Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2,34,Mod(1,2)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 34, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2.1");
S:= CuspForms(chi, 34);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2 \) |
Weight: | \( k \) | \(=\) | \( 34 \) |
Character orbit: | \([\chi]\) | \(=\) | 2.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(13.7965657762\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 2.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −65536.0 | −0.707107 | ||||||||
\(3\) | −1.33006e8 | −1.78389 | −0.891947 | − | 0.452140i | \(-0.850661\pi\) | ||||
−0.891947 | + | 0.452140i | \(0.850661\pi\) | |||||||
\(4\) | 4.29497e9 | 0.500000 | ||||||||
\(5\) | 5.38799e11 | 1.57914 | 0.789572 | − | 0.613658i | \(-0.210303\pi\) | ||||
0.789572 | + | 0.613658i | \(0.210303\pi\) | |||||||
\(6\) | 8.71665e12 | 1.26140 | ||||||||
\(7\) | −3.33473e13 | −0.379265 | −0.189633 | − | 0.981855i | \(-0.560730\pi\) | ||||
−0.189633 | + | 0.981855i | \(0.560730\pi\) | |||||||
\(8\) | −2.81475e14 | −0.353553 | ||||||||
\(9\) | 1.21314e16 | 2.18228 | ||||||||
\(10\) | −3.53107e16 | −1.11662 | ||||||||
\(11\) | −8.58823e16 | −0.563539 | −0.281770 | − | 0.959482i | \(-0.590921\pi\) | ||||
−0.281770 | + | 0.959482i | \(0.590921\pi\) | |||||||
\(12\) | −5.71255e17 | −0.891947 | ||||||||
\(13\) | 1.14405e18 | 0.476849 | 0.238425 | − | 0.971161i | \(-0.423369\pi\) | ||||
0.238425 | + | 0.971161i | \(0.423369\pi\) | |||||||
\(14\) | 2.18545e18 | 0.268181 | ||||||||
\(15\) | −7.16633e19 | −2.81703 | ||||||||
\(16\) | 1.84467e19 | 0.250000 | ||||||||
\(17\) | −1.39114e20 | −0.693366 | −0.346683 | − | 0.937982i | \(-0.612692\pi\) | ||||
−0.346683 | + | 0.937982i | \(0.612692\pi\) | |||||||
\(18\) | −7.95045e20 | −1.54310 | ||||||||
\(19\) | 8.06950e19 | 0.0641818 | 0.0320909 | − | 0.999485i | \(-0.489783\pi\) | ||||
0.0320909 | + | 0.999485i | \(0.489783\pi\) | |||||||
\(20\) | 2.31412e21 | 0.789572 | ||||||||
\(21\) | 4.43538e21 | 0.676569 | ||||||||
\(22\) | 5.62838e21 | 0.398482 | ||||||||
\(23\) | −1.41204e22 | −0.480106 | −0.240053 | − | 0.970760i | \(-0.577165\pi\) | ||||
−0.240053 | + | 0.970760i | \(0.577165\pi\) | |||||||
\(24\) | 3.74377e22 | 0.630702 | ||||||||
\(25\) | 1.73889e23 | 1.49370 | ||||||||
\(26\) | −7.49767e22 | −0.337183 | ||||||||
\(27\) | −8.74160e23 | −2.10906 | ||||||||
\(28\) | −1.43226e23 | −0.189633 | ||||||||
\(29\) | −1.63269e24 | −1.21153 | −0.605767 | − | 0.795642i | \(-0.707134\pi\) | ||||
−0.605767 | + | 0.795642i | \(0.707134\pi\) | |||||||
\(30\) | 4.69652e24 | 1.99194 | ||||||||
\(31\) | −1.89408e24 | −0.467660 | −0.233830 | − | 0.972278i | \(-0.575126\pi\) | ||||
−0.233830 | + | 0.972278i | \(0.575126\pi\) | |||||||
\(32\) | −1.20893e24 | −0.176777 | ||||||||
\(33\) | 1.14228e25 | 1.00529 | ||||||||
\(34\) | 9.11695e24 | 0.490284 | ||||||||
\(35\) | −1.79675e25 | −0.598915 | ||||||||
\(36\) | 5.21040e25 | 1.09114 | ||||||||
\(37\) | −9.64442e25 | −1.28513 | −0.642566 | − | 0.766230i | \(-0.722130\pi\) | ||||
−0.642566 | + | 0.766230i | \(0.722130\pi\) | |||||||
\(38\) | −5.28843e24 | −0.0453834 | ||||||||
\(39\) | −1.52166e26 | −0.850649 | ||||||||
\(40\) | −1.51658e26 | −0.558312 | ||||||||
\(41\) | 6.41768e26 | 1.57197 | 0.785986 | − | 0.618245i | \(-0.212156\pi\) | ||||
0.785986 | + | 0.618245i | \(0.212156\pi\) | |||||||
\(42\) | −2.90677e26 | −0.478407 | ||||||||
\(43\) | −8.17976e26 | −0.913084 | −0.456542 | − | 0.889702i | \(-0.650912\pi\) | ||||
−0.456542 | + | 0.889702i | \(0.650912\pi\) | |||||||
\(44\) | −3.68862e26 | −0.281770 | ||||||||
\(45\) | 6.53640e27 | 3.44613 | ||||||||
\(46\) | 9.25393e26 | 0.339486 | ||||||||
\(47\) | −6.22925e27 | −1.60258 | −0.801292 | − | 0.598273i | \(-0.795854\pi\) | ||||
−0.801292 | + | 0.598273i | \(0.795854\pi\) | |||||||
\(48\) | −2.45352e27 | −0.445974 | ||||||||
\(49\) | −6.61895e27 | −0.856158 | ||||||||
\(50\) | −1.13960e28 | −1.05620 | ||||||||
\(51\) | 1.85029e28 | 1.23689 | ||||||||
\(52\) | 4.91367e27 | 0.238425 | ||||||||
\(53\) | −2.13221e28 | −0.755577 | −0.377788 | − | 0.925892i | \(-0.623315\pi\) | ||||
−0.377788 | + | 0.925892i | \(0.623315\pi\) | |||||||
\(54\) | 5.72890e28 | 1.49133 | ||||||||
\(55\) | −4.62733e28 | −0.889910 | ||||||||
\(56\) | 9.38643e27 | 0.134091 | ||||||||
\(57\) | −1.07329e28 | −0.114494 | ||||||||
\(58\) | 1.07000e29 | 0.856685 | ||||||||
\(59\) | 2.98988e29 | 1.80549 | 0.902746 | − | 0.430175i | \(-0.141548\pi\) | ||||
0.902746 | + | 0.430175i | \(0.141548\pi\) | |||||||
\(60\) | −3.07791e29 | −1.40851 | ||||||||
\(61\) | −4.55882e29 | −1.58822 | −0.794109 | − | 0.607775i | \(-0.792062\pi\) | ||||
−0.794109 | + | 0.607775i | \(0.792062\pi\) | |||||||
\(62\) | 1.24130e29 | 0.330685 | ||||||||
\(63\) | −4.04550e29 | −0.827663 | ||||||||
\(64\) | 7.92282e28 | 0.125000 | ||||||||
\(65\) | 6.16415e29 | 0.753014 | ||||||||
\(66\) | −7.48606e29 | −0.710851 | ||||||||
\(67\) | 1.17233e30 | 0.868593 | 0.434297 | − | 0.900770i | \(-0.356997\pi\) | ||||
0.434297 | + | 0.900770i | \(0.356997\pi\) | |||||||
\(68\) | −5.97489e29 | −0.346683 | ||||||||
\(69\) | 1.87809e30 | 0.856458 | ||||||||
\(70\) | 1.17752e30 | 0.423497 | ||||||||
\(71\) | 2.59152e30 | 0.737552 | 0.368776 | − | 0.929518i | \(-0.379777\pi\) | ||||
0.368776 | + | 0.929518i | \(0.379777\pi\) | |||||||
\(72\) | −3.41469e30 | −0.771552 | ||||||||
\(73\) | −2.82517e30 | −0.508415 | −0.254207 | − | 0.967150i | \(-0.581815\pi\) | ||||
−0.254207 | + | 0.967150i | \(0.581815\pi\) | |||||||
\(74\) | 6.32057e30 | 0.908726 | ||||||||
\(75\) | −2.31282e31 | −2.66460 | ||||||||
\(76\) | 3.46582e29 | 0.0320909 | ||||||||
\(77\) | 2.86394e30 | 0.213731 | ||||||||
\(78\) | 9.97232e30 | 0.601500 | ||||||||
\(79\) | 9.20688e29 | 0.0450055 | 0.0225028 | − | 0.999747i | \(-0.492837\pi\) | ||||
0.0225028 | + | 0.999747i | \(0.492837\pi\) | |||||||
\(80\) | 9.93909e30 | 0.394786 | ||||||||
\(81\) | 4.88289e31 | 1.58006 | ||||||||
\(82\) | −4.20589e31 | −1.11155 | ||||||||
\(83\) | −1.61992e31 | −0.350514 | −0.175257 | − | 0.984523i | \(-0.556076\pi\) | ||||
−0.175257 | + | 0.984523i | \(0.556076\pi\) | |||||||
\(84\) | 1.90498e31 | 0.338285 | ||||||||
\(85\) | −7.49543e31 | −1.09493 | ||||||||
\(86\) | 5.36068e31 | 0.645648 | ||||||||
\(87\) | 2.17156e32 | 2.16125 | ||||||||
\(88\) | 2.41737e31 | 0.199241 | ||||||||
\(89\) | −2.03492e32 | −1.39191 | −0.695955 | − | 0.718085i | \(-0.745019\pi\) | ||||
−0.695955 | + | 0.718085i | \(0.745019\pi\) | |||||||
\(90\) | −4.28369e32 | −2.43678 | ||||||||
\(91\) | −3.81511e31 | −0.180852 | ||||||||
\(92\) | −6.06465e31 | −0.240053 | ||||||||
\(93\) | 2.51923e32 | 0.834256 | ||||||||
\(94\) | 4.08240e32 | 1.13320 | ||||||||
\(95\) | 4.34784e31 | 0.101352 | ||||||||
\(96\) | 1.60794e32 | 0.315351 | ||||||||
\(97\) | 2.26807e32 | 0.374906 | 0.187453 | − | 0.982274i | \(-0.439977\pi\) | ||||
0.187453 | + | 0.982274i | \(0.439977\pi\) | |||||||
\(98\) | 4.33780e32 | 0.605395 | ||||||||
\(99\) | −1.04187e33 | −1.22980 | ||||||||
\(100\) | 7.46848e32 | 0.746848 | ||||||||
\(101\) | 7.19854e32 | 0.610860 | 0.305430 | − | 0.952215i | \(-0.401200\pi\) | ||||
0.305430 | + | 0.952215i | \(0.401200\pi\) | |||||||
\(102\) | −1.21261e33 | −0.874615 | ||||||||
\(103\) | −2.42535e33 | −1.48922 | −0.744611 | − | 0.667499i | \(-0.767365\pi\) | ||||
−0.744611 | + | 0.667499i | \(0.767365\pi\) | |||||||
\(104\) | −3.22023e32 | −0.168592 | ||||||||
\(105\) | 2.38978e33 | 1.06840 | ||||||||
\(106\) | 1.39737e33 | 0.534273 | ||||||||
\(107\) | −4.14367e33 | −1.35692 | −0.678458 | − | 0.734639i | \(-0.737352\pi\) | ||||
−0.678458 | + | 0.734639i | \(0.737352\pi\) | |||||||
\(108\) | −3.75449e33 | −1.05453 | ||||||||
\(109\) | 9.64390e32 | 0.232657 | 0.116328 | − | 0.993211i | \(-0.462888\pi\) | ||||
0.116328 | + | 0.993211i | \(0.462888\pi\) | |||||||
\(110\) | 3.03257e33 | 0.629261 | ||||||||
\(111\) | 1.28276e34 | 2.29254 | ||||||||
\(112\) | −6.15149e32 | −0.0948163 | ||||||||
\(113\) | −1.19165e33 | −0.158619 | −0.0793095 | − | 0.996850i | \(-0.525272\pi\) | ||||
−0.0793095 | + | 0.996850i | \(0.525272\pi\) | |||||||
\(114\) | 7.03390e32 | 0.0809592 | ||||||||
\(115\) | −7.60804e33 | −0.758156 | ||||||||
\(116\) | −7.01234e33 | −0.605767 | ||||||||
\(117\) | 1.38790e34 | 1.04062 | ||||||||
\(118\) | −1.95945e34 | −1.27668 | ||||||||
\(119\) | 4.63907e33 | 0.262970 | ||||||||
\(120\) | 2.01714e34 | 0.995969 | ||||||||
\(121\) | −1.58494e34 | −0.682424 | ||||||||
\(122\) | 2.98767e34 | 1.12304 | ||||||||
\(123\) | −8.53587e34 | −2.80423 | ||||||||
\(124\) | −8.13501e33 | −0.233830 | ||||||||
\(125\) | 3.09669e34 | 0.779618 | ||||||||
\(126\) | 2.65126e34 | 0.585246 | ||||||||
\(127\) | −2.18147e34 | −0.422656 | −0.211328 | − | 0.977415i | \(-0.567779\pi\) | ||||
−0.211328 | + | 0.977415i | \(0.567779\pi\) | |||||||
\(128\) | −5.19230e33 | −0.0883883 | ||||||||
\(129\) | 1.08795e35 | 1.62885 | ||||||||
\(130\) | −4.03974e34 | −0.532461 | ||||||||
\(131\) | 1.54600e35 | 1.79569 | 0.897847 | − | 0.440309i | \(-0.145131\pi\) | ||||
0.897847 | + | 0.440309i | \(0.145131\pi\) | |||||||
\(132\) | 4.90606e34 | 0.502647 | ||||||||
\(133\) | −2.69096e33 | −0.0243420 | ||||||||
\(134\) | −7.68300e34 | −0.614188 | ||||||||
\(135\) | −4.70997e35 | −3.33051 | ||||||||
\(136\) | 3.91570e34 | 0.245142 | ||||||||
\(137\) | 1.66110e35 | 0.921522 | 0.460761 | − | 0.887524i | \(-0.347577\pi\) | ||||
0.460761 | + | 0.887524i | \(0.347577\pi\) | |||||||
\(138\) | −1.23082e35 | −0.605607 | ||||||||
\(139\) | −1.53290e35 | −0.669531 | −0.334766 | − | 0.942301i | \(-0.608657\pi\) | ||||
−0.334766 | + | 0.942301i | \(0.608657\pi\) | |||||||
\(140\) | −7.71698e34 | −0.299457 | ||||||||
\(141\) | 8.28524e35 | 2.85884 | ||||||||
\(142\) | −1.69838e35 | −0.521528 | ||||||||
\(143\) | −9.82539e34 | −0.268723 | ||||||||
\(144\) | 2.23785e35 | 0.545570 | ||||||||
\(145\) | −8.79690e35 | −1.91319 | ||||||||
\(146\) | 1.85151e35 | 0.359503 | ||||||||
\(147\) | 8.80357e35 | 1.52729 | ||||||||
\(148\) | −4.14225e35 | −0.642566 | ||||||||
\(149\) | 3.23613e35 | 0.449213 | 0.224606 | − | 0.974450i | \(-0.427890\pi\) | ||||
0.224606 | + | 0.974450i | \(0.427890\pi\) | |||||||
\(150\) | 1.51573e36 | 1.88415 | ||||||||
\(151\) | −7.40848e35 | −0.825295 | −0.412648 | − | 0.910891i | \(-0.635396\pi\) | ||||
−0.412648 | + | 0.910891i | \(0.635396\pi\) | |||||||
\(152\) | −2.27136e34 | −0.0226917 | ||||||||
\(153\) | −1.68765e36 | −1.51312 | ||||||||
\(154\) | −1.87691e35 | −0.151131 | ||||||||
\(155\) | −1.02053e36 | −0.738502 | ||||||||
\(156\) | −6.53546e35 | −0.425324 | ||||||||
\(157\) | 5.54604e35 | 0.324817 | 0.162408 | − | 0.986724i | \(-0.448074\pi\) | ||||
0.162408 | + | 0.986724i | \(0.448074\pi\) | |||||||
\(158\) | −6.03382e34 | −0.0318237 | ||||||||
\(159\) | 2.83596e36 | 1.34787 | ||||||||
\(160\) | −6.51368e35 | −0.279156 | ||||||||
\(161\) | 4.70876e35 | 0.182087 | ||||||||
\(162\) | −3.20005e36 | −1.11727 | ||||||||
\(163\) | −2.15178e36 | −0.678737 | −0.339369 | − | 0.940653i | \(-0.610213\pi\) | ||||
−0.339369 | + | 0.940653i | \(0.610213\pi\) | |||||||
\(164\) | 2.75637e36 | 0.785986 | ||||||||
\(165\) | 6.15460e36 | 1.58750 | ||||||||
\(166\) | 1.06163e36 | 0.247851 | ||||||||
\(167\) | 9.54101e35 | 0.201731 | 0.100866 | − | 0.994900i | \(-0.467839\pi\) | ||||
0.100866 | + | 0.994900i | \(0.467839\pi\) | |||||||
\(168\) | −1.24845e36 | −0.239203 | ||||||||
\(169\) | −4.44727e36 | −0.772615 | ||||||||
\(170\) | 4.91221e36 | 0.774229 | ||||||||
\(171\) | 9.78945e35 | 0.140063 | ||||||||
\(172\) | −3.51318e36 | −0.456542 | ||||||||
\(173\) | 8.72939e36 | 1.03092 | 0.515458 | − | 0.856915i | \(-0.327622\pi\) | ||||
0.515458 | + | 0.856915i | \(0.327622\pi\) | |||||||
\(174\) | −1.42316e37 | −1.52823 | ||||||||
\(175\) | −5.79874e36 | −0.566507 | ||||||||
\(176\) | −1.58425e36 | −0.140885 | ||||||||
\(177\) | −3.97671e37 | −3.22081 | ||||||||
\(178\) | 1.33360e37 | 0.984230 | ||||||||
\(179\) | 1.44217e37 | 0.970377 | 0.485189 | − | 0.874409i | \(-0.338751\pi\) | ||||
0.485189 | + | 0.874409i | \(0.338751\pi\) | |||||||
\(180\) | 2.80736e37 | 1.72307 | ||||||||
\(181\) | −6.19356e36 | −0.346932 | −0.173466 | − | 0.984840i | \(-0.555497\pi\) | ||||
−0.173466 | + | 0.984840i | \(0.555497\pi\) | |||||||
\(182\) | 2.50027e36 | 0.127882 | ||||||||
\(183\) | 6.06348e37 | 2.83321 | ||||||||
\(184\) | 3.97453e36 | 0.169743 | ||||||||
\(185\) | −5.19641e37 | −2.02941 | ||||||||
\(186\) | −1.65100e37 | −0.589908 | ||||||||
\(187\) | 1.19474e37 | 0.390739 | ||||||||
\(188\) | −2.67544e37 | −0.801292 | ||||||||
\(189\) | 2.91509e37 | 0.799893 | ||||||||
\(190\) | −2.84940e36 | −0.0716670 | ||||||||
\(191\) | −2.37825e37 | −0.548538 | −0.274269 | − | 0.961653i | \(-0.588436\pi\) | ||||
−0.274269 | + | 0.961653i | \(0.588436\pi\) | |||||||
\(192\) | −1.05378e37 | −0.222987 | ||||||||
\(193\) | 7.58741e37 | 1.47366 | 0.736832 | − | 0.676076i | \(-0.236321\pi\) | ||||
0.736832 | + | 0.676076i | \(0.236321\pi\) | |||||||
\(194\) | −1.48640e37 | −0.265098 | ||||||||
\(195\) | −8.19867e37 | −1.34330 | ||||||||
\(196\) | −2.84282e37 | −0.428079 | ||||||||
\(197\) | −1.46746e37 | −0.203177 | −0.101589 | − | 0.994827i | \(-0.532393\pi\) | ||||
−0.101589 | + | 0.994827i | \(0.532393\pi\) | |||||||
\(198\) | 6.82802e37 | 0.869600 | ||||||||
\(199\) | 5.46042e37 | 0.639956 | 0.319978 | − | 0.947425i | \(-0.396324\pi\) | ||||
0.319978 | + | 0.947425i | \(0.396324\pi\) | |||||||
\(200\) | −4.89455e37 | −0.528102 | ||||||||
\(201\) | −1.55927e38 | −1.54948 | ||||||||
\(202\) | −4.71764e37 | −0.431943 | ||||||||
\(203\) | 5.44457e37 | 0.459493 | ||||||||
\(204\) | 7.94693e37 | 0.618446 | ||||||||
\(205\) | 3.45784e38 | 2.48237 | ||||||||
\(206\) | 1.58947e38 | 1.05304 | ||||||||
\(207\) | −1.71300e38 | −1.04772 | ||||||||
\(208\) | 2.11041e37 | 0.119212 | ||||||||
\(209\) | −6.93027e36 | −0.0361690 | ||||||||
\(210\) | −1.56616e38 | −0.755473 | ||||||||
\(211\) | 2.20449e37 | 0.0983213 | 0.0491607 | − | 0.998791i | \(-0.484345\pi\) | ||||
0.0491607 | + | 0.998791i | \(0.484345\pi\) | |||||||
\(212\) | −9.15778e37 | −0.377788 | ||||||||
\(213\) | −3.44687e38 | −1.31571 | ||||||||
\(214\) | 2.71560e38 | 0.959485 | ||||||||
\(215\) | −4.40725e38 | −1.44189 | ||||||||
\(216\) | 2.46054e38 | 0.745665 | ||||||||
\(217\) | 6.31624e37 | 0.177367 | ||||||||
\(218\) | −6.32023e37 | −0.164513 | ||||||||
\(219\) | 3.75764e38 | 0.906958 | ||||||||
\(220\) | −1.98742e38 | −0.444955 | ||||||||
\(221\) | −1.59154e38 | −0.330631 | ||||||||
\(222\) | −8.40671e38 | −1.62107 | ||||||||
\(223\) | −3.00366e38 | −0.537799 | −0.268900 | − | 0.963168i | \(-0.586660\pi\) | ||||
−0.268900 | + | 0.963168i | \(0.586660\pi\) | |||||||
\(224\) | 4.03144e37 | 0.0670453 | ||||||||
\(225\) | 2.10952e39 | 3.25966 | ||||||||
\(226\) | 7.80961e37 | 0.112161 | ||||||||
\(227\) | 7.55693e38 | 1.00906 | 0.504532 | − | 0.863393i | \(-0.331665\pi\) | ||||
0.504532 | + | 0.863393i | \(0.331665\pi\) | |||||||
\(228\) | −4.60974e37 | −0.0572468 | ||||||||
\(229\) | −4.47790e38 | −0.517355 | −0.258678 | − | 0.965964i | \(-0.583287\pi\) | ||||
−0.258678 | + | 0.965964i | \(0.583287\pi\) | |||||||
\(230\) | 4.98601e38 | 0.536097 | ||||||||
\(231\) | −3.80920e38 | −0.381273 | ||||||||
\(232\) | 4.59561e38 | 0.428342 | ||||||||
\(233\) | −8.40517e38 | −0.729750 | −0.364875 | − | 0.931057i | \(-0.618888\pi\) | ||||
−0.364875 | + | 0.931057i | \(0.618888\pi\) | |||||||
\(234\) | −9.09574e38 | −0.735828 | ||||||||
\(235\) | −3.35631e39 | −2.53071 | ||||||||
\(236\) | 1.28414e39 | 0.902746 | ||||||||
\(237\) | −1.22457e38 | −0.0802851 | ||||||||
\(238\) | −3.04026e38 | −0.185948 | ||||||||
\(239\) | 1.59672e39 | 0.911306 | 0.455653 | − | 0.890158i | \(-0.349406\pi\) | ||||
0.455653 | + | 0.890158i | \(0.349406\pi\) | |||||||
\(240\) | −1.32195e39 | −0.704257 | ||||||||
\(241\) | 3.46992e39 | 1.72599 | 0.862996 | − | 0.505212i | \(-0.168586\pi\) | ||||
0.862996 | + | 0.505212i | \(0.168586\pi\) | |||||||
\(242\) | 1.03871e39 | 0.482546 | ||||||||
\(243\) | −1.63500e39 | −0.709603 | ||||||||
\(244\) | −1.95800e39 | −0.794109 | ||||||||
\(245\) | −3.56628e39 | −1.35200 | ||||||||
\(246\) | 5.59407e39 | 1.98289 | ||||||||
\(247\) | 9.23194e37 | 0.0306051 | ||||||||
\(248\) | 5.33136e38 | 0.165343 | ||||||||
\(249\) | 2.15459e39 | 0.625280 | ||||||||
\(250\) | −2.02944e39 | −0.551273 | ||||||||
\(251\) | −1.48419e39 | −0.377461 | −0.188731 | − | 0.982029i | \(-0.560437\pi\) | ||||
−0.188731 | + | 0.982029i | \(0.560437\pi\) | |||||||
\(252\) | −1.73753e39 | −0.413831 | ||||||||
\(253\) | 1.21269e39 | 0.270558 | ||||||||
\(254\) | 1.42965e39 | 0.298863 | ||||||||
\(255\) | 9.96934e39 | 1.95323 | ||||||||
\(256\) | 3.40282e38 | 0.0625000 | ||||||||
\(257\) | −1.36871e39 | −0.235730 | −0.117865 | − | 0.993030i | \(-0.537605\pi\) | ||||
−0.117865 | + | 0.993030i | \(0.537605\pi\) | |||||||
\(258\) | −7.13001e39 | −1.15177 | ||||||||
\(259\) | 3.21616e39 | 0.487406 | ||||||||
\(260\) | 2.64748e39 | 0.376507 | ||||||||
\(261\) | −1.98068e40 | −2.64391 | ||||||||
\(262\) | −1.01318e40 | −1.26975 | ||||||||
\(263\) | 6.59217e39 | 0.775816 | 0.387908 | − | 0.921698i | \(-0.373198\pi\) | ||||
0.387908 | + | 0.921698i | \(0.373198\pi\) | |||||||
\(264\) | −3.21524e39 | −0.355425 | ||||||||
\(265\) | −1.14883e40 | −1.19316 | ||||||||
\(266\) | 1.76355e38 | 0.0172124 | ||||||||
\(267\) | 2.70655e40 | 2.48302 | ||||||||
\(268\) | 5.03513e39 | 0.434297 | ||||||||
\(269\) | 5.00218e39 | 0.405739 | 0.202870 | − | 0.979206i | \(-0.434973\pi\) | ||||
0.202870 | + | 0.979206i | \(0.434973\pi\) | |||||||
\(270\) | 3.08672e40 | 2.35503 | ||||||||
\(271\) | −2.49179e40 | −1.78862 | −0.894308 | − | 0.447451i | \(-0.852332\pi\) | ||||
−0.894308 | + | 0.447451i | \(0.852332\pi\) | |||||||
\(272\) | −2.56619e39 | −0.173342 | ||||||||
\(273\) | 5.07431e39 | 0.322622 | ||||||||
\(274\) | −1.08862e40 | −0.651614 | ||||||||
\(275\) | −1.49340e40 | −0.841757 | ||||||||
\(276\) | 8.06633e39 | 0.428229 | ||||||||
\(277\) | 3.71250e40 | 1.85673 | 0.928367 | − | 0.371665i | \(-0.121213\pi\) | ||||
0.928367 | + | 0.371665i | \(0.121213\pi\) | |||||||
\(278\) | 1.00460e40 | 0.473430 | ||||||||
\(279\) | −2.29779e40 | −1.02056 | ||||||||
\(280\) | 5.05740e39 | 0.211748 | ||||||||
\(281\) | −2.42056e40 | −0.955570 | −0.477785 | − | 0.878477i | \(-0.658560\pi\) | ||||
−0.477785 | + | 0.878477i | \(0.658560\pi\) | |||||||
\(282\) | −5.42982e40 | −2.02151 | ||||||||
\(283\) | 2.77995e40 | 0.976249 | 0.488125 | − | 0.872774i | \(-0.337681\pi\) | ||||
0.488125 | + | 0.872774i | \(0.337681\pi\) | |||||||
\(284\) | 1.11305e40 | 0.368776 | ||||||||
\(285\) | −5.78287e39 | −0.180802 | ||||||||
\(286\) | 6.43917e39 | 0.190016 | ||||||||
\(287\) | −2.14012e40 | −0.596194 | ||||||||
\(288\) | −1.46660e40 | −0.385776 | ||||||||
\(289\) | −2.09019e40 | −0.519243 | ||||||||
\(290\) | 5.76514e40 | 1.35283 | ||||||||
\(291\) | −3.01666e40 | −0.668792 | ||||||||
\(292\) | −1.21340e40 | −0.254207 | ||||||||
\(293\) | 1.14215e40 | 0.226155 | 0.113078 | − | 0.993586i | \(-0.463929\pi\) | ||||
0.113078 | + | 0.993586i | \(0.463929\pi\) | |||||||
\(294\) | −5.76951e40 | −1.07996 | ||||||||
\(295\) | 1.61094e41 | 2.85113 | ||||||||
\(296\) | 2.71466e40 | 0.454363 | ||||||||
\(297\) | 7.50749e40 | 1.18854 | ||||||||
\(298\) | −2.12083e40 | −0.317642 | ||||||||
\(299\) | −1.61545e40 | −0.228938 | ||||||||
\(300\) | −9.93350e40 | −1.33230 | ||||||||
\(301\) | 2.72773e40 | 0.346301 | ||||||||
\(302\) | 4.85522e40 | 0.583572 | ||||||||
\(303\) | −9.57446e40 | −1.08971 | ||||||||
\(304\) | 1.48856e39 | 0.0160455 | ||||||||
\(305\) | −2.45629e41 | −2.50803 | ||||||||
\(306\) | 1.10602e41 | 1.06994 | ||||||||
\(307\) | 1.67395e40 | 0.153447 | 0.0767236 | − | 0.997052i | \(-0.475554\pi\) | ||||
0.0767236 | + | 0.997052i | \(0.475554\pi\) | |||||||
\(308\) | 1.23005e40 | 0.106865 | ||||||||
\(309\) | 3.22584e41 | 2.65661 | ||||||||
\(310\) | 6.68813e40 | 0.522200 | ||||||||
\(311\) | −2.59200e41 | −1.91906 | −0.959528 | − | 0.281612i | \(-0.909131\pi\) | ||||
−0.959528 | + | 0.281612i | \(0.909131\pi\) | |||||||
\(312\) | 4.28308e40 | 0.300750 | ||||||||
\(313\) | −1.65212e41 | −1.10042 | −0.550212 | − | 0.835025i | \(-0.685453\pi\) | ||||
−0.550212 | + | 0.835025i | \(0.685453\pi\) | |||||||
\(314\) | −3.63465e40 | −0.229680 | ||||||||
\(315\) | −2.17971e41 | −1.30700 | ||||||||
\(316\) | 3.95433e39 | 0.0225028 | ||||||||
\(317\) | 5.16289e40 | 0.278879 | 0.139439 | − | 0.990231i | \(-0.455470\pi\) | ||||
0.139439 | + | 0.990231i | \(0.455470\pi\) | |||||||
\(318\) | −1.85858e41 | −0.953087 | ||||||||
\(319\) | 1.40219e41 | 0.682748 | ||||||||
\(320\) | 4.26881e40 | 0.197393 | ||||||||
\(321\) | 5.51131e41 | 2.42060 | ||||||||
\(322\) | −3.08594e40 | −0.128755 | ||||||||
\(323\) | −1.12258e40 | −0.0445015 | ||||||||
\(324\) | 2.09718e41 | 0.790031 | ||||||||
\(325\) | 1.98939e41 | 0.712268 | ||||||||
\(326\) | 1.41019e41 | 0.479940 | ||||||||
\(327\) | −1.28269e41 | −0.415035 | ||||||||
\(328\) | −1.80642e41 | −0.555776 | ||||||||
\(329\) | 2.07729e41 | 0.607805 | ||||||||
\(330\) | −4.03348e41 | −1.12254 | ||||||||
\(331\) | −2.93097e40 | −0.0775977 | −0.0387989 | − | 0.999247i | \(-0.512353\pi\) | ||||
−0.0387989 | + | 0.999247i | \(0.512353\pi\) | |||||||
\(332\) | −6.95751e40 | −0.175257 | ||||||||
\(333\) | −1.17001e42 | −2.80452 | ||||||||
\(334\) | −6.25280e40 | −0.142645 | ||||||||
\(335\) | 6.31652e41 | 1.37163 | ||||||||
\(336\) | 8.18183e40 | 0.169142 | ||||||||
\(337\) | −5.29809e41 | −1.04286 | −0.521429 | − | 0.853294i | \(-0.674601\pi\) | ||||
−0.521429 | + | 0.853294i | \(0.674601\pi\) | |||||||
\(338\) | 2.91456e41 | 0.546321 | ||||||||
\(339\) | 1.58496e41 | 0.282960 | ||||||||
\(340\) | −3.21926e41 | −0.547463 | ||||||||
\(341\) | 1.62668e41 | 0.263545 | ||||||||
\(342\) | −6.41561e40 | −0.0990393 | ||||||||
\(343\) | 4.78532e41 | 0.703976 | ||||||||
\(344\) | 2.30240e41 | 0.322824 | ||||||||
\(345\) | 1.01191e42 | 1.35247 | ||||||||
\(346\) | −5.72089e41 | −0.728967 | ||||||||
\(347\) | 2.52378e40 | 0.0306630 | 0.0153315 | − | 0.999882i | \(-0.495120\pi\) | ||||
0.0153315 | + | 0.999882i | \(0.495120\pi\) | |||||||
\(348\) | 9.32680e41 | 1.08063 | ||||||||
\(349\) | −1.27613e42 | −1.41018 | −0.705092 | − | 0.709116i | \(-0.749094\pi\) | ||||
−0.705092 | + | 0.709116i | \(0.749094\pi\) | |||||||
\(350\) | 3.80026e41 | 0.400581 | ||||||||
\(351\) | −1.00009e42 | −1.00570 | ||||||||
\(352\) | 1.03825e41 | 0.0996206 | ||||||||
\(353\) | −6.97275e41 | −0.638442 | −0.319221 | − | 0.947680i | \(-0.603421\pi\) | ||||
−0.319221 | + | 0.947680i | \(0.603421\pi\) | |||||||
\(354\) | 2.60617e42 | 2.27745 | ||||||||
\(355\) | 1.39631e42 | 1.16470 | ||||||||
\(356\) | −8.73990e41 | −0.695955 | ||||||||
\(357\) | −6.17022e41 | −0.469110 | ||||||||
\(358\) | −9.45139e41 | −0.686160 | ||||||||
\(359\) | 8.87202e41 | 0.615126 | 0.307563 | − | 0.951528i | \(-0.400487\pi\) | ||||
0.307563 | + | 0.951528i | \(0.400487\pi\) | |||||||
\(360\) | −1.83983e42 | −1.21839 | ||||||||
\(361\) | −1.57426e42 | −0.995881 | ||||||||
\(362\) | 4.05901e41 | 0.245318 | ||||||||
\(363\) | 2.10806e42 | 1.21737 | ||||||||
\(364\) | −1.63858e41 | −0.0904262 | ||||||||
\(365\) | −1.52220e42 | −0.802860 | ||||||||
\(366\) | −3.97376e42 | −2.00338 | ||||||||
\(367\) | −3.14846e42 | −1.51743 | −0.758714 | − | 0.651424i | \(-0.774172\pi\) | ||||
−0.758714 | + | 0.651424i | \(0.774172\pi\) | |||||||
\(368\) | −2.60475e41 | −0.120026 | ||||||||
\(369\) | 7.78556e42 | 3.43048 | ||||||||
\(370\) | 3.40552e42 | 1.43501 | ||||||||
\(371\) | 7.11035e41 | 0.286564 | ||||||||
\(372\) | 1.08200e42 | 0.417128 | ||||||||
\(373\) | −9.37335e41 | −0.345700 | −0.172850 | − | 0.984948i | \(-0.555298\pi\) | ||||
−0.172850 | + | 0.984948i | \(0.555298\pi\) | |||||||
\(374\) | −7.82985e41 | −0.276294 | ||||||||
\(375\) | −4.11877e42 | −1.39076 | ||||||||
\(376\) | 1.75338e42 | 0.566599 | ||||||||
\(377\) | −1.86788e42 | −0.577720 | ||||||||
\(378\) | −1.91043e42 | −0.565610 | ||||||||
\(379\) | 3.51502e42 | 0.996278 | 0.498139 | − | 0.867097i | \(-0.334017\pi\) | ||||
0.498139 | + | 0.867097i | \(0.334017\pi\) | |||||||
\(380\) | 1.86738e41 | 0.0506762 | ||||||||
\(381\) | 2.90147e42 | 0.753974 | ||||||||
\(382\) | 1.55861e42 | 0.387875 | ||||||||
\(383\) | 4.14787e42 | 0.988657 | 0.494329 | − | 0.869275i | \(-0.335414\pi\) | ||||
0.494329 | + | 0.869275i | \(0.335414\pi\) | |||||||
\(384\) | 6.90604e41 | 0.157675 | ||||||||
\(385\) | 1.54309e42 | 0.337512 | ||||||||
\(386\) | −4.97249e42 | −1.04204 | ||||||||
\(387\) | −9.92321e42 | −1.99260 | ||||||||
\(388\) | 9.74127e41 | 0.187453 | ||||||||
\(389\) | −1.63044e42 | −0.300703 | −0.150351 | − | 0.988633i | \(-0.548041\pi\) | ||||
−0.150351 | + | 0.988633i | \(0.548041\pi\) | |||||||
\(390\) | 5.37308e42 | 0.949855 | ||||||||
\(391\) | 1.96434e42 | 0.332889 | ||||||||
\(392\) | 1.86307e42 | 0.302697 | ||||||||
\(393\) | −2.05626e43 | −3.20333 | ||||||||
\(394\) | 9.61717e41 | 0.143668 | ||||||||
\(395\) | 4.96066e41 | 0.0710702 | ||||||||
\(396\) | −4.47481e42 | −0.614900 | ||||||||
\(397\) | 7.05205e42 | 0.929548 | 0.464774 | − | 0.885429i | \(-0.346136\pi\) | ||||
0.464774 | + | 0.885429i | \(0.346136\pi\) | |||||||
\(398\) | −3.57854e42 | −0.452517 | ||||||||
\(399\) | 3.57913e41 | 0.0434235 | ||||||||
\(400\) | 3.20769e42 | 0.373424 | ||||||||
\(401\) | 9.06730e42 | 1.01297 | 0.506484 | − | 0.862249i | \(-0.330945\pi\) | ||||
0.506484 | + | 0.862249i | \(0.330945\pi\) | |||||||
\(402\) | 1.02188e43 | 1.09565 | ||||||||
\(403\) | −2.16693e42 | −0.223003 | ||||||||
\(404\) | 3.09175e42 | 0.305430 | ||||||||
\(405\) | 2.63090e43 | 2.49515 | ||||||||
\(406\) | −3.56815e42 | −0.324911 | ||||||||
\(407\) | 8.28285e42 | 0.724222 | ||||||||
\(408\) | −5.20810e42 | −0.437307 | ||||||||
\(409\) | 1.80287e42 | 0.145388 | 0.0726942 | − | 0.997354i | \(-0.476840\pi\) | ||||
0.0726942 | + | 0.997354i | \(0.476840\pi\) | |||||||
\(410\) | −2.26613e43 | −1.75530 | ||||||||
\(411\) | −2.20935e43 | −1.64390 | ||||||||
\(412\) | −1.04168e43 | −0.744611 | ||||||||
\(413\) | −9.97044e42 | −0.684760 | ||||||||
\(414\) | 1.12263e43 | 0.740853 | ||||||||
\(415\) | −8.72813e42 | −0.553512 | ||||||||
\(416\) | −1.38308e42 | −0.0842959 | ||||||||
\(417\) | 2.03885e43 | 1.19437 | ||||||||
\(418\) | 4.54182e41 | 0.0255753 | ||||||||
\(419\) | 2.18879e43 | 1.18488 | 0.592438 | − | 0.805616i | \(-0.298166\pi\) | ||||
0.592438 | + | 0.805616i | \(0.298166\pi\) | |||||||
\(420\) | 1.02640e43 | 0.534200 | ||||||||
\(421\) | 1.25344e43 | 0.627263 | 0.313632 | − | 0.949545i | \(-0.398454\pi\) | ||||
0.313632 | + | 0.949545i | \(0.398454\pi\) | |||||||
\(422\) | −1.44473e42 | −0.0695237 | ||||||||
\(423\) | −7.55696e43 | −3.49729 | ||||||||
\(424\) | 6.00164e42 | 0.267137 | ||||||||
\(425\) | −2.41904e43 | −1.03568 | ||||||||
\(426\) | 2.25894e43 | 0.930351 | ||||||||
\(427\) | 1.52024e43 | 0.602356 | ||||||||
\(428\) | −1.77969e43 | −0.678458 | ||||||||
\(429\) | 1.30683e43 | 0.479374 | ||||||||
\(430\) | 2.88833e43 | 1.01957 | ||||||||
\(431\) | 1.38369e43 | 0.470072 | 0.235036 | − | 0.971987i | \(-0.424479\pi\) | ||||
0.235036 | + | 0.971987i | \(0.424479\pi\) | |||||||
\(432\) | −1.61254e43 | −0.527265 | ||||||||
\(433\) | −4.86806e43 | −1.53216 | −0.766082 | − | 0.642743i | \(-0.777796\pi\) | ||||
−0.766082 | + | 0.642743i | \(0.777796\pi\) | |||||||
\(434\) | −4.13941e42 | −0.125418 | ||||||||
\(435\) | 1.17004e44 | 3.41293 | ||||||||
\(436\) | 4.14203e42 | 0.116328 | ||||||||
\(437\) | −1.13944e42 | −0.0308141 | ||||||||
\(438\) | −2.46261e43 | −0.641316 | ||||||||
\(439\) | 2.44480e43 | 0.613167 | 0.306584 | − | 0.951844i | \(-0.400814\pi\) | ||||
0.306584 | + | 0.951844i | \(0.400814\pi\) | |||||||
\(440\) | 1.30248e43 | 0.314631 | ||||||||
\(441\) | −8.02973e43 | −1.86837 | ||||||||
\(442\) | 1.04303e43 | 0.233792 | ||||||||
\(443\) | 3.59045e43 | 0.775331 | 0.387666 | − | 0.921800i | \(-0.373282\pi\) | ||||
0.387666 | + | 0.921800i | \(0.373282\pi\) | |||||||
\(444\) | 5.50942e43 | 1.14627 | ||||||||
\(445\) | −1.09641e44 | −2.19803 | ||||||||
\(446\) | 1.96848e43 | 0.380282 | ||||||||
\(447\) | −4.30423e43 | −0.801348 | ||||||||
\(448\) | −2.64205e42 | −0.0474082 | ||||||||
\(449\) | 8.52869e43 | 1.47509 | 0.737544 | − | 0.675299i | \(-0.235986\pi\) | ||||
0.737544 | + | 0.675299i | \(0.235986\pi\) | |||||||
\(450\) | −1.38250e44 | −2.30493 | ||||||||
\(451\) | −5.51165e43 | −0.885867 | ||||||||
\(452\) | −5.11811e42 | −0.0793095 | ||||||||
\(453\) | 9.85369e43 | 1.47224 | ||||||||
\(454\) | −4.95251e43 | −0.713516 | ||||||||
\(455\) | −2.05558e43 | −0.285592 | ||||||||
\(456\) | 3.02104e42 | 0.0404796 | ||||||||
\(457\) | 6.07893e43 | 0.785615 | 0.392807 | − | 0.919621i | \(-0.371504\pi\) | ||||
0.392807 | + | 0.919621i | \(0.371504\pi\) | |||||||
\(458\) | 2.93464e43 | 0.365825 | ||||||||
\(459\) | 1.21608e44 | 1.46235 | ||||||||
\(460\) | −3.26763e43 | −0.379078 | ||||||||
\(461\) | −1.43000e44 | −1.60055 | −0.800277 | − | 0.599631i | \(-0.795314\pi\) | ||||
−0.800277 | + | 0.599631i | \(0.795314\pi\) | |||||||
\(462\) | 2.49640e43 | 0.269601 | ||||||||
\(463\) | 1.40454e43 | 0.146369 | 0.0731844 | − | 0.997318i | \(-0.476684\pi\) | ||||
0.0731844 | + | 0.997318i | \(0.476684\pi\) | |||||||
\(464\) | −3.01178e43 | −0.302884 | ||||||||
\(465\) | 1.35736e44 | 1.31741 | ||||||||
\(466\) | 5.50841e43 | 0.516011 | ||||||||
\(467\) | −5.13667e43 | −0.464465 | −0.232233 | − | 0.972660i | \(-0.574603\pi\) | ||||
−0.232233 | + | 0.972660i | \(0.574603\pi\) | |||||||
\(468\) | 5.96098e43 | 0.520309 | ||||||||
\(469\) | −3.90941e43 | −0.329427 | ||||||||
\(470\) | 2.19959e44 | 1.78948 | ||||||||
\(471\) | −7.37654e43 | −0.579439 | ||||||||
\(472\) | −8.41576e43 | −0.638338 | ||||||||
\(473\) | 7.02496e43 | 0.514559 | ||||||||
\(474\) | 8.02532e42 | 0.0567701 | ||||||||
\(475\) | 1.40320e43 | 0.0958682 | ||||||||
\(476\) | 1.99246e43 | 0.131485 | ||||||||
\(477\) | −2.58668e44 | −1.64888 | ||||||||
\(478\) | −1.04643e44 | −0.644390 | ||||||||
\(479\) | −1.67218e44 | −0.994823 | −0.497412 | − | 0.867515i | \(-0.665716\pi\) | ||||
−0.497412 | + | 0.867515i | \(0.665716\pi\) | |||||||
\(480\) | 8.66356e43 | 0.497985 | ||||||||
\(481\) | −1.10337e44 | −0.612814 | ||||||||
\(482\) | −2.27405e44 | −1.22046 | ||||||||
\(483\) | −6.26292e43 | −0.324825 | ||||||||
\(484\) | −6.80726e43 | −0.341212 | ||||||||
\(485\) | 1.22203e44 | 0.592030 | ||||||||
\(486\) | 1.07152e44 | 0.501765 | ||||||||
\(487\) | 1.67480e44 | 0.758117 | 0.379058 | − | 0.925373i | \(-0.376248\pi\) | ||||
0.379058 | + | 0.925373i | \(0.376248\pi\) | |||||||
\(488\) | 1.28319e44 | 0.561520 | ||||||||
\(489\) | 2.86198e44 | 1.21080 | ||||||||
\(490\) | 2.33720e44 | 0.956006 | ||||||||
\(491\) | 2.77223e44 | 1.09644 | 0.548220 | − | 0.836334i | \(-0.315306\pi\) | ||||
0.548220 | + | 0.836334i | \(0.315306\pi\) | |||||||
\(492\) | −3.66613e44 | −1.40212 | ||||||||
\(493\) | 2.27129e44 | 0.840037 | ||||||||
\(494\) | −6.05025e42 | −0.0216411 | ||||||||
\(495\) | −5.61361e44 | −1.94203 | ||||||||
\(496\) | −3.49396e43 | −0.116915 | ||||||||
\(497\) | −8.64204e43 | −0.279728 | ||||||||
\(498\) | −1.41203e44 | −0.442140 | ||||||||
\(499\) | 4.56174e44 | 1.38188 | 0.690942 | − | 0.722910i | \(-0.257196\pi\) | ||||
0.690942 | + | 0.722910i | \(0.257196\pi\) | |||||||
\(500\) | 1.33002e44 | 0.389809 | ||||||||
\(501\) | −1.26901e44 | −0.359867 | ||||||||
\(502\) | 9.72677e43 | 0.266905 | ||||||||
\(503\) | −5.38096e44 | −1.42885 | −0.714427 | − | 0.699710i | \(-0.753312\pi\) | ||||
−0.714427 | + | 0.699710i | \(0.753312\pi\) | |||||||
\(504\) | 1.13871e44 | 0.292623 | ||||||||
\(505\) | 3.87857e44 | 0.964636 | ||||||||
\(506\) | −7.94748e43 | −0.191314 | ||||||||
\(507\) | 5.91512e44 | 1.37826 | ||||||||
\(508\) | −9.36933e43 | −0.211328 | ||||||||
\(509\) | 6.21555e43 | 0.135718 | 0.0678588 | − | 0.997695i | \(-0.478383\pi\) | ||||
0.0678588 | + | 0.997695i | \(0.478383\pi\) | |||||||
\(510\) | −6.53351e44 | −1.38114 | ||||||||
\(511\) | 9.42120e43 | 0.192824 | ||||||||
\(512\) | −2.23007e43 | −0.0441942 | ||||||||
\(513\) | −7.05404e43 | −0.135363 | ||||||||
\(514\) | 8.96998e43 | 0.166686 | ||||||||
\(515\) | −1.30677e45 | −2.35170 | ||||||||
\(516\) | 4.67272e44 | 0.814423 | ||||||||
\(517\) | 5.34982e44 | 0.903119 | ||||||||
\(518\) | −2.10774e44 | −0.344648 | ||||||||
\(519\) | −1.16106e45 | −1.83904 | ||||||||
\(520\) | −1.73505e44 | −0.266231 | ||||||||
\(521\) | −7.97253e44 | −1.18515 | −0.592576 | − | 0.805515i | \(-0.701889\pi\) | ||||
−0.592576 | + | 0.805515i | \(0.701889\pi\) | |||||||
\(522\) | 1.29806e45 | 1.86952 | ||||||||
\(523\) | 1.35653e44 | 0.189301 | 0.0946504 | − | 0.995511i | \(-0.469827\pi\) | ||||
0.0946504 | + | 0.995511i | \(0.469827\pi\) | |||||||
\(524\) | 6.64000e44 | 0.897847 | ||||||||
\(525\) | 7.71264e44 | 1.01059 | ||||||||
\(526\) | −4.32025e44 | −0.548585 | ||||||||
\(527\) | 2.63492e44 | 0.324260 | ||||||||
\(528\) | 2.10714e44 | 0.251324 | ||||||||
\(529\) | −6.65620e44 | −0.769499 | ||||||||
\(530\) | 7.52900e44 | 0.843695 | ||||||||
\(531\) | 3.62715e45 | 3.94009 | ||||||||
\(532\) | −1.15576e43 | −0.0121710 | ||||||||
\(533\) | 7.34218e44 | 0.749593 | ||||||||
\(534\) | −1.77377e45 | −1.75576 | ||||||||
\(535\) | −2.23261e45 | −2.14277 | ||||||||
\(536\) | −3.29982e44 | −0.307094 | ||||||||
\(537\) | −1.91816e45 | −1.73105 | ||||||||
\(538\) | −3.27823e44 | −0.286901 | ||||||||
\(539\) | 5.68450e44 | 0.482479 | ||||||||
\(540\) | −2.02292e45 | −1.66526 | ||||||||
\(541\) | 1.73198e45 | 1.38289 | 0.691445 | − | 0.722429i | \(-0.256974\pi\) | ||||
0.691445 | + | 0.722429i | \(0.256974\pi\) | |||||||
\(542\) | 1.63302e45 | 1.26474 | ||||||||
\(543\) | 8.23778e44 | 0.618889 | ||||||||
\(544\) | 1.68178e44 | 0.122571 | ||||||||
\(545\) | 5.19613e44 | 0.367399 | ||||||||
\(546\) | −3.32550e44 | −0.228128 | ||||||||
\(547\) | −1.10462e45 | −0.735227 | −0.367614 | − | 0.929979i | \(-0.619825\pi\) | ||||
−0.367614 | + | 0.929979i | \(0.619825\pi\) | |||||||
\(548\) | 7.13436e44 | 0.460761 | ||||||||
\(549\) | −5.53049e45 | −3.46593 | ||||||||
\(550\) | 9.78714e44 | 0.595212 | ||||||||
\(551\) | −1.31750e44 | −0.0777586 | ||||||||
\(552\) | −5.28635e44 | −0.302804 | ||||||||
\(553\) | −3.07025e43 | −0.0170690 | ||||||||
\(554\) | −2.43302e45 | −1.31291 | ||||||||
\(555\) | 6.91151e45 | 3.62025 | ||||||||
\(556\) | −6.58378e44 | −0.334766 | ||||||||
\(557\) | 1.13068e45 | 0.558120 | 0.279060 | − | 0.960274i | \(-0.409977\pi\) | ||||
0.279060 | + | 0.960274i | \(0.409977\pi\) | |||||||
\(558\) | 1.50588e45 | 0.721648 | ||||||||
\(559\) | −9.35808e44 | −0.435404 | ||||||||
\(560\) | −3.31442e44 | −0.149729 | ||||||||
\(561\) | −1.58907e45 | −0.697037 | ||||||||
\(562\) | 1.58634e45 | 0.675690 | ||||||||
\(563\) | 2.85343e45 | 1.18026 | 0.590131 | − | 0.807307i | \(-0.299076\pi\) | ||||
0.590131 | + | 0.807307i | \(0.299076\pi\) | |||||||
\(564\) | 3.55849e45 | 1.42942 | ||||||||
\(565\) | −6.42061e44 | −0.250482 | ||||||||
\(566\) | −1.82187e45 | −0.690312 | ||||||||
\(567\) | −1.62831e45 | −0.599263 | ||||||||
\(568\) | −7.29449e44 | −0.260764 | ||||||||
\(569\) | 4.66376e44 | 0.161951 | 0.0809756 | − | 0.996716i | \(-0.474196\pi\) | ||||
0.0809756 | + | 0.996716i | \(0.474196\pi\) | |||||||
\(570\) | 3.78986e44 | 0.127846 | ||||||||
\(571\) | −5.04939e45 | −1.65479 | −0.827396 | − | 0.561619i | \(-0.810179\pi\) | ||||
−0.827396 | + | 0.561619i | \(0.810179\pi\) | |||||||
\(572\) | −4.21997e44 | −0.134362 | ||||||||
\(573\) | 3.16320e45 | 0.978533 | ||||||||
\(574\) | 1.40255e45 | 0.421573 | ||||||||
\(575\) | −2.45538e45 | −0.717132 | ||||||||
\(576\) | 9.61150e44 | 0.272785 | ||||||||
\(577\) | 2.74486e44 | 0.0757040 | 0.0378520 | − | 0.999283i | \(-0.487948\pi\) | ||||
0.0378520 | + | 0.999283i | \(0.487948\pi\) | |||||||
\(578\) | 1.36983e45 | 0.367161 | ||||||||
\(579\) | −1.00917e46 | −2.62886 | ||||||||
\(580\) | −3.77824e45 | −0.956594 | ||||||||
\(581\) | 5.40200e44 | 0.132938 | ||||||||
\(582\) | 1.97700e45 | 0.472908 | ||||||||
\(583\) | 1.83119e45 | 0.425797 | ||||||||
\(584\) | 7.95216e44 | 0.179752 | ||||||||
\(585\) | 7.47799e45 | 1.64329 | ||||||||
\(586\) | −7.48518e44 | −0.159916 | ||||||||
\(587\) | 3.25926e45 | 0.677002 | 0.338501 | − | 0.940966i | \(-0.390080\pi\) | ||||
0.338501 | + | 0.940966i | \(0.390080\pi\) | |||||||
\(588\) | 3.78111e45 | 0.763647 | ||||||||
\(589\) | −1.52843e44 | −0.0300153 | ||||||||
\(590\) | −1.05575e46 | −2.01605 | ||||||||
\(591\) | 1.95181e45 | 0.362446 | ||||||||
\(592\) | −1.77908e45 | −0.321283 | ||||||||
\(593\) | 1.56542e45 | 0.274933 | 0.137467 | − | 0.990506i | \(-0.456104\pi\) | ||||
0.137467 | + | 0.990506i | \(0.456104\pi\) | |||||||
\(594\) | −4.92011e45 | −0.840423 | ||||||||
\(595\) | 2.49953e45 | 0.415267 | ||||||||
\(596\) | 1.38991e45 | 0.224606 | ||||||||
\(597\) | −7.26266e45 | −1.14161 | ||||||||
\(598\) | 1.05870e45 | 0.161884 | ||||||||
\(599\) | 2.66724e45 | 0.396753 | 0.198376 | − | 0.980126i | \(-0.436433\pi\) | ||||
0.198376 | + | 0.980126i | \(0.436433\pi\) | |||||||
\(600\) | 6.51002e45 | 0.942077 | ||||||||
\(601\) | 1.01736e46 | 1.43234 | 0.716170 | − | 0.697926i | \(-0.245893\pi\) | ||||
0.716170 | + | 0.697926i | \(0.245893\pi\) | |||||||
\(602\) | −1.78764e45 | −0.244872 | ||||||||
\(603\) | 1.42221e46 | 1.89551 | ||||||||
\(604\) | −3.18192e45 | −0.412648 | ||||||||
\(605\) | −8.53964e45 | −1.07765 | ||||||||
\(606\) | 6.27472e45 | 0.770541 | ||||||||
\(607\) | −1.91910e45 | −0.229343 | −0.114671 | − | 0.993403i | \(-0.536581\pi\) | ||||
−0.114671 | + | 0.993403i | \(0.536581\pi\) | |||||||
\(608\) | −9.75543e43 | −0.0113459 | ||||||||
\(609\) | −7.24158e45 | −0.819687 | ||||||||
\(610\) | 1.60975e46 | 1.77344 | ||||||||
\(611\) | −7.12659e45 | −0.764191 | ||||||||
\(612\) | −7.24839e45 | −0.756559 | ||||||||
\(613\) | −9.21265e45 | −0.936023 | −0.468012 | − | 0.883722i | \(-0.655029\pi\) | ||||
−0.468012 | + | 0.883722i | \(0.655029\pi\) | |||||||
\(614\) | −1.09704e45 | −0.108504 | ||||||||
\(615\) | −4.59912e46 | −4.42828 | ||||||||
\(616\) | −8.06128e44 | −0.0755653 | ||||||||
\(617\) | 1.85344e46 | 1.69150 | 0.845752 | − | 0.533577i | \(-0.179152\pi\) | ||||
0.845752 | + | 0.533577i | \(0.179152\pi\) | |||||||
\(618\) | −2.11409e46 | −1.87851 | ||||||||
\(619\) | 1.79796e46 | 1.55555 | 0.777777 | − | 0.628540i | \(-0.216347\pi\) | ||||
0.777777 | + | 0.628540i | \(0.216347\pi\) | |||||||
\(620\) | −4.38313e45 | −0.369251 | ||||||||
\(621\) | 1.23435e46 | 1.01257 | ||||||||
\(622\) | 1.69869e46 | 1.35698 | ||||||||
\(623\) | 6.78590e45 | 0.527904 | ||||||||
\(624\) | −2.80696e45 | −0.212662 | ||||||||
\(625\) | −3.55844e45 | −0.262567 | ||||||||
\(626\) | 1.08273e46 | 0.778117 | ||||||||
\(627\) | 9.21764e44 | 0.0645217 | ||||||||
\(628\) | 2.38200e45 | 0.162408 | ||||||||
\(629\) | 1.34167e46 | 0.891067 | ||||||||
\(630\) | 1.42850e46 | 0.924188 | ||||||||
\(631\) | −1.17228e46 | −0.738831 | −0.369416 | − | 0.929264i | \(-0.620442\pi\) | ||||
−0.369416 | + | 0.929264i | \(0.620442\pi\) | |||||||
\(632\) | −2.59151e44 | −0.0159119 | ||||||||
\(633\) | −2.93209e45 | −0.175395 | ||||||||
\(634\) | −3.38355e45 | −0.197197 | ||||||||
\(635\) | −1.17537e46 | −0.667435 | ||||||||
\(636\) | 1.21804e46 | 0.673934 | ||||||||
\(637\) | −7.57244e45 | −0.408258 | ||||||||
\(638\) | −9.18938e45 | −0.482775 | ||||||||
\(639\) | 3.14389e46 | 1.60954 | ||||||||
\(640\) | −2.79761e45 | −0.139578 | ||||||||
\(641\) | −1.41216e46 | −0.686638 | −0.343319 | − | 0.939219i | \(-0.611551\pi\) | ||||
−0.343319 | + | 0.939219i | \(0.611551\pi\) | |||||||
\(642\) | −3.61190e46 | −1.71162 | ||||||||
\(643\) | −4.07405e45 | −0.188168 | −0.0940838 | − | 0.995564i | \(-0.529992\pi\) | ||||
−0.0940838 | + | 0.995564i | \(0.529992\pi\) | |||||||
\(644\) | 2.02240e45 | 0.0910437 | ||||||||
\(645\) | 5.86188e46 | 2.57218 | ||||||||
\(646\) | 7.35693e44 | 0.0314673 | ||||||||
\(647\) | −3.65004e45 | −0.152187 | −0.0760933 | − | 0.997101i | \(-0.524245\pi\) | ||||
−0.0760933 | + | 0.997101i | \(0.524245\pi\) | |||||||
\(648\) | −1.37441e46 | −0.558636 | ||||||||
\(649\) | −2.56778e46 | −1.01747 | ||||||||
\(650\) | −1.30376e46 | −0.503650 | ||||||||
\(651\) | −8.40096e45 | −0.316404 | ||||||||
\(652\) | −9.24181e45 | −0.339369 | ||||||||
\(653\) | −5.21698e46 | −1.86789 | −0.933946 | − | 0.357414i | \(-0.883659\pi\) | ||||
−0.933946 | + | 0.357414i | \(0.883659\pi\) | |||||||
\(654\) | 8.40626e45 | 0.293474 | ||||||||
\(655\) | 8.32982e46 | 2.83566 | ||||||||
\(656\) | 1.18385e46 | 0.392993 | ||||||||
\(657\) | −3.42734e46 | −1.10950 | ||||||||
\(658\) | −1.36137e46 | −0.429783 | ||||||||
\(659\) | −5.05202e45 | −0.155545 | −0.0777724 | − | 0.996971i | \(-0.524781\pi\) | ||||
−0.0777724 | + | 0.996971i | \(0.524781\pi\) | |||||||
\(660\) | 2.64338e46 | 0.793752 | ||||||||
\(661\) | −5.49372e46 | −1.60895 | −0.804475 | − | 0.593987i | \(-0.797553\pi\) | ||||
−0.804475 | + | 0.593987i | \(0.797553\pi\) | |||||||
\(662\) | 1.92084e45 | 0.0548699 | ||||||||
\(663\) | 2.11683e46 | 0.589811 | ||||||||
\(664\) | 4.55968e45 | 0.123925 | ||||||||
\(665\) | −1.44989e45 | −0.0384395 | ||||||||
\(666\) | 7.66775e46 | 1.98309 | ||||||||
\(667\) | 2.30541e46 | 0.581665 | ||||||||
\(668\) | 4.09783e45 | 0.100866 | ||||||||
\(669\) | 3.99503e46 | 0.959377 | ||||||||
\(670\) | −4.13959e46 | −0.969892 | ||||||||
\(671\) | 3.91522e46 | 0.895023 | ||||||||
\(672\) | −5.36204e45 | −0.119602 | ||||||||
\(673\) | 3.75226e45 | 0.0816666 | 0.0408333 | − | 0.999166i | \(-0.486999\pi\) | ||||
0.0408333 | + | 0.999166i | \(0.486999\pi\) | |||||||
\(674\) | 3.47215e46 | 0.737413 | ||||||||
\(675\) | −1.52007e47 | −3.15030 | ||||||||
\(676\) | −1.91009e46 | −0.386307 | ||||||||
\(677\) | 4.64616e46 | 0.917025 | 0.458513 | − | 0.888688i | \(-0.348382\pi\) | ||||
0.458513 | + | 0.888688i | \(0.348382\pi\) | |||||||
\(678\) | −1.03872e46 | −0.200083 | ||||||||
\(679\) | −7.56339e45 | −0.142189 | ||||||||
\(680\) | 2.10978e46 | 0.387115 | ||||||||
\(681\) | −1.00511e47 | −1.80006 | ||||||||
\(682\) | −1.06606e46 | −0.186354 | ||||||||
\(683\) | 8.92876e46 | 1.52352 | 0.761762 | − | 0.647857i | \(-0.224334\pi\) | ||||
0.761762 | + | 0.647857i | \(0.224334\pi\) | |||||||
\(684\) | 4.20454e45 | 0.0700313 | ||||||||
\(685\) | 8.94997e46 | 1.45522 | ||||||||
\(686\) | −3.13611e46 | −0.497786 | ||||||||
\(687\) | 5.95585e46 | 0.922907 | ||||||||
\(688\) | −1.50890e46 | −0.228271 | ||||||||
\(689\) | −2.43937e46 | −0.360296 | ||||||||
\(690\) | −6.63167e46 | −0.956341 | ||||||||
\(691\) | −1.40554e47 | −1.97904 | −0.989522 | − | 0.144382i | \(-0.953881\pi\) | ||||
−0.989522 | + | 0.144382i | \(0.953881\pi\) | |||||||
\(692\) | 3.74924e46 | 0.515458 | ||||||||
\(693\) | 3.47437e46 | 0.466420 | ||||||||
\(694\) | −1.65398e45 | −0.0216820 | ||||||||
\(695\) | −8.25928e46 | −1.05729 | ||||||||
\(696\) | −6.11241e46 | −0.764117 | ||||||||
\(697\) | −8.92787e46 | −1.08995 | ||||||||
\(698\) | 8.36325e46 | 0.997150 | ||||||||
\(699\) | 1.11793e47 | 1.30180 | ||||||||
\(700\) | −2.49054e46 | −0.283254 | ||||||||
\(701\) | −5.92277e46 | −0.657926 | −0.328963 | − | 0.944343i | \(-0.606699\pi\) | ||||
−0.328963 | + | 0.944343i | \(0.606699\pi\) | |||||||
\(702\) | 6.55417e46 | 0.711140 | ||||||||
\(703\) | −7.78257e45 | −0.0824821 | ||||||||
\(704\) | −6.80429e45 | −0.0704424 | ||||||||
\(705\) | 4.46408e47 | 4.51452 | ||||||||
\(706\) | 4.56966e46 | 0.451447 | ||||||||
\(707\) | −2.40052e46 | −0.231678 | ||||||||
\(708\) | −1.70798e47 | −1.61040 | ||||||||
\(709\) | 6.19740e46 | 0.570882 | 0.285441 | − | 0.958396i | \(-0.407860\pi\) | ||||
0.285441 | + | 0.958396i | \(0.407860\pi\) | |||||||
\(710\) | −9.15086e46 | −0.823568 | ||||||||
\(711\) | 1.11693e46 | 0.0982146 | ||||||||
\(712\) | 5.72778e46 | 0.492115 | ||||||||
\(713\) | 2.67451e46 | 0.224526 | ||||||||
\(714\) | 4.04371e46 | 0.331711 | ||||||||
\(715\) | −5.29391e46 | −0.424353 | ||||||||
\(716\) | 6.19406e46 | 0.485189 | ||||||||
\(717\) | −2.12373e47 | −1.62567 | ||||||||
\(718\) | −5.81436e46 | −0.434960 | ||||||||
\(719\) | −2.33935e46 | −0.171028 | −0.0855142 | − | 0.996337i | \(-0.527253\pi\) | ||||
−0.0855142 | + | 0.996337i | \(0.527253\pi\) | |||||||
\(720\) | 1.20575e47 | 0.861533 | ||||||||
\(721\) | 8.08787e46 | 0.564810 | ||||||||
\(722\) | 1.03171e47 | 0.704194 | ||||||||
\(723\) | −4.61519e47 | −3.07899 | ||||||||
\(724\) | −2.66011e46 | −0.173466 | ||||||||
\(725\) | −2.83907e47 | −1.80967 | ||||||||
\(726\) | −1.38154e47 | −0.860812 | ||||||||
\(727\) | 3.68313e46 | 0.224336 | 0.112168 | − | 0.993689i | \(-0.464220\pi\) | ||||
0.112168 | + | 0.993689i | \(0.464220\pi\) | |||||||
\(728\) | 1.07386e46 | 0.0639410 | ||||||||
\(729\) | −5.39781e46 | −0.314205 | ||||||||
\(730\) | 9.97590e46 | 0.567708 | ||||||||
\(731\) | 1.13792e47 | 0.633102 | ||||||||
\(732\) | 2.60425e47 | 1.41661 | ||||||||
\(733\) | 1.06749e47 | 0.567740 | 0.283870 | − | 0.958863i | \(-0.408382\pi\) | ||||
0.283870 | + | 0.958863i | \(0.408382\pi\) | |||||||
\(734\) | 2.06337e47 | 1.07298 | ||||||||
\(735\) | 4.74336e47 | 2.41182 | ||||||||
\(736\) | 1.70705e46 | 0.0848715 | ||||||||
\(737\) | −1.00683e47 | −0.489486 | ||||||||
\(738\) | −5.10234e47 | −2.42572 | ||||||||
\(739\) | 1.86383e47 | 0.866509 | 0.433254 | − | 0.901272i | \(-0.357365\pi\) | ||||
0.433254 | + | 0.901272i | \(0.357365\pi\) | |||||||
\(740\) | −2.23184e47 | −1.01470 | ||||||||
\(741\) | −1.22790e46 | −0.0545962 | ||||||||
\(742\) | −4.65984e46 | −0.202631 | ||||||||
\(743\) | −1.41560e47 | −0.602040 | −0.301020 | − | 0.953618i | \(-0.597327\pi\) | ||||
−0.301020 | + | 0.953618i | \(0.597327\pi\) | |||||||
\(744\) | −7.09100e46 | −0.294954 | ||||||||
\(745\) | 1.74362e47 | 0.709372 | ||||||||
\(746\) | 6.14292e46 | 0.244447 | ||||||||
\(747\) | −1.96520e47 | −0.764920 | ||||||||
\(748\) | 5.13137e46 | 0.195370 | ||||||||
\(749\) | 1.38180e47 | 0.514631 | ||||||||
\(750\) | 2.69927e47 | 0.983413 | ||||||||
\(751\) | 2.61886e47 | 0.933368 | 0.466684 | − | 0.884424i | \(-0.345449\pi\) | ||||
0.466684 | + | 0.884424i | \(0.345449\pi\) | |||||||
\(752\) | −1.14909e47 | −0.400646 | ||||||||
\(753\) | 1.97405e47 | 0.673351 | ||||||||
\(754\) | 1.22414e47 | 0.408509 | ||||||||
\(755\) | −3.99168e47 | −1.30326 | ||||||||
\(756\) | 1.25202e47 | 0.399947 | ||||||||
\(757\) | 2.21676e47 | 0.692846 | 0.346423 | − | 0.938078i | \(-0.387396\pi\) | ||||
0.346423 | + | 0.938078i | \(0.387396\pi\) | |||||||
\(758\) | −2.30360e47 | −0.704475 | ||||||||
\(759\) | −1.61294e47 | −0.482648 | ||||||||
\(760\) | −1.22381e46 | −0.0358335 | ||||||||
\(761\) | 1.15570e47 | 0.331131 | 0.165565 | − | 0.986199i | \(-0.447055\pi\) | ||||
0.165565 | + | 0.986199i | \(0.447055\pi\) | |||||||
\(762\) | −1.90151e47 | −0.533140 | ||||||||
\(763\) | −3.21598e46 | −0.0882386 | ||||||||
\(764\) | −1.02145e47 | −0.274269 | ||||||||
\(765\) | −9.09302e47 | −2.38943 | ||||||||
\(766\) | −2.71835e47 | −0.699086 | ||||||||
\(767\) | 3.42058e47 | 0.860947 | ||||||||
\(768\) | −4.52594e46 | −0.111493 | ||||||||
\(769\) | −3.82649e47 | −0.922605 | −0.461302 | − | 0.887243i | \(-0.652618\pi\) | ||||
−0.461302 | + | 0.887243i | \(0.652618\pi\) | |||||||
\(770\) | −1.01128e47 | −0.238657 | ||||||||
\(771\) | 1.82046e47 | 0.420518 | ||||||||
\(772\) | 3.25877e47 | 0.736832 | ||||||||
\(773\) | 7.89533e47 | 1.74746 | 0.873732 | − | 0.486407i | \(-0.161693\pi\) | ||||
0.873732 | + | 0.486407i | \(0.161693\pi\) | |||||||
\(774\) | 6.50327e47 | 1.40898 | ||||||||
\(775\) | −3.29360e47 | −0.698542 | ||||||||
\(776\) | −6.38404e46 | −0.132549 | ||||||||
\(777\) | −4.27767e47 | −0.869481 | ||||||||
\(778\) | 1.06853e47 | 0.212629 | ||||||||
\(779\) | 5.17875e46 | 0.100892 | ||||||||
\(780\) | −3.52130e47 | −0.671649 | ||||||||
\(781\) | −2.22566e47 | −0.415639 | ||||||||
\(782\) | −1.28735e47 | −0.235388 | ||||||||
\(783\) | 1.42723e48 | 2.55520 | ||||||||
\(784\) | −1.22098e47 | −0.214039 | ||||||||
\(785\) | 2.98820e47 | 0.512933 | ||||||||
\(786\) | 1.34759e48 | 2.26509 | ||||||||
\(787\) | −1.15500e48 | −1.90107 | −0.950534 | − | 0.310620i | \(-0.899463\pi\) | ||||
−0.950534 | + | 0.310620i | \(0.899463\pi\) | |||||||
\(788\) | −6.30271e46 | −0.101589 | ||||||||
\(789\) | −8.76795e47 | −1.38397 | ||||||||
\(790\) | −3.25102e46 | −0.0502542 | ||||||||
\(791\) | 3.97384e46 | 0.0601587 | ||||||||
\(792\) | 2.93261e47 | 0.434800 | ||||||||
\(793\) | −5.21554e47 | −0.757341 | ||||||||
\(794\) | −4.62163e47 | −0.657290 | ||||||||
\(795\) | 1.52801e48 | 2.12848 | ||||||||
\(796\) | 2.34523e47 | 0.319978 | ||||||||
\(797\) | 4.08413e47 | 0.545805 | 0.272902 | − | 0.962042i | \(-0.412016\pi\) | ||||
0.272902 | + | 0.962042i | \(0.412016\pi\) | |||||||
\(798\) | −2.34562e46 | −0.0307050 | ||||||||
\(799\) | 8.66573e47 | 1.11118 | ||||||||
\(800\) | −2.10219e47 | −0.264051 | ||||||||
\(801\) | −2.46864e48 | −3.03754 | ||||||||
\(802\) | −5.94235e47 | −0.716277 | ||||||||
\(803\) | 2.42632e47 | 0.286512 | ||||||||
\(804\) | −6.69700e47 | −0.774739 | ||||||||
\(805\) | 2.53708e47 | 0.287542 | ||||||||
\(806\) | 1.42012e47 | 0.157687 | ||||||||
\(807\) | −6.65318e47 | −0.723796 | ||||||||
\(808\) | −2.02621e47 | −0.215972 | ||||||||
\(809\) | 7.61932e47 | 0.795730 | 0.397865 | − | 0.917444i | \(-0.369751\pi\) | ||||
0.397865 | + | 0.917444i | \(0.369751\pi\) | |||||||
\(810\) | −1.72418e48 | −1.76433 | ||||||||
\(811\) | −1.03654e48 | −1.03930 | −0.519651 | − | 0.854378i | \(-0.673938\pi\) | ||||
−0.519651 | + | 0.854378i | \(0.673938\pi\) | |||||||
\(812\) | 2.33843e47 | 0.229747 | ||||||||
\(813\) | 3.31421e48 | 3.19070 | ||||||||
\(814\) | −5.42825e47 | −0.512103 | ||||||||
\(815\) | −1.15938e48 | −1.07182 | ||||||||
\(816\) | 3.41318e47 | 0.309223 | ||||||||
\(817\) | −6.60065e46 | −0.0586034 | ||||||||
\(818\) | −1.18153e47 | −0.102805 | ||||||||
\(819\) | −4.62827e47 | −0.394670 | ||||||||
\(820\) | 1.48513e48 | 1.24118 | ||||||||
\(821\) | 8.66860e47 | 0.710047 | 0.355023 | − | 0.934857i | \(-0.384473\pi\) | ||||
0.355023 | + | 0.934857i | \(0.384473\pi\) | |||||||
\(822\) | 1.44792e48 | 1.16241 | ||||||||
\(823\) | 6.30492e47 | 0.496115 | 0.248058 | − | 0.968745i | \(-0.420208\pi\) | ||||
0.248058 | + | 0.968745i | \(0.420208\pi\) | |||||||
\(824\) | 6.82674e47 | 0.526519 | ||||||||
\(825\) | 1.98630e48 | 1.50161 | ||||||||
\(826\) | 6.53423e47 | 0.484199 | ||||||||
\(827\) | 2.94601e47 | 0.213990 | 0.106995 | − | 0.994260i | \(-0.465877\pi\) | ||||
0.106995 | + | 0.994260i | \(0.465877\pi\) | |||||||
\(828\) | −7.35729e47 | −0.523862 | ||||||||
\(829\) | −1.63460e48 | −1.14094 | −0.570470 | − | 0.821318i | \(-0.693239\pi\) | ||||
−0.570470 | + | 0.821318i | \(0.693239\pi\) | |||||||
\(830\) | 5.72006e47 | 0.391392 | ||||||||
\(831\) | −4.93782e48 | −3.31222 | ||||||||
\(832\) | 9.06413e46 | 0.0596062 | ||||||||
\(833\) | 9.20787e47 | 0.593631 | ||||||||
\(834\) | −1.33618e48 | −0.844549 | ||||||||
\(835\) | 5.14069e47 | 0.318562 | ||||||||
\(836\) | −2.97653e46 | −0.0180845 | ||||||||
\(837\) | 1.65573e48 | 0.986323 | ||||||||
\(838\) | −1.43445e48 | −0.837833 | ||||||||
\(839\) | −2.42256e48 | −1.38740 | −0.693702 | − | 0.720262i | \(-0.744021\pi\) | ||||
−0.693702 | + | 0.720262i | \(0.744021\pi\) | |||||||
\(840\) | −6.72663e47 | −0.377737 | ||||||||
\(841\) | 8.49591e47 | 0.467817 | ||||||||
\(842\) | −8.21456e47 | −0.443542 | ||||||||
\(843\) | 3.21949e48 | 1.70464 | ||||||||
\(844\) | 9.46821e46 | 0.0491607 | ||||||||
\(845\) | −2.39619e48 | −1.22007 | ||||||||
\(846\) | 4.95253e48 | 2.47295 | ||||||||
\(847\) | 5.28535e47 | 0.258820 | ||||||||
\(848\) | −3.93324e47 | −0.188894 | ||||||||
\(849\) | −3.69749e48 | −1.74153 | ||||||||
\(850\) | 1.58534e48 | 0.732335 | ||||||||
\(851\) | 1.36183e48 | 0.616999 | ||||||||
\(852\) | −1.48042e48 | −0.657857 | ||||||||
\(853\) | −2.74926e48 | −1.19827 | −0.599137 | − | 0.800647i | \(-0.704489\pi\) | ||||
−0.599137 | + | 0.800647i | \(0.704489\pi\) | |||||||
\(854\) | −9.96307e47 | −0.425930 | ||||||||
\(855\) | 5.27455e47 | 0.221179 | ||||||||
\(856\) | 1.16634e48 | 0.479742 | ||||||||
\(857\) | −7.23564e47 | −0.291940 | −0.145970 | − | 0.989289i | \(-0.546630\pi\) | ||||
−0.145970 | + | 0.989289i | \(0.546630\pi\) | |||||||
\(858\) | −8.56446e47 | −0.338969 | ||||||||
\(859\) | −8.35479e47 | −0.324376 | −0.162188 | − | 0.986760i | \(-0.551855\pi\) | ||||
−0.162188 | + | 0.986760i | \(0.551855\pi\) | |||||||
\(860\) | −1.89290e48 | −0.720946 | ||||||||
\(861\) | 2.84648e48 | 1.06355 | ||||||||
\(862\) | −9.06816e47 | −0.332391 | ||||||||
\(863\) | 6.91469e46 | 0.0248653 | 0.0124327 | − | 0.999923i | \(-0.496042\pi\) | ||||
0.0124327 | + | 0.999923i | \(0.496042\pi\) | |||||||
\(864\) | 1.05679e48 | 0.372833 | ||||||||
\(865\) | 4.70339e48 | 1.62796 | ||||||||
\(866\) | 3.19033e48 | 1.08340 | ||||||||
\(867\) | 2.78007e48 | 0.926275 | ||||||||
\(868\) | 2.71281e47 | 0.0886836 | ||||||||
\(869\) | −7.90708e46 | −0.0253624 | ||||||||
\(870\) | −7.66795e48 | −2.41330 | ||||||||
\(871\) | 1.34121e48 | 0.414188 | ||||||||
\(872\) | −2.71452e47 | −0.0822566 | ||||||||
\(873\) | 2.75149e48 | 0.818149 | ||||||||
\(874\) | 7.46746e46 | 0.0217888 | ||||||||
\(875\) | −1.03266e48 | −0.295682 | ||||||||
\(876\) | 1.61389e48 | 0.453479 | ||||||||
\(877\) | 4.76181e48 | 1.31304 | 0.656521 | − | 0.754308i | \(-0.272027\pi\) | ||||
0.656521 | + | 0.754308i | \(0.272027\pi\) | |||||||
\(878\) | −1.60222e48 | −0.433575 | ||||||||
\(879\) | −1.51912e48 | −0.403437 | ||||||||
\(880\) | −8.53592e47 | −0.222477 | ||||||||
\(881\) | 1.74378e48 | 0.446055 | 0.223028 | − | 0.974812i | \(-0.428406\pi\) | ||||
0.223028 | + | 0.974812i | \(0.428406\pi\) | |||||||
\(882\) | 5.26236e48 | 1.32114 | ||||||||
\(883\) | −7.49080e47 | −0.184577 | −0.0922883 | − | 0.995732i | \(-0.529418\pi\) | ||||
−0.0922883 | + | 0.995732i | \(0.529418\pi\) | |||||||
\(884\) | −6.83559e47 | −0.165316 | ||||||||
\(885\) | −2.14265e49 | −5.08612 | ||||||||
\(886\) | −2.35304e48 | −0.548242 | ||||||||
\(887\) | 1.36136e47 | 0.0311338 | 0.0155669 | − | 0.999879i | \(-0.495045\pi\) | ||||
0.0155669 | + | 0.999879i | \(0.495045\pi\) | |||||||
\(888\) | −3.61065e48 | −0.810535 | ||||||||
\(889\) | 7.27461e47 | 0.160299 | ||||||||
\(890\) | 7.18544e48 | 1.55424 | ||||||||
\(891\) | −4.19354e48 | −0.890427 | ||||||||
\(892\) | −1.29006e48 | −0.268900 | ||||||||
\(893\) | −5.02669e47 | −0.102857 | ||||||||
\(894\) | 2.82082e48 | 0.566639 | ||||||||
\(895\) | 7.77039e48 | 1.53237 | ||||||||
\(896\) | 1.73149e47 | 0.0335226 | ||||||||
\(897\) | 2.14863e48 | 0.408401 | ||||||||
\(898\) | −5.58936e48 | −1.04304 | ||||||||
\(899\) | 3.09244e48 | 0.566586 | ||||||||
\(900\) | 9.06033e48 | 1.62983 | ||||||||
\(901\) | 2.96620e48 | 0.523891 | ||||||||
\(902\) | 3.61212e48 | 0.626403 | ||||||||
\(903\) | −3.62803e48 | −0.617765 | ||||||||
\(904\) | 3.35420e47 | 0.0560803 | ||||||||
\(905\) | −3.33708e48 | −0.547855 | ||||||||
\(906\) | −6.45771e48 | −1.04103 | ||||||||
\(907\) | −6.26172e48 | −0.991228 | −0.495614 | − | 0.868543i | \(-0.665057\pi\) | ||||
−0.495614 | + | 0.868543i | \(0.665057\pi\) | |||||||
\(908\) | 3.24568e48 | 0.504532 | ||||||||
\(909\) | 8.73285e48 | 1.33307 | ||||||||
\(910\) | 1.34714e48 | 0.201944 | ||||||||
\(911\) | −1.10745e49 | −1.63031 | −0.815155 | − | 0.579243i | \(-0.803348\pi\) | ||||
−0.815155 | + | 0.579243i | \(0.803348\pi\) | |||||||
\(912\) | −1.97987e47 | −0.0286234 | ||||||||
\(913\) | 1.39123e48 | 0.197528 | ||||||||
\(914\) | −3.98389e48 | −0.555514 | ||||||||
\(915\) | 3.26700e49 | 4.47405 | ||||||||
\(916\) | −1.92324e48 | −0.258678 | ||||||||
\(917\) | −5.15548e48 | −0.681044 | ||||||||
\(918\) | −7.96968e48 | −1.03404 | ||||||||
\(919\) | 6.88858e48 | 0.877857 | 0.438929 | − | 0.898522i | \(-0.355358\pi\) | ||||
0.438929 | + | 0.898522i | \(0.355358\pi\) | |||||||
\(920\) | 2.14147e48 | 0.268049 | ||||||||
\(921\) | −2.22644e48 | −0.273733 | ||||||||
\(922\) | 9.37164e48 | 1.13176 | ||||||||
\(923\) | 2.96484e48 | 0.351701 | ||||||||
\(924\) | −1.63604e48 | −0.190637 | ||||||||
\(925\) | −1.67706e49 | −1.91960 | ||||||||
\(926\) | −9.20481e47 | −0.103498 | ||||||||
\(927\) | −2.94229e49 | −3.24990 | ||||||||
\(928\) | 1.97380e48 | 0.214171 | ||||||||
\(929\) | −1.62943e49 | −1.73691 | −0.868456 | − | 0.495767i | \(-0.834887\pi\) | ||||
−0.868456 | + | 0.495767i | \(0.834887\pi\) | |||||||
\(930\) | −8.89559e48 | −0.931550 | ||||||||
\(931\) | −5.34116e47 | −0.0549498 | ||||||||
\(932\) | −3.60999e48 | −0.364875 | ||||||||
\(933\) | 3.44750e49 | 3.42339 | ||||||||
\(934\) | 3.36637e48 | 0.328426 | ||||||||
\(935\) | 6.43725e48 | 0.617033 | ||||||||
\(936\) | −3.90659e48 | −0.367914 | ||||||||
\(937\) | −1.49919e49 | −1.38724 | −0.693621 | − | 0.720340i | \(-0.743986\pi\) | ||||
−0.693621 | + | 0.720340i | \(0.743986\pi\) | |||||||
\(938\) | 2.56207e48 | 0.232940 | ||||||||
\(939\) | 2.19741e49 | 1.96304 | ||||||||
\(940\) | −1.44153e49 | −1.26536 | ||||||||
\(941\) | 8.73939e48 | 0.753794 | 0.376897 | − | 0.926255i | \(-0.376991\pi\) | ||||
0.376897 | + | 0.926255i | \(0.376991\pi\) | |||||||
\(942\) | 4.83429e48 | 0.409725 | ||||||||
\(943\) | −9.06201e48 | −0.754712 | ||||||||
\(944\) | 5.51535e48 | 0.451373 | ||||||||
\(945\) | 1.57065e49 | 1.26315 | ||||||||
\(946\) | −4.60388e48 | −0.363848 | ||||||||
\(947\) | 7.24316e48 | 0.562540 | 0.281270 | − | 0.959629i | \(-0.409244\pi\) | ||||
0.281270 | + | 0.959629i | \(0.409244\pi\) | |||||||
\(948\) | −5.25947e47 | −0.0401425 | ||||||||
\(949\) | −3.23215e48 | −0.242437 | ||||||||
\(950\) | −9.19600e47 | −0.0677891 | ||||||||
\(951\) | −6.86694e48 | −0.497490 | ||||||||
\(952\) | −1.30578e48 | −0.0929738 | ||||||||
\(953\) | 8.48504e48 | 0.593774 | 0.296887 | − | 0.954913i | \(-0.404052\pi\) | ||||
0.296887 | + | 0.954913i | \(0.404052\pi\) | |||||||
\(954\) | 1.69520e49 | 1.16593 | ||||||||
\(955\) | −1.28140e49 | −0.866220 | ||||||||
\(956\) | 6.85787e48 | 0.455653 | ||||||||
\(957\) | −1.86499e49 | −1.21795 | ||||||||
\(958\) | 1.09588e49 | 0.703446 | ||||||||
\(959\) | −5.53931e48 | −0.349501 | ||||||||
\(960\) | −5.67775e48 | −0.352128 | ||||||||
\(961\) | −1.28159e49 | −0.781294 | ||||||||
\(962\) | 7.23107e48 | 0.433325 | ||||||||
\(963\) | −5.02686e49 | −2.96117 | ||||||||
\(964\) | 1.49032e49 | 0.862996 | ||||||||
\(965\) | 4.08809e49 | 2.32713 | ||||||||
\(966\) | 4.10447e48 | 0.229686 | ||||||||
\(967\) | 3.55845e49 | 1.95760 | 0.978800 | − | 0.204820i | \(-0.0656608\pi\) | ||||
0.978800 | + | 0.204820i | \(0.0656608\pi\) | |||||||
\(968\) | 4.46121e48 | 0.241273 | ||||||||
\(969\) | 1.49309e48 | 0.0793860 | ||||||||
\(970\) | −8.00871e48 | −0.418629 | ||||||||
\(971\) | −1.83055e49 | −0.940728 | −0.470364 | − | 0.882473i | \(-0.655877\pi\) | ||||
−0.470364 | + | 0.882473i | \(0.655877\pi\) | |||||||
\(972\) | −7.02229e48 | −0.354801 | ||||||||
\(973\) | 5.11183e48 | 0.253930 | ||||||||
\(974\) | −1.09760e49 | −0.536069 | ||||||||
\(975\) | −2.64599e49 | −1.27061 | ||||||||
\(976\) | −8.40954e48 | −0.397054 | ||||||||
\(977\) | 9.99310e48 | 0.463916 | 0.231958 | − | 0.972726i | \(-0.425487\pi\) | ||||
0.231958 | + | 0.972726i | \(0.425487\pi\) | |||||||
\(978\) | −1.87563e49 | −0.856162 | ||||||||
\(979\) | 1.74763e49 | 0.784396 | ||||||||
\(980\) | −1.53171e49 | −0.675998 | ||||||||
\(981\) | 1.16994e49 | 0.507722 | ||||||||
\(982\) | −1.81681e49 | −0.775300 | ||||||||
\(983\) | −2.70444e49 | −1.13487 | −0.567434 | − | 0.823419i | \(-0.692064\pi\) | ||||
−0.567434 | + | 0.823419i | \(0.692064\pi\) | |||||||
\(984\) | 2.40264e49 | 0.991445 | ||||||||
\(985\) | −7.90668e48 | −0.320846 | ||||||||
\(986\) | −1.48851e49 | −0.593996 | ||||||||
\(987\) | −2.76291e49 | −1.08426 | ||||||||
\(988\) | 3.96509e47 | 0.0153025 | ||||||||
\(989\) | 1.15501e49 | 0.438377 | ||||||||
\(990\) | 3.67893e49 | 1.37322 | ||||||||
\(991\) | 2.95819e49 | 1.08595 | 0.542977 | − | 0.839748i | \(-0.317297\pi\) | ||||
0.542977 | + | 0.839748i | \(0.317297\pi\) | |||||||
\(992\) | 2.28980e48 | 0.0826714 | ||||||||
\(993\) | 3.89835e48 | 0.138426 | ||||||||
\(994\) | 5.66364e48 | 0.197797 | ||||||||
\(995\) | 2.94207e49 | 1.01058 | ||||||||
\(996\) | 9.25388e48 | 0.312640 | ||||||||
\(997\) | 4.00799e49 | 1.33185 | 0.665927 | − | 0.746017i | \(-0.268036\pi\) | ||||
0.665927 | + | 0.746017i | \(0.268036\pi\) | |||||||
\(998\) | −2.98958e49 | −0.977140 | ||||||||
\(999\) | 8.43077e49 | 2.71042 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2.34.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 18.34.a.c.1.1 | 1 | |||
4.3 | odd | 2 | 16.34.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.34.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
16.34.a.a.1.1 | 1 | 4.3 | odd | 2 | |||
18.34.a.c.1.1 | 1 | 3.2 | odd | 2 |