Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,18,Mod(1,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.1");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.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: | \(53.1344053299\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 29.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 327.881 | 0.905653 | 0.452826 | − | 0.891599i | \(-0.350416\pi\) | ||||
0.452826 | + | 0.891599i | \(0.350416\pi\) | |||||||
\(3\) | 6727.77 | 0.592026 | 0.296013 | − | 0.955184i | \(-0.404343\pi\) | ||||
0.296013 | + | 0.955184i | \(0.404343\pi\) | |||||||
\(4\) | −23565.9 | −0.179793 | ||||||||
\(5\) | 1.45971e6 | 1.67117 | 0.835584 | − | 0.549362i | \(-0.185129\pi\) | ||||
0.835584 | + | 0.549362i | \(0.185129\pi\) | |||||||
\(6\) | 2.20591e6 | 0.536169 | ||||||||
\(7\) | 2.18126e7 | 1.43013 | 0.715063 | − | 0.699060i | \(-0.246398\pi\) | ||||
0.715063 | + | 0.699060i | \(0.246398\pi\) | |||||||
\(8\) | −5.07029e7 | −1.06848 | ||||||||
\(9\) | −8.38773e7 | −0.649506 | ||||||||
\(10\) | 4.78610e8 | 1.51350 | ||||||||
\(11\) | 9.06517e8 | 1.27508 | 0.637541 | − | 0.770417i | \(-0.279952\pi\) | ||||
0.637541 | + | 0.770417i | \(0.279952\pi\) | |||||||
\(12\) | −1.58546e8 | −0.106442 | ||||||||
\(13\) | 1.99314e9 | 0.677672 | 0.338836 | − | 0.940845i | \(-0.389967\pi\) | ||||
0.338836 | + | 0.940845i | \(0.389967\pi\) | |||||||
\(14\) | 7.15194e9 | 1.29520 | ||||||||
\(15\) | 9.82056e9 | 0.989374 | ||||||||
\(16\) | −1.35357e10 | −0.787881 | ||||||||
\(17\) | 2.19793e10 | 0.764183 | 0.382092 | − | 0.924124i | \(-0.375204\pi\) | ||||
0.382092 | + | 0.924124i | \(0.375204\pi\) | |||||||
\(18\) | −2.75018e10 | −0.588227 | ||||||||
\(19\) | −1.22325e11 | −1.65238 | −0.826188 | − | 0.563394i | \(-0.809495\pi\) | ||||
−0.826188 | + | 0.563394i | \(0.809495\pi\) | |||||||
\(20\) | −3.43992e10 | −0.300465 | ||||||||
\(21\) | 1.46750e11 | 0.846671 | ||||||||
\(22\) | 2.97230e11 | 1.15478 | ||||||||
\(23\) | 1.06484e11 | 0.283528 | 0.141764 | − | 0.989900i | \(-0.454723\pi\) | ||||
0.141764 | + | 0.989900i | \(0.454723\pi\) | |||||||
\(24\) | −3.41117e11 | −0.632569 | ||||||||
\(25\) | 1.36780e12 | 1.79280 | ||||||||
\(26\) | 6.53514e11 | 0.613736 | ||||||||
\(27\) | −1.43313e12 | −0.976550 | ||||||||
\(28\) | −5.14033e11 | −0.257127 | ||||||||
\(29\) | 5.00246e11 | 0.185695 | ||||||||
\(30\) | 3.21998e12 | 0.896029 | ||||||||
\(31\) | 4.28486e11 | 0.0902323 | 0.0451162 | − | 0.998982i | \(-0.485634\pi\) | ||||
0.0451162 | + | 0.998982i | \(0.485634\pi\) | |||||||
\(32\) | 2.20763e12 | 0.354936 | ||||||||
\(33\) | 6.09884e12 | 0.754881 | ||||||||
\(34\) | 7.20659e12 | 0.692084 | ||||||||
\(35\) | 3.18400e13 | 2.38998 | ||||||||
\(36\) | 1.97664e12 | 0.116777 | ||||||||
\(37\) | −3.72444e13 | −1.74320 | −0.871598 | − | 0.490221i | \(-0.836916\pi\) | ||||
−0.871598 | + | 0.490221i | \(0.836916\pi\) | |||||||
\(38\) | −4.01080e13 | −1.49648 | ||||||||
\(39\) | 1.34094e13 | 0.401199 | ||||||||
\(40\) | −7.40112e13 | −1.78561 | ||||||||
\(41\) | 6.35703e13 | 1.24334 | 0.621672 | − | 0.783278i | \(-0.286454\pi\) | ||||
0.621672 | + | 0.783278i | \(0.286454\pi\) | |||||||
\(42\) | 4.81166e13 | 0.766789 | ||||||||
\(43\) | 8.68501e13 | 1.13315 | 0.566576 | − | 0.824009i | \(-0.308268\pi\) | ||||
0.566576 | + | 0.824009i | \(0.308268\pi\) | |||||||
\(44\) | −2.13629e13 | −0.229251 | ||||||||
\(45\) | −1.22436e14 | −1.08543 | ||||||||
\(46\) | 3.49140e13 | 0.256778 | ||||||||
\(47\) | 2.38379e14 | 1.46028 | 0.730139 | − | 0.683298i | \(-0.239455\pi\) | ||||
0.730139 | + | 0.683298i | \(0.239455\pi\) | |||||||
\(48\) | −9.10650e13 | −0.466446 | ||||||||
\(49\) | 2.43159e14 | 1.04526 | ||||||||
\(50\) | 4.48476e14 | 1.62366 | ||||||||
\(51\) | 1.47871e14 | 0.452416 | ||||||||
\(52\) | −4.69701e13 | −0.121841 | ||||||||
\(53\) | −4.92045e14 | −1.08558 | −0.542788 | − | 0.839870i | \(-0.682631\pi\) | ||||
−0.542788 | + | 0.839870i | \(0.682631\pi\) | |||||||
\(54\) | −4.69897e14 | −0.884415 | ||||||||
\(55\) | 1.32325e15 | 2.13088 | ||||||||
\(56\) | −1.10596e15 | −1.52806 | ||||||||
\(57\) | −8.22973e14 | −0.978249 | ||||||||
\(58\) | 1.64021e14 | 0.168175 | ||||||||
\(59\) | −8.09233e13 | −0.0717516 | −0.0358758 | − | 0.999356i | \(-0.511422\pi\) | ||||
−0.0358758 | + | 0.999356i | \(0.511422\pi\) | |||||||
\(60\) | −2.31430e14 | −0.177883 | ||||||||
\(61\) | 7.00512e14 | 0.467856 | 0.233928 | − | 0.972254i | \(-0.424842\pi\) | ||||
0.233928 | + | 0.972254i | \(0.424842\pi\) | |||||||
\(62\) | 1.40492e14 | 0.0817191 | ||||||||
\(63\) | −1.82958e15 | −0.928875 | ||||||||
\(64\) | 2.49799e15 | 1.10933 | ||||||||
\(65\) | 2.90940e15 | 1.13250 | ||||||||
\(66\) | 1.99969e15 | 0.683660 | ||||||||
\(67\) | 1.84485e14 | 0.0555043 | 0.0277521 | − | 0.999615i | \(-0.491165\pi\) | ||||
0.0277521 | + | 0.999615i | \(0.491165\pi\) | |||||||
\(68\) | −5.17961e14 | −0.137395 | ||||||||
\(69\) | 7.16397e14 | 0.167856 | ||||||||
\(70\) | 1.04397e16 | 2.16449 | ||||||||
\(71\) | 2.30383e14 | 0.0423403 | 0.0211702 | − | 0.999776i | \(-0.493261\pi\) | ||||
0.0211702 | + | 0.999776i | \(0.493261\pi\) | |||||||
\(72\) | 4.25282e15 | 0.693986 | ||||||||
\(73\) | 6.34133e15 | 0.920314 | 0.460157 | − | 0.887837i | \(-0.347793\pi\) | ||||
0.460157 | + | 0.887837i | \(0.347793\pi\) | |||||||
\(74\) | −1.22117e16 | −1.57873 | ||||||||
\(75\) | 9.20225e15 | 1.06139 | ||||||||
\(76\) | 2.88269e15 | 0.297086 | ||||||||
\(77\) | 1.97735e16 | 1.82353 | ||||||||
\(78\) | 4.39669e15 | 0.363347 | ||||||||
\(79\) | −1.59594e16 | −1.18355 | −0.591775 | − | 0.806103i | \(-0.701572\pi\) | ||||
−0.591775 | + | 0.806103i | \(0.701572\pi\) | |||||||
\(80\) | −1.97581e16 | −1.31668 | ||||||||
\(81\) | 1.19014e15 | 0.0713635 | ||||||||
\(82\) | 2.08435e16 | 1.12604 | ||||||||
\(83\) | 3.22884e16 | 1.57356 | 0.786779 | − | 0.617234i | \(-0.211747\pi\) | ||||
0.786779 | + | 0.617234i | \(0.211747\pi\) | |||||||
\(84\) | −3.45830e15 | −0.152226 | ||||||||
\(85\) | 3.20833e16 | 1.27708 | ||||||||
\(86\) | 2.84765e16 | 1.02624 | ||||||||
\(87\) | 3.36554e15 | 0.109936 | ||||||||
\(88\) | −4.59630e16 | −1.36240 | ||||||||
\(89\) | −3.38978e16 | −0.912761 | −0.456380 | − | 0.889785i | \(-0.650854\pi\) | ||||
−0.456380 | + | 0.889785i | \(0.650854\pi\) | |||||||
\(90\) | −4.01445e16 | −0.983026 | ||||||||
\(91\) | 4.34756e16 | 0.969156 | ||||||||
\(92\) | −2.50938e15 | −0.0509764 | ||||||||
\(93\) | 2.88275e15 | 0.0534198 | ||||||||
\(94\) | 7.81599e16 | 1.32251 | ||||||||
\(95\) | −1.78558e17 | −2.76140 | ||||||||
\(96\) | 1.48524e16 | 0.210131 | ||||||||
\(97\) | −5.54890e16 | −0.718865 | −0.359432 | − | 0.933171i | \(-0.617030\pi\) | ||||
−0.359432 | + | 0.933171i | \(0.617030\pi\) | |||||||
\(98\) | 7.97273e16 | 0.946641 | ||||||||
\(99\) | −7.60362e16 | −0.828173 | ||||||||
\(100\) | −3.22334e16 | −0.322334 | ||||||||
\(101\) | −5.98576e16 | −0.550031 | −0.275016 | − | 0.961440i | \(-0.588683\pi\) | ||||
−0.275016 | + | 0.961440i | \(0.588683\pi\) | |||||||
\(102\) | 4.84843e16 | 0.409732 | ||||||||
\(103\) | −2.31102e17 | −1.79757 | −0.898787 | − | 0.438385i | \(-0.855551\pi\) | ||||
−0.898787 | + | 0.438385i | \(0.855551\pi\) | |||||||
\(104\) | −1.01058e17 | −0.724081 | ||||||||
\(105\) | 2.14212e17 | 1.41493 | ||||||||
\(106\) | −1.61332e17 | −0.983155 | ||||||||
\(107\) | −1.28964e17 | −0.725616 | −0.362808 | − | 0.931864i | \(-0.618182\pi\) | ||||
−0.362808 | + | 0.931864i | \(0.618182\pi\) | |||||||
\(108\) | 3.37730e16 | 0.175577 | ||||||||
\(109\) | −9.68812e16 | −0.465709 | −0.232854 | − | 0.972512i | \(-0.574807\pi\) | ||||
−0.232854 | + | 0.972512i | \(0.574807\pi\) | |||||||
\(110\) | 4.33868e17 | 1.92983 | ||||||||
\(111\) | −2.50572e17 | −1.03202 | ||||||||
\(112\) | −2.95249e17 | −1.12677 | ||||||||
\(113\) | 1.63216e17 | 0.577557 | 0.288779 | − | 0.957396i | \(-0.406751\pi\) | ||||
0.288779 | + | 0.957396i | \(0.406751\pi\) | |||||||
\(114\) | −2.69837e17 | −0.885954 | ||||||||
\(115\) | 1.55435e17 | 0.473823 | ||||||||
\(116\) | −1.17887e16 | −0.0333868 | ||||||||
\(117\) | −1.67179e17 | −0.440152 | ||||||||
\(118\) | −2.65332e16 | −0.0649820 | ||||||||
\(119\) | 4.79425e17 | 1.09288 | ||||||||
\(120\) | −4.97931e17 | −1.05713 | ||||||||
\(121\) | 3.16326e17 | 0.625833 | ||||||||
\(122\) | 2.29685e17 | 0.423715 | ||||||||
\(123\) | 4.27686e17 | 0.736091 | ||||||||
\(124\) | −1.00976e16 | −0.0162232 | ||||||||
\(125\) | 8.82919e17 | 1.32491 | ||||||||
\(126\) | −5.99885e17 | −0.841238 | ||||||||
\(127\) | −1.01659e18 | −1.33295 | −0.666473 | − | 0.745529i | \(-0.732197\pi\) | ||||
−0.666473 | + | 0.745529i | \(0.732197\pi\) | |||||||
\(128\) | 5.29686e17 | 0.649731 | ||||||||
\(129\) | 5.84307e17 | 0.670855 | ||||||||
\(130\) | 9.53938e17 | 1.02566 | ||||||||
\(131\) | 4.10599e17 | 0.413629 | 0.206815 | − | 0.978380i | \(-0.433690\pi\) | ||||
0.206815 | + | 0.978380i | \(0.433690\pi\) | |||||||
\(132\) | −1.43724e17 | −0.135723 | ||||||||
\(133\) | −2.66822e18 | −2.36310 | ||||||||
\(134\) | 6.04893e16 | 0.0502676 | ||||||||
\(135\) | −2.09195e18 | −1.63198 | ||||||||
\(136\) | −1.11441e18 | −0.816517 | ||||||||
\(137\) | −8.86837e17 | −0.610547 | −0.305273 | − | 0.952265i | \(-0.598748\pi\) | ||||
−0.305273 | + | 0.952265i | \(0.598748\pi\) | |||||||
\(138\) | 2.34893e17 | 0.152019 | ||||||||
\(139\) | −2.95476e17 | −0.179844 | −0.0899220 | − | 0.995949i | \(-0.528662\pi\) | ||||
−0.0899220 | + | 0.995949i | \(0.528662\pi\) | |||||||
\(140\) | −7.50337e17 | −0.429703 | ||||||||
\(141\) | 1.60376e18 | 0.864522 | ||||||||
\(142\) | 7.55382e16 | 0.0383456 | ||||||||
\(143\) | 1.80682e18 | 0.864087 | ||||||||
\(144\) | 1.13534e18 | 0.511733 | ||||||||
\(145\) | 7.30212e17 | 0.310328 | ||||||||
\(146\) | 2.07920e18 | 0.833485 | ||||||||
\(147\) | 1.63592e18 | 0.618819 | ||||||||
\(148\) | 8.77697e17 | 0.313415 | ||||||||
\(149\) | 6.39723e17 | 0.215729 | 0.107865 | − | 0.994166i | \(-0.465599\pi\) | ||||
0.107865 | + | 0.994166i | \(0.465599\pi\) | |||||||
\(150\) | 3.01724e18 | 0.961247 | ||||||||
\(151\) | −3.05483e18 | −0.919779 | −0.459890 | − | 0.887976i | \(-0.652111\pi\) | ||||
−0.459890 | + | 0.887976i | \(0.652111\pi\) | |||||||
\(152\) | 6.20222e18 | 1.76554 | ||||||||
\(153\) | −1.84356e18 | −0.496341 | ||||||||
\(154\) | 6.48336e18 | 1.65148 | ||||||||
\(155\) | 6.25463e17 | 0.150793 | ||||||||
\(156\) | −3.16004e17 | −0.0721330 | ||||||||
\(157\) | −3.98069e18 | −0.860619 | −0.430310 | − | 0.902681i | \(-0.641596\pi\) | ||||
−0.430310 | + | 0.902681i | \(0.641596\pi\) | |||||||
\(158\) | −5.23279e18 | −1.07188 | ||||||||
\(159\) | −3.31037e18 | −0.642689 | ||||||||
\(160\) | 3.22248e18 | 0.593159 | ||||||||
\(161\) | 2.32268e18 | 0.405480 | ||||||||
\(162\) | 3.90225e17 | 0.0646306 | ||||||||
\(163\) | −1.23420e19 | −1.93996 | −0.969979 | − | 0.243187i | \(-0.921807\pi\) | ||||
−0.969979 | + | 0.243187i | \(0.921807\pi\) | |||||||
\(164\) | −1.49809e18 | −0.223545 | ||||||||
\(165\) | 8.90250e18 | 1.26153 | ||||||||
\(166\) | 1.05868e19 | 1.42510 | ||||||||
\(167\) | −7.73936e18 | −0.989954 | −0.494977 | − | 0.868906i | \(-0.664823\pi\) | ||||
−0.494977 | + | 0.868906i | \(0.664823\pi\) | |||||||
\(168\) | −7.44065e18 | −0.904653 | ||||||||
\(169\) | −4.67780e18 | −0.540760 | ||||||||
\(170\) | 1.05195e19 | 1.15659 | ||||||||
\(171\) | 1.02603e19 | 1.07323 | ||||||||
\(172\) | −2.04670e18 | −0.203733 | ||||||||
\(173\) | 1.56524e19 | 1.48316 | 0.741582 | − | 0.670862i | \(-0.234076\pi\) | ||||
0.741582 | + | 0.670862i | \(0.234076\pi\) | |||||||
\(174\) | 1.10350e18 | 0.0995642 | ||||||||
\(175\) | 2.98353e19 | 2.56393 | ||||||||
\(176\) | −1.22703e19 | −1.00461 | ||||||||
\(177\) | −5.44433e17 | −0.0424788 | ||||||||
\(178\) | −1.11145e19 | −0.826644 | ||||||||
\(179\) | −2.02080e19 | −1.43308 | −0.716542 | − | 0.697544i | \(-0.754276\pi\) | ||||
−0.716542 | + | 0.697544i | \(0.754276\pi\) | |||||||
\(180\) | 2.88531e18 | 0.195154 | ||||||||
\(181\) | 1.00683e19 | 0.649661 | 0.324831 | − | 0.945772i | \(-0.394693\pi\) | ||||
0.324831 | + | 0.945772i | \(0.394693\pi\) | |||||||
\(182\) | 1.42548e19 | 0.877719 | ||||||||
\(183\) | 4.71289e18 | 0.276983 | ||||||||
\(184\) | −5.39902e18 | −0.302945 | ||||||||
\(185\) | −5.43658e19 | −2.91317 | ||||||||
\(186\) | 9.45201e17 | 0.0483798 | ||||||||
\(187\) | 1.99246e19 | 0.974396 | ||||||||
\(188\) | −5.61760e18 | −0.262548 | ||||||||
\(189\) | −3.12603e19 | −1.39659 | ||||||||
\(190\) | −5.85459e19 | −2.50087 | ||||||||
\(191\) | 3.28029e19 | 1.34007 | 0.670036 | − | 0.742329i | \(-0.266279\pi\) | ||||
0.670036 | + | 0.742329i | \(0.266279\pi\) | |||||||
\(192\) | 1.68059e19 | 0.656752 | ||||||||
\(193\) | 3.04161e18 | 0.113728 | 0.0568638 | − | 0.998382i | \(-0.481890\pi\) | ||||
0.0568638 | + | 0.998382i | \(0.481890\pi\) | |||||||
\(194\) | −1.81938e19 | −0.651042 | ||||||||
\(195\) | 1.95738e19 | 0.670471 | ||||||||
\(196\) | −5.73025e18 | −0.187930 | ||||||||
\(197\) | 2.46461e19 | 0.774079 | 0.387039 | − | 0.922063i | \(-0.373498\pi\) | ||||
0.387039 | + | 0.922063i | \(0.373498\pi\) | |||||||
\(198\) | −2.49308e19 | −0.750037 | ||||||||
\(199\) | −5.32537e19 | −1.53496 | −0.767482 | − | 0.641070i | \(-0.778491\pi\) | ||||
−0.767482 | + | 0.641070i | \(0.778491\pi\) | |||||||
\(200\) | −6.93514e19 | −1.91558 | ||||||||
\(201\) | 1.24118e18 | 0.0328599 | ||||||||
\(202\) | −1.96262e19 | −0.498137 | ||||||||
\(203\) | 1.09117e19 | 0.265568 | ||||||||
\(204\) | −3.48472e18 | −0.0813414 | ||||||||
\(205\) | 9.27939e19 | 2.07784 | ||||||||
\(206\) | −7.57739e19 | −1.62798 | ||||||||
\(207\) | −8.93155e18 | −0.184153 | ||||||||
\(208\) | −2.69786e19 | −0.533925 | ||||||||
\(209\) | −1.10889e20 | −2.10691 | ||||||||
\(210\) | 7.02361e19 | 1.28143 | ||||||||
\(211\) | 9.36675e19 | 1.64130 | 0.820650 | − | 0.571431i | \(-0.193612\pi\) | ||||
0.820650 | + | 0.571431i | \(0.193612\pi\) | |||||||
\(212\) | 1.15955e19 | 0.195179 | ||||||||
\(213\) | 1.54996e18 | 0.0250666 | ||||||||
\(214\) | −4.22849e19 | −0.657156 | ||||||||
\(215\) | 1.26776e20 | 1.89369 | ||||||||
\(216\) | 7.26639e19 | 1.04343 | ||||||||
\(217\) | 9.34639e18 | 0.129043 | ||||||||
\(218\) | −3.17655e19 | −0.421770 | ||||||||
\(219\) | 4.26630e19 | 0.544850 | ||||||||
\(220\) | −3.11835e19 | −0.383117 | ||||||||
\(221\) | 4.38078e19 | 0.517866 | ||||||||
\(222\) | −8.21577e19 | −0.934648 | ||||||||
\(223\) | −6.28942e19 | −0.688682 | −0.344341 | − | 0.938845i | \(-0.611898\pi\) | ||||
−0.344341 | + | 0.938845i | \(0.611898\pi\) | |||||||
\(224\) | 4.81540e19 | 0.507604 | ||||||||
\(225\) | −1.14727e20 | −1.16444 | ||||||||
\(226\) | 5.35154e19 | 0.523066 | ||||||||
\(227\) | −1.04145e20 | −0.980436 | −0.490218 | − | 0.871600i | \(-0.663083\pi\) | ||||
−0.490218 | + | 0.871600i | \(0.663083\pi\) | |||||||
\(228\) | 1.93941e19 | 0.175883 | ||||||||
\(229\) | −1.51162e20 | −1.32081 | −0.660404 | − | 0.750911i | \(-0.729615\pi\) | ||||
−0.660404 | + | 0.750911i | \(0.729615\pi\) | |||||||
\(230\) | 5.09641e19 | 0.429119 | ||||||||
\(231\) | 1.33031e20 | 1.07957 | ||||||||
\(232\) | −2.53639e19 | −0.198412 | ||||||||
\(233\) | 1.43579e20 | 1.08284 | 0.541422 | − | 0.840751i | \(-0.317886\pi\) | ||||
0.541422 | + | 0.840751i | \(0.317886\pi\) | |||||||
\(234\) | −5.48150e19 | −0.398625 | ||||||||
\(235\) | 3.47963e20 | 2.44037 | ||||||||
\(236\) | 1.90703e18 | 0.0129005 | ||||||||
\(237\) | −1.07371e20 | −0.700691 | ||||||||
\(238\) | 1.57194e20 | 0.989767 | ||||||||
\(239\) | 1.15025e20 | 0.698892 | 0.349446 | − | 0.936957i | \(-0.386370\pi\) | ||||
0.349446 | + | 0.936957i | \(0.386370\pi\) | |||||||
\(240\) | −1.32928e20 | −0.779509 | ||||||||
\(241\) | −6.01272e19 | −0.340350 | −0.170175 | − | 0.985414i | \(-0.554433\pi\) | ||||
−0.170175 | + | 0.985414i | \(0.554433\pi\) | |||||||
\(242\) | 1.03717e20 | 0.566788 | ||||||||
\(243\) | 1.93082e20 | 1.01880 | ||||||||
\(244\) | −1.65082e19 | −0.0841174 | ||||||||
\(245\) | 3.54940e20 | 1.74680 | ||||||||
\(246\) | 1.40230e20 | 0.666643 | ||||||||
\(247\) | −2.43811e20 | −1.11977 | ||||||||
\(248\) | −2.17255e19 | −0.0964117 | ||||||||
\(249\) | 2.17229e20 | 0.931587 | ||||||||
\(250\) | 2.89493e20 | 1.19991 | ||||||||
\(251\) | −1.05912e20 | −0.424343 | −0.212172 | − | 0.977232i | \(-0.568054\pi\) | ||||
−0.212172 | + | 0.977232i | \(0.568054\pi\) | |||||||
\(252\) | 4.31157e19 | 0.167005 | ||||||||
\(253\) | 9.65291e19 | 0.361521 | ||||||||
\(254\) | −3.33320e20 | −1.20719 | ||||||||
\(255\) | 2.15849e20 | 0.756063 | ||||||||
\(256\) | −1.53742e20 | −0.520899 | ||||||||
\(257\) | 1.68953e20 | 0.553775 | 0.276888 | − | 0.960902i | \(-0.410697\pi\) | ||||
0.276888 | + | 0.960902i | \(0.410697\pi\) | |||||||
\(258\) | 1.91583e20 | 0.607562 | ||||||||
\(259\) | −8.12397e20 | −2.49299 | ||||||||
\(260\) | −6.85625e19 | −0.203617 | ||||||||
\(261\) | −4.19593e19 | −0.120610 | ||||||||
\(262\) | 1.34628e20 | 0.374605 | ||||||||
\(263\) | 3.52541e20 | 0.949698 | 0.474849 | − | 0.880067i | \(-0.342503\pi\) | ||||
0.474849 | + | 0.880067i | \(0.342503\pi\) | |||||||
\(264\) | −3.09228e20 | −0.806577 | ||||||||
\(265\) | −7.18241e20 | −1.81418 | ||||||||
\(266\) | −8.74860e20 | −2.14015 | ||||||||
\(267\) | −2.28057e20 | −0.540378 | ||||||||
\(268\) | −4.34756e18 | −0.00997930 | ||||||||
\(269\) | 8.82157e20 | 1.96178 | 0.980892 | − | 0.194551i | \(-0.0623251\pi\) | ||||
0.980892 | + | 0.194551i | \(0.0623251\pi\) | |||||||
\(270\) | −6.85912e20 | −1.47801 | ||||||||
\(271\) | 2.81024e20 | 0.586820 | 0.293410 | − | 0.955987i | \(-0.405210\pi\) | ||||
0.293410 | + | 0.955987i | \(0.405210\pi\) | |||||||
\(272\) | −2.97505e20 | −0.602085 | ||||||||
\(273\) | 2.92494e20 | 0.573765 | ||||||||
\(274\) | −2.90777e20 | −0.552943 | ||||||||
\(275\) | 1.23993e21 | 2.28597 | ||||||||
\(276\) | −1.68825e19 | −0.0301794 | ||||||||
\(277\) | −7.85707e20 | −1.36202 | −0.681008 | − | 0.732276i | \(-0.738458\pi\) | ||||
−0.681008 | + | 0.732276i | \(0.738458\pi\) | |||||||
\(278\) | −9.68809e19 | −0.162876 | ||||||||
\(279\) | −3.59402e19 | −0.0586064 | ||||||||
\(280\) | −1.61438e21 | −2.55365 | ||||||||
\(281\) | 3.04537e20 | 0.467343 | 0.233672 | − | 0.972316i | \(-0.424926\pi\) | ||||
0.233672 | + | 0.972316i | \(0.424926\pi\) | |||||||
\(282\) | 5.25842e20 | 0.782957 | ||||||||
\(283\) | 7.30789e20 | 1.05586 | 0.527931 | − | 0.849287i | \(-0.322968\pi\) | ||||
0.527931 | + | 0.849287i | \(0.322968\pi\) | |||||||
\(284\) | −5.42917e18 | −0.00761251 | ||||||||
\(285\) | −1.20130e21 | −1.63482 | ||||||||
\(286\) | 5.92421e20 | 0.782563 | ||||||||
\(287\) | 1.38663e21 | 1.77814 | ||||||||
\(288\) | −1.85170e20 | −0.230533 | ||||||||
\(289\) | −3.44152e20 | −0.416024 | ||||||||
\(290\) | 2.39423e20 | 0.281050 | ||||||||
\(291\) | −3.73317e20 | −0.425586 | ||||||||
\(292\) | −1.49439e20 | −0.165466 | ||||||||
\(293\) | −1.31610e21 | −1.41552 | −0.707759 | − | 0.706454i | \(-0.750294\pi\) | ||||
−0.707759 | + | 0.706454i | \(0.750294\pi\) | |||||||
\(294\) | 5.36387e20 | 0.560435 | ||||||||
\(295\) | −1.18124e20 | −0.119909 | ||||||||
\(296\) | 1.88840e21 | 1.86257 | ||||||||
\(297\) | −1.29916e21 | −1.24518 | ||||||||
\(298\) | 2.09753e20 | 0.195376 | ||||||||
\(299\) | 2.12237e20 | 0.192139 | ||||||||
\(300\) | −2.16859e20 | −0.190830 | ||||||||
\(301\) | 1.89443e21 | 1.62055 | ||||||||
\(302\) | −1.00162e21 | −0.833000 | ||||||||
\(303\) | −4.02708e20 | −0.325633 | ||||||||
\(304\) | 1.65575e21 | 1.30188 | ||||||||
\(305\) | 1.02254e21 | 0.781866 | ||||||||
\(306\) | −6.04469e20 | −0.449513 | ||||||||
\(307\) | 1.80622e20 | 0.130645 | 0.0653227 | − | 0.997864i | \(-0.479192\pi\) | ||||
0.0653227 | + | 0.997864i | \(0.479192\pi\) | |||||||
\(308\) | −4.65979e20 | −0.327858 | ||||||||
\(309\) | −1.55480e21 | −1.06421 | ||||||||
\(310\) | 2.05078e20 | 0.136566 | ||||||||
\(311\) | −1.91012e21 | −1.23765 | −0.618826 | − | 0.785528i | \(-0.712391\pi\) | ||||
−0.618826 | + | 0.785528i | \(0.712391\pi\) | |||||||
\(312\) | −6.79895e20 | −0.428675 | ||||||||
\(313\) | −6.59463e20 | −0.404635 | −0.202318 | − | 0.979320i | \(-0.564847\pi\) | ||||
−0.202318 | + | 0.979320i | \(0.564847\pi\) | |||||||
\(314\) | −1.30519e21 | −0.779422 | ||||||||
\(315\) | −2.67065e21 | −1.55231 | ||||||||
\(316\) | 3.76097e20 | 0.212794 | ||||||||
\(317\) | 2.78486e21 | 1.53391 | 0.766956 | − | 0.641700i | \(-0.221770\pi\) | ||||
0.766956 | + | 0.641700i | \(0.221770\pi\) | |||||||
\(318\) | −1.08541e21 | −0.582053 | ||||||||
\(319\) | 4.53482e20 | 0.236777 | ||||||||
\(320\) | 3.64633e21 | 1.85388 | ||||||||
\(321\) | −8.67641e20 | −0.429583 | ||||||||
\(322\) | 7.61564e20 | 0.367224 | ||||||||
\(323\) | −2.68861e21 | −1.26272 | ||||||||
\(324\) | −2.80467e19 | −0.0128307 | ||||||||
\(325\) | 2.72622e21 | 1.21493 | ||||||||
\(326\) | −4.04673e21 | −1.75693 | ||||||||
\(327\) | −6.51794e20 | −0.275711 | ||||||||
\(328\) | −3.22320e21 | −1.32849 | ||||||||
\(329\) | 5.19966e21 | 2.08838 | ||||||||
\(330\) | 2.91896e21 | 1.14251 | ||||||||
\(331\) | −8.37974e20 | −0.319663 | −0.159832 | − | 0.987144i | \(-0.551095\pi\) | ||||
−0.159832 | + | 0.987144i | \(0.551095\pi\) | |||||||
\(332\) | −7.60905e20 | −0.282915 | ||||||||
\(333\) | 3.12396e21 | 1.13222 | ||||||||
\(334\) | −2.53759e21 | −0.896554 | ||||||||
\(335\) | 2.69294e20 | 0.0927570 | ||||||||
\(336\) | −1.98636e21 | −0.667076 | ||||||||
\(337\) | 4.10587e21 | 1.34447 | 0.672235 | − | 0.740338i | \(-0.265334\pi\) | ||||
0.672235 | + | 0.740338i | \(0.265334\pi\) | |||||||
\(338\) | −1.53376e21 | −0.489741 | ||||||||
\(339\) | 1.09808e21 | 0.341929 | ||||||||
\(340\) | −7.56070e20 | −0.229610 | ||||||||
\(341\) | 3.88430e20 | 0.115054 | ||||||||
\(342\) | 3.36415e21 | 0.971972 | ||||||||
\(343\) | 2.29652e20 | 0.0647247 | ||||||||
\(344\) | −4.40355e21 | −1.21075 | ||||||||
\(345\) | 1.04573e21 | 0.280515 | ||||||||
\(346\) | 5.13213e21 | 1.34323 | ||||||||
\(347\) | −1.00068e21 | −0.255560 | −0.127780 | − | 0.991803i | \(-0.540785\pi\) | ||||
−0.127780 | + | 0.991803i | \(0.540785\pi\) | |||||||
\(348\) | −7.93120e19 | −0.0197658 | ||||||||
\(349\) | −3.27750e21 | −0.797126 | −0.398563 | − | 0.917141i | \(-0.630491\pi\) | ||||
−0.398563 | + | 0.917141i | \(0.630491\pi\) | |||||||
\(350\) | 9.78243e21 | 2.32203 | ||||||||
\(351\) | −2.85644e21 | −0.661780 | ||||||||
\(352\) | 2.00125e21 | 0.452573 | ||||||||
\(353\) | 4.58335e20 | 0.101181 | 0.0505903 | − | 0.998719i | \(-0.483890\pi\) | ||||
0.0505903 | + | 0.998719i | \(0.483890\pi\) | |||||||
\(354\) | −1.78509e20 | −0.0384710 | ||||||||
\(355\) | 3.36291e20 | 0.0707578 | ||||||||
\(356\) | 7.98832e20 | 0.164108 | ||||||||
\(357\) | 3.22546e21 | 0.647011 | ||||||||
\(358\) | −6.62581e21 | −1.29788 | ||||||||
\(359\) | 5.03266e20 | 0.0962709 | 0.0481354 | − | 0.998841i | \(-0.484672\pi\) | ||||
0.0481354 | + | 0.998841i | \(0.484672\pi\) | |||||||
\(360\) | 6.20786e21 | 1.15977 | ||||||||
\(361\) | 9.48297e21 | 1.73035 | ||||||||
\(362\) | 3.30120e21 | 0.588368 | ||||||||
\(363\) | 2.12817e21 | 0.370509 | ||||||||
\(364\) | −1.02454e21 | −0.174248 | ||||||||
\(365\) | 9.25648e21 | 1.53800 | ||||||||
\(366\) | 1.54527e21 | 0.250850 | ||||||||
\(367\) | −8.94361e21 | −1.41857 | −0.709286 | − | 0.704921i | \(-0.750982\pi\) | ||||
−0.709286 | + | 0.704921i | \(0.750982\pi\) | |||||||
\(368\) | −1.44133e21 | −0.223386 | ||||||||
\(369\) | −5.33210e21 | −0.807559 | ||||||||
\(370\) | −1.78255e22 | −2.63832 | ||||||||
\(371\) | −1.07328e22 | −1.55251 | ||||||||
\(372\) | −6.79346e19 | −0.00960453 | ||||||||
\(373\) | 3.36625e21 | 0.465181 | 0.232590 | − | 0.972575i | \(-0.425280\pi\) | ||||
0.232590 | + | 0.972575i | \(0.425280\pi\) | |||||||
\(374\) | 6.53290e21 | 0.882464 | ||||||||
\(375\) | 5.94008e21 | 0.784379 | ||||||||
\(376\) | −1.20865e22 | −1.56028 | ||||||||
\(377\) | 9.97062e20 | 0.125841 | ||||||||
\(378\) | −1.02497e22 | −1.26482 | ||||||||
\(379\) | 3.28121e19 | 0.00395914 | 0.00197957 | − | 0.999998i | \(-0.499370\pi\) | ||||
0.00197957 | + | 0.999998i | \(0.499370\pi\) | |||||||
\(380\) | 4.20788e21 | 0.496481 | ||||||||
\(381\) | −6.83936e21 | −0.789138 | ||||||||
\(382\) | 1.07554e22 | 1.21364 | ||||||||
\(383\) | 9.55720e21 | 1.05473 | 0.527365 | − | 0.849639i | \(-0.323180\pi\) | ||||
0.527365 | + | 0.849639i | \(0.323180\pi\) | |||||||
\(384\) | 3.56361e21 | 0.384657 | ||||||||
\(385\) | 2.88635e22 | 3.04742 | ||||||||
\(386\) | 9.97286e20 | 0.102998 | ||||||||
\(387\) | −7.28475e21 | −0.735989 | ||||||||
\(388\) | 1.30765e21 | 0.129247 | ||||||||
\(389\) | 7.02922e21 | 0.679728 | 0.339864 | − | 0.940475i | \(-0.389619\pi\) | ||||
0.339864 | + | 0.940475i | \(0.389619\pi\) | |||||||
\(390\) | 6.41787e21 | 0.607214 | ||||||||
\(391\) | 2.34043e21 | 0.216667 | ||||||||
\(392\) | −1.23289e22 | −1.11684 | ||||||||
\(393\) | 2.76241e21 | 0.244879 | ||||||||
\(394\) | 8.08099e21 | 0.701046 | ||||||||
\(395\) | −2.32960e22 | −1.97791 | ||||||||
\(396\) | 1.79186e21 | 0.148900 | ||||||||
\(397\) | −1.96775e22 | −1.60048 | −0.800242 | − | 0.599677i | \(-0.795296\pi\) | ||||
−0.800242 | + | 0.599677i | \(0.795296\pi\) | |||||||
\(398\) | −1.74609e22 | −1.39014 | ||||||||
\(399\) | −1.79512e22 | −1.39902 | ||||||||
\(400\) | −1.85141e22 | −1.41252 | ||||||||
\(401\) | −2.13267e22 | −1.59293 | −0.796465 | − | 0.604685i | \(-0.793299\pi\) | ||||
−0.796465 | + | 0.604685i | \(0.793299\pi\) | |||||||
\(402\) | 4.06958e20 | 0.0297597 | ||||||||
\(403\) | 8.54033e20 | 0.0611479 | ||||||||
\(404\) | 1.41060e21 | 0.0988920 | ||||||||
\(405\) | 1.73726e21 | 0.119260 | ||||||||
\(406\) | 3.57773e21 | 0.240512 | ||||||||
\(407\) | −3.37627e22 | −2.22272 | ||||||||
\(408\) | −7.49751e21 | −0.483399 | ||||||||
\(409\) | −3.03623e22 | −1.91729 | −0.958643 | − | 0.284610i | \(-0.908136\pi\) | ||||
−0.958643 | + | 0.284610i | \(0.908136\pi\) | |||||||
\(410\) | 3.04254e22 | 1.88180 | ||||||||
\(411\) | −5.96644e21 | −0.361459 | ||||||||
\(412\) | 5.44612e21 | 0.323192 | ||||||||
\(413\) | −1.76515e21 | −0.102614 | ||||||||
\(414\) | −2.92849e21 | −0.166779 | ||||||||
\(415\) | 4.71316e22 | 2.62968 | ||||||||
\(416\) | 4.40011e21 | 0.240531 | ||||||||
\(417\) | −1.98789e21 | −0.106472 | ||||||||
\(418\) | −3.63586e22 | −1.90813 | ||||||||
\(419\) | 1.69166e22 | 0.869947 | 0.434973 | − | 0.900443i | \(-0.356758\pi\) | ||||
0.434973 | + | 0.900443i | \(0.356758\pi\) | |||||||
\(420\) | −5.04809e21 | −0.254395 | ||||||||
\(421\) | −3.38430e22 | −1.67136 | −0.835681 | − | 0.549215i | \(-0.814927\pi\) | ||||
−0.835681 | + | 0.549215i | \(0.814927\pi\) | |||||||
\(422\) | 3.07118e22 | 1.48645 | ||||||||
\(423\) | −1.99946e22 | −0.948459 | ||||||||
\(424\) | 2.49481e22 | 1.15992 | ||||||||
\(425\) | 3.00633e22 | 1.37003 | ||||||||
\(426\) | 5.08204e20 | 0.0227016 | ||||||||
\(427\) | 1.52800e22 | 0.669093 | ||||||||
\(428\) | 3.03915e21 | 0.130461 | ||||||||
\(429\) | 1.21558e22 | 0.511562 | ||||||||
\(430\) | 4.15673e22 | 1.71502 | ||||||||
\(431\) | −2.53815e22 | −1.02674 | −0.513371 | − | 0.858167i | \(-0.671603\pi\) | ||||
−0.513371 | + | 0.858167i | \(0.671603\pi\) | |||||||
\(432\) | 1.93984e22 | 0.769405 | ||||||||
\(433\) | 2.00085e22 | 0.778158 | 0.389079 | − | 0.921204i | \(-0.372793\pi\) | ||||
0.389079 | + | 0.921204i | \(0.372793\pi\) | |||||||
\(434\) | 3.06451e21 | 0.116869 | ||||||||
\(435\) | 4.91270e21 | 0.183722 | ||||||||
\(436\) | 2.28309e21 | 0.0837313 | ||||||||
\(437\) | −1.30256e22 | −0.468495 | ||||||||
\(438\) | 1.39884e22 | 0.493444 | ||||||||
\(439\) | 3.67625e22 | 1.27191 | 0.635955 | − | 0.771726i | \(-0.280606\pi\) | ||||
0.635955 | + | 0.771726i | \(0.280606\pi\) | |||||||
\(440\) | −6.70924e22 | −2.27680 | ||||||||
\(441\) | −2.03955e22 | −0.678901 | ||||||||
\(442\) | 1.43638e22 | 0.469006 | ||||||||
\(443\) | −2.72263e20 | −0.00872082 | −0.00436041 | − | 0.999990i | \(-0.501388\pi\) | ||||
−0.00436041 | + | 0.999990i | \(0.501388\pi\) | |||||||
\(444\) | 5.90494e21 | 0.185550 | ||||||||
\(445\) | −4.94809e22 | −1.52538 | ||||||||
\(446\) | −2.06218e22 | −0.623707 | ||||||||
\(447\) | 4.30391e21 | 0.127717 | ||||||||
\(448\) | 5.44876e22 | 1.58648 | ||||||||
\(449\) | 3.00571e22 | 0.858723 | 0.429361 | − | 0.903133i | \(-0.358739\pi\) | ||||
0.429361 | + | 0.903133i | \(0.358739\pi\) | |||||||
\(450\) | −3.76170e22 | −1.05457 | ||||||||
\(451\) | 5.76275e22 | 1.58537 | ||||||||
\(452\) | −3.84632e21 | −0.103841 | ||||||||
\(453\) | −2.05522e22 | −0.544533 | ||||||||
\(454\) | −3.41473e22 | −0.887935 | ||||||||
\(455\) | 6.34616e22 | 1.61962 | ||||||||
\(456\) | 4.17271e22 | 1.04524 | ||||||||
\(457\) | −1.65823e22 | −0.407715 | −0.203858 | − | 0.979001i | \(-0.565348\pi\) | ||||
−0.203858 | + | 0.979001i | \(0.565348\pi\) | |||||||
\(458\) | −4.95630e22 | −1.19619 | ||||||||
\(459\) | −3.14992e22 | −0.746263 | ||||||||
\(460\) | −3.66295e21 | −0.0851902 | ||||||||
\(461\) | −1.23592e22 | −0.282185 | −0.141093 | − | 0.989996i | \(-0.545062\pi\) | ||||
−0.141093 | + | 0.989996i | \(0.545062\pi\) | |||||||
\(462\) | 4.36185e22 | 0.977719 | ||||||||
\(463\) | 4.77741e22 | 1.05137 | 0.525683 | − | 0.850680i | \(-0.323810\pi\) | ||||
0.525683 | + | 0.850680i | \(0.323810\pi\) | |||||||
\(464\) | −6.77118e21 | −0.146306 | ||||||||
\(465\) | 4.20797e21 | 0.0892735 | ||||||||
\(466\) | 4.70769e22 | 0.980680 | ||||||||
\(467\) | 1.00133e21 | 0.0204825 | 0.0102412 | − | 0.999948i | \(-0.496740\pi\) | ||||
0.0102412 | + | 0.999948i | \(0.496740\pi\) | |||||||
\(468\) | 3.93973e21 | 0.0791364 | ||||||||
\(469\) | 4.02411e21 | 0.0793780 | ||||||||
\(470\) | 1.14090e23 | 2.21013 | ||||||||
\(471\) | −2.67811e22 | −0.509509 | ||||||||
\(472\) | 4.10304e21 | 0.0766653 | ||||||||
\(473\) | 7.87310e22 | 1.44486 | ||||||||
\(474\) | −3.52050e22 | −0.634583 | ||||||||
\(475\) | −1.67316e23 | −2.96239 | ||||||||
\(476\) | −1.12981e22 | −0.196492 | ||||||||
\(477\) | 4.12714e22 | 0.705088 | ||||||||
\(478\) | 3.77145e22 | 0.632953 | ||||||||
\(479\) | 6.34545e22 | 1.04619 | 0.523095 | − | 0.852274i | \(-0.324777\pi\) | ||||
0.523095 | + | 0.852274i | \(0.324777\pi\) | |||||||
\(480\) | 2.16801e22 | 0.351165 | ||||||||
\(481\) | −7.42333e22 | −1.18132 | ||||||||
\(482\) | −1.97146e22 | −0.308239 | ||||||||
\(483\) | 1.56265e22 | 0.240055 | ||||||||
\(484\) | −7.45449e21 | −0.112521 | ||||||||
\(485\) | −8.09976e22 | −1.20134 | ||||||||
\(486\) | 6.33080e22 | 0.922678 | ||||||||
\(487\) | 3.63304e22 | 0.520325 | 0.260162 | − | 0.965565i | \(-0.416224\pi\) | ||||
0.260162 | + | 0.965565i | \(0.416224\pi\) | |||||||
\(488\) | −3.55180e22 | −0.499896 | ||||||||
\(489\) | −8.30344e22 | −1.14851 | ||||||||
\(490\) | 1.16378e23 | 1.58200 | ||||||||
\(491\) | 1.21537e22 | 0.162373 | 0.0811866 | − | 0.996699i | \(-0.474129\pi\) | ||||
0.0811866 | + | 0.996699i | \(0.474129\pi\) | |||||||
\(492\) | −1.00788e22 | −0.132344 | ||||||||
\(493\) | 1.09951e22 | 0.141905 | ||||||||
\(494\) | −7.99409e22 | −1.01412 | ||||||||
\(495\) | −1.10990e23 | −1.38402 | ||||||||
\(496\) | −5.79985e21 | −0.0710923 | ||||||||
\(497\) | 5.02525e21 | 0.0605520 | ||||||||
\(498\) | 7.12253e22 | 0.843694 | ||||||||
\(499\) | −3.17479e22 | −0.369710 | −0.184855 | − | 0.982766i | \(-0.559182\pi\) | ||||
−0.184855 | + | 0.982766i | \(0.559182\pi\) | |||||||
\(500\) | −2.08068e22 | −0.238210 | ||||||||
\(501\) | −5.20686e22 | −0.586078 | ||||||||
\(502\) | −3.47265e22 | −0.384308 | ||||||||
\(503\) | 1.05072e22 | 0.114329 | 0.0571646 | − | 0.998365i | \(-0.481794\pi\) | ||||
0.0571646 | + | 0.998365i | \(0.481794\pi\) | |||||||
\(504\) | 9.27650e22 | 0.992487 | ||||||||
\(505\) | −8.73744e22 | −0.919195 | ||||||||
\(506\) | 3.16501e22 | 0.327413 | ||||||||
\(507\) | −3.14712e22 | −0.320144 | ||||||||
\(508\) | 2.39567e22 | 0.239655 | ||||||||
\(509\) | −1.93166e23 | −1.90033 | −0.950166 | − | 0.311744i | \(-0.899087\pi\) | ||||
−0.950166 | + | 0.311744i | \(0.899087\pi\) | |||||||
\(510\) | 7.07728e22 | 0.684731 | ||||||||
\(511\) | 1.38321e23 | 1.31616 | ||||||||
\(512\) | −1.19836e23 | −1.12149 | ||||||||
\(513\) | 1.75308e23 | 1.61363 | ||||||||
\(514\) | 5.53964e22 | 0.501528 | ||||||||
\(515\) | −3.37341e23 | −3.00405 | ||||||||
\(516\) | −1.37697e22 | −0.120615 | ||||||||
\(517\) | 2.16094e23 | 1.86197 | ||||||||
\(518\) | −2.66370e23 | −2.25778 | ||||||||
\(519\) | 1.05306e23 | 0.878071 | ||||||||
\(520\) | −1.47515e23 | −1.21006 | ||||||||
\(521\) | −2.17012e23 | −1.75131 | −0.875654 | − | 0.482938i | \(-0.839570\pi\) | ||||
−0.875654 | + | 0.482938i | \(0.839570\pi\) | |||||||
\(522\) | −1.37577e22 | −0.109231 | ||||||||
\(523\) | 7.80323e22 | 0.609551 | 0.304775 | − | 0.952424i | \(-0.401419\pi\) | ||||
0.304775 | + | 0.952424i | \(0.401419\pi\) | |||||||
\(524\) | −9.67611e21 | −0.0743678 | ||||||||
\(525\) | 2.00725e23 | 1.51791 | ||||||||
\(526\) | 1.15592e23 | 0.860096 | ||||||||
\(527\) | 9.41781e21 | 0.0689540 | ||||||||
\(528\) | −8.25520e22 | −0.594756 | ||||||||
\(529\) | −1.29711e23 | −0.919612 | ||||||||
\(530\) | −2.35498e23 | −1.64302 | ||||||||
\(531\) | 6.78762e21 | 0.0466031 | ||||||||
\(532\) | 6.28790e22 | 0.424871 | ||||||||
\(533\) | 1.26705e23 | 0.842580 | ||||||||
\(534\) | −7.47756e22 | −0.489395 | ||||||||
\(535\) | −1.88250e23 | −1.21263 | ||||||||
\(536\) | −9.35394e21 | −0.0593054 | ||||||||
\(537\) | −1.35954e23 | −0.848422 | ||||||||
\(538\) | 2.89243e23 | 1.77670 | ||||||||
\(539\) | 2.20428e23 | 1.33279 | ||||||||
\(540\) | 4.92987e22 | 0.293419 | ||||||||
\(541\) | 1.21903e23 | 0.714229 | 0.357115 | − | 0.934061i | \(-0.383761\pi\) | ||||
0.357115 | + | 0.934061i | \(0.383761\pi\) | |||||||
\(542\) | 9.21426e22 | 0.531455 | ||||||||
\(543\) | 6.77370e22 | 0.384616 | ||||||||
\(544\) | 4.85220e22 | 0.271236 | ||||||||
\(545\) | −1.41418e23 | −0.778278 | ||||||||
\(546\) | 9.59032e22 | 0.519632 | ||||||||
\(547\) | 2.98026e23 | 1.58987 | 0.794936 | − | 0.606693i | \(-0.207504\pi\) | ||||
0.794936 | + | 0.606693i | \(0.207504\pi\) | |||||||
\(548\) | 2.08991e22 | 0.109772 | ||||||||
\(549\) | −5.87571e22 | −0.303875 | ||||||||
\(550\) | 4.06551e23 | 2.07030 | ||||||||
\(551\) | −6.11925e22 | −0.306839 | ||||||||
\(552\) | −3.63234e22 | −0.179351 | ||||||||
\(553\) | −3.48116e23 | −1.69262 | ||||||||
\(554\) | −2.57619e23 | −1.23351 | ||||||||
\(555\) | −3.65761e23 | −1.72467 | ||||||||
\(556\) | 6.96314e21 | 0.0323347 | ||||||||
\(557\) | −1.66559e23 | −0.761728 | −0.380864 | − | 0.924631i | \(-0.624373\pi\) | ||||
−0.380864 | + | 0.924631i | \(0.624373\pi\) | |||||||
\(558\) | −1.17841e22 | −0.0530770 | ||||||||
\(559\) | 1.73104e23 | 0.767906 | ||||||||
\(560\) | −4.30976e23 | −1.88302 | ||||||||
\(561\) | 1.34048e23 | 0.576867 | ||||||||
\(562\) | 9.98519e22 | 0.423251 | ||||||||
\(563\) | 4.20849e23 | 1.75714 | 0.878568 | − | 0.477618i | \(-0.158500\pi\) | ||||
0.878568 | + | 0.477618i | \(0.158500\pi\) | |||||||
\(564\) | −3.77939e22 | −0.155435 | ||||||||
\(565\) | 2.38247e23 | 0.965196 | ||||||||
\(566\) | 2.39612e23 | 0.956245 | ||||||||
\(567\) | 2.59601e22 | 0.102059 | ||||||||
\(568\) | −1.16811e22 | −0.0452399 | ||||||||
\(569\) | 6.24767e22 | 0.238377 | 0.119188 | − | 0.992872i | \(-0.461971\pi\) | ||||
0.119188 | + | 0.992872i | \(0.461971\pi\) | |||||||
\(570\) | −3.93883e23 | −1.48058 | ||||||||
\(571\) | −3.83744e23 | −1.42113 | −0.710566 | − | 0.703631i | \(-0.751561\pi\) | ||||
−0.710566 | + | 0.703631i | \(0.751561\pi\) | |||||||
\(572\) | −4.25792e22 | −0.155357 | ||||||||
\(573\) | 2.20690e23 | 0.793357 | ||||||||
\(574\) | 4.54651e23 | 1.61038 | ||||||||
\(575\) | 1.45648e23 | 0.508310 | ||||||||
\(576\) | −2.09525e23 | −0.720516 | ||||||||
\(577\) | −1.10564e23 | −0.374646 | −0.187323 | − | 0.982298i | \(-0.559981\pi\) | ||||
−0.187323 | + | 0.982298i | \(0.559981\pi\) | |||||||
\(578\) | −1.12841e23 | −0.376773 | ||||||||
\(579\) | 2.04632e22 | 0.0673297 | ||||||||
\(580\) | −1.72081e22 | −0.0557949 | ||||||||
\(581\) | 7.04294e23 | 2.25039 | ||||||||
\(582\) | −1.22404e23 | −0.385433 | ||||||||
\(583\) | −4.46047e23 | −1.38420 | ||||||||
\(584\) | −3.21524e23 | −0.983340 | ||||||||
\(585\) | −2.44033e23 | −0.735568 | ||||||||
\(586\) | −4.31526e23 | −1.28197 | ||||||||
\(587\) | 4.47105e23 | 1.30914 | 0.654570 | − | 0.756002i | \(-0.272850\pi\) | ||||
0.654570 | + | 0.756002i | \(0.272850\pi\) | |||||||
\(588\) | −3.85518e22 | −0.111260 | ||||||||
\(589\) | −5.24144e22 | −0.149098 | ||||||||
\(590\) | −3.87307e22 | −0.108596 | ||||||||
\(591\) | 1.65813e23 | 0.458274 | ||||||||
\(592\) | 5.04129e23 | 1.37343 | ||||||||
\(593\) | 1.77200e23 | 0.475882 | 0.237941 | − | 0.971280i | \(-0.423527\pi\) | ||||
0.237941 | + | 0.971280i | \(0.423527\pi\) | |||||||
\(594\) | −4.25970e23 | −1.12770 | ||||||||
\(595\) | 6.99819e23 | 1.82638 | ||||||||
\(596\) | −1.50756e22 | −0.0387867 | ||||||||
\(597\) | −3.58278e23 | −0.908738 | ||||||||
\(598\) | 6.95885e22 | 0.174011 | ||||||||
\(599\) | −5.19820e22 | −0.128152 | −0.0640760 | − | 0.997945i | \(-0.520410\pi\) | ||||
−0.0640760 | + | 0.997945i | \(0.520410\pi\) | |||||||
\(600\) | −4.66580e23 | −1.13407 | ||||||||
\(601\) | 9.35878e22 | 0.224278 | 0.112139 | − | 0.993693i | \(-0.464230\pi\) | ||||
0.112139 | + | 0.993693i | \(0.464230\pi\) | |||||||
\(602\) | 6.21147e23 | 1.46765 | ||||||||
\(603\) | −1.54741e22 | −0.0360503 | ||||||||
\(604\) | 7.19898e22 | 0.165370 | ||||||||
\(605\) | 4.61742e23 | 1.04587 | ||||||||
\(606\) | −1.32040e23 | −0.294910 | ||||||||
\(607\) | 1.50667e23 | 0.331829 | 0.165915 | − | 0.986140i | \(-0.446942\pi\) | ||||
0.165915 | + | 0.986140i | \(0.446942\pi\) | |||||||
\(608\) | −2.70047e23 | −0.586489 | ||||||||
\(609\) | 7.34112e22 | 0.157223 | ||||||||
\(610\) | 3.35272e23 | 0.708099 | ||||||||
\(611\) | 4.75123e23 | 0.989590 | ||||||||
\(612\) | 4.34451e22 | 0.0892389 | ||||||||
\(613\) | 7.36068e23 | 1.49109 | 0.745545 | − | 0.666455i | \(-0.232189\pi\) | ||||
0.745545 | + | 0.666455i | \(0.232189\pi\) | |||||||
\(614\) | 5.92225e22 | 0.118319 | ||||||||
\(615\) | 6.24296e23 | 1.23013 | ||||||||
\(616\) | −1.00257e24 | −1.94841 | ||||||||
\(617\) | 7.03580e23 | 1.34862 | 0.674310 | − | 0.738449i | \(-0.264441\pi\) | ||||
0.674310 | + | 0.738449i | \(0.264441\pi\) | |||||||
\(618\) | −5.09790e23 | −0.963804 | ||||||||
\(619\) | 9.58495e23 | 1.78739 | 0.893695 | − | 0.448675i | \(-0.148104\pi\) | ||||
0.893695 | + | 0.448675i | \(0.148104\pi\) | |||||||
\(620\) | −1.47396e22 | −0.0271116 | ||||||||
\(621\) | −1.52605e23 | −0.276879 | ||||||||
\(622\) | −6.26294e23 | −1.12088 | ||||||||
\(623\) | −7.39400e23 | −1.30536 | ||||||||
\(624\) | −1.81505e23 | −0.316097 | ||||||||
\(625\) | 2.45253e23 | 0.421341 | ||||||||
\(626\) | −2.16226e23 | −0.366459 | ||||||||
\(627\) | −7.46039e23 | −1.24735 | ||||||||
\(628\) | 9.38084e22 | 0.154734 | ||||||||
\(629\) | −8.18605e23 | −1.33212 | ||||||||
\(630\) | −8.75656e23 | −1.40585 | ||||||||
\(631\) | −2.26530e23 | −0.358819 | −0.179410 | − | 0.983774i | \(-0.557419\pi\) | ||||
−0.179410 | + | 0.983774i | \(0.557419\pi\) | |||||||
\(632\) | 8.09187e23 | 1.26460 | ||||||||
\(633\) | 6.30173e23 | 0.971691 | ||||||||
\(634\) | 9.13105e23 | 1.38919 | ||||||||
\(635\) | −1.48392e24 | −2.22758 | ||||||||
\(636\) | 7.80117e22 | 0.115551 | ||||||||
\(637\) | 4.84650e23 | 0.708342 | ||||||||
\(638\) | 1.48688e23 | 0.214437 | ||||||||
\(639\) | −1.93239e22 | −0.0275003 | ||||||||
\(640\) | 7.73186e23 | 1.08581 | ||||||||
\(641\) | −5.22645e23 | −0.724292 | −0.362146 | − | 0.932121i | \(-0.617956\pi\) | ||||
−0.362146 | + | 0.932121i | \(0.617956\pi\) | |||||||
\(642\) | −2.84483e23 | −0.389053 | ||||||||
\(643\) | −6.48185e23 | −0.874794 | −0.437397 | − | 0.899268i | \(-0.644100\pi\) | ||||
−0.437397 | + | 0.899268i | \(0.644100\pi\) | |||||||
\(644\) | −5.47361e22 | −0.0729027 | ||||||||
\(645\) | 8.52916e23 | 1.12111 | ||||||||
\(646\) | −8.81545e23 | −1.14358 | ||||||||
\(647\) | −1.29109e23 | −0.165300 | −0.0826498 | − | 0.996579i | \(-0.526338\pi\) | ||||
−0.0826498 | + | 0.996579i | \(0.526338\pi\) | |||||||
\(648\) | −6.03436e22 | −0.0762507 | ||||||||
\(649\) | −7.33583e22 | −0.0914891 | ||||||||
\(650\) | 8.93877e23 | 1.10031 | ||||||||
\(651\) | 6.28804e22 | 0.0763970 | ||||||||
\(652\) | 2.90851e23 | 0.348792 | ||||||||
\(653\) | 1.49980e24 | 1.77529 | 0.887647 | − | 0.460525i | \(-0.152339\pi\) | ||||
0.887647 | + | 0.460525i | \(0.152339\pi\) | |||||||
\(654\) | −2.13711e23 | −0.249699 | ||||||||
\(655\) | 5.99353e23 | 0.691244 | ||||||||
\(656\) | −8.60468e23 | −0.979607 | ||||||||
\(657\) | −5.31894e23 | −0.597749 | ||||||||
\(658\) | 1.70487e24 | 1.89135 | ||||||||
\(659\) | 3.48779e23 | 0.381965 | 0.190983 | − | 0.981593i | \(-0.438833\pi\) | ||||
0.190983 | + | 0.981593i | \(0.438833\pi\) | |||||||
\(660\) | −2.09795e23 | −0.226815 | ||||||||
\(661\) | −2.57921e23 | −0.275280 | −0.137640 | − | 0.990482i | \(-0.543952\pi\) | ||||
−0.137640 | + | 0.990482i | \(0.543952\pi\) | |||||||
\(662\) | −2.74756e23 | −0.289504 | ||||||||
\(663\) | 2.94729e23 | 0.306590 | ||||||||
\(664\) | −1.63712e24 | −1.68132 | ||||||||
\(665\) | −3.89482e24 | −3.94915 | ||||||||
\(666\) | 1.02429e24 | 1.02539 | ||||||||
\(667\) | 5.32680e22 | 0.0526498 | ||||||||
\(668\) | 1.82385e23 | 0.177987 | ||||||||
\(669\) | −4.23137e23 | −0.407718 | ||||||||
\(670\) | 8.82966e22 | 0.0840056 | ||||||||
\(671\) | 6.35026e23 | 0.596555 | ||||||||
\(672\) | 3.23969e23 | 0.300514 | ||||||||
\(673\) | −8.97036e23 | −0.821641 | −0.410820 | − | 0.911716i | \(-0.634758\pi\) | ||||
−0.410820 | + | 0.911716i | \(0.634758\pi\) | |||||||
\(674\) | 1.34624e24 | 1.21762 | ||||||||
\(675\) | −1.96024e24 | −1.75076 | ||||||||
\(676\) | 1.10237e23 | 0.0972251 | ||||||||
\(677\) | 4.13358e23 | 0.360017 | 0.180008 | − | 0.983665i | \(-0.442388\pi\) | ||||
0.180008 | + | 0.983665i | \(0.442388\pi\) | |||||||
\(678\) | 3.60039e23 | 0.309669 | ||||||||
\(679\) | −1.21036e24 | −1.02807 | ||||||||
\(680\) | −1.62671e24 | −1.36454 | ||||||||
\(681\) | −7.00665e23 | −0.580443 | ||||||||
\(682\) | 1.27359e23 | 0.104199 | ||||||||
\(683\) | −8.83551e23 | −0.713930 | −0.356965 | − | 0.934118i | \(-0.616188\pi\) | ||||
−0.356965 | + | 0.934118i | \(0.616188\pi\) | |||||||
\(684\) | −2.41792e23 | −0.192959 | ||||||||
\(685\) | −1.29452e24 | −1.02033 | ||||||||
\(686\) | 7.52986e22 | 0.0586181 | ||||||||
\(687\) | −1.01698e24 | −0.781952 | ||||||||
\(688\) | −1.17558e24 | −0.892789 | ||||||||
\(689\) | −9.80716e23 | −0.735665 | ||||||||
\(690\) | 3.42875e23 | 0.254049 | ||||||||
\(691\) | 3.85744e23 | 0.282316 | 0.141158 | − | 0.989987i | \(-0.454917\pi\) | ||||
0.141158 | + | 0.989987i | \(0.454917\pi\) | |||||||
\(692\) | −3.68863e23 | −0.266663 | ||||||||
\(693\) | −1.65855e24 | −1.18439 | ||||||||
\(694\) | −3.28103e23 | −0.231448 | ||||||||
\(695\) | −4.31307e23 | −0.300549 | ||||||||
\(696\) | −1.70643e23 | −0.117465 | ||||||||
\(697\) | 1.39723e24 | 0.950143 | ||||||||
\(698\) | −1.07463e24 | −0.721919 | ||||||||
\(699\) | 9.65967e23 | 0.641071 | ||||||||
\(700\) | −7.03095e23 | −0.460978 | ||||||||
\(701\) | 1.43098e24 | 0.926893 | 0.463446 | − | 0.886125i | \(-0.346613\pi\) | ||||
0.463446 | + | 0.886125i | \(0.346613\pi\) | |||||||
\(702\) | −9.36572e23 | −0.599343 | ||||||||
\(703\) | 4.55591e24 | 2.88042 | ||||||||
\(704\) | 2.26447e24 | 1.41449 | ||||||||
\(705\) | 2.34101e24 | 1.44476 | ||||||||
\(706\) | 1.50279e23 | 0.0916346 | ||||||||
\(707\) | −1.30565e24 | −0.786614 | ||||||||
\(708\) | 1.28300e22 | 0.00763740 | ||||||||
\(709\) | 4.46129e22 | 0.0262402 | 0.0131201 | − | 0.999914i | \(-0.495824\pi\) | ||||
0.0131201 | + | 0.999914i | \(0.495824\pi\) | |||||||
\(710\) | 1.10264e23 | 0.0640820 | ||||||||
\(711\) | 1.33863e24 | 0.768722 | ||||||||
\(712\) | 1.71872e24 | 0.975269 | ||||||||
\(713\) | 4.56267e22 | 0.0255834 | ||||||||
\(714\) | 1.05757e24 | 0.585968 | ||||||||
\(715\) | 2.63742e24 | 1.44404 | ||||||||
\(716\) | 4.76218e23 | 0.257659 | ||||||||
\(717\) | 7.73861e23 | 0.413762 | ||||||||
\(718\) | 1.65012e23 | 0.0871880 | ||||||||
\(719\) | 2.71624e24 | 1.41831 | 0.709157 | − | 0.705050i | \(-0.249076\pi\) | ||||
0.709157 | + | 0.705050i | \(0.249076\pi\) | |||||||
\(720\) | 1.65726e24 | 0.855192 | ||||||||
\(721\) | −5.04093e24 | −2.57076 | ||||||||
\(722\) | 3.10929e24 | 1.56709 | ||||||||
\(723\) | −4.04522e23 | −0.201496 | ||||||||
\(724\) | −2.37268e23 | −0.116805 | ||||||||
\(725\) | 6.84237e23 | 0.332915 | ||||||||
\(726\) | 6.97786e23 | 0.335553 | ||||||||
\(727\) | 1.96738e24 | 0.935073 | 0.467537 | − | 0.883974i | \(-0.345142\pi\) | ||||
0.467537 | + | 0.883974i | \(0.345142\pi\) | |||||||
\(728\) | −2.20434e24 | −1.03553 | ||||||||
\(729\) | 1.14532e24 | 0.531791 | ||||||||
\(730\) | 3.03503e24 | 1.39289 | ||||||||
\(731\) | 1.90890e24 | 0.865936 | ||||||||
\(732\) | −1.11063e23 | −0.0497997 | ||||||||
\(733\) | 3.28195e23 | 0.145462 | 0.0727309 | − | 0.997352i | \(-0.476829\pi\) | ||||
0.0727309 | + | 0.997352i | \(0.476829\pi\) | |||||||
\(734\) | −2.93244e24 | −1.28473 | ||||||||
\(735\) | 2.38796e24 | 1.03415 | ||||||||
\(736\) | 2.35076e23 | 0.100634 | ||||||||
\(737\) | 1.67239e23 | 0.0707725 | ||||||||
\(738\) | −1.74830e24 | −0.731368 | ||||||||
\(739\) | −1.77329e24 | −0.733335 | −0.366668 | − | 0.930352i | \(-0.619501\pi\) | ||||
−0.366668 | + | 0.930352i | \(0.619501\pi\) | |||||||
\(740\) | 1.28118e24 | 0.523769 | ||||||||
\(741\) | −1.64030e24 | −0.662932 | ||||||||
\(742\) | −3.51908e24 | −1.40603 | ||||||||
\(743\) | 1.63750e24 | 0.646811 | 0.323405 | − | 0.946260i | \(-0.395172\pi\) | ||||
0.323405 | + | 0.946260i | \(0.395172\pi\) | |||||||
\(744\) | −1.46164e23 | −0.0570782 | ||||||||
\(745\) | 9.33807e23 | 0.360520 | ||||||||
\(746\) | 1.10373e24 | 0.421292 | ||||||||
\(747\) | −2.70826e24 | −1.02204 | ||||||||
\(748\) | −4.69540e23 | −0.175190 | ||||||||
\(749\) | −2.81304e24 | −1.03772 | ||||||||
\(750\) | 1.94764e24 | 0.710375 | ||||||||
\(751\) | −1.26189e24 | −0.455075 | −0.227537 | − | 0.973769i | \(-0.573067\pi\) | ||||
−0.227537 | + | 0.973769i | \(0.573067\pi\) | |||||||
\(752\) | −3.22662e24 | −1.15053 | ||||||||
\(753\) | −7.12549e23 | −0.251222 | ||||||||
\(754\) | 3.26918e23 | 0.113968 | ||||||||
\(755\) | −4.45916e24 | −1.53711 | ||||||||
\(756\) | 7.36677e23 | 0.251097 | ||||||||
\(757\) | 4.84738e24 | 1.63377 | 0.816887 | − | 0.576797i | \(-0.195698\pi\) | ||||
0.816887 | + | 0.576797i | \(0.195698\pi\) | |||||||
\(758\) | 1.07585e22 | 0.00358561 | ||||||||
\(759\) | 6.49426e23 | 0.214030 | ||||||||
\(760\) | 9.05341e24 | 2.95051 | ||||||||
\(761\) | −3.16525e24 | −1.02009 | −0.510045 | − | 0.860148i | \(-0.670371\pi\) | ||||
−0.510045 | + | 0.860148i | \(0.670371\pi\) | |||||||
\(762\) | −2.24250e24 | −0.714685 | ||||||||
\(763\) | −2.11323e24 | −0.666022 | ||||||||
\(764\) | −7.73028e23 | −0.240936 | ||||||||
\(765\) | −2.69106e24 | −0.829470 | ||||||||
\(766\) | 3.13363e24 | 0.955218 | ||||||||
\(767\) | −1.61292e23 | −0.0486240 | ||||||||
\(768\) | −1.03434e24 | −0.308386 | ||||||||
\(769\) | −1.29823e24 | −0.382804 | −0.191402 | − | 0.981512i | \(-0.561303\pi\) | ||||
−0.191402 | + | 0.981512i | \(0.561303\pi\) | |||||||
\(770\) | 9.46379e24 | 2.75990 | ||||||||
\(771\) | 1.13667e24 | 0.327849 | ||||||||
\(772\) | −7.16781e22 | −0.0204475 | ||||||||
\(773\) | 3.55520e24 | 1.00309 | 0.501544 | − | 0.865132i | \(-0.332766\pi\) | ||||
0.501544 | + | 0.865132i | \(0.332766\pi\) | |||||||
\(774\) | −2.38853e24 | −0.666550 | ||||||||
\(775\) | 5.86083e23 | 0.161769 | ||||||||
\(776\) | 2.81345e24 | 0.768094 | ||||||||
\(777\) | −5.46562e24 | −1.47591 | ||||||||
\(778\) | 2.30475e24 | 0.615598 | ||||||||
\(779\) | −7.77622e24 | −2.05447 | ||||||||
\(780\) | −4.61273e23 | −0.120546 | ||||||||
\(781\) | 2.08846e23 | 0.0539874 | ||||||||
\(782\) | 7.67383e23 | 0.196225 | ||||||||
\(783\) | −7.16919e23 | −0.181341 | ||||||||
\(784\) | −3.29132e24 | −0.823539 | ||||||||
\(785\) | −5.81063e24 | −1.43824 | ||||||||
\(786\) | 9.05743e23 | 0.221775 | ||||||||
\(787\) | 1.61751e24 | 0.391797 | 0.195898 | − | 0.980624i | \(-0.437238\pi\) | ||||
0.195898 | + | 0.980624i | \(0.437238\pi\) | |||||||
\(788\) | −5.80807e23 | −0.139174 | ||||||||
\(789\) | 2.37181e24 | 0.562245 | ||||||||
\(790\) | −7.63833e24 | −1.79130 | ||||||||
\(791\) | 3.56016e24 | 0.825979 | ||||||||
\(792\) | 3.85525e24 | 0.884889 | ||||||||
\(793\) | 1.39622e24 | 0.317053 | ||||||||
\(794\) | −6.45190e24 | −1.44948 | ||||||||
\(795\) | −4.83216e24 | −1.07404 | ||||||||
\(796\) | 1.25497e24 | 0.275976 | ||||||||
\(797\) | −4.85450e24 | −1.05621 | −0.528103 | − | 0.849180i | \(-0.677096\pi\) | ||||
−0.528103 | + | 0.849180i | \(0.677096\pi\) | |||||||
\(798\) | −5.88586e24 | −1.26702 | ||||||||
\(799\) | 5.23939e24 | 1.11592 | ||||||||
\(800\) | 3.01959e24 | 0.636331 | ||||||||
\(801\) | 2.84326e24 | 0.592843 | ||||||||
\(802\) | −6.99262e24 | −1.44264 | ||||||||
\(803\) | 5.74852e24 | 1.17348 | ||||||||
\(804\) | −2.92494e22 | −0.00590800 | ||||||||
\(805\) | 3.39043e24 | 0.677626 | ||||||||
\(806\) | 2.80021e23 | 0.0553788 | ||||||||
\(807\) | 5.93495e24 | 1.16143 | ||||||||
\(808\) | 3.03495e24 | 0.587699 | ||||||||
\(809\) | 4.71065e24 | 0.902648 | 0.451324 | − | 0.892360i | \(-0.350952\pi\) | ||||
0.451324 | + | 0.892360i | \(0.350952\pi\) | |||||||
\(810\) | 5.69614e23 | 0.108009 | ||||||||
\(811\) | 3.62987e24 | 0.681105 | 0.340553 | − | 0.940225i | \(-0.389386\pi\) | ||||
0.340553 | + | 0.940225i | \(0.389386\pi\) | |||||||
\(812\) | −2.57143e23 | −0.0477473 | ||||||||
\(813\) | 1.89067e24 | 0.347412 | ||||||||
\(814\) | −1.10701e25 | −2.01301 | ||||||||
\(815\) | −1.80157e25 | −3.24200 | ||||||||
\(816\) | −2.00154e24 | −0.356450 | ||||||||
\(817\) | −1.06239e25 | −1.87239 | ||||||||
\(818\) | −9.95524e24 | −1.73640 | ||||||||
\(819\) | −3.64661e24 | −0.629472 | ||||||||
\(820\) | −2.18677e24 | −0.373581 | ||||||||
\(821\) | 1.21391e24 | 0.205243 | 0.102621 | − | 0.994720i | \(-0.467277\pi\) | ||||
0.102621 | + | 0.994720i | \(0.467277\pi\) | |||||||
\(822\) | −1.95628e24 | −0.327357 | ||||||||
\(823\) | 5.81195e24 | 0.962550 | 0.481275 | − | 0.876570i | \(-0.340174\pi\) | ||||
0.481275 | + | 0.876570i | \(0.340174\pi\) | |||||||
\(824\) | 1.17175e25 | 1.92068 | ||||||||
\(825\) | 8.34199e24 | 1.35335 | ||||||||
\(826\) | −5.78759e23 | −0.0929324 | ||||||||
\(827\) | 4.75053e24 | 0.754997 | 0.377498 | − | 0.926010i | \(-0.376784\pi\) | ||||
0.377498 | + | 0.926010i | \(0.376784\pi\) | |||||||
\(828\) | 2.10480e23 | 0.0331095 | ||||||||
\(829\) | −8.41454e24 | −1.31014 | −0.655069 | − | 0.755569i | \(-0.727360\pi\) | ||||
−0.655069 | + | 0.755569i | \(0.727360\pi\) | |||||||
\(830\) | 1.54536e25 | 2.38158 | ||||||||
\(831\) | −5.28605e24 | −0.806349 | ||||||||
\(832\) | 4.97885e24 | 0.751762 | ||||||||
\(833\) | 5.34446e24 | 0.798769 | ||||||||
\(834\) | −6.51792e23 | −0.0964268 | ||||||||
\(835\) | −1.12972e25 | −1.65438 | ||||||||
\(836\) | 2.61321e24 | 0.378809 | ||||||||
\(837\) | −6.14077e23 | −0.0881163 | ||||||||
\(838\) | 5.54662e24 | 0.787869 | ||||||||
\(839\) | 3.50641e24 | 0.493045 | 0.246522 | − | 0.969137i | \(-0.420712\pi\) | ||||
0.246522 | + | 0.969137i | \(0.420712\pi\) | |||||||
\(840\) | −1.08612e25 | −1.51183 | ||||||||
\(841\) | 2.50246e23 | 0.0344828 | ||||||||
\(842\) | −1.10965e25 | −1.51367 | ||||||||
\(843\) | 2.04885e24 | 0.276679 | ||||||||
\(844\) | −2.20736e24 | −0.295095 | ||||||||
\(845\) | −6.82821e24 | −0.903702 | ||||||||
\(846\) | −6.55584e24 | −0.858975 | ||||||||
\(847\) | 6.89988e24 | 0.895020 | ||||||||
\(848\) | 6.66017e24 | 0.855305 | ||||||||
\(849\) | 4.91658e24 | 0.625098 | ||||||||
\(850\) | 9.85718e24 | 1.24077 | ||||||||
\(851\) | −3.96591e24 | −0.494245 | ||||||||
\(852\) | −3.65262e22 | −0.00450680 | ||||||||
\(853\) | 2.01835e24 | 0.246564 | 0.123282 | − | 0.992372i | \(-0.460658\pi\) | ||||
0.123282 | + | 0.992372i | \(0.460658\pi\) | |||||||
\(854\) | 5.01002e24 | 0.605966 | ||||||||
\(855\) | 1.49770e25 | 1.79354 | ||||||||
\(856\) | 6.53885e24 | 0.775308 | ||||||||
\(857\) | −1.13064e25 | −1.32736 | −0.663680 | − | 0.748016i | \(-0.731006\pi\) | ||||
−0.663680 | + | 0.748016i | \(0.731006\pi\) | |||||||
\(858\) | 3.98567e24 | 0.463297 | ||||||||
\(859\) | −1.04837e25 | −1.20663 | −0.603313 | − | 0.797505i | \(-0.706153\pi\) | ||||
−0.603313 | + | 0.797505i | \(0.706153\pi\) | |||||||
\(860\) | −2.98758e24 | −0.340473 | ||||||||
\(861\) | 9.32895e24 | 1.05270 | ||||||||
\(862\) | −8.32213e24 | −0.929871 | ||||||||
\(863\) | −6.81348e24 | −0.753836 | −0.376918 | − | 0.926247i | \(-0.623016\pi\) | ||||
−0.376918 | + | 0.926247i | \(0.623016\pi\) | |||||||
\(864\) | −3.16382e24 | −0.346613 | ||||||||
\(865\) | 2.28479e25 | 2.47862 | ||||||||
\(866\) | 6.56042e24 | 0.704741 | ||||||||
\(867\) | −2.31537e24 | −0.246297 | ||||||||
\(868\) | −2.20256e23 | −0.0232012 | ||||||||
\(869\) | −1.44675e25 | −1.50912 | ||||||||
\(870\) | 1.61078e24 | 0.166388 | ||||||||
\(871\) | 3.67706e23 | 0.0376137 | ||||||||
\(872\) | 4.91215e24 | 0.497602 | ||||||||
\(873\) | 4.65427e24 | 0.466907 | ||||||||
\(874\) | −4.27084e24 | −0.424294 | ||||||||
\(875\) | 1.92588e25 | 1.89478 | ||||||||
\(876\) | −1.00539e24 | −0.0979603 | ||||||||
\(877\) | 4.94993e24 | 0.477642 | 0.238821 | − | 0.971064i | \(-0.423239\pi\) | ||||
0.238821 | + | 0.971064i | \(0.423239\pi\) | |||||||
\(878\) | 1.20537e25 | 1.15191 | ||||||||
\(879\) | −8.85445e24 | −0.838023 | ||||||||
\(880\) | −1.79111e25 | −1.67888 | ||||||||
\(881\) | 4.20081e24 | 0.389975 | 0.194988 | − | 0.980806i | \(-0.437533\pi\) | ||||
0.194988 | + | 0.980806i | \(0.437533\pi\) | |||||||
\(882\) | −6.68731e24 | −0.614849 | ||||||||
\(883\) | 1.26234e25 | 1.14950 | 0.574751 | − | 0.818328i | \(-0.305099\pi\) | ||||
0.574751 | + | 0.818328i | \(0.305099\pi\) | |||||||
\(884\) | −1.03237e24 | −0.0931088 | ||||||||
\(885\) | −7.94712e23 | −0.0709891 | ||||||||
\(886\) | −8.92700e22 | −0.00789803 | ||||||||
\(887\) | 3.60457e24 | 0.315866 | 0.157933 | − | 0.987450i | \(-0.449517\pi\) | ||||
0.157933 | + | 0.987450i | \(0.449517\pi\) | |||||||
\(888\) | 1.27047e25 | 1.10269 | ||||||||
\(889\) | −2.21744e25 | −1.90628 | ||||||||
\(890\) | −1.62238e25 | −1.38146 | ||||||||
\(891\) | 1.07888e24 | 0.0909943 | ||||||||
\(892\) | 1.48216e24 | 0.123821 | ||||||||
\(893\) | −2.91596e25 | −2.41293 | ||||||||
\(894\) | 1.41117e24 | 0.115667 | ||||||||
\(895\) | −2.94977e25 | −2.39492 | ||||||||
\(896\) | 1.15538e25 | 0.929197 | ||||||||
\(897\) | 1.42788e24 | 0.113751 | ||||||||
\(898\) | 9.85516e24 | 0.777705 | ||||||||
\(899\) | 2.14348e23 | 0.0167557 | ||||||||
\(900\) | 2.70365e24 | 0.209358 | ||||||||
\(901\) | −1.08148e25 | −0.829579 | ||||||||
\(902\) | 1.88950e25 | 1.43579 | ||||||||
\(903\) | 1.27453e25 | 0.959407 | ||||||||
\(904\) | −8.27550e24 | −0.617110 | ||||||||
\(905\) | 1.46967e25 | 1.08569 | ||||||||
\(906\) | −6.73869e24 | −0.493157 | ||||||||
\(907\) | 1.71250e25 | 1.24156 | 0.620782 | − | 0.783983i | \(-0.286815\pi\) | ||||
0.620782 | + | 0.783983i | \(0.286815\pi\) | |||||||
\(908\) | 2.45427e24 | 0.176276 | ||||||||
\(909\) | 5.02069e24 | 0.357249 | ||||||||
\(910\) | 2.08079e25 | 1.46682 | ||||||||
\(911\) | −1.07652e25 | −0.751826 | −0.375913 | − | 0.926655i | \(-0.622671\pi\) | ||||
−0.375913 | + | 0.926655i | \(0.622671\pi\) | |||||||
\(912\) | 1.11395e25 | 0.770744 | ||||||||
\(913\) | 2.92700e25 | 2.00642 | ||||||||
\(914\) | −5.43702e24 | −0.369248 | ||||||||
\(915\) | 6.87943e24 | 0.462885 | ||||||||
\(916\) | 3.56225e24 | 0.237472 | ||||||||
\(917\) | 8.95622e24 | 0.591542 | ||||||||
\(918\) | −1.03280e25 | −0.675855 | ||||||||
\(919\) | 1.37024e25 | 0.888416 | 0.444208 | − | 0.895924i | \(-0.353485\pi\) | ||||
0.444208 | + | 0.895924i | \(0.353485\pi\) | |||||||
\(920\) | −7.88098e24 | −0.506272 | ||||||||
\(921\) | 1.21518e24 | 0.0773454 | ||||||||
\(922\) | −4.05236e24 | −0.255562 | ||||||||
\(923\) | 4.59186e23 | 0.0286929 | ||||||||
\(924\) | −3.13500e24 | −0.194100 | ||||||||
\(925\) | −5.09429e25 | −3.12521 | ||||||||
\(926\) | 1.56642e25 | 0.952173 | ||||||||
\(927\) | 1.93842e25 | 1.16753 | ||||||||
\(928\) | 1.10436e24 | 0.0659100 | ||||||||
\(929\) | −1.43769e25 | −0.850219 | −0.425109 | − | 0.905142i | \(-0.639764\pi\) | ||||
−0.425109 | + | 0.905142i | \(0.639764\pi\) | |||||||
\(930\) | 1.37972e24 | 0.0808508 | ||||||||
\(931\) | −2.97444e25 | −1.72716 | ||||||||
\(932\) | −3.38357e24 | −0.194688 | ||||||||
\(933\) | −1.28509e25 | −0.732721 | ||||||||
\(934\) | 3.28316e23 | 0.0185500 | ||||||||
\(935\) | 2.90840e25 | 1.62838 | ||||||||
\(936\) | 8.47647e24 | 0.470295 | ||||||||
\(937\) | 2.47776e25 | 1.36230 | 0.681150 | − | 0.732144i | \(-0.261480\pi\) | ||||
0.681150 | + | 0.732144i | \(0.261480\pi\) | |||||||
\(938\) | 1.31943e24 | 0.0718889 | ||||||||
\(939\) | −4.43672e24 | −0.239554 | ||||||||
\(940\) | −8.20005e24 | −0.438763 | ||||||||
\(941\) | −9.20959e24 | −0.488347 | −0.244174 | − | 0.969732i | \(-0.578517\pi\) | ||||
−0.244174 | + | 0.969732i | \(0.578517\pi\) | |||||||
\(942\) | −8.78104e24 | −0.461438 | ||||||||
\(943\) | 6.76919e24 | 0.352523 | ||||||||
\(944\) | 1.09535e24 | 0.0565317 | ||||||||
\(945\) | −4.56309e25 | −2.33393 | ||||||||
\(946\) | 2.58144e25 | 1.30854 | ||||||||
\(947\) | −1.03683e25 | −0.520874 | −0.260437 | − | 0.965491i | \(-0.583867\pi\) | ||||
−0.260437 | + | 0.965491i | \(0.583867\pi\) | |||||||
\(948\) | 2.53030e24 | 0.125980 | ||||||||
\(949\) | 1.26392e25 | 0.623671 | ||||||||
\(950\) | −5.48598e25 | −2.68289 | ||||||||
\(951\) | 1.87359e25 | 0.908115 | ||||||||
\(952\) | −2.43082e25 | −1.16772 | ||||||||
\(953\) | 2.35634e25 | 1.12188 | 0.560942 | − | 0.827855i | \(-0.310439\pi\) | ||||
0.560942 | + | 0.827855i | \(0.310439\pi\) | |||||||
\(954\) | 1.35321e25 | 0.638565 | ||||||||
\(955\) | 4.78825e25 | 2.23949 | ||||||||
\(956\) | −2.71066e24 | −0.125656 | ||||||||
\(957\) | 3.05092e24 | 0.140178 | ||||||||
\(958\) | 2.08055e25 | 0.947485 | ||||||||
\(959\) | −1.93442e25 | −0.873159 | ||||||||
\(960\) | 2.45317e25 | 1.09754 | ||||||||
\(961\) | −2.23665e25 | −0.991858 | ||||||||
\(962\) | −2.43397e25 | −1.06986 | ||||||||
\(963\) | 1.08172e25 | 0.471292 | ||||||||
\(964\) | 1.41695e24 | 0.0611927 | ||||||||
\(965\) | 4.43985e24 | 0.190058 | ||||||||
\(966\) | 5.12363e24 | 0.217406 | ||||||||
\(967\) | 1.78014e25 | 0.748736 | 0.374368 | − | 0.927280i | \(-0.377860\pi\) | ||||
0.374368 | + | 0.927280i | \(0.377860\pi\) | |||||||
\(968\) | −1.60386e25 | −0.668692 | ||||||||
\(969\) | −1.80884e25 | −0.747561 | ||||||||
\(970\) | −2.65576e25 | −1.08800 | ||||||||
\(971\) | −2.84221e25 | −1.15423 | −0.577116 | − | 0.816662i | \(-0.695822\pi\) | ||||
−0.577116 | + | 0.816662i | \(0.695822\pi\) | |||||||
\(972\) | −4.55014e24 | −0.183173 | ||||||||
\(973\) | −6.44509e24 | −0.257199 | ||||||||
\(974\) | 1.19121e25 | 0.471233 | ||||||||
\(975\) | 1.83414e25 | 0.719271 | ||||||||
\(976\) | −9.48192e24 | −0.368615 | ||||||||
\(977\) | 2.63061e25 | 1.01380 | 0.506901 | − | 0.862004i | \(-0.330791\pi\) | ||||
0.506901 | + | 0.862004i | \(0.330791\pi\) | |||||||
\(978\) | −2.72254e25 | −1.04015 | ||||||||
\(979\) | −3.07290e25 | −1.16384 | ||||||||
\(980\) | −8.36448e24 | −0.314063 | ||||||||
\(981\) | 8.12613e24 | 0.302480 | ||||||||
\(982\) | 3.98496e24 | 0.147054 | ||||||||
\(983\) | −4.87916e25 | −1.78501 | −0.892504 | − | 0.451039i | \(-0.851053\pi\) | ||||
−0.892504 | + | 0.451039i | \(0.851053\pi\) | |||||||
\(984\) | −2.16849e25 | −0.786501 | ||||||||
\(985\) | 3.59760e25 | 1.29362 | ||||||||
\(986\) | 3.60507e24 | 0.128517 | ||||||||
\(987\) | 3.49821e25 | 1.23638 | ||||||||
\(988\) | 5.74561e24 | 0.201327 | ||||||||
\(989\) | 9.24810e24 | 0.321280 | ||||||||
\(990\) | −3.63917e25 | −1.25344 | ||||||||
\(991\) | 1.94268e25 | 0.663401 | 0.331701 | − | 0.943385i | \(-0.392378\pi\) | ||||
0.331701 | + | 0.943385i | \(0.392378\pi\) | |||||||
\(992\) | 9.45936e23 | 0.0320267 | ||||||||
\(993\) | −5.63770e24 | −0.189249 | ||||||||
\(994\) | 1.64768e24 | 0.0548390 | ||||||||
\(995\) | −7.77346e25 | −2.56518 | ||||||||
\(996\) | −5.11919e24 | −0.167493 | ||||||||
\(997\) | −1.27472e25 | −0.413530 | −0.206765 | − | 0.978391i | \(-0.566294\pi\) | ||||
−0.206765 | + | 0.978391i | \(0.566294\pi\) | |||||||
\(998\) | −1.04096e25 | −0.334829 | ||||||||
\(999\) | 5.33761e25 | 1.70232 |
(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 | 29.18.a.b.1.15 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.18.a.b.1.15 | ✓ | 21 | 1.1 | even | 1 | trivial |