Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,32,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, 32, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 32);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 32 \) |
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: | \(60.8771328190\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{337159}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 337159 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(580.654\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −32768.0 | −0.707107 | ||||||||
\(3\) | 1.82748e7 | 0.735313 | 0.367656 | − | 0.929962i | \(-0.380160\pi\) | ||||
0.367656 | + | 0.929962i | \(0.380160\pi\) | |||||||
\(4\) | 1.07374e9 | 0.500000 | ||||||||
\(5\) | −3.05176e10 | −0.447214 | ||||||||
\(6\) | −5.98827e11 | −0.519945 | ||||||||
\(7\) | −9.80486e12 | −0.780587 | −0.390294 | − | 0.920690i | \(-0.627627\pi\) | ||||
−0.390294 | + | 0.920690i | \(0.627627\pi\) | |||||||
\(8\) | −3.51844e13 | −0.353553 | ||||||||
\(9\) | −2.83707e14 | −0.459315 | ||||||||
\(10\) | 1.00000e15 | 0.316228 | ||||||||
\(11\) | −2.50417e16 | −1.80750 | −0.903749 | − | 0.428063i | \(-0.859196\pi\) | ||||
−0.903749 | + | 0.428063i | \(0.859196\pi\) | |||||||
\(12\) | 1.96224e16 | 0.367656 | ||||||||
\(13\) | −5.10202e16 | −0.276453 | −0.138226 | − | 0.990401i | \(-0.544140\pi\) | ||||
−0.138226 | + | 0.990401i | \(0.544140\pi\) | |||||||
\(14\) | 3.21285e17 | 0.551959 | ||||||||
\(15\) | −5.57701e17 | −0.328842 | ||||||||
\(16\) | 1.15292e18 | 0.250000 | ||||||||
\(17\) | 5.39972e17 | 0.0457523 | 0.0228762 | − | 0.999738i | \(-0.492718\pi\) | ||||
0.0228762 | + | 0.999738i | \(0.492718\pi\) | |||||||
\(18\) | 9.29650e18 | 0.324785 | ||||||||
\(19\) | 8.95940e19 | 1.35394 | 0.676968 | − | 0.736012i | \(-0.263293\pi\) | ||||
0.676968 | + | 0.736012i | \(0.263293\pi\) | |||||||
\(20\) | −3.27680e19 | −0.223607 | ||||||||
\(21\) | −1.79181e20 | −0.573976 | ||||||||
\(22\) | 8.20567e20 | 1.27809 | ||||||||
\(23\) | 3.91328e20 | 0.306026 | 0.153013 | − | 0.988224i | \(-0.451102\pi\) | ||||
0.153013 | + | 0.988224i | \(0.451102\pi\) | |||||||
\(24\) | −6.42986e20 | −0.259972 | ||||||||
\(25\) | 9.31323e20 | 0.200000 | ||||||||
\(26\) | 1.67183e21 | 0.195481 | ||||||||
\(27\) | −1.64725e22 | −1.07305 | ||||||||
\(28\) | −1.05279e22 | −0.390294 | ||||||||
\(29\) | 7.65729e22 | 1.64781 | 0.823903 | − | 0.566731i | \(-0.191792\pi\) | ||||
0.823903 | + | 0.566731i | \(0.191792\pi\) | |||||||
\(30\) | 1.82748e22 | 0.232526 | ||||||||
\(31\) | −1.67730e23 | −1.28382 | −0.641912 | − | 0.766778i | \(-0.721858\pi\) | ||||
−0.641912 | + | 0.766778i | \(0.721858\pi\) | |||||||
\(32\) | −3.77789e22 | −0.176777 | ||||||||
\(33\) | −4.57632e23 | −1.32908 | ||||||||
\(34\) | −1.76938e22 | −0.0323518 | ||||||||
\(35\) | 2.99220e23 | 0.349089 | ||||||||
\(36\) | −3.04628e23 | −0.229657 | ||||||||
\(37\) | −2.35029e24 | −1.15876 | −0.579382 | − | 0.815056i | \(-0.696706\pi\) | ||||
−0.579382 | + | 0.815056i | \(0.696706\pi\) | |||||||
\(38\) | −2.93582e24 | −0.957378 | ||||||||
\(39\) | −9.32383e23 | −0.203279 | ||||||||
\(40\) | 1.07374e24 | 0.158114 | ||||||||
\(41\) | 4.23536e24 | 0.425344 | 0.212672 | − | 0.977124i | \(-0.431783\pi\) | ||||
0.212672 | + | 0.977124i | \(0.431783\pi\) | |||||||
\(42\) | 5.87142e24 | 0.405862 | ||||||||
\(43\) | 2.21121e25 | 1.06138 | 0.530688 | − | 0.847567i | \(-0.321934\pi\) | ||||
0.530688 | + | 0.847567i | \(0.321934\pi\) | |||||||
\(44\) | −2.68884e25 | −0.903749 | ||||||||
\(45\) | 8.65804e24 | 0.205412 | ||||||||
\(46\) | −1.28230e25 | −0.216393 | ||||||||
\(47\) | 9.02140e25 | 1.09083 | 0.545415 | − | 0.838166i | \(-0.316372\pi\) | ||||
0.545415 | + | 0.838166i | \(0.316372\pi\) | |||||||
\(48\) | 2.10694e25 | 0.183828 | ||||||||
\(49\) | −6.16402e25 | −0.390683 | ||||||||
\(50\) | −3.05176e25 | −0.141421 | ||||||||
\(51\) | 9.86786e24 | 0.0336423 | ||||||||
\(52\) | −5.47826e25 | −0.138226 | ||||||||
\(53\) | 8.66817e25 | 0.162799 | 0.0813994 | − | 0.996682i | \(-0.474061\pi\) | ||||
0.0813994 | + | 0.996682i | \(0.474061\pi\) | |||||||
\(54\) | 5.39771e26 | 0.758763 | ||||||||
\(55\) | 7.64213e26 | 0.808337 | ||||||||
\(56\) | 3.44978e26 | 0.275979 | ||||||||
\(57\) | 1.63731e27 | 0.995567 | ||||||||
\(58\) | −2.50914e27 | −1.16517 | ||||||||
\(59\) | 3.37162e27 | 1.20125 | 0.600624 | − | 0.799532i | \(-0.294919\pi\) | ||||
0.600624 | + | 0.799532i | \(0.294919\pi\) | |||||||
\(60\) | −5.98827e26 | −0.164421 | ||||||||
\(61\) | −3.72439e27 | −0.791485 | −0.395742 | − | 0.918362i | \(-0.629513\pi\) | ||||
−0.395742 | + | 0.918362i | \(0.629513\pi\) | |||||||
\(62\) | 5.49619e27 | 0.907800 | ||||||||
\(63\) | 2.78170e27 | 0.358535 | ||||||||
\(64\) | 1.23794e27 | 0.125000 | ||||||||
\(65\) | 1.55701e27 | 0.123633 | ||||||||
\(66\) | 1.49957e28 | 0.939799 | ||||||||
\(67\) | −1.08156e28 | −0.536900 | −0.268450 | − | 0.963294i | \(-0.586511\pi\) | ||||
−0.268450 | + | 0.963294i | \(0.586511\pi\) | |||||||
\(68\) | 5.79791e26 | 0.0228762 | ||||||||
\(69\) | 7.15142e27 | 0.225025 | ||||||||
\(70\) | −9.80486e27 | −0.246843 | ||||||||
\(71\) | 3.01084e28 | 0.608393 | 0.304196 | − | 0.952609i | \(-0.401612\pi\) | ||||
0.304196 | + | 0.952609i | \(0.401612\pi\) | |||||||
\(72\) | 9.98204e27 | 0.162392 | ||||||||
\(73\) | 1.41961e29 | 1.86494 | 0.932471 | − | 0.361246i | \(-0.117648\pi\) | ||||
0.932471 | + | 0.361246i | \(0.117648\pi\) | |||||||
\(74\) | 7.70144e28 | 0.819370 | ||||||||
\(75\) | 1.70197e28 | 0.147063 | ||||||||
\(76\) | 9.62009e28 | 0.676968 | ||||||||
\(77\) | 2.45531e29 | 1.41091 | ||||||||
\(78\) | 3.05523e28 | 0.143740 | ||||||||
\(79\) | 4.24928e29 | 1.64095 | 0.820475 | − | 0.571682i | \(-0.193709\pi\) | ||||
0.820475 | + | 0.571682i | \(0.193709\pi\) | |||||||
\(80\) | −3.51844e28 | −0.111803 | ||||||||
\(81\) | −1.25793e29 | −0.329715 | ||||||||
\(82\) | −1.38784e29 | −0.300764 | ||||||||
\(83\) | −2.61223e29 | −0.469138 | −0.234569 | − | 0.972099i | \(-0.575368\pi\) | ||||
−0.234569 | + | 0.972099i | \(0.575368\pi\) | |||||||
\(84\) | −1.92395e29 | −0.286988 | ||||||||
\(85\) | −1.64786e28 | −0.0204611 | ||||||||
\(86\) | −7.24570e29 | −0.750506 | ||||||||
\(87\) | 1.39935e30 | 1.21165 | ||||||||
\(88\) | 8.81077e29 | 0.639047 | ||||||||
\(89\) | −1.92566e30 | −1.17229 | −0.586144 | − | 0.810207i | \(-0.699355\pi\) | ||||
−0.586144 | + | 0.810207i | \(0.699355\pi\) | |||||||
\(90\) | −2.83707e29 | −0.145248 | ||||||||
\(91\) | 5.00246e29 | 0.215795 | ||||||||
\(92\) | 4.20185e29 | 0.153013 | ||||||||
\(93\) | −3.06523e30 | −0.944012 | ||||||||
\(94\) | −2.95613e30 | −0.771333 | ||||||||
\(95\) | −2.73419e30 | −0.605499 | ||||||||
\(96\) | −6.90401e29 | −0.129986 | ||||||||
\(97\) | −1.19769e30 | −0.192035 | −0.0960177 | − | 0.995380i | \(-0.530611\pi\) | ||||
−0.0960177 | + | 0.995380i | \(0.530611\pi\) | |||||||
\(98\) | 2.01983e30 | 0.276255 | ||||||||
\(99\) | 7.10450e30 | 0.830210 | ||||||||
\(100\) | 1.00000e30 | 0.100000 | ||||||||
\(101\) | −1.82554e30 | −0.156462 | −0.0782311 | − | 0.996935i | \(-0.524927\pi\) | ||||
−0.0782311 | + | 0.996935i | \(0.524927\pi\) | |||||||
\(102\) | −3.23350e29 | −0.0237887 | ||||||||
\(103\) | −3.09796e31 | −1.95929 | −0.979644 | − | 0.200744i | \(-0.935664\pi\) | ||||
−0.979644 | + | 0.200744i | \(0.935664\pi\) | |||||||
\(104\) | 1.79512e30 | 0.0977407 | ||||||||
\(105\) | 5.46818e30 | 0.256690 | ||||||||
\(106\) | −2.84038e30 | −0.115116 | ||||||||
\(107\) | −7.75249e30 | −0.271639 | −0.135820 | − | 0.990734i | \(-0.543367\pi\) | ||||
−0.135820 | + | 0.990734i | \(0.543367\pi\) | |||||||
\(108\) | −1.76872e31 | −0.536527 | ||||||||
\(109\) | 2.74905e31 | 0.722890 | 0.361445 | − | 0.932393i | \(-0.382284\pi\) | ||||
0.361445 | + | 0.932393i | \(0.382284\pi\) | |||||||
\(110\) | −2.50417e31 | −0.571581 | ||||||||
\(111\) | −4.29510e31 | −0.852055 | ||||||||
\(112\) | −1.13042e31 | −0.195147 | ||||||||
\(113\) | 3.04360e31 | 0.457796 | 0.228898 | − | 0.973450i | \(-0.426488\pi\) | ||||
0.228898 | + | 0.973450i | \(0.426488\pi\) | |||||||
\(114\) | −5.36514e31 | −0.703972 | ||||||||
\(115\) | −1.19424e31 | −0.136859 | ||||||||
\(116\) | 8.22195e31 | 0.823903 | ||||||||
\(117\) | 1.44748e31 | 0.126979 | ||||||||
\(118\) | −1.10481e32 | −0.849410 | ||||||||
\(119\) | −5.29435e30 | −0.0357137 | ||||||||
\(120\) | 1.96224e31 | 0.116263 | ||||||||
\(121\) | 4.35145e32 | 2.26705 | ||||||||
\(122\) | 1.22041e32 | 0.559664 | ||||||||
\(123\) | 7.74002e31 | 0.312761 | ||||||||
\(124\) | −1.80099e32 | −0.641912 | ||||||||
\(125\) | −2.84217e31 | −0.0894427 | ||||||||
\(126\) | −9.11508e31 | −0.253523 | ||||||||
\(127\) | 5.99688e32 | 1.47560 | 0.737798 | − | 0.675021i | \(-0.235865\pi\) | ||||
0.737798 | + | 0.675021i | \(0.235865\pi\) | |||||||
\(128\) | −4.05648e31 | −0.0883883 | ||||||||
\(129\) | 4.04094e32 | 0.780444 | ||||||||
\(130\) | −5.10202e31 | −0.0874220 | ||||||||
\(131\) | 8.06361e32 | 1.22694 | 0.613471 | − | 0.789717i | \(-0.289773\pi\) | ||||
0.613471 | + | 0.789717i | \(0.289773\pi\) | |||||||
\(132\) | −4.91378e32 | −0.664538 | ||||||||
\(133\) | −8.78457e32 | −1.05687 | ||||||||
\(134\) | 3.54407e32 | 0.379645 | ||||||||
\(135\) | 5.02701e32 | 0.479884 | ||||||||
\(136\) | −1.89986e31 | −0.0161759 | ||||||||
\(137\) | 1.25859e33 | 0.956566 | 0.478283 | − | 0.878206i | \(-0.341259\pi\) | ||||
0.478283 | + | 0.878206i | \(0.341259\pi\) | |||||||
\(138\) | −2.34338e32 | −0.159117 | ||||||||
\(139\) | −1.28760e33 | −0.781721 | −0.390861 | − | 0.920450i | \(-0.627823\pi\) | ||||
−0.390861 | + | 0.920450i | \(0.627823\pi\) | |||||||
\(140\) | 3.21285e32 | 0.174545 | ||||||||
\(141\) | 1.64864e33 | 0.802102 | ||||||||
\(142\) | −9.86593e32 | −0.430198 | ||||||||
\(143\) | 1.27764e33 | 0.499687 | ||||||||
\(144\) | −3.27091e32 | −0.114829 | ||||||||
\(145\) | −2.33682e33 | −0.736921 | ||||||||
\(146\) | −4.65178e33 | −1.31871 | ||||||||
\(147\) | −1.12646e33 | −0.287274 | ||||||||
\(148\) | −2.52361e33 | −0.579382 | ||||||||
\(149\) | −4.23721e31 | −0.00876380 | −0.00438190 | − | 0.999990i | \(-0.501395\pi\) | ||||
−0.00438190 | + | 0.999990i | \(0.501395\pi\) | |||||||
\(150\) | −5.57701e32 | −0.103989 | ||||||||
\(151\) | −7.07794e33 | −1.19060 | −0.595298 | − | 0.803505i | \(-0.702966\pi\) | ||||
−0.595298 | + | 0.803505i | \(0.702966\pi\) | |||||||
\(152\) | −3.15231e33 | −0.478689 | ||||||||
\(153\) | −1.53194e32 | −0.0210147 | ||||||||
\(154\) | −8.04554e33 | −0.997664 | ||||||||
\(155\) | 5.11872e33 | 0.574143 | ||||||||
\(156\) | −1.00114e33 | −0.101640 | ||||||||
\(157\) | 1.32372e34 | 1.21717 | 0.608583 | − | 0.793490i | \(-0.291738\pi\) | ||||
0.608583 | + | 0.793490i | \(0.291738\pi\) | |||||||
\(158\) | −1.39240e34 | −1.16033 | ||||||||
\(159\) | 1.58409e33 | 0.119708 | ||||||||
\(160\) | 1.15292e33 | 0.0790569 | ||||||||
\(161\) | −3.83691e33 | −0.238880 | ||||||||
\(162\) | 4.12199e33 | 0.233144 | ||||||||
\(163\) | 1.78685e34 | 0.918715 | 0.459358 | − | 0.888251i | \(-0.348080\pi\) | ||||
0.459358 | + | 0.888251i | \(0.348080\pi\) | |||||||
\(164\) | 4.54768e33 | 0.212672 | ||||||||
\(165\) | 1.39658e34 | 0.594381 | ||||||||
\(166\) | 8.55975e33 | 0.331731 | ||||||||
\(167\) | 1.88144e34 | 0.664331 | 0.332165 | − | 0.943221i | \(-0.392221\pi\) | ||||
0.332165 | + | 0.943221i | \(0.392221\pi\) | |||||||
\(168\) | 6.30438e33 | 0.202931 | ||||||||
\(169\) | −3.14569e34 | −0.923574 | ||||||||
\(170\) | 5.39972e32 | 0.0144682 | ||||||||
\(171\) | −2.54184e34 | −0.621883 | ||||||||
\(172\) | 2.37427e34 | 0.530688 | ||||||||
\(173\) | 3.38111e34 | 0.690789 | 0.345394 | − | 0.938458i | \(-0.387745\pi\) | ||||
0.345394 | + | 0.938458i | \(0.387745\pi\) | |||||||
\(174\) | −4.58539e34 | −0.856768 | ||||||||
\(175\) | −9.13148e33 | −0.156117 | ||||||||
\(176\) | −2.88711e34 | −0.451874 | ||||||||
\(177\) | 6.16155e34 | 0.883293 | ||||||||
\(178\) | 6.31000e34 | 0.828932 | ||||||||
\(179\) | −2.41562e34 | −0.290942 | −0.145471 | − | 0.989362i | \(-0.546470\pi\) | ||||
−0.145471 | + | 0.989362i | \(0.546470\pi\) | |||||||
\(180\) | 9.29650e33 | 0.102706 | ||||||||
\(181\) | 3.12629e34 | 0.316965 | 0.158482 | − | 0.987362i | \(-0.449340\pi\) | ||||
0.158482 | + | 0.987362i | \(0.449340\pi\) | |||||||
\(182\) | −1.63921e34 | −0.152590 | ||||||||
\(183\) | −6.80623e34 | −0.581989 | ||||||||
\(184\) | −1.37686e34 | −0.108197 | ||||||||
\(185\) | 7.17253e34 | 0.518215 | ||||||||
\(186\) | 1.00442e35 | 0.667517 | ||||||||
\(187\) | −1.35218e34 | −0.0826972 | ||||||||
\(188\) | 9.68666e34 | 0.545415 | ||||||||
\(189\) | 1.61510e35 | 0.837612 | ||||||||
\(190\) | 8.95940e34 | 0.428152 | ||||||||
\(191\) | −5.87939e33 | −0.0259009 | −0.0129504 | − | 0.999916i | \(-0.504122\pi\) | ||||
−0.0129504 | + | 0.999916i | \(0.504122\pi\) | |||||||
\(192\) | 2.26231e34 | 0.0919141 | ||||||||
\(193\) | −2.74156e35 | −1.02768 | −0.513841 | − | 0.857885i | \(-0.671778\pi\) | ||||
−0.513841 | + | 0.857885i | \(0.671778\pi\) | |||||||
\(194\) | 3.92458e34 | 0.135790 | ||||||||
\(195\) | 2.84541e34 | 0.0909092 | ||||||||
\(196\) | −6.61857e34 | −0.195342 | ||||||||
\(197\) | 2.83335e35 | 0.772812 | 0.386406 | − | 0.922329i | \(-0.373716\pi\) | ||||
0.386406 | + | 0.922329i | \(0.373716\pi\) | |||||||
\(198\) | −2.32800e35 | −0.587047 | ||||||||
\(199\) | −5.63487e35 | −1.31420 | −0.657100 | − | 0.753803i | \(-0.728217\pi\) | ||||
−0.657100 | + | 0.753803i | \(0.728217\pi\) | |||||||
\(200\) | −3.27680e34 | −0.0707107 | ||||||||
\(201\) | −1.97653e35 | −0.394789 | ||||||||
\(202\) | 5.98192e34 | 0.110636 | ||||||||
\(203\) | −7.50786e35 | −1.28626 | ||||||||
\(204\) | 1.05955e34 | 0.0168211 | ||||||||
\(205\) | −1.29253e35 | −0.190220 | ||||||||
\(206\) | 1.01514e36 | 1.38543 | ||||||||
\(207\) | −1.11022e35 | −0.140562 | ||||||||
\(208\) | −5.88223e34 | −0.0691131 | ||||||||
\(209\) | −2.24359e36 | −2.44724 | ||||||||
\(210\) | −1.79181e35 | −0.181507 | ||||||||
\(211\) | −1.37274e36 | −1.29184 | −0.645920 | − | 0.763405i | \(-0.723526\pi\) | ||||
−0.645920 | + | 0.763405i | \(0.723526\pi\) | |||||||
\(212\) | 9.30737e34 | 0.0813994 | ||||||||
\(213\) | 5.50225e35 | 0.447359 | ||||||||
\(214\) | 2.54034e35 | 0.192078 | ||||||||
\(215\) | −6.74809e35 | −0.474662 | ||||||||
\(216\) | 5.79575e35 | 0.379382 | ||||||||
\(217\) | 1.64457e36 | 1.00214 | ||||||||
\(218\) | −9.00809e35 | −0.511160 | ||||||||
\(219\) | 2.59431e36 | 1.37132 | ||||||||
\(220\) | 8.20567e35 | 0.404169 | ||||||||
\(221\) | −2.75495e34 | −0.0126483 | ||||||||
\(222\) | 1.40742e36 | 0.602494 | ||||||||
\(223\) | 5.24242e34 | 0.0209318 | 0.0104659 | − | 0.999945i | \(-0.496669\pi\) | ||||
0.0104659 | + | 0.999945i | \(0.496669\pi\) | |||||||
\(224\) | 3.70417e35 | 0.137990 | ||||||||
\(225\) | −2.64222e35 | −0.0918630 | ||||||||
\(226\) | −9.97327e35 | −0.323710 | ||||||||
\(227\) | −2.30435e36 | −0.698471 | −0.349235 | − | 0.937035i | \(-0.613559\pi\) | ||||
−0.349235 | + | 0.937035i | \(0.613559\pi\) | |||||||
\(228\) | 1.75805e36 | 0.497784 | ||||||||
\(229\) | 3.22039e36 | 0.852037 | 0.426019 | − | 0.904714i | \(-0.359916\pi\) | ||||
0.426019 | + | 0.904714i | \(0.359916\pi\) | |||||||
\(230\) | 3.91328e35 | 0.0967740 | ||||||||
\(231\) | 4.48701e36 | 1.03746 | ||||||||
\(232\) | −2.69417e36 | −0.582587 | ||||||||
\(233\) | 3.35115e36 | 0.677917 | 0.338959 | − | 0.940801i | \(-0.389925\pi\) | ||||
0.338959 | + | 0.940801i | \(0.389925\pi\) | |||||||
\(234\) | −4.74310e35 | −0.0897875 | ||||||||
\(235\) | −2.75311e36 | −0.487834 | ||||||||
\(236\) | 3.62025e36 | 0.600624 | ||||||||
\(237\) | 7.76546e36 | 1.20661 | ||||||||
\(238\) | 1.73485e35 | 0.0252534 | ||||||||
\(239\) | 5.41220e36 | 0.738255 | 0.369127 | − | 0.929379i | \(-0.379657\pi\) | ||||
0.369127 | + | 0.929379i | \(0.379657\pi\) | |||||||
\(240\) | −6.42986e35 | −0.0822105 | ||||||||
\(241\) | −3.64065e36 | −0.436430 | −0.218215 | − | 0.975901i | \(-0.570023\pi\) | ||||
−0.218215 | + | 0.975901i | \(0.570023\pi\) | |||||||
\(242\) | −1.42588e37 | −1.60304 | ||||||||
\(243\) | 7.87579e36 | 0.830609 | ||||||||
\(244\) | −3.99903e36 | −0.395742 | ||||||||
\(245\) | 1.88111e36 | 0.174719 | ||||||||
\(246\) | −2.53625e36 | −0.221155 | ||||||||
\(247\) | −4.57111e36 | −0.374299 | ||||||||
\(248\) | 5.90149e36 | 0.453900 | ||||||||
\(249\) | −4.77379e36 | −0.344963 | ||||||||
\(250\) | 9.31323e35 | 0.0632456 | ||||||||
\(251\) | −6.60375e36 | −0.421549 | −0.210774 | − | 0.977535i | \(-0.567599\pi\) | ||||
−0.210774 | + | 0.977535i | \(0.567599\pi\) | |||||||
\(252\) | 2.98683e36 | 0.179268 | ||||||||
\(253\) | −9.79952e36 | −0.553142 | ||||||||
\(254\) | −1.96506e37 | −1.04340 | ||||||||
\(255\) | −3.01143e35 | −0.0150453 | ||||||||
\(256\) | 1.32923e36 | 0.0625000 | ||||||||
\(257\) | −1.70943e37 | −0.756638 | −0.378319 | − | 0.925675i | \(-0.623498\pi\) | ||||
−0.378319 | + | 0.925675i | \(0.623498\pi\) | |||||||
\(258\) | −1.32413e37 | −0.551857 | ||||||||
\(259\) | 2.30443e37 | 0.904517 | ||||||||
\(260\) | 1.67183e36 | 0.0618167 | ||||||||
\(261\) | −2.17242e37 | −0.756862 | ||||||||
\(262\) | −2.64228e37 | −0.867580 | ||||||||
\(263\) | 6.06914e37 | 1.87851 | 0.939254 | − | 0.343224i | \(-0.111519\pi\) | ||||
0.939254 | + | 0.343224i | \(0.111519\pi\) | |||||||
\(264\) | 1.61015e37 | 0.469899 | ||||||||
\(265\) | −2.64531e36 | −0.0728058 | ||||||||
\(266\) | 2.87853e37 | 0.747317 | ||||||||
\(267\) | −3.51909e37 | −0.861998 | ||||||||
\(268\) | −1.16132e37 | −0.268450 | ||||||||
\(269\) | −4.69833e37 | −1.02514 | −0.512570 | − | 0.858646i | \(-0.671306\pi\) | ||||
−0.512570 | + | 0.858646i | \(0.671306\pi\) | |||||||
\(270\) | −1.64725e37 | −0.339329 | ||||||||
\(271\) | −2.99460e37 | −0.582526 | −0.291263 | − | 0.956643i | \(-0.594075\pi\) | ||||
−0.291263 | + | 0.956643i | \(0.594075\pi\) | |||||||
\(272\) | 6.22546e35 | 0.0114381 | ||||||||
\(273\) | 9.14188e36 | 0.158677 | ||||||||
\(274\) | −4.12414e37 | −0.676394 | ||||||||
\(275\) | −2.33219e37 | −0.361499 | ||||||||
\(276\) | 7.67877e36 | 0.112513 | ||||||||
\(277\) | 7.82408e37 | 1.08392 | 0.541960 | − | 0.840404i | \(-0.317682\pi\) | ||||
0.541960 | + | 0.840404i | \(0.317682\pi\) | |||||||
\(278\) | 4.21921e37 | 0.552760 | ||||||||
\(279\) | 4.75862e37 | 0.589679 | ||||||||
\(280\) | −1.05279e37 | −0.123422 | ||||||||
\(281\) | 1.79861e38 | 1.99522 | 0.997608 | − | 0.0691186i | \(-0.0220187\pi\) | ||||
0.997608 | + | 0.0691186i | \(0.0220187\pi\) | |||||||
\(282\) | −5.40226e37 | −0.567172 | ||||||||
\(283\) | 1.02428e38 | 1.01796 | 0.508979 | − | 0.860779i | \(-0.330023\pi\) | ||||
0.508979 | + | 0.860779i | \(0.330023\pi\) | |||||||
\(284\) | 3.23287e37 | 0.304196 | ||||||||
\(285\) | −4.99667e37 | −0.445231 | ||||||||
\(286\) | −4.18655e37 | −0.353332 | ||||||||
\(287\) | −4.15271e37 | −0.332018 | ||||||||
\(288\) | 1.07181e37 | 0.0811962 | ||||||||
\(289\) | −1.38997e38 | −0.997907 | ||||||||
\(290\) | 7.65729e37 | 0.521082 | ||||||||
\(291\) | −2.18874e37 | −0.141206 | ||||||||
\(292\) | 1.52430e38 | 0.932471 | ||||||||
\(293\) | −2.65665e38 | −1.54129 | −0.770647 | − | 0.637262i | \(-0.780067\pi\) | ||||
−0.770647 | + | 0.637262i | \(0.780067\pi\) | |||||||
\(294\) | 3.69118e37 | 0.203134 | ||||||||
\(295\) | −1.02894e38 | −0.537214 | ||||||||
\(296\) | 8.26936e37 | 0.409685 | ||||||||
\(297\) | 4.12500e38 | 1.93954 | ||||||||
\(298\) | 1.38845e36 | 0.00619694 | ||||||||
\(299\) | −1.99656e37 | −0.0846018 | ||||||||
\(300\) | 1.82748e37 | 0.0735313 | ||||||||
\(301\) | −2.16806e38 | −0.828497 | ||||||||
\(302\) | 2.31930e38 | 0.841879 | ||||||||
\(303\) | −3.33613e37 | −0.115049 | ||||||||
\(304\) | 1.03295e38 | 0.338484 | ||||||||
\(305\) | 1.13659e38 | 0.353963 | ||||||||
\(306\) | 5.01985e36 | 0.0148597 | ||||||||
\(307\) | −1.23731e38 | −0.348204 | −0.174102 | − | 0.984728i | \(-0.555702\pi\) | ||||
−0.174102 | + | 0.984728i | \(0.555702\pi\) | |||||||
\(308\) | 2.63636e38 | 0.705455 | ||||||||
\(309\) | −5.66144e38 | −1.44069 | ||||||||
\(310\) | −1.67730e38 | −0.405981 | ||||||||
\(311\) | 7.02325e38 | 1.61716 | 0.808579 | − | 0.588388i | \(-0.200237\pi\) | ||||
0.808579 | + | 0.588388i | \(0.200237\pi\) | |||||||
\(312\) | 3.28053e37 | 0.0718700 | ||||||||
\(313\) | 6.10426e38 | 1.27261 | 0.636306 | − | 0.771437i | \(-0.280462\pi\) | ||||
0.636306 | + | 0.771437i | \(0.280462\pi\) | |||||||
\(314\) | −4.33755e38 | −0.860667 | ||||||||
\(315\) | −8.48908e37 | −0.160342 | ||||||||
\(316\) | 4.56263e38 | 0.820475 | ||||||||
\(317\) | −5.90092e38 | −1.01042 | −0.505209 | − | 0.862997i | \(-0.668585\pi\) | ||||
−0.505209 | + | 0.862997i | \(0.668585\pi\) | |||||||
\(318\) | −5.19073e37 | −0.0846464 | ||||||||
\(319\) | −1.91752e39 | −2.97840 | ||||||||
\(320\) | −3.77789e37 | −0.0559017 | ||||||||
\(321\) | −1.41675e38 | −0.199740 | ||||||||
\(322\) | 1.25728e38 | 0.168914 | ||||||||
\(323\) | 4.83783e37 | 0.0619457 | ||||||||
\(324\) | −1.35069e38 | −0.164858 | ||||||||
\(325\) | −4.75163e37 | −0.0552905 | ||||||||
\(326\) | −5.85516e38 | −0.649630 | ||||||||
\(327\) | 5.02383e38 | 0.531550 | ||||||||
\(328\) | −1.49018e38 | −0.150382 | ||||||||
\(329\) | −8.84535e38 | −0.851488 | ||||||||
\(330\) | −4.57632e38 | −0.420291 | ||||||||
\(331\) | −1.26563e39 | −1.10910 | −0.554552 | − | 0.832149i | \(-0.687110\pi\) | ||||
−0.554552 | + | 0.832149i | \(0.687110\pi\) | |||||||
\(332\) | −2.80486e38 | −0.234569 | ||||||||
\(333\) | 6.66794e38 | 0.532238 | ||||||||
\(334\) | −6.16509e38 | −0.469753 | ||||||||
\(335\) | 3.30067e38 | 0.240109 | ||||||||
\(336\) | −2.06582e38 | −0.143494 | ||||||||
\(337\) | −1.15260e39 | −0.764565 | −0.382283 | − | 0.924045i | \(-0.624862\pi\) | ||||
−0.382283 | + | 0.924045i | \(0.624862\pi\) | |||||||
\(338\) | 1.03078e39 | 0.653065 | ||||||||
\(339\) | 5.56211e38 | 0.336623 | ||||||||
\(340\) | −1.76938e37 | −0.0102305 | ||||||||
\(341\) | 4.20026e39 | 2.32051 | ||||||||
\(342\) | 8.32911e38 | 0.439738 | ||||||||
\(343\) | 2.15134e39 | 1.08555 | ||||||||
\(344\) | −7.78001e38 | −0.375253 | ||||||||
\(345\) | −2.18244e38 | −0.100634 | ||||||||
\(346\) | −1.10792e39 | −0.488461 | ||||||||
\(347\) | 3.25921e39 | 1.37406 | 0.687029 | − | 0.726630i | \(-0.258914\pi\) | ||||
0.687029 | + | 0.726630i | \(0.258914\pi\) | |||||||
\(348\) | 1.50254e39 | 0.605826 | ||||||||
\(349\) | 6.30486e37 | 0.0243154 | 0.0121577 | − | 0.999926i | \(-0.496130\pi\) | ||||
0.0121577 | + | 0.999926i | \(0.496130\pi\) | |||||||
\(350\) | 2.99220e38 | 0.110392 | ||||||||
\(351\) | 8.40431e38 | 0.296648 | ||||||||
\(352\) | 9.46050e38 | 0.319523 | ||||||||
\(353\) | 4.15083e39 | 1.34161 | 0.670807 | − | 0.741632i | \(-0.265948\pi\) | ||||
0.670807 | + | 0.741632i | \(0.265948\pi\) | |||||||
\(354\) | −2.01902e39 | −0.624582 | ||||||||
\(355\) | −9.18837e38 | −0.272081 | ||||||||
\(356\) | −2.06766e39 | −0.586144 | ||||||||
\(357\) | −9.67530e37 | −0.0262607 | ||||||||
\(358\) | 7.91551e38 | 0.205727 | ||||||||
\(359\) | −7.62845e39 | −1.89877 | −0.949385 | − | 0.314114i | \(-0.898293\pi\) | ||||
−0.949385 | + | 0.314114i | \(0.898293\pi\) | |||||||
\(360\) | −3.04628e38 | −0.0726241 | ||||||||
\(361\) | 3.64823e39 | 0.833144 | ||||||||
\(362\) | −1.02442e39 | −0.224128 | ||||||||
\(363\) | 7.95217e39 | 1.66699 | ||||||||
\(364\) | 5.37135e38 | 0.107898 | ||||||||
\(365\) | −4.33231e39 | −0.834027 | ||||||||
\(366\) | 2.23027e39 | 0.411528 | ||||||||
\(367\) | −4.70956e38 | −0.0833021 | −0.0416510 | − | 0.999132i | \(-0.513262\pi\) | ||||
−0.0416510 | + | 0.999132i | \(0.513262\pi\) | |||||||
\(368\) | 4.51170e38 | 0.0765066 | ||||||||
\(369\) | −1.20160e39 | −0.195367 | ||||||||
\(370\) | −2.35029e39 | −0.366434 | ||||||||
\(371\) | −8.49901e38 | −0.127079 | ||||||||
\(372\) | −3.29127e39 | −0.472006 | ||||||||
\(373\) | 5.24767e38 | 0.0721904 | 0.0360952 | − | 0.999348i | \(-0.488508\pi\) | ||||
0.0360952 | + | 0.999348i | \(0.488508\pi\) | |||||||
\(374\) | 4.43084e38 | 0.0584757 | ||||||||
\(375\) | −5.19400e38 | −0.0657684 | ||||||||
\(376\) | −3.17412e39 | −0.385667 | ||||||||
\(377\) | −3.90677e39 | −0.455540 | ||||||||
\(378\) | −5.29238e39 | −0.592281 | ||||||||
\(379\) | −4.30594e39 | −0.462551 | −0.231276 | − | 0.972888i | \(-0.574290\pi\) | ||||
−0.231276 | + | 0.972888i | \(0.574290\pi\) | |||||||
\(380\) | −2.93582e39 | −0.302749 | ||||||||
\(381\) | 1.09592e40 | 1.08503 | ||||||||
\(382\) | 1.92656e38 | 0.0183147 | ||||||||
\(383\) | 2.43638e39 | 0.222415 | 0.111208 | − | 0.993797i | \(-0.464528\pi\) | ||||
0.111208 | + | 0.993797i | \(0.464528\pi\) | |||||||
\(384\) | −7.41312e38 | −0.0649931 | ||||||||
\(385\) | −7.49300e39 | −0.630978 | ||||||||
\(386\) | 8.98354e39 | 0.726682 | ||||||||
\(387\) | −6.27336e39 | −0.487506 | ||||||||
\(388\) | −1.28601e39 | −0.0960177 | ||||||||
\(389\) | −1.05964e40 | −0.760219 | −0.380110 | − | 0.924941i | \(-0.624114\pi\) | ||||
−0.380110 | + | 0.924941i | \(0.624114\pi\) | |||||||
\(390\) | −9.32383e38 | −0.0642825 | ||||||||
\(391\) | 2.11306e38 | 0.0140014 | ||||||||
\(392\) | 2.16877e39 | 0.138127 | ||||||||
\(393\) | 1.47361e40 | 0.902187 | ||||||||
\(394\) | −9.28432e39 | −0.546461 | ||||||||
\(395\) | −1.29678e40 | −0.733855 | ||||||||
\(396\) | 7.62840e39 | 0.415105 | ||||||||
\(397\) | −2.43442e40 | −1.27392 | −0.636962 | − | 0.770896i | \(-0.719809\pi\) | ||||
−0.636962 | + | 0.770896i | \(0.719809\pi\) | |||||||
\(398\) | 1.84644e40 | 0.929280 | ||||||||
\(399\) | −1.60536e40 | −0.777127 | ||||||||
\(400\) | 1.07374e39 | 0.0500000 | ||||||||
\(401\) | −1.19933e40 | −0.537279 | −0.268639 | − | 0.963241i | \(-0.586574\pi\) | ||||
−0.268639 | + | 0.963241i | \(0.586574\pi\) | |||||||
\(402\) | 6.47670e39 | 0.279158 | ||||||||
\(403\) | 8.55764e39 | 0.354916 | ||||||||
\(404\) | −1.96016e39 | −0.0782311 | ||||||||
\(405\) | 3.83890e39 | 0.147453 | ||||||||
\(406\) | 2.46018e40 | 0.909521 | ||||||||
\(407\) | 5.88554e40 | 2.09446 | ||||||||
\(408\) | −3.47195e38 | −0.0118943 | ||||||||
\(409\) | −5.19301e40 | −1.71281 | −0.856403 | − | 0.516308i | \(-0.827306\pi\) | ||||
−0.856403 | + | 0.516308i | \(0.827306\pi\) | |||||||
\(410\) | 4.23536e39 | 0.134506 | ||||||||
\(411\) | 2.30004e40 | 0.703376 | ||||||||
\(412\) | −3.32640e40 | −0.979644 | ||||||||
\(413\) | −3.30582e40 | −0.937678 | ||||||||
\(414\) | 3.63797e39 | 0.0993927 | ||||||||
\(415\) | 7.97189e39 | 0.209805 | ||||||||
\(416\) | 1.92749e39 | 0.0488704 | ||||||||
\(417\) | −2.35306e40 | −0.574810 | ||||||||
\(418\) | 7.35179e40 | 1.73046 | ||||||||
\(419\) | 5.00033e40 | 1.13418 | 0.567089 | − | 0.823656i | \(-0.308069\pi\) | ||||
0.567089 | + | 0.823656i | \(0.308069\pi\) | |||||||
\(420\) | 5.87142e39 | 0.128345 | ||||||||
\(421\) | −9.66156e39 | −0.203552 | −0.101776 | − | 0.994807i | \(-0.532452\pi\) | ||||
−0.101776 | + | 0.994807i | \(0.532452\pi\) | |||||||
\(422\) | 4.49818e40 | 0.913469 | ||||||||
\(423\) | −2.55943e40 | −0.501035 | ||||||||
\(424\) | −3.04984e39 | −0.0575581 | ||||||||
\(425\) | 5.02888e38 | 0.00915046 | ||||||||
\(426\) | −1.80298e40 | −0.316331 | ||||||||
\(427\) | 3.65171e40 | 0.617823 | ||||||||
\(428\) | −8.32417e39 | −0.135820 | ||||||||
\(429\) | 2.33485e40 | 0.367427 | ||||||||
\(430\) | 2.21121e40 | 0.335637 | ||||||||
\(431\) | −6.30614e40 | −0.923350 | −0.461675 | − | 0.887049i | \(-0.652751\pi\) | ||||
−0.461675 | + | 0.887049i | \(0.652751\pi\) | |||||||
\(432\) | −1.89915e40 | −0.268263 | ||||||||
\(433\) | 1.25919e41 | 1.71605 | 0.858026 | − | 0.513606i | \(-0.171691\pi\) | ||||
0.858026 | + | 0.513606i | \(0.171691\pi\) | |||||||
\(434\) | −5.38893e40 | −0.708618 | ||||||||
\(435\) | −4.27048e40 | −0.541868 | ||||||||
\(436\) | 2.95177e40 | 0.361445 | ||||||||
\(437\) | 3.50606e40 | 0.414340 | ||||||||
\(438\) | −8.50102e40 | −0.969667 | ||||||||
\(439\) | −8.26623e39 | −0.0910138 | −0.0455069 | − | 0.998964i | \(-0.514490\pi\) | ||||
−0.0455069 | + | 0.998964i | \(0.514490\pi\) | |||||||
\(440\) | −2.68884e40 | −0.285790 | ||||||||
\(441\) | 1.74877e40 | 0.179447 | ||||||||
\(442\) | 9.02742e38 | 0.00894373 | ||||||||
\(443\) | 1.43030e41 | 1.36826 | 0.684132 | − | 0.729358i | \(-0.260181\pi\) | ||||
0.684132 | + | 0.729358i | \(0.260181\pi\) | |||||||
\(444\) | −4.61183e40 | −0.426027 | ||||||||
\(445\) | 5.87664e40 | 0.524263 | ||||||||
\(446\) | −1.71784e39 | −0.0148010 | ||||||||
\(447\) | −7.74339e38 | −0.00644414 | ||||||||
\(448\) | −1.21378e40 | −0.0975734 | ||||||||
\(449\) | −1.81047e41 | −1.40596 | −0.702980 | − | 0.711210i | \(-0.748148\pi\) | ||||
−0.702980 | + | 0.711210i | \(0.748148\pi\) | |||||||
\(450\) | 8.65804e39 | 0.0649569 | ||||||||
\(451\) | −1.06061e41 | −0.768808 | ||||||||
\(452\) | 3.26804e40 | 0.228898 | ||||||||
\(453\) | −1.29348e41 | −0.875461 | ||||||||
\(454\) | 7.55091e40 | 0.493893 | ||||||||
\(455\) | −1.52663e40 | −0.0965066 | ||||||||
\(456\) | −5.76077e40 | −0.351986 | ||||||||
\(457\) | 1.94398e41 | 1.14813 | 0.574064 | − | 0.818810i | \(-0.305366\pi\) | ||||
0.574064 | + | 0.818810i | \(0.305366\pi\) | |||||||
\(458\) | −1.05526e41 | −0.602481 | ||||||||
\(459\) | −8.89469e39 | −0.0490947 | ||||||||
\(460\) | −1.28230e40 | −0.0684296 | ||||||||
\(461\) | −1.15427e41 | −0.595582 | −0.297791 | − | 0.954631i | \(-0.596250\pi\) | ||||
−0.297791 | + | 0.954631i | \(0.596250\pi\) | |||||||
\(462\) | −1.47030e41 | −0.733595 | ||||||||
\(463\) | −1.83772e41 | −0.886694 | −0.443347 | − | 0.896350i | \(-0.646209\pi\) | ||||
−0.443347 | + | 0.896350i | \(0.646209\pi\) | |||||||
\(464\) | 8.82825e40 | 0.411951 | ||||||||
\(465\) | 9.35434e40 | 0.422175 | ||||||||
\(466\) | −1.09810e41 | −0.479360 | ||||||||
\(467\) | −1.32162e41 | −0.558078 | −0.279039 | − | 0.960280i | \(-0.590016\pi\) | ||||
−0.279039 | + | 0.960280i | \(0.590016\pi\) | |||||||
\(468\) | 1.55422e40 | 0.0634894 | ||||||||
\(469\) | 1.06046e41 | 0.419097 | ||||||||
\(470\) | 9.02140e40 | 0.344951 | ||||||||
\(471\) | 2.41906e41 | 0.894998 | ||||||||
\(472\) | −1.18628e41 | −0.424705 | ||||||||
\(473\) | −5.53726e41 | −1.91844 | ||||||||
\(474\) | −2.54458e41 | −0.853203 | ||||||||
\(475\) | 8.34410e40 | 0.270787 | ||||||||
\(476\) | −5.68476e39 | −0.0178568 | ||||||||
\(477\) | −2.45922e40 | −0.0747759 | ||||||||
\(478\) | −1.77347e41 | −0.522025 | ||||||||
\(479\) | 6.48535e41 | 1.84813 | 0.924066 | − | 0.382233i | \(-0.124845\pi\) | ||||
0.924066 | + | 0.382233i | \(0.124845\pi\) | |||||||
\(480\) | 2.10694e40 | 0.0581316 | ||||||||
\(481\) | 1.19913e41 | 0.320343 | ||||||||
\(482\) | 1.19297e41 | 0.308603 | ||||||||
\(483\) | −7.01186e40 | −0.175652 | ||||||||
\(484\) | 4.67233e41 | 1.13352 | ||||||||
\(485\) | 3.65505e40 | 0.0858809 | ||||||||
\(486\) | −2.58074e41 | −0.587330 | ||||||||
\(487\) | 1.77648e41 | 0.391617 | 0.195808 | − | 0.980642i | \(-0.437267\pi\) | ||||
0.195808 | + | 0.980642i | \(0.437267\pi\) | |||||||
\(488\) | 1.31040e41 | 0.279832 | ||||||||
\(489\) | 3.26543e41 | 0.675543 | ||||||||
\(490\) | −6.16402e40 | −0.123545 | ||||||||
\(491\) | 7.79527e41 | 1.51380 | 0.756900 | − | 0.653531i | \(-0.226713\pi\) | ||||
0.756900 | + | 0.653531i | \(0.226713\pi\) | |||||||
\(492\) | 8.31078e40 | 0.156381 | ||||||||
\(493\) | 4.13472e40 | 0.0753909 | ||||||||
\(494\) | 1.49786e41 | 0.264669 | ||||||||
\(495\) | −2.16812e41 | −0.371281 | ||||||||
\(496\) | −1.93380e41 | −0.320956 | ||||||||
\(497\) | −2.95209e41 | −0.474904 | ||||||||
\(498\) | 1.56427e41 | 0.243926 | ||||||||
\(499\) | 8.45266e41 | 1.27772 | 0.638859 | − | 0.769324i | \(-0.279407\pi\) | ||||
0.638859 | + | 0.769324i | \(0.279407\pi\) | |||||||
\(500\) | −3.05176e40 | −0.0447214 | ||||||||
\(501\) | 3.43828e41 | 0.488491 | ||||||||
\(502\) | 2.16392e41 | 0.298080 | ||||||||
\(503\) | −2.43928e41 | −0.325805 | −0.162903 | − | 0.986642i | \(-0.552086\pi\) | ||||
−0.162903 | + | 0.986642i | \(0.552086\pi\) | |||||||
\(504\) | −9.78724e40 | −0.126761 | ||||||||
\(505\) | 5.57110e40 | 0.0699720 | ||||||||
\(506\) | 3.21111e41 | 0.391130 | ||||||||
\(507\) | −5.74867e41 | −0.679116 | ||||||||
\(508\) | 6.43910e41 | 0.737798 | ||||||||
\(509\) | 9.04219e41 | 1.00496 | 0.502479 | − | 0.864589i | \(-0.332421\pi\) | ||||
0.502479 | + | 0.864589i | \(0.332421\pi\) | |||||||
\(510\) | 9.86786e39 | 0.0106386 | ||||||||
\(511\) | −1.39191e42 | −1.45575 | ||||||||
\(512\) | −4.35561e40 | −0.0441942 | ||||||||
\(513\) | −1.47584e42 | −1.45285 | ||||||||
\(514\) | 5.60146e41 | 0.535024 | ||||||||
\(515\) | 9.45421e41 | 0.876220 | ||||||||
\(516\) | 4.33892e41 | 0.390222 | ||||||||
\(517\) | −2.25911e42 | −1.97167 | ||||||||
\(518\) | −7.55115e41 | −0.639590 | ||||||||
\(519\) | 6.17890e41 | 0.507946 | ||||||||
\(520\) | −5.47826e40 | −0.0437110 | ||||||||
\(521\) | −1.32797e42 | −1.02850 | −0.514249 | − | 0.857641i | \(-0.671929\pi\) | ||||
−0.514249 | + | 0.857641i | \(0.671929\pi\) | |||||||
\(522\) | 7.11859e41 | 0.535182 | ||||||||
\(523\) | −6.64786e41 | −0.485183 | −0.242591 | − | 0.970129i | \(-0.577997\pi\) | ||||
−0.242591 | + | 0.970129i | \(0.577997\pi\) | |||||||
\(524\) | 8.65823e41 | 0.613471 | ||||||||
\(525\) | −1.66876e41 | −0.114795 | ||||||||
\(526\) | −1.98874e42 | −1.32831 | ||||||||
\(527\) | −9.05697e40 | −0.0587379 | ||||||||
\(528\) | −5.27613e41 | −0.332269 | ||||||||
\(529\) | −1.48203e42 | −0.906348 | ||||||||
\(530\) | 8.66817e40 | 0.0514815 | ||||||||
\(531\) | −9.56551e41 | −0.551751 | ||||||||
\(532\) | −9.43236e41 | −0.528433 | ||||||||
\(533\) | −2.16089e41 | −0.117587 | ||||||||
\(534\) | 1.15314e42 | 0.609525 | ||||||||
\(535\) | 2.36587e41 | 0.121481 | ||||||||
\(536\) | 3.80542e41 | 0.189823 | ||||||||
\(537\) | −4.41449e41 | −0.213934 | ||||||||
\(538\) | 1.53955e42 | 0.724883 | ||||||||
\(539\) | 1.54358e42 | 0.706159 | ||||||||
\(540\) | 5.39771e41 | 0.239942 | ||||||||
\(541\) | −3.24428e42 | −1.40140 | −0.700699 | − | 0.713457i | \(-0.747128\pi\) | ||||
−0.700699 | + | 0.713457i | \(0.747128\pi\) | |||||||
\(542\) | 9.81271e41 | 0.411908 | ||||||||
\(543\) | 5.71322e41 | 0.233068 | ||||||||
\(544\) | −2.03996e40 | −0.00808794 | ||||||||
\(545\) | −8.38944e41 | −0.323286 | ||||||||
\(546\) | −2.99561e41 | −0.112202 | ||||||||
\(547\) | 4.67015e42 | 1.70031 | 0.850153 | − | 0.526536i | \(-0.176510\pi\) | ||||
0.850153 | + | 0.526536i | \(0.176510\pi\) | |||||||
\(548\) | 1.35140e42 | 0.478283 | ||||||||
\(549\) | 1.05663e42 | 0.363541 | ||||||||
\(550\) | 7.64213e41 | 0.255619 | ||||||||
\(551\) | 6.86047e42 | 2.23102 | ||||||||
\(552\) | −2.51618e41 | −0.0795584 | ||||||||
\(553\) | −4.16636e42 | −1.28091 | ||||||||
\(554\) | −2.56380e42 | −0.766447 | ||||||||
\(555\) | 1.31076e42 | 0.381050 | ||||||||
\(556\) | −1.38255e42 | −0.390861 | ||||||||
\(557\) | −3.04905e42 | −0.838320 | −0.419160 | − | 0.907912i | \(-0.637675\pi\) | ||||
−0.419160 | + | 0.907912i | \(0.637675\pi\) | |||||||
\(558\) | −1.55930e42 | −0.416966 | ||||||||
\(559\) | −1.12817e42 | −0.293420 | ||||||||
\(560\) | 3.44978e41 | 0.0872723 | ||||||||
\(561\) | −2.47108e41 | −0.0608083 | ||||||||
\(562\) | −5.89370e42 | −1.41083 | ||||||||
\(563\) | 6.25531e41 | 0.145669 | 0.0728347 | − | 0.997344i | \(-0.476795\pi\) | ||||
0.0728347 | + | 0.997344i | \(0.476795\pi\) | |||||||
\(564\) | 1.77021e42 | 0.401051 | ||||||||
\(565\) | −9.28833e41 | −0.204732 | ||||||||
\(566\) | −3.35637e42 | −0.719805 | ||||||||
\(567\) | 1.23338e42 | 0.257371 | ||||||||
\(568\) | −1.05935e42 | −0.215099 | ||||||||
\(569\) | 6.38935e42 | 1.26246 | 0.631228 | − | 0.775597i | \(-0.282551\pi\) | ||||
0.631228 | + | 0.775597i | \(0.282551\pi\) | |||||||
\(570\) | 1.63731e42 | 0.314826 | ||||||||
\(571\) | 4.53027e42 | 0.847744 | 0.423872 | − | 0.905722i | \(-0.360671\pi\) | ||||
0.423872 | + | 0.905722i | \(0.360671\pi\) | |||||||
\(572\) | 1.37185e42 | 0.249844 | ||||||||
\(573\) | −1.07444e41 | −0.0190453 | ||||||||
\(574\) | 1.36076e42 | 0.234772 | ||||||||
\(575\) | 3.64452e41 | 0.0612053 | ||||||||
\(576\) | −3.51212e41 | −0.0574144 | ||||||||
\(577\) | 9.48731e42 | 1.50980 | 0.754898 | − | 0.655843i | \(-0.227687\pi\) | ||||
0.754898 | + | 0.655843i | \(0.227687\pi\) | |||||||
\(578\) | 4.55467e42 | 0.705627 | ||||||||
\(579\) | −5.01013e42 | −0.755669 | ||||||||
\(580\) | −2.50914e42 | −0.368461 | ||||||||
\(581\) | 2.56125e42 | 0.366203 | ||||||||
\(582\) | 7.17208e41 | 0.0998478 | ||||||||
\(583\) | −2.17066e42 | −0.294258 | ||||||||
\(584\) | −4.99481e42 | −0.659356 | ||||||||
\(585\) | −4.41735e41 | −0.0567866 | ||||||||
\(586\) | 8.70530e42 | 1.08986 | ||||||||
\(587\) | 1.48304e43 | 1.80827 | 0.904134 | − | 0.427250i | \(-0.140518\pi\) | ||||
0.904134 | + | 0.427250i | \(0.140518\pi\) | |||||||
\(588\) | −1.20953e42 | −0.143637 | ||||||||
\(589\) | −1.50276e43 | −1.73822 | ||||||||
\(590\) | 3.37162e42 | 0.379868 | ||||||||
\(591\) | 5.17788e42 | 0.568259 | ||||||||
\(592\) | −2.70970e42 | −0.289691 | ||||||||
\(593\) | 6.85391e42 | 0.713823 | 0.356912 | − | 0.934138i | \(-0.383830\pi\) | ||||
0.356912 | + | 0.934138i | \(0.383830\pi\) | |||||||
\(594\) | −1.35168e43 | −1.37146 | ||||||||
\(595\) | 1.61571e41 | 0.0159716 | ||||||||
\(596\) | −4.54967e40 | −0.00438190 | ||||||||
\(597\) | −1.02976e43 | −0.966349 | ||||||||
\(598\) | 6.54234e41 | 0.0598225 | ||||||||
\(599\) | 1.05394e43 | 0.939078 | 0.469539 | − | 0.882912i | \(-0.344420\pi\) | ||||
0.469539 | + | 0.882912i | \(0.344420\pi\) | |||||||
\(600\) | −5.98827e41 | −0.0519945 | ||||||||
\(601\) | −4.18011e42 | −0.353698 | −0.176849 | − | 0.984238i | \(-0.556591\pi\) | ||||
−0.176849 | + | 0.984238i | \(0.556591\pi\) | |||||||
\(602\) | 7.10431e42 | 0.585836 | ||||||||
\(603\) | 3.06847e42 | 0.246606 | ||||||||
\(604\) | −7.59988e42 | −0.595298 | ||||||||
\(605\) | −1.32796e43 | −1.01385 | ||||||||
\(606\) | 1.09318e42 | 0.0813517 | ||||||||
\(607\) | 4.39468e40 | 0.00318788 | 0.00159394 | − | 0.999999i | \(-0.499493\pi\) | ||||
0.00159394 | + | 0.999999i | \(0.499493\pi\) | |||||||
\(608\) | −3.38477e42 | −0.239344 | ||||||||
\(609\) | −1.37204e43 | −0.945801 | ||||||||
\(610\) | −3.72439e42 | −0.250289 | ||||||||
\(611\) | −4.60274e42 | −0.301563 | ||||||||
\(612\) | −1.64490e41 | −0.0105074 | ||||||||
\(613\) | −2.74553e43 | −1.70997 | −0.854985 | − | 0.518653i | \(-0.826434\pi\) | ||||
−0.854985 | + | 0.518653i | \(0.826434\pi\) | |||||||
\(614\) | 4.05442e42 | 0.246217 | ||||||||
\(615\) | −2.36207e42 | −0.139871 | ||||||||
\(616\) | −8.63884e42 | −0.498832 | ||||||||
\(617\) | 2.93144e43 | 1.65067 | 0.825336 | − | 0.564641i | \(-0.190986\pi\) | ||||
0.825336 | + | 0.564641i | \(0.190986\pi\) | |||||||
\(618\) | 1.85514e43 | 1.01872 | ||||||||
\(619\) | −5.48823e42 | −0.293919 | −0.146959 | − | 0.989143i | \(-0.546949\pi\) | ||||
−0.146959 | + | 0.989143i | \(0.546949\pi\) | |||||||
\(620\) | 5.49619e42 | 0.287072 | ||||||||
\(621\) | −6.44614e42 | −0.328383 | ||||||||
\(622\) | −2.30138e43 | −1.14350 | ||||||||
\(623\) | 1.88808e43 | 0.915073 | ||||||||
\(624\) | −1.07496e42 | −0.0508198 | ||||||||
\(625\) | 8.67362e41 | 0.0400000 | ||||||||
\(626\) | −2.00024e43 | −0.899873 | ||||||||
\(627\) | −4.10011e43 | −1.79948 | ||||||||
\(628\) | 1.42133e43 | 0.608583 | ||||||||
\(629\) | −1.26909e42 | −0.0530162 | ||||||||
\(630\) | 2.78170e42 | 0.113379 | ||||||||
\(631\) | 2.48327e43 | 0.987572 | 0.493786 | − | 0.869583i | \(-0.335613\pi\) | ||||
0.493786 | + | 0.869583i | \(0.335613\pi\) | |||||||
\(632\) | −1.49508e43 | −0.580163 | ||||||||
\(633\) | −2.50864e43 | −0.949907 | ||||||||
\(634\) | 1.93361e43 | 0.714474 | ||||||||
\(635\) | −1.83010e43 | −0.659907 | ||||||||
\(636\) | 1.70090e42 | 0.0598540 | ||||||||
\(637\) | 3.14490e42 | 0.108005 | ||||||||
\(638\) | 6.28332e43 | 2.10605 | ||||||||
\(639\) | −8.54196e42 | −0.279444 | ||||||||
\(640\) | 1.23794e42 | 0.0395285 | ||||||||
\(641\) | 2.55989e43 | 0.797850 | 0.398925 | − | 0.916984i | \(-0.369383\pi\) | ||||
0.398925 | + | 0.916984i | \(0.369383\pi\) | |||||||
\(642\) | 4.64240e42 | 0.141237 | ||||||||
\(643\) | 4.50652e43 | 1.33836 | 0.669178 | − | 0.743103i | \(-0.266647\pi\) | ||||
0.669178 | + | 0.743103i | \(0.266647\pi\) | |||||||
\(644\) | −4.11985e42 | −0.119440 | ||||||||
\(645\) | −1.23320e43 | −0.349025 | ||||||||
\(646\) | −1.58526e42 | −0.0438022 | ||||||||
\(647\) | 7.99244e42 | 0.215607 | 0.107804 | − | 0.994172i | \(-0.465618\pi\) | ||||
0.107804 | + | 0.994172i | \(0.465618\pi\) | |||||||
\(648\) | 4.42595e42 | 0.116572 | ||||||||
\(649\) | −8.44312e43 | −2.17125 | ||||||||
\(650\) | 1.55701e42 | 0.0390963 | ||||||||
\(651\) | 3.00542e43 | 0.736884 | ||||||||
\(652\) | 1.91862e43 | 0.459358 | ||||||||
\(653\) | 6.70562e43 | 1.56778 | 0.783890 | − | 0.620900i | \(-0.213233\pi\) | ||||
0.783890 | + | 0.620900i | \(0.213233\pi\) | |||||||
\(654\) | −1.64621e43 | −0.375863 | ||||||||
\(655\) | −2.46082e43 | −0.548706 | ||||||||
\(656\) | 4.88304e42 | 0.106336 | ||||||||
\(657\) | −4.02753e43 | −0.856595 | ||||||||
\(658\) | 2.89845e43 | 0.602093 | ||||||||
\(659\) | 2.04703e43 | 0.415337 | 0.207668 | − | 0.978199i | \(-0.433412\pi\) | ||||
0.207668 | + | 0.978199i | \(0.433412\pi\) | |||||||
\(660\) | 1.49957e43 | 0.297190 | ||||||||
\(661\) | 1.02079e43 | 0.197611 | 0.0988057 | − | 0.995107i | \(-0.468498\pi\) | ||||
0.0988057 | + | 0.995107i | \(0.468498\pi\) | |||||||
\(662\) | 4.14721e43 | 0.784254 | ||||||||
\(663\) | −5.03461e41 | −0.00930049 | ||||||||
\(664\) | 9.19096e42 | 0.165865 | ||||||||
\(665\) | 2.68084e43 | 0.472645 | ||||||||
\(666\) | −2.18495e43 | −0.376349 | ||||||||
\(667\) | 2.99651e43 | 0.504272 | ||||||||
\(668\) | 2.02018e43 | 0.332165 | ||||||||
\(669\) | 9.58040e41 | 0.0153914 | ||||||||
\(670\) | −1.08156e43 | −0.169783 | ||||||||
\(671\) | 9.32651e43 | 1.43061 | ||||||||
\(672\) | 6.76928e42 | 0.101466 | ||||||||
\(673\) | −1.16828e43 | −0.171125 | −0.0855623 | − | 0.996333i | \(-0.527269\pi\) | ||||
−0.0855623 | + | 0.996333i | \(0.527269\pi\) | |||||||
\(674\) | 3.77683e43 | 0.540629 | ||||||||
\(675\) | −1.53412e43 | −0.214611 | ||||||||
\(676\) | −3.37766e43 | −0.461787 | ||||||||
\(677\) | −5.20282e43 | −0.695208 | −0.347604 | − | 0.937641i | \(-0.613005\pi\) | ||||
−0.347604 | + | 0.937641i | \(0.613005\pi\) | |||||||
\(678\) | −1.82259e43 | −0.238029 | ||||||||
\(679\) | 1.17431e43 | 0.149900 | ||||||||
\(680\) | 5.79791e41 | 0.00723408 | ||||||||
\(681\) | −4.21115e43 | −0.513595 | ||||||||
\(682\) | −1.37634e44 | −1.64085 | ||||||||
\(683\) | −1.36522e44 | −1.59104 | −0.795521 | − | 0.605926i | \(-0.792803\pi\) | ||||
−0.795521 | + | 0.605926i | \(0.792803\pi\) | |||||||
\(684\) | −2.72928e43 | −0.310942 | ||||||||
\(685\) | −3.84091e43 | −0.427789 | ||||||||
\(686\) | −7.04950e43 | −0.767600 | ||||||||
\(687\) | 5.88519e43 | 0.626514 | ||||||||
\(688\) | 2.54935e43 | 0.265344 | ||||||||
\(689\) | −4.42252e42 | −0.0450061 | ||||||||
\(690\) | 7.15142e42 | 0.0711592 | ||||||||
\(691\) | 1.03195e44 | 1.00404 | 0.502020 | − | 0.864856i | \(-0.332590\pi\) | ||||
0.502020 | + | 0.864856i | \(0.332590\pi\) | |||||||
\(692\) | 3.63044e43 | 0.345394 | ||||||||
\(693\) | −6.96586e43 | −0.648052 | ||||||||
\(694\) | −1.06798e44 | −0.971606 | ||||||||
\(695\) | 3.92945e43 | 0.349596 | ||||||||
\(696\) | −4.92353e43 | −0.428384 | ||||||||
\(697\) | 2.28698e42 | 0.0194605 | ||||||||
\(698\) | −2.06598e42 | −0.0171936 | ||||||||
\(699\) | 6.12414e43 | 0.498482 | ||||||||
\(700\) | −9.80486e42 | −0.0780587 | ||||||||
\(701\) | 1.21223e44 | 0.943967 | 0.471983 | − | 0.881607i | \(-0.343538\pi\) | ||||
0.471983 | + | 0.881607i | \(0.343538\pi\) | |||||||
\(702\) | −2.75392e43 | −0.209762 | ||||||||
\(703\) | −2.10572e44 | −1.56889 | ||||||||
\(704\) | −3.10002e43 | −0.225937 | ||||||||
\(705\) | −5.03125e43 | −0.358711 | ||||||||
\(706\) | −1.36015e44 | −0.948664 | ||||||||
\(707\) | 1.78991e43 | 0.122132 | ||||||||
\(708\) | 6.61592e43 | 0.441646 | ||||||||
\(709\) | −2.19198e43 | −0.143159 | −0.0715797 | − | 0.997435i | \(-0.522804\pi\) | ||||
−0.0715797 | + | 0.997435i | \(0.522804\pi\) | |||||||
\(710\) | 3.01084e43 | 0.192391 | ||||||||
\(711\) | −1.20555e44 | −0.753713 | ||||||||
\(712\) | 6.77531e43 | 0.414466 | ||||||||
\(713\) | −6.56375e43 | −0.392884 | ||||||||
\(714\) | 3.17040e42 | 0.0185691 | ||||||||
\(715\) | −3.89903e43 | −0.223467 | ||||||||
\(716\) | −2.59375e43 | −0.145471 | ||||||||
\(717\) | 9.89066e43 | 0.542848 | ||||||||
\(718\) | 2.49969e44 | 1.34263 | ||||||||
\(719\) | 9.40579e43 | 0.494422 | 0.247211 | − | 0.968962i | \(-0.420486\pi\) | ||||
0.247211 | + | 0.968962i | \(0.420486\pi\) | |||||||
\(720\) | 9.98204e42 | 0.0513530 | ||||||||
\(721\) | 3.03750e44 | 1.52940 | ||||||||
\(722\) | −1.19545e44 | −0.589122 | ||||||||
\(723\) | −6.65320e43 | −0.320913 | ||||||||
\(724\) | 3.35683e43 | 0.158482 | ||||||||
\(725\) | 7.13140e43 | 0.329561 | ||||||||
\(726\) | −2.60577e44 | −1.17874 | ||||||||
\(727\) | 4.09641e44 | 1.81393 | 0.906965 | − | 0.421207i | \(-0.138393\pi\) | ||||
0.906965 | + | 0.421207i | \(0.138393\pi\) | |||||||
\(728\) | −1.76008e43 | −0.0762952 | ||||||||
\(729\) | 2.21627e44 | 0.940473 | ||||||||
\(730\) | 1.41961e44 | 0.589746 | ||||||||
\(731\) | 1.19399e43 | 0.0485604 | ||||||||
\(732\) | −7.30813e43 | −0.290994 | ||||||||
\(733\) | −4.57092e44 | −1.78194 | −0.890968 | − | 0.454067i | \(-0.849973\pi\) | ||||
−0.890968 | + | 0.454067i | \(0.849973\pi\) | |||||||
\(734\) | 1.54323e43 | 0.0589035 | ||||||||
\(735\) | 3.43768e43 | 0.128473 | ||||||||
\(736\) | −1.47839e43 | −0.0540983 | ||||||||
\(737\) | 2.70842e44 | 0.970445 | ||||||||
\(738\) | 3.93740e43 | 0.138145 | ||||||||
\(739\) | 1.00404e44 | 0.344957 | 0.172478 | − | 0.985013i | \(-0.444823\pi\) | ||||
0.172478 | + | 0.985013i | \(0.444823\pi\) | |||||||
\(740\) | 7.70144e43 | 0.259108 | ||||||||
\(741\) | −8.35359e43 | −0.275227 | ||||||||
\(742\) | 2.78496e43 | 0.0898582 | ||||||||
\(743\) | −7.43485e43 | −0.234934 | −0.117467 | − | 0.993077i | \(-0.537477\pi\) | ||||
−0.117467 | + | 0.993077i | \(0.537477\pi\) | |||||||
\(744\) | 1.07848e44 | 0.333759 | ||||||||
\(745\) | 1.29309e42 | 0.00391929 | ||||||||
\(746\) | −1.71956e43 | −0.0510463 | ||||||||
\(747\) | 7.41106e43 | 0.215482 | ||||||||
\(748\) | −1.45190e43 | −0.0413486 | ||||||||
\(749\) | 7.60121e43 | 0.212038 | ||||||||
\(750\) | 1.70197e43 | 0.0465053 | ||||||||
\(751\) | −5.97546e44 | −1.59938 | −0.799691 | − | 0.600411i | \(-0.795003\pi\) | ||||
−0.799691 | + | 0.600411i | \(0.795003\pi\) | |||||||
\(752\) | 1.04010e44 | 0.272708 | ||||||||
\(753\) | −1.20682e44 | −0.309970 | ||||||||
\(754\) | 1.28017e44 | 0.322115 | ||||||||
\(755\) | 2.16002e44 | 0.532451 | ||||||||
\(756\) | 1.73421e44 | 0.418806 | ||||||||
\(757\) | −6.25091e44 | −1.47896 | −0.739481 | − | 0.673177i | \(-0.764929\pi\) | ||||
−0.739481 | + | 0.673177i | \(0.764929\pi\) | |||||||
\(758\) | 1.41097e44 | 0.327073 | ||||||||
\(759\) | −1.79084e44 | −0.406732 | ||||||||
\(760\) | 9.62009e43 | 0.214076 | ||||||||
\(761\) | 8.11145e44 | 1.76863 | 0.884314 | − | 0.466892i | \(-0.154626\pi\) | ||||
0.884314 | + | 0.466892i | \(0.154626\pi\) | |||||||
\(762\) | −3.59110e44 | −0.767229 | ||||||||
\(763\) | −2.69541e44 | −0.564279 | ||||||||
\(764\) | −6.31294e42 | −0.0129504 | ||||||||
\(765\) | 4.67510e42 | 0.00939807 | ||||||||
\(766\) | −7.98354e43 | −0.157271 | ||||||||
\(767\) | −1.72021e44 | −0.332088 | ||||||||
\(768\) | 2.42913e43 | 0.0459571 | ||||||||
\(769\) | 4.74855e44 | 0.880446 | 0.440223 | − | 0.897888i | \(-0.354899\pi\) | ||||
0.440223 | + | 0.897888i | \(0.354899\pi\) | |||||||
\(770\) | 2.45531e44 | 0.446169 | ||||||||
\(771\) | −3.12394e44 | −0.556366 | ||||||||
\(772\) | −2.94373e44 | −0.513841 | ||||||||
\(773\) | 3.40400e44 | 0.582380 | 0.291190 | − | 0.956665i | \(-0.405949\pi\) | ||||
0.291190 | + | 0.956665i | \(0.405949\pi\) | |||||||
\(774\) | 2.05565e44 | 0.344719 | ||||||||
\(775\) | −1.56211e44 | −0.256765 | ||||||||
\(776\) | 4.21399e43 | 0.0678948 | ||||||||
\(777\) | 4.21129e44 | 0.665103 | ||||||||
\(778\) | 3.47222e44 | 0.537556 | ||||||||
\(779\) | 3.79463e44 | 0.575889 | ||||||||
\(780\) | 3.05523e43 | 0.0454546 | ||||||||
\(781\) | −7.53967e44 | −1.09967 | ||||||||
\(782\) | −6.92407e42 | −0.00990050 | ||||||||
\(783\) | −1.26135e45 | −1.76818 | ||||||||
\(784\) | −7.10663e43 | −0.0976708 | ||||||||
\(785\) | −4.03966e44 | −0.544334 | ||||||||
\(786\) | −4.82871e44 | −0.637943 | ||||||||
\(787\) | −1.06793e45 | −1.38336 | −0.691678 | − | 0.722206i | \(-0.743128\pi\) | ||||
−0.691678 | + | 0.722206i | \(0.743128\pi\) | |||||||
\(788\) | 3.04229e44 | 0.386406 | ||||||||
\(789\) | 1.10912e45 | 1.38129 | ||||||||
\(790\) | 4.24928e44 | 0.518914 | ||||||||
\(791\) | −2.98421e44 | −0.357350 | ||||||||
\(792\) | −2.49967e44 | −0.293524 | ||||||||
\(793\) | 1.90019e44 | 0.218808 | ||||||||
\(794\) | 7.97712e44 | 0.900800 | ||||||||
\(795\) | −4.83425e43 | −0.0535351 | ||||||||
\(796\) | −6.05040e44 | −0.657100 | ||||||||
\(797\) | −9.48957e43 | −0.101075 | −0.0505374 | − | 0.998722i | \(-0.516093\pi\) | ||||
−0.0505374 | + | 0.998722i | \(0.516093\pi\) | |||||||
\(798\) | 5.26044e44 | 0.549512 | ||||||||
\(799\) | 4.87131e43 | 0.0499080 | ||||||||
\(800\) | −3.51844e43 | −0.0353553 | ||||||||
\(801\) | 5.46322e44 | 0.538449 | ||||||||
\(802\) | 3.92995e44 | 0.379913 | ||||||||
\(803\) | −3.55495e45 | −3.37088 | ||||||||
\(804\) | −2.12229e44 | −0.197395 | ||||||||
\(805\) | 1.17093e44 | 0.106831 | ||||||||
\(806\) | −2.80417e44 | −0.250964 | ||||||||
\(807\) | −8.58608e44 | −0.753798 | ||||||||
\(808\) | 6.42304e43 | 0.0553178 | ||||||||
\(809\) | 5.97219e44 | 0.504582 | 0.252291 | − | 0.967651i | \(-0.418816\pi\) | ||||
0.252291 | + | 0.967651i | \(0.418816\pi\) | |||||||
\(810\) | −1.25793e44 | −0.104265 | ||||||||
\(811\) | 9.30989e44 | 0.757045 | 0.378522 | − | 0.925592i | \(-0.376432\pi\) | ||||
0.378522 | + | 0.925592i | \(0.376432\pi\) | |||||||
\(812\) | −8.06150e44 | −0.643128 | ||||||||
\(813\) | −5.47256e44 | −0.428339 | ||||||||
\(814\) | −1.92857e45 | −1.48101 | ||||||||
\(815\) | −5.45304e44 | −0.410862 | ||||||||
\(816\) | 1.13769e43 | 0.00841057 | ||||||||
\(817\) | 1.98111e45 | 1.43704 | ||||||||
\(818\) | 1.70165e45 | 1.21114 | ||||||||
\(819\) | −1.41923e44 | −0.0991180 | ||||||||
\(820\) | −1.38784e44 | −0.0951098 | ||||||||
\(821\) | 4.88604e44 | 0.328578 | 0.164289 | − | 0.986412i | \(-0.447467\pi\) | ||||
0.164289 | + | 0.986412i | \(0.447467\pi\) | |||||||
\(822\) | −7.53677e44 | −0.497362 | ||||||||
\(823\) | 2.61589e45 | 1.69403 | 0.847017 | − | 0.531566i | \(-0.178396\pi\) | ||||
0.847017 | + | 0.531566i | \(0.178396\pi\) | |||||||
\(824\) | 1.09000e45 | 0.692713 | ||||||||
\(825\) | −4.26203e44 | −0.265815 | ||||||||
\(826\) | 1.08325e45 | 0.663039 | ||||||||
\(827\) | 2.59698e45 | 1.56003 | 0.780015 | − | 0.625761i | \(-0.215211\pi\) | ||||
0.780015 | + | 0.625761i | \(0.215211\pi\) | |||||||
\(828\) | −1.19209e44 | −0.0702812 | ||||||||
\(829\) | −2.36709e45 | −1.36968 | −0.684842 | − | 0.728692i | \(-0.740129\pi\) | ||||
−0.684842 | + | 0.728692i | \(0.740129\pi\) | |||||||
\(830\) | −2.61223e44 | −0.148355 | ||||||||
\(831\) | 1.42983e45 | 0.797020 | ||||||||
\(832\) | −6.31600e43 | −0.0345566 | ||||||||
\(833\) | −3.32840e43 | −0.0178747 | ||||||||
\(834\) | 7.71051e44 | 0.406452 | ||||||||
\(835\) | −5.74169e44 | −0.297098 | ||||||||
\(836\) | −2.40904e45 | −1.22362 | ||||||||
\(837\) | 2.76294e45 | 1.37761 | ||||||||
\(838\) | −1.63851e45 | −0.801985 | ||||||||
\(839\) | 2.59287e45 | 1.24586 | 0.622930 | − | 0.782277i | \(-0.285942\pi\) | ||||
0.622930 | + | 0.782277i | \(0.285942\pi\) | |||||||
\(840\) | −1.92395e44 | −0.0907536 | ||||||||
\(841\) | 3.70398e45 | 1.71526 | ||||||||
\(842\) | 3.16590e44 | 0.143933 | ||||||||
\(843\) | 3.28692e45 | 1.46711 | ||||||||
\(844\) | −1.47396e45 | −0.645920 | ||||||||
\(845\) | 9.59988e44 | 0.413035 | ||||||||
\(846\) | 8.38674e44 | 0.354285 | ||||||||
\(847\) | −4.26653e45 | −1.76963 | ||||||||
\(848\) | 9.99371e43 | 0.0406997 | ||||||||
\(849\) | 1.87185e45 | 0.748518 | ||||||||
\(850\) | −1.64786e43 | −0.00647035 | ||||||||
\(851\) | −9.19734e44 | −0.354613 | ||||||||
\(852\) | 5.90799e44 | 0.223679 | ||||||||
\(853\) | 1.97911e45 | 0.735799 | 0.367900 | − | 0.929866i | \(-0.380077\pi\) | ||||
0.367900 | + | 0.929866i | \(0.380077\pi\) | |||||||
\(854\) | −1.19659e45 | −0.436867 | ||||||||
\(855\) | 7.75709e44 | 0.278115 | ||||||||
\(856\) | 2.72767e44 | 0.0960390 | ||||||||
\(857\) | −2.57732e45 | −0.891181 | −0.445591 | − | 0.895237i | \(-0.647006\pi\) | ||||
−0.445591 | + | 0.895237i | \(0.647006\pi\) | |||||||
\(858\) | −7.65083e44 | −0.259810 | ||||||||
\(859\) | 5.92532e44 | 0.197614 | 0.0988069 | − | 0.995107i | \(-0.468497\pi\) | ||||
0.0988069 | + | 0.995107i | \(0.468497\pi\) | |||||||
\(860\) | −7.24570e44 | −0.237331 | ||||||||
\(861\) | −7.58897e44 | −0.244137 | ||||||||
\(862\) | 2.06640e45 | 0.652907 | ||||||||
\(863\) | −3.98009e45 | −1.23517 | −0.617583 | − | 0.786506i | \(-0.711888\pi\) | ||||
−0.617583 | + | 0.786506i | \(0.711888\pi\) | |||||||
\(864\) | 6.22314e44 | 0.189691 | ||||||||
\(865\) | −1.03183e45 | −0.308930 | ||||||||
\(866\) | −4.12613e45 | −1.21343 | ||||||||
\(867\) | −2.54014e45 | −0.733774 | ||||||||
\(868\) | 1.76585e45 | 0.501068 | ||||||||
\(869\) | −1.06409e46 | −2.96601 | ||||||||
\(870\) | 1.39935e45 | 0.383158 | ||||||||
\(871\) | 5.51817e44 | 0.148427 | ||||||||
\(872\) | −9.67237e44 | −0.255580 | ||||||||
\(873\) | 3.39792e44 | 0.0882047 | ||||||||
\(874\) | −1.14887e45 | −0.292983 | ||||||||
\(875\) | 2.78671e44 | 0.0698179 | ||||||||
\(876\) | 2.78561e45 | 0.685658 | ||||||||
\(877\) | 6.85482e45 | 1.65769 | 0.828844 | − | 0.559480i | \(-0.188999\pi\) | ||||
0.828844 | + | 0.559480i | \(0.188999\pi\) | |||||||
\(878\) | 2.70868e44 | 0.0643565 | ||||||||
\(879\) | −4.85496e45 | −1.13333 | ||||||||
\(880\) | 8.81077e44 | 0.202084 | ||||||||
\(881\) | −1.78938e44 | −0.0403251 | −0.0201625 | − | 0.999797i | \(-0.506418\pi\) | ||||
−0.0201625 | + | 0.999797i | \(0.506418\pi\) | |||||||
\(882\) | −5.73038e44 | −0.126888 | ||||||||
\(883\) | 1.67939e45 | 0.365393 | 0.182696 | − | 0.983169i | \(-0.441518\pi\) | ||||
0.182696 | + | 0.983169i | \(0.441518\pi\) | |||||||
\(884\) | −2.95811e43 | −0.00632417 | ||||||||
\(885\) | −1.88036e45 | −0.395020 | ||||||||
\(886\) | −4.68681e45 | −0.967509 | ||||||||
\(887\) | 9.72650e43 | 0.0197306 | 0.00986530 | − | 0.999951i | \(-0.496860\pi\) | ||||
0.00986530 | + | 0.999951i | \(0.496860\pi\) | |||||||
\(888\) | 1.51121e45 | 0.301247 | ||||||||
\(889\) | −5.87986e45 | −1.15183 | ||||||||
\(890\) | −1.92566e45 | −0.370710 | ||||||||
\(891\) | 3.15007e45 | 0.595959 | ||||||||
\(892\) | 5.62901e43 | 0.0104659 | ||||||||
\(893\) | 8.08264e45 | 1.47691 | ||||||||
\(894\) | 2.53736e43 | 0.00455669 | ||||||||
\(895\) | 7.37189e44 | 0.130113 | ||||||||
\(896\) | 3.97732e44 | 0.0689948 | ||||||||
\(897\) | −3.64867e44 | −0.0622088 | ||||||||
\(898\) | 5.93255e45 | 0.994164 | ||||||||
\(899\) | −1.28436e46 | −2.11549 | ||||||||
\(900\) | −2.83707e44 | −0.0459315 | ||||||||
\(901\) | 4.68057e43 | 0.00744842 | ||||||||
\(902\) | 3.47540e45 | 0.543630 | ||||||||
\(903\) | −3.96208e45 | −0.609205 | ||||||||
\(904\) | −1.07087e45 | −0.161855 | ||||||||
\(905\) | −9.54068e44 | −0.141751 | ||||||||
\(906\) | 4.23847e45 | 0.619044 | ||||||||
\(907\) | 5.07003e44 | 0.0727943 | 0.0363972 | − | 0.999337i | \(-0.488412\pi\) | ||||
0.0363972 | + | 0.999337i | \(0.488412\pi\) | |||||||
\(908\) | −2.47428e45 | −0.349235 | ||||||||
\(909\) | 5.17917e44 | 0.0718654 | ||||||||
\(910\) | 5.00246e44 | 0.0682405 | ||||||||
\(911\) | −8.33096e44 | −0.111728 | −0.0558638 | − | 0.998438i | \(-0.517791\pi\) | ||||
−0.0558638 | + | 0.998438i | \(0.517791\pi\) | |||||||
\(912\) | 1.88769e45 | 0.248892 | ||||||||
\(913\) | 6.54147e45 | 0.847966 | ||||||||
\(914\) | −6.37003e45 | −0.811850 | ||||||||
\(915\) | 2.07710e45 | 0.260273 | ||||||||
\(916\) | 3.45787e45 | 0.426019 | ||||||||
\(917\) | −7.90625e45 | −0.957736 | ||||||||
\(918\) | 2.91461e44 | 0.0347152 | ||||||||
\(919\) | 7.80049e45 | 0.913549 | 0.456774 | − | 0.889583i | \(-0.349005\pi\) | ||||
0.456774 | + | 0.889583i | \(0.349005\pi\) | |||||||
\(920\) | 4.20185e44 | 0.0483870 | ||||||||
\(921\) | −2.26115e45 | −0.256039 | ||||||||
\(922\) | 3.78230e45 | 0.421140 | ||||||||
\(923\) | −1.53614e45 | −0.168192 | ||||||||
\(924\) | 4.81789e45 | 0.518730 | ||||||||
\(925\) | −2.18888e45 | −0.231753 | ||||||||
\(926\) | 6.02184e45 | 0.626987 | ||||||||
\(927\) | 8.78910e45 | 0.899930 | ||||||||
\(928\) | −2.89284e45 | −0.291294 | ||||||||
\(929\) | 9.20353e45 | 0.911404 | 0.455702 | − | 0.890133i | \(-0.349388\pi\) | ||||
0.455702 | + | 0.890133i | \(0.349388\pi\) | |||||||
\(930\) | −3.06523e45 | −0.298523 | ||||||||
\(931\) | −5.52259e45 | −0.528960 | ||||||||
\(932\) | 3.59827e45 | 0.338959 | ||||||||
\(933\) | 1.28348e46 | 1.18912 | ||||||||
\(934\) | 4.33068e45 | 0.394621 | ||||||||
\(935\) | 4.12654e44 | 0.0369833 | ||||||||
\(936\) | −5.09286e44 | −0.0448938 | ||||||||
\(937\) | 1.17829e46 | 1.02162 | 0.510808 | − | 0.859695i | \(-0.329346\pi\) | ||||
0.510808 | + | 0.859695i | \(0.329346\pi\) | |||||||
\(938\) | −3.47491e45 | −0.296346 | ||||||||
\(939\) | 1.11554e46 | 0.935768 | ||||||||
\(940\) | −2.95613e45 | −0.243917 | ||||||||
\(941\) | −6.87236e45 | −0.557785 | −0.278892 | − | 0.960322i | \(-0.589967\pi\) | ||||
−0.278892 | + | 0.960322i | \(0.589967\pi\) | |||||||
\(942\) | −7.92677e45 | −0.632859 | ||||||||
\(943\) | 1.65741e45 | 0.130167 | ||||||||
\(944\) | 3.88721e45 | 0.300312 | ||||||||
\(945\) | −4.92891e45 | −0.374591 | ||||||||
\(946\) | 1.81445e46 | 1.35654 | ||||||||
\(947\) | −8.94323e45 | −0.657763 | −0.328882 | − | 0.944371i | \(-0.606672\pi\) | ||||
−0.328882 | + | 0.944371i | \(0.606672\pi\) | |||||||
\(948\) | 8.33810e45 | 0.603306 | ||||||||
\(949\) | −7.24289e45 | −0.515568 | ||||||||
\(950\) | −2.73419e45 | −0.191476 | ||||||||
\(951\) | −1.07838e46 | −0.742974 | ||||||||
\(952\) | 1.86278e44 | 0.0126267 | ||||||||
\(953\) | −7.57551e45 | −0.505210 | −0.252605 | − | 0.967569i | \(-0.581287\pi\) | ||||
−0.252605 | + | 0.967569i | \(0.581287\pi\) | |||||||
\(954\) | 8.05836e44 | 0.0528746 | ||||||||
\(955\) | 1.79425e44 | 0.0115832 | ||||||||
\(956\) | 5.81130e45 | 0.369127 | ||||||||
\(957\) | −3.50422e46 | −2.19006 | ||||||||
\(958\) | −2.12512e46 | −1.30683 | ||||||||
\(959\) | −1.23403e46 | −0.746684 | ||||||||
\(960\) | −6.90401e44 | −0.0411052 | ||||||||
\(961\) | 1.10643e46 | 0.648203 | ||||||||
\(962\) | −3.92929e45 | −0.226517 | ||||||||
\(963\) | 2.19943e45 | 0.124768 | ||||||||
\(964\) | −3.90912e45 | −0.218215 | ||||||||
\(965\) | 8.36657e45 | 0.459594 | ||||||||
\(966\) | 2.29765e45 | 0.124205 | ||||||||
\(967\) | 3.23805e46 | 1.72255 | 0.861277 | − | 0.508136i | \(-0.169665\pi\) | ||||
0.861277 | + | 0.508136i | \(0.169665\pi\) | |||||||
\(968\) | −1.53103e46 | −0.801522 | ||||||||
\(969\) | 8.84102e44 | 0.0455495 | ||||||||
\(970\) | −1.19769e45 | −0.0607270 | ||||||||
\(971\) | −9.38917e44 | −0.0468521 | −0.0234260 | − | 0.999726i | \(-0.507457\pi\) | ||||
−0.0234260 | + | 0.999726i | \(0.507457\pi\) | |||||||
\(972\) | 8.45656e45 | 0.415305 | ||||||||
\(973\) | 1.26247e46 | 0.610202 | ||||||||
\(974\) | −5.82117e45 | −0.276915 | ||||||||
\(975\) | −8.68349e44 | −0.0406558 | ||||||||
\(976\) | −4.29393e45 | −0.197871 | ||||||||
\(977\) | −2.21995e46 | −1.00688 | −0.503441 | − | 0.864030i | \(-0.667933\pi\) | ||||
−0.503441 | + | 0.864030i | \(0.667933\pi\) | |||||||
\(978\) | −1.07002e46 | −0.477681 | ||||||||
\(979\) | 4.82218e46 | 2.11891 | ||||||||
\(980\) | 2.01983e45 | 0.0873594 | ||||||||
\(981\) | −7.79924e45 | −0.332034 | ||||||||
\(982\) | −2.55436e46 | −1.07042 | ||||||||
\(983\) | −9.42127e45 | −0.388624 | −0.194312 | − | 0.980940i | \(-0.562247\pi\) | ||||
−0.194312 | + | 0.980940i | \(0.562247\pi\) | |||||||
\(984\) | −2.72328e45 | −0.110578 | ||||||||
\(985\) | −8.64670e45 | −0.345612 | ||||||||
\(986\) | −1.35487e45 | −0.0533094 | ||||||||
\(987\) | −1.61647e46 | −0.626110 | ||||||||
\(988\) | −4.90819e45 | −0.187150 | ||||||||
\(989\) | 8.65308e45 | 0.324809 | ||||||||
\(990\) | 7.10450e45 | 0.262536 | ||||||||
\(991\) | −5.11507e44 | −0.0186084 | −0.00930422 | − | 0.999957i | \(-0.502962\pi\) | ||||
−0.00930422 | + | 0.999957i | \(0.502962\pi\) | |||||||
\(992\) | 6.33667e45 | 0.226950 | ||||||||
\(993\) | −2.31290e46 | −0.815538 | ||||||||
\(994\) | 9.67341e45 | 0.335808 | ||||||||
\(995\) | 1.71963e46 | 0.587728 | ||||||||
\(996\) | −5.12581e45 | −0.172482 | ||||||||
\(997\) | 9.34514e45 | 0.309607 | 0.154804 | − | 0.987945i | \(-0.450526\pi\) | ||||
0.154804 | + | 0.987945i | \(0.450526\pi\) | |||||||
\(998\) | −2.76977e46 | −0.903483 | ||||||||
\(999\) | 3.87152e46 | 1.24342 |
(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 | 10.32.a.b.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.32.a.b.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial |