e46 | 0.0353553 | ||||||||
\(801\) | 1.05775e47 | 0.130151 | ||||||||
\(802\) | 3.90671e47 | 0.470906 | ||||||||
\(803\) | −8.43851e47 | −0.996459 | ||||||||
\(804\) | 6.61919e47 | 0.765737 | ||||||||
\(805\) | 4.69835e46 | 0.0532492 | ||||||||
\(806\) | 1.17075e48 | 1.29998 | ||||||||
\(807\) | 4.49682e47 | 0.489206 | ||||||||
\(808\) | 4.88231e46 | 0.0520400 | ||||||||
\(809\) | 9.08440e47 | 0.948737 | 0.474368 | − | 0.880326i | \(-0.342676\pi\) | ||||
0.474368 | + | 0.880326i | \(0.342676\pi\) | |||||||
\(810\) | −2.79487e47 | −0.285995 | ||||||||
\(811\) | 1.62541e48 | 1.62974 | 0.814869 | − | 0.579646i | \(-0.196809\pi\) | ||||
0.814869 | + | 0.579646i | \(0.196809\pi\) | |||||||
\(812\) | −4.33763e46 | −0.0426166 | ||||||||
\(813\) | −7.73654e47 | −0.744822 | ||||||||
\(814\) | −3.46593e47 | −0.326977 | ||||||||
\(815\) | 2.45929e47 | 0.227357 | ||||||||
\(816\) | 2.55757e47 | 0.231708 | ||||||||
\(817\) | −7.26214e47 | −0.644764 | ||||||||
\(818\) | −1.35844e48 | −1.18198 | ||||||||
\(819\) | 1.46004e47 | 0.124503 | ||||||||
\(820\) | −2.78563e47 | −0.232807 | ||||||||
\(821\) | −1.89976e48 | −1.55610 | −0.778048 | − | 0.628205i | \(-0.783790\pi\) | ||||
−0.778048 | + | 0.628205i | \(0.783790\pi\) | |||||||
\(822\) | 9.05852e47 | 0.727231 | ||||||||
\(823\) | 1.15896e48 | 0.911950 | 0.455975 | − | 0.889992i | \(-0.349291\pi\) | ||||
0.455975 | + | 0.889992i | \(0.349291\pi\) | |||||||
\(824\) | 5.76689e47 | 0.444778 | ||||||||
\(825\) | −1.89581e47 | −0.143319 | ||||||||
\(826\) | 9.29509e47 | 0.688784 | ||||||||
\(827\) | −7.78559e47 | −0.565524 | −0.282762 | − | 0.959190i | \(-0.591251\pi\) | ||||
−0.282762 | + | 0.959190i | \(0.591251\pi\) | |||||||
\(828\) | 8.47122e45 | 0.00603178 | ||||||||
\(829\) | 2.22673e48 | 1.55424 | 0.777120 | − | 0.629353i | \(-0.216680\pi\) | ||||
0.777120 | + | 0.629353i | \(0.216680\pi\) | |||||||
\(830\) | 5.09132e47 | 0.348371 | ||||||||
\(831\) | −1.66266e48 | −1.11528 | ||||||||
\(832\) | 3.10457e47 | 0.204158 | ||||||||
\(833\) | 3.72717e47 | 0.240290 | ||||||||
\(834\) | 1.15026e48 | 0.727037 | ||||||||
\(835\) | 7.29677e47 | 0.452172 | ||||||||
\(836\) | −5.98540e47 | −0.363655 | ||||||||
\(837\) | 1.96324e48 | 1.16951 | ||||||||
\(838\) | −5.22219e47 | −0.305019 | ||||||||
\(839\) | −1.12708e48 | −0.645478 | −0.322739 | − | 0.946488i | \(-0.604604\pi\) | ||||
−0.322739 | + | 0.946488i | \(0.604604\pi\) | |||||||
\(840\) | 2.33253e47 | 0.130984 | ||||||||
\(841\) | −1.79854e48 | −0.990345 | ||||||||
\(842\) | −9.17732e47 | −0.495526 | ||||||||
\(843\) | −2.49734e48 | −1.32228 | ||||||||
\(844\) | −7.99118e47 | −0.414916 | ||||||||
\(845\) | 1.46464e48 | 0.745752 | ||||||||
\(846\) | 9.86298e46 | 0.0492490 | ||||||||
\(847\) | 7.74097e47 | 0.379070 | ||||||||
\(848\) | −1.02492e48 | −0.492221 | ||||||||
\(849\) | −1.66626e48 | −0.784814 | ||||||||
\(850\) | −2.97099e47 | −0.137243 | ||||||||
\(851\) | 1.86722e47 | 0.0845978 | ||||||||
\(852\) | 9.50871e47 | 0.422540 | ||||||||
\(853\) | 3.65470e48 | 1.59292 | 0.796459 | − | 0.604693i | \(-0.206704\pi\) | ||||
0.796459 | + | 0.604693i | \(0.206704\pi\) | |||||||
\(854\) | 7.76208e47 | 0.331836 | ||||||||
\(855\) | 9.08505e46 | 0.0380966 | ||||||||
\(856\) | 8.41986e47 | 0.346328 | ||||||||
\(857\) | 1.20507e48 | 0.486214 | 0.243107 | − | 0.969999i | \(-0.421833\pi\) | ||||
0.243107 | + | 0.969999i | \(0.421833\pi\) | |||||||
\(858\) | −2.09101e48 | −0.827590 | ||||||||
\(859\) | −1.13686e48 | −0.441389 | −0.220694 | − | 0.975343i | \(-0.570832\pi\) | ||||
−0.220694 | + | 0.975343i | \(0.570832\pi\) | |||||||
\(860\) | 3.90516e47 | 0.148735 | ||||||||
\(861\) | −2.30840e48 | −0.862498 | ||||||||
\(862\) | −1.43706e47 | −0.0526750 | ||||||||
\(863\) | 3.08439e46 | 0.0110915 | 0.00554576 | − | 0.999985i | \(-0.498235\pi\) | ||||
0.00554576 | + | 0.999985i | \(0.498235\pi\) | |||||||
\(864\) | 5.20606e47 | 0.183668 | ||||||||
\(865\) | 4.91055e47 | 0.169967 | ||||||||
\(866\) | 3.24304e48 | 1.10130 | ||||||||
\(867\) | 1.66885e47 | 0.0556034 | ||||||||
\(868\) | −1.49336e48 | −0.488189 | ||||||||
\(869\) | 7.88294e47 | 0.252849 | ||||||||
\(870\) | −9.42929e46 | −0.0296764 | ||||||||
\(871\) | −8.48087e48 | −2.61903 | ||||||||
\(872\) | 2.84845e47 | 0.0863151 | ||||||||
\(873\) | −7.16831e46 | −0.0213148 | ||||||||
\(874\) | 3.22456e47 | 0.0940875 | ||||||||
\(875\) | −2.70957e47 | −0.0775832 | ||||||||
\(876\) | 2.25696e48 | 0.634171 | ||||||||
\(877\) | −3.96964e48 | −1.09461 | −0.547303 | − | 0.836935i | \(-0.684345\pi\) | ||||
−0.547303 | + | 0.836935i | \(0.684345\pi\) | |||||||
\(878\) | −3.47097e48 | −0.939272 | ||||||||
\(879\) | 2.21485e48 | 0.588204 | ||||||||
\(880\) | 3.21860e47 | 0.0838887 | ||||||||
\(881\) | −1.10851e48 | −0.283556 | −0.141778 | − | 0.989898i | \(-0.545282\pi\) | ||||
−0.141778 | + | 0.989898i | \(0.545282\pi\) | |||||||
\(882\) | 6.12884e46 | 0.0153867 | ||||||||
\(883\) | 3.17298e48 | 0.781836 | 0.390918 | − | 0.920426i | \(-0.372158\pi\) | ||||
0.390918 | + | 0.920426i | \(0.372158\pi\) | |||||||
\(884\) | −3.27690e48 | −0.792503 | ||||||||
\(885\) | 2.02060e48 | 0.479641 | ||||||||
\(886\) | −4.30888e48 | −1.00394 | ||||||||
\(887\) | 5.58665e47 | 0.127765 | 0.0638824 | − | 0.997957i | \(-0.479652\pi\) | ||||
0.0638824 | + | 0.997957i | \(0.479652\pi\) | |||||||
\(888\) | 9.26996e47 | 0.208096 | ||||||||
\(889\) | 3.00418e47 | 0.0661984 | ||||||||
\(890\) | −2.16513e48 | −0.468326 | ||||||||
\(891\) | −3.19586e48 | −0.678588 | ||||||||
\(892\) | 1.01335e48 | 0.211222 | ||||||||
\(893\) | 3.75434e48 | 0.768217 | ||||||||
\(894\) | −1.45314e48 | −0.291903 | ||||||||
\(895\) | 1.13472e47 | 0.0223773 | ||||||||
\(896\) | −3.96004e47 | −0.0766686 | ||||||||
\(897\) | 1.12650e48 | 0.214120 | ||||||||
\(898\) | −4.58823e48 | −0.856220 | ||||||||
\(899\) | 6.03693e47 | 0.110607 | ||||||||
\(900\) | −4.88541e46 | −0.00878820 | ||||||||
\(901\) | 1.08182e49 | 1.91071 | ||||||||
\(902\) | −3.18531e48 | −0.552387 | ||||||||
\(903\) | 3.23612e48 | 0.551033 | ||||||||
\(904\) | 3.14704e48 | 0.526166 | ||||||||
\(905\) | 2.26942e48 | 0.372575 | ||||||||
\(906\) | −4.23433e47 | −0.0682605 | ||||||||
\(907\) | −1.20858e49 | −1.91318 | −0.956589 | − | 0.291441i | \(-0.905865\pi\) | ||||
−0.956589 | + | 0.291441i | \(0.905865\pi\) | |||||||
\(908\) | 1.67257e48 | 0.259997 | ||||||||
\(909\) | −8.47396e46 | −0.0129355 | ||||||||
\(910\) | −2.98856e48 | −0.448001 | ||||||||
\(911\) | 2.56704e48 | 0.377902 | 0.188951 | − | 0.981986i | \(-0.439491\pi\) | ||||
0.188951 | + | 0.981986i | \(0.439491\pi\) | |||||||
\(912\) | 1.60086e48 | 0.231439 | ||||||||
\(913\) | 5.82181e48 | 0.826590 | ||||||||
\(914\) | −2.67843e47 | −0.0373480 | ||||||||
\(915\) | 1.68735e48 | 0.231077 | ||||||||
\(916\) | −2.75972e48 | −0.371184 | ||||||||
\(917\) | 1.12847e49 | 1.49072 | ||||||||
\(918\) | −5.49504e48 | −0.712963 | ||||||||
\(919\) | −5.63209e47 | −0.0717734 | −0.0358867 | − | 0.999356i | \(-0.511426\pi\) | ||||
−0.0358867 | + | 0.999356i | \(0.511426\pi\) | |||||||
\(920\) | −1.73398e47 | −0.0217043 | ||||||||
\(921\) | 1.11675e49 | 1.37300 | ||||||||
\(922\) | 3.89285e48 | 0.470118 | ||||||||
\(923\) | −1.21831e49 | −1.44520 | ||||||||
\(924\) | 2.66719e48 | 0.310790 | ||||||||
\(925\) | −1.07684e48 | −0.123258 | ||||||||
\(926\) | 8.55860e48 | 0.962324 | ||||||||
\(927\) | −1.00093e48 | −0.110557 | ||||||||
\(928\) | 1.60086e47 | 0.0173704 | ||||||||
\(929\) | 3.29801e47 | 0.0351555 | 0.0175777 | − | 0.999845i | \(-0.494405\pi\) | ||||
0.0175777 | + | 0.999845i | \(0.494405\pi\) | |||||||
\(930\) | −3.24631e48 | −0.339954 | ||||||||
\(931\) | 2.33294e48 | 0.240012 | ||||||||
\(932\) | 4.28029e48 | 0.432624 | ||||||||
\(933\) | 1.35571e49 | 1.34623 | ||||||||
\(934\) | −2.40370e48 | −0.234507 | ||||||||
\(935\) | −3.39727e48 | −0.325640 | ||||||||
\(936\) | −5.38844e47 | −0.0507471 | ||||||||
\(937\) | −3.91522e48 | −0.362287 | −0.181144 | − | 0.983457i | \(-0.557980\pi\) | ||||
−0.181144 | + | 0.983457i | \(0.557980\pi\) | |||||||
\(938\) | 1.08178e49 | 0.983540 | ||||||||
\(939\) | −2.44467e48 | −0.218392 | ||||||||
\(940\) | −2.01886e48 | −0.177214 | ||||||||
\(941\) | 1.08951e49 | 0.939731 | 0.469866 | − | 0.882738i | \(-0.344302\pi\) | ||||
0.469866 | + | 0.882738i | \(0.344302\pi\) | |||||||
\(942\) | 7.82708e48 | 0.663376 | ||||||||
\(943\) | 1.71604e48 | 0.142918 | ||||||||
\(944\) | −3.43047e48 | −0.280747 | ||||||||
\(945\) | −5.01152e48 | −0.403037 | ||||||||
\(946\) | 4.46546e48 | 0.352909 | ||||||||
\(947\) | −1.05116e49 | −0.816382 | −0.408191 | − | 0.912897i | \(-0.633840\pi\) | ||||
−0.408191 | + | 0.912897i | \(0.633840\pi\) | |||||||
\(948\) | −2.10837e48 | −0.160920 | ||||||||
\(949\) | −2.89175e49 | −2.16904 | ||||||||
\(950\) | −1.85963e48 | −0.137084 | ||||||||
\(951\) | −1.91956e49 | −1.39067 | ||||||||
\(952\) | 4.17986e48 | 0.297613 | ||||||||
\(953\) | 1.01486e49 | 0.710190 | 0.355095 | − | 0.934830i | \(-0.384449\pi\) | ||||
0.355095 | + | 0.934830i | \(0.384449\pi\) | |||||||
\(954\) | 1.77891e48 | 0.122350 | ||||||||
\(955\) | −7.44292e47 | −0.0503138 | ||||||||
\(956\) | 8.87922e48 | 0.589956 | ||||||||
\(957\) | −1.07822e48 | −0.0704141 | ||||||||
\(958\) | 1.17403e49 | 0.753613 | ||||||||
\(959\) | 1.48044e49 | 0.934081 | ||||||||
\(960\) | −8.60847e47 | −0.0533888 | ||||||||
\(961\) | 4.38039e48 | 0.267040 | ||||||||
\(962\) | −1.18772e49 | −0.711746 | ||||||||
\(963\) | −1.46139e48 | −0.0860860 | ||||||||
\(964\) | −1.26700e49 | −0.733677 | ||||||||
\(965\) | −1.08538e49 | −0.617849 | ||||||||
\(966\) | −1.43692e48 | −0.0804097 | ||||||||
\(967\) | 7.23400e47 | 0.0397962 | 0.0198981 | − | 0.999802i | \(-0.493666\pi\) | ||||
0.0198981 | + | 0.999802i | \(0.493666\pi\) | |||||||
\(968\) | −2.85690e48 | −0.154508 | ||||||||
\(969\) | −1.68972e49 | −0.898404 | ||||||||
\(970\) | 1.46729e48 | 0.0766976 | ||||||||
\(971\) | 7.86578e47 | 0.0404226 | 0.0202113 | − | 0.999796i | \(-0.493566\pi\) | ||||
0.0202113 | + | 0.999796i | \(0.493566\pi\) | |||||||
\(972\) | −1.73418e48 | −0.0876196 | ||||||||
\(973\) | 1.87988e49 | 0.933832 | ||||||||
\(974\) | 1.86984e49 | 0.913233 | ||||||||
\(975\) | −6.49663e48 | −0.311969 | ||||||||
\(976\) | −2.86469e48 | −0.135256 | ||||||||
\(977\) | −2.61058e49 | −1.21193 | −0.605964 | − | 0.795492i | \(-0.707213\pi\) | ||||
−0.605964 | + | 0.795492i | \(0.707213\pi\) | |||||||
\(978\) | −7.52134e48 | −0.343324 | ||||||||
\(979\) | −2.47577e49 | −1.11121 | ||||||||
\(980\) | −1.25452e48 | −0.0553664 | ||||||||
\(981\) | −4.94391e47 | −0.0214552 | ||||||||
\(982\) | 1.25706e49 | 0.536433 | ||||||||
\(983\) | −7.33769e48 | −0.307912 | −0.153956 | − | 0.988078i | \(-0.549201\pi\) | ||||
−0.153956 | + | 0.988078i | \(0.549201\pi\) | |||||||
\(984\) | 8.51941e48 | 0.351553 | ||||||||
\(985\) | −1.85427e49 | −0.752446 | ||||||||
\(986\) | −1.68972e48 | −0.0674288 | ||||||||
\(987\) | −1.67299e49 | −0.656539 | ||||||||
\(988\) | −2.05110e49 | −0.791586 | ||||||||
\(989\) | −2.40571e48 | −0.0913071 | ||||||||
\(990\) | −5.58636e47 | −0.0208520 | ||||||||
\(991\) | −2.29393e49 | −0.842102 | −0.421051 | − | 0.907037i | \(-0.638339\pi\) | ||||
−0.421051 | + | 0.907037i | \(0.638339\pi\) | |||||||
\(992\) | 5.51141e48 | 0.198985 | ||||||||
\(993\) | −8.00902e48 | −0.284391 | ||||||||
\(994\) | 1.55402e49 | 0.542726 | ||||||||
\(995\) | 2.43145e49 | 0.835188 | ||||||||
\(996\) | −1.55710e49 | −0.526063 | ||||||||
\(997\) | 1.96710e49 | 0.653665 | 0.326833 | − | 0.945082i | \(-0.394019\pi\) | ||||
0.326833 | + | 0.945082i | \(0.394019\pi\) | |||||||
\(998\) | 1.96104e49 | 0.640961 | ||||||||
\(999\) | −1.99169e49 | −0.640311 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 10.34.a.a.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.34.a.a.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial |