Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,40,Mod(1,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 40, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.1");
S:= CuspForms(chi, 40);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 40 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.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: | \(28.9018654169\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 3876249523x - 18467420411022 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{6}\cdot 5\cdot 7\cdot 13 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(64517.4\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −983454. | −1.32638 | −0.663192 | − | 0.748449i | \(-0.730799\pi\) | ||||
−0.663192 | + | 0.748449i | \(0.730799\pi\) | |||||||
\(3\) | −1.16226e9 | −0.577350 | ||||||||
\(4\) | 4.17427e11 | 0.759295 | ||||||||
\(5\) | 1.57969e13 | 0.370387 | 0.185193 | − | 0.982702i | \(-0.440709\pi\) | ||||
0.185193 | + | 0.982702i | \(0.440709\pi\) | |||||||
\(6\) | 1.14303e15 | 0.765788 | ||||||||
\(7\) | 5.39162e15 | 0.178775 | 0.0893877 | − | 0.995997i | \(-0.471509\pi\) | ||||
0.0893877 | + | 0.995997i | \(0.471509\pi\) | |||||||
\(8\) | 1.30140e17 | 0.319268 | ||||||||
\(9\) | 1.35085e18 | 0.333333 | ||||||||
\(10\) | −1.55355e19 | −0.491275 | ||||||||
\(11\) | −1.89252e20 | −0.933001 | −0.466501 | − | 0.884521i | \(-0.654485\pi\) | ||||
−0.466501 | + | 0.884521i | \(0.654485\pi\) | |||||||
\(12\) | −4.85159e20 | −0.438379 | ||||||||
\(13\) | −1.17129e21 | −0.222214 | −0.111107 | − | 0.993808i | \(-0.535440\pi\) | ||||
−0.111107 | + | 0.993808i | \(0.535440\pi\) | |||||||
\(14\) | −5.30242e21 | −0.237125 | ||||||||
\(15\) | −1.83601e22 | −0.213843 | ||||||||
\(16\) | −3.57469e23 | −1.18277 | ||||||||
\(17\) | −1.39600e24 | −1.41623 | −0.708113 | − | 0.706099i | \(-0.750453\pi\) | ||||
−0.708113 | + | 0.706099i | \(0.750453\pi\) | |||||||
\(18\) | −1.32850e24 | −0.442128 | ||||||||
\(19\) | −2.79398e24 | −0.323988 | −0.161994 | − | 0.986792i | \(-0.551792\pi\) | ||||
−0.161994 | + | 0.986792i | \(0.551792\pi\) | |||||||
\(20\) | 6.59403e24 | 0.281233 | ||||||||
\(21\) | −6.26648e24 | −0.103216 | ||||||||
\(22\) | 1.86120e26 | 1.23752 | ||||||||
\(23\) | 5.34440e26 | 1.49350 | 0.746751 | − | 0.665103i | \(-0.231613\pi\) | ||||
0.746751 | + | 0.665103i | \(0.231613\pi\) | |||||||
\(24\) | −1.51256e26 | −0.184329 | ||||||||
\(25\) | −1.56945e27 | −0.862813 | ||||||||
\(26\) | 1.15191e27 | 0.294741 | ||||||||
\(27\) | −1.57004e27 | −0.192450 | ||||||||
\(28\) | 2.25061e27 | 0.135743 | ||||||||
\(29\) | 2.12460e28 | 0.646422 | 0.323211 | − | 0.946327i | \(-0.395238\pi\) | ||||
0.323211 | + | 0.946327i | \(0.395238\pi\) | |||||||
\(30\) | 1.80563e28 | 0.283638 | ||||||||
\(31\) | 1.34079e29 | 1.11124 | 0.555618 | − | 0.831438i | \(-0.312482\pi\) | ||||
0.555618 | + | 0.831438i | \(0.312482\pi\) | |||||||
\(32\) | 2.80010e29 | 1.24953 | ||||||||
\(33\) | 2.19960e29 | 0.538669 | ||||||||
\(34\) | 1.37291e30 | 1.87846 | ||||||||
\(35\) | 8.51707e28 | 0.0662161 | ||||||||
\(36\) | 5.63882e29 | 0.253098 | ||||||||
\(37\) | −4.34673e30 | −1.14348 | −0.571741 | − | 0.820434i | \(-0.693732\pi\) | ||||
−0.571741 | + | 0.820434i | \(0.693732\pi\) | |||||||
\(38\) | 2.74775e30 | 0.429732 | ||||||||
\(39\) | 1.36135e30 | 0.128295 | ||||||||
\(40\) | 2.05580e30 | 0.118253 | ||||||||
\(41\) | 3.17213e31 | 1.12737 | 0.563684 | − | 0.825990i | \(-0.309384\pi\) | ||||
0.563684 | + | 0.825990i | \(0.309384\pi\) | |||||||
\(42\) | 6.16279e30 | 0.136904 | ||||||||
\(43\) | −8.86307e31 | −1.24437 | −0.622184 | − | 0.782871i | \(-0.713755\pi\) | ||||
−0.622184 | + | 0.782871i | \(0.713755\pi\) | |||||||
\(44\) | −7.89987e31 | −0.708423 | ||||||||
\(45\) | 2.13392e31 | 0.123462 | ||||||||
\(46\) | −5.25597e32 | −1.98096 | ||||||||
\(47\) | −3.38028e32 | −0.837616 | −0.418808 | − | 0.908075i | \(-0.637552\pi\) | ||||
−0.418808 | + | 0.908075i | \(0.637552\pi\) | |||||||
\(48\) | 4.15473e32 | 0.682870 | ||||||||
\(49\) | −8.80474e32 | −0.968039 | ||||||||
\(50\) | 1.54348e33 | 1.14442 | ||||||||
\(51\) | 1.62252e33 | 0.817659 | ||||||||
\(52\) | −4.88930e32 | −0.168726 | ||||||||
\(53\) | 7.04033e33 | 1.67577 | 0.837883 | − | 0.545849i | \(-0.183793\pi\) | ||||
0.837883 | + | 0.545849i | \(0.183793\pi\) | |||||||
\(54\) | 1.54407e33 | 0.255263 | ||||||||
\(55\) | −2.98958e33 | −0.345572 | ||||||||
\(56\) | 7.01664e32 | 0.0570772 | ||||||||
\(57\) | 3.24734e33 | 0.187054 | ||||||||
\(58\) | −2.08945e34 | −0.857404 | ||||||||
\(59\) | 1.96619e34 | 0.578110 | 0.289055 | − | 0.957313i | \(-0.406659\pi\) | ||||
0.289055 | + | 0.957313i | \(0.406659\pi\) | |||||||
\(60\) | −7.66399e33 | −0.162370 | ||||||||
\(61\) | 6.79380e34 | 1.04275 | 0.521376 | − | 0.853327i | \(-0.325419\pi\) | ||||
0.521376 | + | 0.853327i | \(0.325419\pi\) | |||||||
\(62\) | −1.31860e35 | −1.47393 | ||||||||
\(63\) | 7.28328e33 | 0.0595918 | ||||||||
\(64\) | −7.88559e34 | −0.474597 | ||||||||
\(65\) | −1.85028e34 | −0.0823050 | ||||||||
\(66\) | −2.16320e35 | −0.714481 | ||||||||
\(67\) | 4.10558e35 | 1.01138 | 0.505691 | − | 0.862714i | \(-0.331237\pi\) | ||||
0.505691 | + | 0.862714i | \(0.331237\pi\) | |||||||
\(68\) | −5.82729e35 | −1.07533 | ||||||||
\(69\) | −6.21159e35 | −0.862274 | ||||||||
\(70\) | −8.37615e34 | −0.0878280 | ||||||||
\(71\) | 8.69914e35 | 0.691733 | 0.345867 | − | 0.938284i | \(-0.387585\pi\) | ||||
0.345867 | + | 0.938284i | \(0.387585\pi\) | |||||||
\(72\) | 1.75799e35 | 0.106423 | ||||||||
\(73\) | 3.39418e36 | 1.57014 | 0.785071 | − | 0.619405i | \(-0.212626\pi\) | ||||
0.785071 | + | 0.619405i | \(0.212626\pi\) | |||||||
\(74\) | 4.27481e36 | 1.51670 | ||||||||
\(75\) | 1.82411e36 | 0.498146 | ||||||||
\(76\) | −1.16628e36 | −0.246002 | ||||||||
\(77\) | −1.02037e36 | −0.166798 | ||||||||
\(78\) | −1.33883e36 | −0.170169 | ||||||||
\(79\) | −1.47904e37 | −1.46639 | −0.733197 | − | 0.680016i | \(-0.761973\pi\) | ||||
−0.733197 | + | 0.680016i | \(0.761973\pi\) | |||||||
\(80\) | −5.64689e36 | −0.438081 | ||||||||
\(81\) | 1.82480e36 | 0.111111 | ||||||||
\(82\) | −3.11965e37 | −1.49532 | ||||||||
\(83\) | 1.98587e37 | 0.751500 | 0.375750 | − | 0.926721i | \(-0.377385\pi\) | ||||
0.375750 | + | 0.926721i | \(0.377385\pi\) | |||||||
\(84\) | −2.61579e36 | −0.0783714 | ||||||||
\(85\) | −2.20525e37 | −0.524552 | ||||||||
\(86\) | 8.71642e37 | 1.65051 | ||||||||
\(87\) | −2.46934e37 | −0.373212 | ||||||||
\(88\) | −2.46291e37 | −0.297877 | ||||||||
\(89\) | −1.95350e37 | −0.189543 | −0.0947717 | − | 0.995499i | \(-0.530212\pi\) | ||||
−0.0947717 | + | 0.995499i | \(0.530212\pi\) | |||||||
\(90\) | −2.09861e37 | −0.163758 | ||||||||
\(91\) | −6.31518e36 | −0.0397263 | ||||||||
\(92\) | 2.23089e38 | 1.13401 | ||||||||
\(93\) | −1.55834e38 | −0.641572 | ||||||||
\(94\) | 3.32435e38 | 1.11100 | ||||||||
\(95\) | −4.41362e37 | −0.120001 | ||||||||
\(96\) | −3.25444e38 | −0.721419 | ||||||||
\(97\) | 3.46965e38 | 0.628400 | 0.314200 | − | 0.949357i | \(-0.398264\pi\) | ||||
0.314200 | + | 0.949357i | \(0.398264\pi\) | |||||||
\(98\) | 8.65906e38 | 1.28399 | ||||||||
\(99\) | −2.55651e38 | −0.311000 | ||||||||
\(100\) | −6.55130e38 | −0.655130 | ||||||||
\(101\) | 9.43292e38 | 0.776925 | 0.388463 | − | 0.921464i | \(-0.373006\pi\) | ||||
0.388463 | + | 0.921464i | \(0.373006\pi\) | |||||||
\(102\) | −1.59568e39 | −1.08453 | ||||||||
\(103\) | −1.80882e39 | −1.01641 | −0.508205 | − | 0.861236i | \(-0.669691\pi\) | ||||
−0.508205 | + | 0.861236i | \(0.669691\pi\) | |||||||
\(104\) | −1.52432e38 | −0.0709456 | ||||||||
\(105\) | −9.89907e37 | −0.0382299 | ||||||||
\(106\) | −6.92384e39 | −2.22271 | ||||||||
\(107\) | 4.01033e39 | 1.07201 | 0.536003 | − | 0.844216i | \(-0.319934\pi\) | ||||
0.536003 | + | 0.844216i | \(0.319934\pi\) | |||||||
\(108\) | −6.55378e38 | −0.146126 | ||||||||
\(109\) | 2.19571e39 | 0.409033 | 0.204517 | − | 0.978863i | \(-0.434438\pi\) | ||||
0.204517 | + | 0.978863i | \(0.434438\pi\) | |||||||
\(110\) | 2.94012e39 | 0.458361 | ||||||||
\(111\) | 5.05204e39 | 0.660190 | ||||||||
\(112\) | −1.92734e39 | −0.211450 | ||||||||
\(113\) | 1.80870e40 | 1.66854 | 0.834272 | − | 0.551353i | \(-0.185888\pi\) | ||||
0.834272 | + | 0.551353i | \(0.185888\pi\) | |||||||
\(114\) | −3.19361e39 | −0.248106 | ||||||||
\(115\) | 8.44247e39 | 0.553174 | ||||||||
\(116\) | 8.86865e39 | 0.490825 | ||||||||
\(117\) | −1.58225e39 | −0.0740712 | ||||||||
\(118\) | −1.93365e40 | −0.766796 | ||||||||
\(119\) | −7.52673e39 | −0.253186 | ||||||||
\(120\) | −2.38937e39 | −0.0682731 | ||||||||
\(121\) | −5.32861e39 | −0.129509 | ||||||||
\(122\) | −6.68140e40 | −1.38309 | ||||||||
\(123\) | −3.68685e40 | −0.650886 | ||||||||
\(124\) | 5.59680e40 | 0.843756 | ||||||||
\(125\) | −5.35267e40 | −0.689962 | ||||||||
\(126\) | −7.16278e39 | −0.0790416 | ||||||||
\(127\) | 1.44477e41 | 1.36655 | 0.683277 | − | 0.730159i | \(-0.260554\pi\) | ||||
0.683277 | + | 0.730159i | \(0.260554\pi\) | |||||||
\(128\) | −7.63857e40 | −0.620037 | ||||||||
\(129\) | 1.03012e41 | 0.718437 | ||||||||
\(130\) | 1.81966e40 | 0.109168 | ||||||||
\(131\) | −1.14560e41 | −0.591892 | −0.295946 | − | 0.955205i | \(-0.595635\pi\) | ||||
−0.295946 | + | 0.955205i | \(0.595635\pi\) | |||||||
\(132\) | 9.18171e40 | 0.409008 | ||||||||
\(133\) | −1.50641e40 | −0.0579210 | ||||||||
\(134\) | −4.03765e41 | −1.34148 | ||||||||
\(135\) | −2.48017e40 | −0.0712810 | ||||||||
\(136\) | −1.81675e41 | −0.452155 | ||||||||
\(137\) | 6.64327e41 | 1.43328 | 0.716640 | − | 0.697443i | \(-0.245679\pi\) | ||||
0.716640 | + | 0.697443i | \(0.245679\pi\) | |||||||
\(138\) | 6.10881e41 | 1.14371 | ||||||||
\(139\) | 6.31930e41 | 1.02773 | 0.513867 | − | 0.857870i | \(-0.328213\pi\) | ||||
0.513867 | + | 0.857870i | \(0.328213\pi\) | |||||||
\(140\) | 3.55525e40 | 0.0502775 | ||||||||
\(141\) | 3.92877e41 | 0.483598 | ||||||||
\(142\) | −8.55521e41 | −0.917504 | ||||||||
\(143\) | 2.21669e41 | 0.207326 | ||||||||
\(144\) | −4.82888e41 | −0.394255 | ||||||||
\(145\) | 3.35620e41 | 0.239426 | ||||||||
\(146\) | −3.33802e42 | −2.08261 | ||||||||
\(147\) | 1.02334e42 | 0.558898 | ||||||||
\(148\) | −1.81444e42 | −0.868240 | ||||||||
\(149\) | −3.63083e41 | −0.152361 | −0.0761805 | − | 0.997094i | \(-0.524273\pi\) | ||||
−0.0761805 | + | 0.997094i | \(0.524273\pi\) | |||||||
\(150\) | −1.79393e42 | −0.660732 | ||||||||
\(151\) | 1.34108e42 | 0.433913 | 0.216957 | − | 0.976181i | \(-0.430387\pi\) | ||||
0.216957 | + | 0.976181i | \(0.430387\pi\) | |||||||
\(152\) | −3.63608e41 | −0.103439 | ||||||||
\(153\) | −1.88579e42 | −0.472076 | ||||||||
\(154\) | 1.00349e42 | 0.221238 | ||||||||
\(155\) | 2.11802e42 | 0.411587 | ||||||||
\(156\) | 5.68264e41 | 0.0974138 | ||||||||
\(157\) | 7.18671e42 | 1.08764 | 0.543822 | − | 0.839200i | \(-0.316977\pi\) | ||||
0.543822 | + | 0.839200i | \(0.316977\pi\) | |||||||
\(158\) | 1.45457e43 | 1.94500 | ||||||||
\(159\) | −8.18270e42 | −0.967504 | ||||||||
\(160\) | 4.42327e42 | 0.462811 | ||||||||
\(161\) | 2.88150e42 | 0.267002 | ||||||||
\(162\) | −1.79461e42 | −0.147376 | ||||||||
\(163\) | −1.01241e43 | −0.737395 | −0.368697 | − | 0.929549i | \(-0.620196\pi\) | ||||
−0.368697 | + | 0.929549i | \(0.620196\pi\) | |||||||
\(164\) | 1.32413e43 | 0.856005 | ||||||||
\(165\) | 3.47468e42 | 0.199516 | ||||||||
\(166\) | −1.95302e43 | −0.996777 | ||||||||
\(167\) | −1.84485e43 | −0.837511 | −0.418756 | − | 0.908099i | \(-0.637534\pi\) | ||||
−0.418756 | + | 0.908099i | \(0.637534\pi\) | |||||||
\(168\) | −8.15517e41 | −0.0329535 | ||||||||
\(169\) | −2.64118e43 | −0.950621 | ||||||||
\(170\) | 2.16876e43 | 0.695757 | ||||||||
\(171\) | −3.77426e42 | −0.107996 | ||||||||
\(172\) | −3.69968e43 | −0.944843 | ||||||||
\(173\) | 1.26682e43 | 0.288944 | 0.144472 | − | 0.989509i | \(-0.453852\pi\) | ||||
0.144472 | + | 0.989509i | \(0.453852\pi\) | |||||||
\(174\) | 2.42848e43 | 0.495022 | ||||||||
\(175\) | −8.46188e42 | −0.154250 | ||||||||
\(176\) | 6.76516e43 | 1.10352 | ||||||||
\(177\) | −2.28522e43 | −0.333772 | ||||||||
\(178\) | 1.92118e43 | 0.251407 | ||||||||
\(179\) | −1.09111e44 | −1.28008 | −0.640038 | − | 0.768343i | \(-0.721081\pi\) | ||||
−0.640038 | + | 0.768343i | \(0.721081\pi\) | |||||||
\(180\) | 8.90756e42 | 0.0937443 | ||||||||
\(181\) | 7.55663e43 | 0.713832 | 0.356916 | − | 0.934136i | \(-0.383828\pi\) | ||||
0.356916 | + | 0.934136i | \(0.383828\pi\) | |||||||
\(182\) | 6.21069e42 | 0.0526924 | ||||||||
\(183\) | −7.89618e43 | −0.602033 | ||||||||
\(184\) | 6.95518e43 | 0.476827 | ||||||||
\(185\) | −6.86647e43 | −0.423531 | ||||||||
\(186\) | 1.53256e44 | 0.850971 | ||||||||
\(187\) | 2.64196e44 | 1.32134 | ||||||||
\(188\) | −1.41102e44 | −0.635997 | ||||||||
\(189\) | −8.46508e42 | −0.0344053 | ||||||||
\(190\) | 4.34059e43 | 0.159167 | ||||||||
\(191\) | −1.39897e44 | −0.463081 | −0.231540 | − | 0.972825i | \(-0.574377\pi\) | ||||
−0.231540 | + | 0.972825i | \(0.574377\pi\) | |||||||
\(192\) | 9.16512e43 | 0.274009 | ||||||||
\(193\) | 6.10898e44 | 1.65044 | 0.825222 | − | 0.564808i | \(-0.191050\pi\) | ||||
0.825222 | + | 0.564808i | \(0.191050\pi\) | |||||||
\(194\) | −3.41224e44 | −0.833500 | ||||||||
\(195\) | 2.15051e43 | 0.0475188 | ||||||||
\(196\) | −3.67533e44 | −0.735027 | ||||||||
\(197\) | −4.59710e44 | −0.832517 | −0.416258 | − | 0.909246i | \(-0.636659\pi\) | ||||
−0.416258 | + | 0.909246i | \(0.636659\pi\) | |||||||
\(198\) | 2.51421e44 | 0.412506 | ||||||||
\(199\) | −1.14245e45 | −1.69903 | −0.849514 | − | 0.527566i | \(-0.823105\pi\) | ||||
−0.849514 | + | 0.527566i | \(0.823105\pi\) | |||||||
\(200\) | −2.04247e44 | −0.275468 | ||||||||
\(201\) | −4.77175e44 | −0.583922 | ||||||||
\(202\) | −9.27685e44 | −1.03050 | ||||||||
\(203\) | 1.14550e44 | 0.115564 | ||||||||
\(204\) | 6.77284e44 | 0.620844 | ||||||||
\(205\) | 5.01097e44 | 0.417563 | ||||||||
\(206\) | 1.77889e45 | 1.34815 | ||||||||
\(207\) | 7.21949e44 | 0.497834 | ||||||||
\(208\) | 4.18702e44 | 0.262827 | ||||||||
\(209\) | 5.28766e44 | 0.302281 | ||||||||
\(210\) | 9.73528e43 | 0.0507075 | ||||||||
\(211\) | 2.97530e45 | 1.41261 | 0.706307 | − | 0.707906i | \(-0.250360\pi\) | ||||
0.706307 | + | 0.707906i | \(0.250360\pi\) | |||||||
\(212\) | 2.93882e45 | 1.27240 | ||||||||
\(213\) | −1.01107e45 | −0.399372 | ||||||||
\(214\) | −3.94398e45 | −1.42189 | ||||||||
\(215\) | −1.40009e45 | −0.460898 | ||||||||
\(216\) | −2.04325e44 | −0.0614431 | ||||||||
\(217\) | 7.22901e44 | 0.198662 | ||||||||
\(218\) | −2.15938e45 | −0.542535 | ||||||||
\(219\) | −3.94493e45 | −0.906522 | ||||||||
\(220\) | −1.24793e45 | −0.262391 | ||||||||
\(221\) | 1.63513e45 | 0.314705 | ||||||||
\(222\) | −4.96845e45 | −0.875665 | ||||||||
\(223\) | 9.60122e45 | 1.55018 | 0.775089 | − | 0.631852i | \(-0.217705\pi\) | ||||
0.775089 | + | 0.631852i | \(0.217705\pi\) | |||||||
\(224\) | 1.50971e45 | 0.223386 | ||||||||
\(225\) | −2.12009e45 | −0.287604 | ||||||||
\(226\) | −1.77878e46 | −2.21313 | ||||||||
\(227\) | 8.83193e45 | 1.00821 | 0.504105 | − | 0.863642i | \(-0.331822\pi\) | ||||
0.504105 | + | 0.863642i | \(0.331822\pi\) | |||||||
\(228\) | 1.35553e45 | 0.142029 | ||||||||
\(229\) | 5.23661e45 | 0.503800 | 0.251900 | − | 0.967753i | \(-0.418945\pi\) | ||||
0.251900 | + | 0.967753i | \(0.418945\pi\) | |||||||
\(230\) | −8.30279e45 | −0.733721 | ||||||||
\(231\) | 1.18594e45 | 0.0963007 | ||||||||
\(232\) | 2.76495e45 | 0.206382 | ||||||||
\(233\) | 4.92640e45 | 0.338134 | 0.169067 | − | 0.985605i | \(-0.445925\pi\) | ||||
0.169067 | + | 0.985605i | \(0.445925\pi\) | |||||||
\(234\) | 1.55607e45 | 0.0982469 | ||||||||
\(235\) | −5.33979e45 | −0.310242 | ||||||||
\(236\) | 8.20739e45 | 0.438956 | ||||||||
\(237\) | 1.71903e46 | 0.846623 | ||||||||
\(238\) | 7.40219e45 | 0.335823 | ||||||||
\(239\) | −1.38643e46 | −0.579613 | −0.289806 | − | 0.957085i | \(-0.593591\pi\) | ||||
−0.289806 | + | 0.957085i | \(0.593591\pi\) | |||||||
\(240\) | 6.56316e45 | 0.252926 | ||||||||
\(241\) | −2.68139e46 | −0.952857 | −0.476429 | − | 0.879213i | \(-0.658069\pi\) | ||||
−0.476429 | + | 0.879213i | \(0.658069\pi\) | |||||||
\(242\) | 5.24044e45 | 0.171778 | ||||||||
\(243\) | −2.12090e45 | −0.0641500 | ||||||||
\(244\) | 2.83591e46 | 0.791756 | ||||||||
\(245\) | −1.39087e46 | −0.358549 | ||||||||
\(246\) | 3.62584e46 | 0.863325 | ||||||||
\(247\) | 3.27258e45 | 0.0719945 | ||||||||
\(248\) | 1.74489e46 | 0.354782 | ||||||||
\(249\) | −2.30810e46 | −0.433879 | ||||||||
\(250\) | 5.26411e46 | 0.915154 | ||||||||
\(251\) | −3.67189e46 | −0.590544 | −0.295272 | − | 0.955413i | \(-0.595410\pi\) | ||||
−0.295272 | + | 0.955413i | \(0.595410\pi\) | |||||||
\(252\) | 3.04024e45 | 0.0452477 | ||||||||
\(253\) | −1.01144e47 | −1.39344 | ||||||||
\(254\) | −1.42087e47 | −1.81258 | ||||||||
\(255\) | 2.56308e46 | 0.302850 | ||||||||
\(256\) | 1.18473e47 | 1.29700 | ||||||||
\(257\) | −1.07481e47 | −1.09052 | −0.545262 | − | 0.838266i | \(-0.683570\pi\) | ||||
−0.545262 | + | 0.838266i | \(0.683570\pi\) | |||||||
\(258\) | −1.01308e47 | −0.952923 | ||||||||
\(259\) | −2.34359e46 | −0.204426 | ||||||||
\(260\) | −7.72355e45 | −0.0624938 | ||||||||
\(261\) | 2.87002e46 | 0.215474 | ||||||||
\(262\) | 1.12665e47 | 0.785077 | ||||||||
\(263\) | 4.28852e46 | 0.277441 | 0.138720 | − | 0.990332i | \(-0.455701\pi\) | ||||
0.138720 | + | 0.990332i | \(0.455701\pi\) | |||||||
\(264\) | 2.86255e46 | 0.171979 | ||||||||
\(265\) | 1.11215e47 | 0.620682 | ||||||||
\(266\) | 1.48149e46 | 0.0768255 | ||||||||
\(267\) | 2.27048e46 | 0.109433 | ||||||||
\(268\) | 1.71378e47 | 0.767938 | ||||||||
\(269\) | 3.54634e47 | 1.47779 | 0.738893 | − | 0.673823i | \(-0.235349\pi\) | ||||
0.738893 | + | 0.673823i | \(0.235349\pi\) | |||||||
\(270\) | 2.43914e46 | 0.0945460 | ||||||||
\(271\) | −1.75773e47 | −0.633944 | −0.316972 | − | 0.948435i | \(-0.602666\pi\) | ||||
−0.316972 | + | 0.948435i | \(0.602666\pi\) | |||||||
\(272\) | 4.99028e47 | 1.67506 | ||||||||
\(273\) | 7.33989e45 | 0.0229360 | ||||||||
\(274\) | −6.53336e47 | −1.90108 | ||||||||
\(275\) | 2.97021e47 | 0.805006 | ||||||||
\(276\) | −2.59288e47 | −0.654720 | ||||||||
\(277\) | −4.57384e47 | −1.07628 | −0.538140 | − | 0.842856i | \(-0.680873\pi\) | ||||
−0.538140 | + | 0.842856i | \(0.680873\pi\) | |||||||
\(278\) | −6.21475e47 | −1.36317 | ||||||||
\(279\) | 1.81120e47 | 0.370412 | ||||||||
\(280\) | 1.10841e46 | 0.0211406 | ||||||||
\(281\) | 8.97102e46 | 0.159613 | 0.0798065 | − | 0.996810i | \(-0.474570\pi\) | ||||
0.0798065 | + | 0.996810i | \(0.474570\pi\) | |||||||
\(282\) | −3.86377e47 | −0.641436 | ||||||||
\(283\) | −6.02752e47 | −0.933906 | −0.466953 | − | 0.884282i | \(-0.654648\pi\) | ||||
−0.466953 | + | 0.884282i | \(0.654648\pi\) | |||||||
\(284\) | 3.63126e47 | 0.525230 | ||||||||
\(285\) | 5.12978e46 | 0.0692825 | ||||||||
\(286\) | −2.18002e47 | −0.274993 | ||||||||
\(287\) | 1.71029e47 | 0.201546 | ||||||||
\(288\) | 3.78251e47 | 0.416512 | ||||||||
\(289\) | 9.77182e47 | 1.00570 | ||||||||
\(290\) | −3.30067e47 | −0.317571 | ||||||||
\(291\) | −4.03264e47 | −0.362807 | ||||||||
\(292\) | 1.41682e48 | 1.19220 | ||||||||
\(293\) | 5.28590e47 | 0.416102 | 0.208051 | − | 0.978118i | \(-0.433288\pi\) | ||||
0.208051 | + | 0.978118i | \(0.433288\pi\) | |||||||
\(294\) | −1.00641e48 | −0.741313 | ||||||||
\(295\) | 3.10596e47 | 0.214124 | ||||||||
\(296\) | −5.65682e47 | −0.365077 | ||||||||
\(297\) | 2.97133e47 | 0.179556 | ||||||||
\(298\) | 3.57076e47 | 0.202089 | ||||||||
\(299\) | −6.25986e47 | −0.331877 | ||||||||
\(300\) | 7.61432e47 | 0.378239 | ||||||||
\(301\) | −4.77863e47 | −0.222463 | ||||||||
\(302\) | −1.31889e48 | −0.575535 | ||||||||
\(303\) | −1.09635e48 | −0.448558 | ||||||||
\(304\) | 9.98763e47 | 0.383202 | ||||||||
\(305\) | 1.07321e48 | 0.386222 | ||||||||
\(306\) | 1.85459e48 | 0.626153 | ||||||||
\(307\) | 4.29049e48 | 1.35928 | 0.679639 | − | 0.733547i | \(-0.262136\pi\) | ||||
0.679639 | + | 0.733547i | \(0.262136\pi\) | |||||||
\(308\) | −4.25931e47 | −0.126649 | ||||||||
\(309\) | 2.10232e48 | 0.586824 | ||||||||
\(310\) | −2.08298e48 | −0.545923 | ||||||||
\(311\) | −2.42927e48 | −0.597928 | −0.298964 | − | 0.954264i | \(-0.596641\pi\) | ||||
−0.298964 | + | 0.954264i | \(0.596641\pi\) | |||||||
\(312\) | 1.77166e47 | 0.0409605 | ||||||||
\(313\) | −1.42549e48 | −0.309635 | −0.154818 | − | 0.987943i | \(-0.549479\pi\) | ||||
−0.154818 | + | 0.987943i | \(0.549479\pi\) | |||||||
\(314\) | −7.06780e48 | −1.44263 | ||||||||
\(315\) | 1.15053e47 | 0.0220720 | ||||||||
\(316\) | −6.17390e48 | −1.11343 | ||||||||
\(317\) | −7.18697e47 | −0.121868 | −0.0609341 | − | 0.998142i | \(-0.519408\pi\) | ||||
−0.0609341 | + | 0.998142i | \(0.519408\pi\) | |||||||
\(318\) | 8.04732e48 | 1.28328 | ||||||||
\(319\) | −4.02084e48 | −0.603113 | ||||||||
\(320\) | −1.24568e48 | −0.175784 | ||||||||
\(321\) | −4.66106e48 | −0.618922 | ||||||||
\(322\) | −2.83382e48 | −0.354147 | ||||||||
\(323\) | 3.90041e48 | 0.458840 | ||||||||
\(324\) | 7.61720e47 | 0.0843661 | ||||||||
\(325\) | 1.83829e48 | 0.191729 | ||||||||
\(326\) | 9.95663e48 | 0.978069 | ||||||||
\(327\) | −2.55199e48 | −0.236155 | ||||||||
\(328\) | 4.12820e48 | 0.359932 | ||||||||
\(329\) | −1.82252e48 | −0.149745 | ||||||||
\(330\) | −3.41718e48 | −0.264635 | ||||||||
\(331\) | 1.29273e49 | 0.943759 | 0.471880 | − | 0.881663i | \(-0.343576\pi\) | ||||
0.471880 | + | 0.881663i | \(0.343576\pi\) | |||||||
\(332\) | 8.28957e48 | 0.570610 | ||||||||
\(333\) | −5.87179e48 | −0.381161 | ||||||||
\(334\) | 1.81433e49 | 1.11086 | ||||||||
\(335\) | 6.48552e48 | 0.374603 | ||||||||
\(336\) | 2.24007e48 | 0.122080 | ||||||||
\(337\) | 1.11373e48 | 0.0572792 | 0.0286396 | − | 0.999590i | \(-0.490882\pi\) | ||||
0.0286396 | + | 0.999590i | \(0.490882\pi\) | |||||||
\(338\) | 2.59748e49 | 1.26089 | ||||||||
\(339\) | −2.10219e49 | −0.963334 | ||||||||
\(340\) | −9.20530e48 | −0.398290 | ||||||||
\(341\) | −2.53746e49 | −1.03678 | ||||||||
\(342\) | 3.71181e48 | 0.143244 | ||||||||
\(343\) | −9.65110e48 | −0.351837 | ||||||||
\(344\) | −1.15344e49 | −0.397287 | ||||||||
\(345\) | −9.81236e48 | −0.319375 | ||||||||
\(346\) | −1.24586e49 | −0.383251 | ||||||||
\(347\) | −2.89424e49 | −0.841608 | −0.420804 | − | 0.907152i | \(-0.638252\pi\) | ||||
−0.420804 | + | 0.907152i | \(0.638252\pi\) | |||||||
\(348\) | −1.03077e49 | −0.283378 | ||||||||
\(349\) | −4.65598e49 | −1.21036 | −0.605181 | − | 0.796088i | \(-0.706899\pi\) | ||||
−0.605181 | + | 0.796088i | \(0.706899\pi\) | |||||||
\(350\) | 8.32187e48 | 0.204595 | ||||||||
\(351\) | 1.83898e48 | 0.0427650 | ||||||||
\(352\) | −5.29923e49 | −1.16582 | ||||||||
\(353\) | 9.33522e49 | 1.94320 | 0.971600 | − | 0.236628i | \(-0.0760422\pi\) | ||||
0.971600 | + | 0.236628i | \(0.0760422\pi\) | |||||||
\(354\) | 2.24741e49 | 0.442710 | ||||||||
\(355\) | 1.37419e49 | 0.256209 | ||||||||
\(356\) | −8.15444e48 | −0.143919 | ||||||||
\(357\) | 8.74803e48 | 0.146177 | ||||||||
\(358\) | 1.07306e50 | 1.69787 | ||||||||
\(359\) | 8.40096e49 | 1.25889 | 0.629444 | − | 0.777046i | \(-0.283283\pi\) | ||||
0.629444 | + | 0.777046i | \(0.283283\pi\) | |||||||
\(360\) | 2.77708e48 | 0.0394175 | ||||||||
\(361\) | −6.65624e49 | −0.895032 | ||||||||
\(362\) | −7.43161e49 | −0.946816 | ||||||||
\(363\) | 6.19323e48 | 0.0747719 | ||||||||
\(364\) | −2.63612e48 | −0.0301640 | ||||||||
\(365\) | 5.36174e49 | 0.581560 | ||||||||
\(366\) | 7.76553e49 | 0.798527 | ||||||||
\(367\) | −5.51580e49 | −0.537799 | −0.268900 | − | 0.963168i | \(-0.586660\pi\) | ||||
−0.268900 | + | 0.963168i | \(0.586660\pi\) | |||||||
\(368\) | −1.91046e50 | −1.76646 | ||||||||
\(369\) | 4.28508e49 | 0.375789 | ||||||||
\(370\) | 6.75286e49 | 0.561765 | ||||||||
\(371\) | 3.79588e49 | 0.299586 | ||||||||
\(372\) | −6.50494e49 | −0.487143 | ||||||||
\(373\) | 2.65526e50 | 1.88706 | 0.943529 | − | 0.331291i | \(-0.107484\pi\) | ||||
0.943529 | + | 0.331291i | \(0.107484\pi\) | |||||||
\(374\) | −2.59825e50 | −1.75261 | ||||||||
\(375\) | 6.22120e49 | 0.398350 | ||||||||
\(376\) | −4.39909e49 | −0.267423 | ||||||||
\(377\) | −2.48853e49 | −0.143644 | ||||||||
\(378\) | 8.32502e48 | 0.0456347 | ||||||||
\(379\) | 2.97919e49 | 0.155108 | 0.0775539 | − | 0.996988i | \(-0.475289\pi\) | ||||
0.0775539 | + | 0.996988i | \(0.475289\pi\) | |||||||
\(380\) | −1.84236e49 | −0.0911160 | ||||||||
\(381\) | −1.67920e50 | −0.788980 | ||||||||
\(382\) | 1.37582e50 | 0.614223 | ||||||||
\(383\) | 1.50203e50 | 0.637240 | 0.318620 | − | 0.947883i | \(-0.396781\pi\) | ||||
0.318620 | + | 0.947883i | \(0.396781\pi\) | |||||||
\(384\) | 8.87802e49 | 0.357979 | ||||||||
\(385\) | −1.61187e49 | −0.0617797 | ||||||||
\(386\) | −6.00790e50 | −2.18912 | ||||||||
\(387\) | −1.19727e50 | −0.414790 | ||||||||
\(388\) | 1.44832e50 | 0.477141 | ||||||||
\(389\) | 3.70754e50 | 1.16163 | 0.580816 | − | 0.814035i | \(-0.302734\pi\) | ||||
0.580816 | + | 0.814035i | \(0.302734\pi\) | |||||||
\(390\) | −2.11492e49 | −0.0630282 | ||||||||
\(391\) | −7.46080e50 | −2.11514 | ||||||||
\(392\) | −1.14585e50 | −0.309064 | ||||||||
\(393\) | 1.33149e50 | 0.341729 | ||||||||
\(394\) | 4.52104e50 | 1.10424 | ||||||||
\(395\) | −2.33641e50 | −0.543133 | ||||||||
\(396\) | −1.06716e50 | −0.236141 | ||||||||
\(397\) | −6.45741e50 | −1.36033 | −0.680164 | − | 0.733060i | \(-0.738091\pi\) | ||||
−0.680164 | + | 0.733060i | \(0.738091\pi\) | |||||||
\(398\) | 1.12354e51 | 2.25356 | ||||||||
\(399\) | 1.75084e49 | 0.0334407 | ||||||||
\(400\) | 5.61029e50 | 1.02051 | ||||||||
\(401\) | 4.44619e50 | 0.770322 | 0.385161 | − | 0.922849i | \(-0.374146\pi\) | ||||
0.385161 | + | 0.922849i | \(0.374146\pi\) | |||||||
\(402\) | 4.69280e50 | 0.774505 | ||||||||
\(403\) | −1.57045e50 | −0.246932 | ||||||||
\(404\) | 3.93755e50 | 0.589915 | ||||||||
\(405\) | 2.88261e49 | 0.0411541 | ||||||||
\(406\) | −1.12655e50 | −0.153283 | ||||||||
\(407\) | 8.22626e50 | 1.06687 | ||||||||
\(408\) | 2.11154e50 | 0.261052 | ||||||||
\(409\) | −6.28638e50 | −0.740963 | −0.370481 | − | 0.928840i | \(-0.620807\pi\) | ||||
−0.370481 | + | 0.928840i | \(0.620807\pi\) | |||||||
\(410\) | −4.92806e50 | −0.553848 | ||||||||
\(411\) | −7.72122e50 | −0.827505 | ||||||||
\(412\) | −7.55049e50 | −0.771755 | ||||||||
\(413\) | 1.06009e50 | 0.103352 | ||||||||
\(414\) | −7.10004e50 | −0.660319 | ||||||||
\(415\) | 3.13706e50 | 0.278346 | ||||||||
\(416\) | −3.27974e50 | −0.277664 | ||||||||
\(417\) | −7.34468e50 | −0.593362 | ||||||||
\(418\) | −5.20017e50 | −0.400941 | ||||||||
\(419\) | −3.74717e49 | −0.0275759 | −0.0137879 | − | 0.999905i | \(-0.504389\pi\) | ||||
−0.0137879 | + | 0.999905i | \(0.504389\pi\) | |||||||
\(420\) | −4.13213e49 | −0.0290277 | ||||||||
\(421\) | −1.68026e50 | −0.112687 | −0.0563437 | − | 0.998411i | \(-0.517944\pi\) | ||||
−0.0563437 | + | 0.998411i | \(0.517944\pi\) | |||||||
\(422\) | −2.92607e51 | −1.87367 | ||||||||
\(423\) | −4.56626e50 | −0.279205 | ||||||||
\(424\) | 9.16226e50 | 0.535018 | ||||||||
\(425\) | 2.19096e51 | 1.22194 | ||||||||
\(426\) | 9.94339e50 | 0.529721 | ||||||||
\(427\) | 3.66296e50 | 0.186418 | ||||||||
\(428\) | 1.67402e51 | 0.813968 | ||||||||
\(429\) | −2.57638e50 | −0.119699 | ||||||||
\(430\) | 1.37692e51 | 0.611328 | ||||||||
\(431\) | −3.10054e51 | −1.31562 | −0.657809 | − | 0.753184i | \(-0.728517\pi\) | ||||
−0.657809 | + | 0.753184i | \(0.728517\pi\) | |||||||
\(432\) | 5.61242e50 | 0.227623 | ||||||||
\(433\) | 5.11038e51 | 1.98125 | 0.990624 | − | 0.136616i | \(-0.0436225\pi\) | ||||
0.990624 | + | 0.136616i | \(0.0436225\pi\) | |||||||
\(434\) | −7.10940e50 | −0.263502 | ||||||||
\(435\) | −3.90078e50 | −0.138233 | ||||||||
\(436\) | 9.16548e50 | 0.310577 | ||||||||
\(437\) | −1.49322e51 | −0.483876 | ||||||||
\(438\) | 3.87965e51 | 1.20240 | ||||||||
\(439\) | −2.58440e51 | −0.766129 | −0.383065 | − | 0.923722i | \(-0.625131\pi\) | ||||
−0.383065 | + | 0.923722i | \(0.625131\pi\) | |||||||
\(440\) | −3.89063e50 | −0.110330 | ||||||||
\(441\) | −1.18939e51 | −0.322680 | ||||||||
\(442\) | −1.60808e51 | −0.417420 | ||||||||
\(443\) | 7.44976e51 | 1.85042 | 0.925209 | − | 0.379459i | \(-0.123890\pi\) | ||||
0.925209 | + | 0.379459i | \(0.123890\pi\) | |||||||
\(444\) | 2.10886e51 | 0.501278 | ||||||||
\(445\) | −3.08592e50 | −0.0702044 | ||||||||
\(446\) | −9.44236e51 | −2.05613 | ||||||||
\(447\) | 4.21997e50 | 0.0879657 | ||||||||
\(448\) | −4.25161e50 | −0.0848462 | ||||||||
\(449\) | −5.14327e51 | −0.982733 | −0.491366 | − | 0.870953i | \(-0.663502\pi\) | ||||
−0.491366 | + | 0.870953i | \(0.663502\pi\) | |||||||
\(450\) | 2.08501e51 | 0.381474 | ||||||||
\(451\) | −6.00331e51 | −1.05184 | ||||||||
\(452\) | 7.55001e51 | 1.26692 | ||||||||
\(453\) | −1.55868e51 | −0.250520 | ||||||||
\(454\) | −8.68580e51 | −1.33727 | ||||||||
\(455\) | −9.97600e49 | −0.0147141 | ||||||||
\(456\) | 4.22607e50 | 0.0597204 | ||||||||
\(457\) | 7.10120e51 | 0.961536 | 0.480768 | − | 0.876848i | \(-0.340358\pi\) | ||||
0.480768 | + | 0.876848i | \(0.340358\pi\) | |||||||
\(458\) | −5.14996e51 | −0.668232 | ||||||||
\(459\) | 2.19179e51 | 0.272553 | ||||||||
\(460\) | 3.52411e51 | 0.420022 | ||||||||
\(461\) | 1.14310e52 | 1.30592 | 0.652961 | − | 0.757392i | \(-0.273527\pi\) | ||||
0.652961 | + | 0.757392i | \(0.273527\pi\) | |||||||
\(462\) | −1.16632e51 | −0.127732 | ||||||||
\(463\) | 6.36169e51 | 0.667948 | 0.333974 | − | 0.942582i | \(-0.391610\pi\) | ||||
0.333974 | + | 0.942582i | \(0.391610\pi\) | |||||||
\(464\) | −7.59479e51 | −0.764566 | ||||||||
\(465\) | −2.46169e51 | −0.237630 | ||||||||
\(466\) | −4.84489e51 | −0.448496 | ||||||||
\(467\) | −1.61556e52 | −1.43431 | −0.717155 | − | 0.696913i | \(-0.754556\pi\) | ||||
−0.717155 | + | 0.696913i | \(0.754556\pi\) | |||||||
\(468\) | −6.60471e50 | −0.0562419 | ||||||||
\(469\) | 2.21357e51 | 0.180810 | ||||||||
\(470\) | 5.25144e51 | 0.411500 | ||||||||
\(471\) | −8.35284e51 | −0.627952 | ||||||||
\(472\) | 2.55879e51 | 0.184572 | ||||||||
\(473\) | 1.67735e52 | 1.16100 | ||||||||
\(474\) | −1.69059e52 | −1.12295 | ||||||||
\(475\) | 4.38501e51 | 0.279541 | ||||||||
\(476\) | −3.14186e51 | −0.192243 | ||||||||
\(477\) | 9.51044e51 | 0.558589 | ||||||||
\(478\) | 1.36349e52 | 0.768789 | ||||||||
\(479\) | 2.76529e52 | 1.49692 | 0.748459 | − | 0.663181i | \(-0.230794\pi\) | ||||
0.748459 | + | 0.663181i | \(0.230794\pi\) | |||||||
\(480\) | −5.14100e51 | −0.267204 | ||||||||
\(481\) | 5.09130e51 | 0.254097 | ||||||||
\(482\) | 2.63703e52 | 1.26385 | ||||||||
\(483\) | −3.34905e51 | −0.154153 | ||||||||
\(484\) | −2.22430e51 | −0.0983353 | ||||||||
\(485\) | 5.48095e51 | 0.232751 | ||||||||
\(486\) | 2.08580e51 | 0.0850876 | ||||||||
\(487\) | −4.32447e52 | −1.69480 | −0.847398 | − | 0.530957i | \(-0.821832\pi\) | ||||
−0.847398 | + | 0.530957i | \(0.821832\pi\) | |||||||
\(488\) | 8.84143e51 | 0.332917 | ||||||||
\(489\) | 1.17669e52 | 0.425735 | ||||||||
\(490\) | 1.36786e52 | 0.475574 | ||||||||
\(491\) | −4.34756e52 | −1.45264 | −0.726318 | − | 0.687359i | \(-0.758770\pi\) | ||||
−0.726318 | + | 0.687359i | \(0.758770\pi\) | |||||||
\(492\) | −1.53899e52 | −0.494215 | ||||||||
\(493\) | −2.96595e52 | −0.915480 | ||||||||
\(494\) | −3.21843e51 | −0.0954923 | ||||||||
\(495\) | −4.03848e51 | −0.115191 | ||||||||
\(496\) | −4.79289e52 | −1.31433 | ||||||||
\(497\) | 4.69025e51 | 0.123665 | ||||||||
\(498\) | 2.26992e52 | 0.575490 | ||||||||
\(499\) | −3.90961e52 | −0.953176 | −0.476588 | − | 0.879127i | \(-0.658127\pi\) | ||||
−0.476588 | + | 0.879127i | \(0.658127\pi\) | |||||||
\(500\) | −2.23435e52 | −0.523884 | ||||||||
\(501\) | 2.14420e52 | 0.483537 | ||||||||
\(502\) | 3.61114e52 | 0.783288 | ||||||||
\(503\) | −9.26181e52 | −1.93250 | −0.966252 | − | 0.257599i | \(-0.917069\pi\) | ||||
−0.966252 | + | 0.257599i | \(0.917069\pi\) | |||||||
\(504\) | 9.47844e50 | 0.0190257 | ||||||||
\(505\) | 1.49011e52 | 0.287763 | ||||||||
\(506\) | 9.94701e52 | 1.84824 | ||||||||
\(507\) | 3.06974e52 | 0.548841 | ||||||||
\(508\) | 6.03087e52 | 1.03762 | ||||||||
\(509\) | 4.50967e52 | 0.746703 | 0.373351 | − | 0.927690i | \(-0.378209\pi\) | ||||
0.373351 | + | 0.927690i | \(0.378209\pi\) | |||||||
\(510\) | −2.52067e52 | −0.401696 | ||||||||
\(511\) | 1.83001e52 | 0.280703 | ||||||||
\(512\) | −7.45197e52 | −1.10029 | ||||||||
\(513\) | 4.38667e51 | 0.0623515 | ||||||||
\(514\) | 1.05702e53 | 1.44645 | ||||||||
\(515\) | −2.85736e52 | −0.376465 | ||||||||
\(516\) | 4.30000e52 | 0.545505 | ||||||||
\(517\) | 6.39724e52 | 0.781496 | ||||||||
\(518\) | 2.30482e52 | 0.271148 | ||||||||
\(519\) | −1.47237e52 | −0.166822 | ||||||||
\(520\) | −2.40794e51 | −0.0262773 | ||||||||
\(521\) | 1.49958e52 | 0.157629 | 0.0788143 | − | 0.996889i | \(-0.474887\pi\) | ||||
0.0788143 | + | 0.996889i | \(0.474887\pi\) | |||||||
\(522\) | −2.82253e52 | −0.285801 | ||||||||
\(523\) | −7.38472e52 | −0.720363 | −0.360181 | − | 0.932882i | \(-0.617285\pi\) | ||||
−0.360181 | + | 0.932882i | \(0.617285\pi\) | |||||||
\(524\) | −4.78204e52 | −0.449421 | ||||||||
\(525\) | 9.83491e51 | 0.0890562 | ||||||||
\(526\) | −4.21757e52 | −0.367993 | ||||||||
\(527\) | −1.87174e53 | −1.57376 | ||||||||
\(528\) | −7.86289e52 | −0.637119 | ||||||||
\(529\) | 1.57574e53 | 1.23055 | ||||||||
\(530\) | −1.09375e53 | −0.823263 | ||||||||
\(531\) | 2.65603e52 | 0.192703 | ||||||||
\(532\) | −6.28816e51 | −0.0439791 | ||||||||
\(533\) | −3.71550e52 | −0.250517 | ||||||||
\(534\) | −2.23291e52 | −0.145150 | ||||||||
\(535\) | 6.33507e52 | 0.397057 | ||||||||
\(536\) | 5.34298e52 | 0.322902 | ||||||||
\(537\) | 1.26816e53 | 0.739052 | ||||||||
\(538\) | −3.48767e53 | −1.96011 | ||||||||
\(539\) | 1.66631e53 | 0.903182 | ||||||||
\(540\) | −1.03529e52 | −0.0541233 | ||||||||
\(541\) | 2.27671e53 | 1.14805 | 0.574026 | − | 0.818837i | \(-0.305381\pi\) | ||||
0.574026 | + | 0.818837i | \(0.305381\pi\) | |||||||
\(542\) | 1.72865e53 | 0.840854 | ||||||||
\(543\) | −8.78279e52 | −0.412131 | ||||||||
\(544\) | −3.90895e53 | −1.76962 | ||||||||
\(545\) | 3.46853e52 | 0.151501 | ||||||||
\(546\) | −7.21845e51 | −0.0304220 | ||||||||
\(547\) | −5.88442e52 | −0.239305 | −0.119652 | − | 0.992816i | \(-0.538178\pi\) | ||||
−0.119652 | + | 0.992816i | \(0.538178\pi\) | |||||||
\(548\) | 2.77308e53 | 1.08828 | ||||||||
\(549\) | 9.17742e52 | 0.347584 | ||||||||
\(550\) | −2.92106e53 | −1.06775 | ||||||||
\(551\) | −5.93610e52 | −0.209433 | ||||||||
\(552\) | −8.08374e52 | −0.275296 | ||||||||
\(553\) | −7.97441e52 | −0.262155 | ||||||||
\(554\) | 4.49816e53 | 1.42756 | ||||||||
\(555\) | 7.98064e52 | 0.244526 | ||||||||
\(556\) | 2.63785e53 | 0.780353 | ||||||||
\(557\) | 2.92686e53 | 0.836036 | 0.418018 | − | 0.908439i | \(-0.362725\pi\) | ||||
0.418018 | + | 0.908439i | \(0.362725\pi\) | |||||||
\(558\) | −1.78123e53 | −0.491309 | ||||||||
\(559\) | 1.03813e53 | 0.276516 | ||||||||
\(560\) | −3.04459e52 | −0.0783181 | ||||||||
\(561\) | −3.07065e53 | −0.762877 | ||||||||
\(562\) | −8.82259e52 | −0.211708 | ||||||||
\(563\) | −4.41627e53 | −1.02363 | −0.511813 | − | 0.859097i | \(-0.671026\pi\) | ||||
−0.511813 | + | 0.859097i | \(0.671026\pi\) | |||||||
\(564\) | 1.63997e53 | 0.367193 | ||||||||
\(565\) | 2.85718e53 | 0.618007 | ||||||||
\(566\) | 5.92779e53 | 1.23872 | ||||||||
\(567\) | 9.83864e51 | 0.0198639 | ||||||||
\(568\) | 1.13210e53 | 0.220848 | ||||||||
\(569\) | −5.05383e53 | −0.952646 | −0.476323 | − | 0.879270i | \(-0.658031\pi\) | ||||
−0.476323 | + | 0.879270i | \(0.658031\pi\) | |||||||
\(570\) | −5.04490e52 | −0.0918952 | ||||||||
\(571\) | 2.64819e53 | 0.466170 | 0.233085 | − | 0.972456i | \(-0.425118\pi\) | ||||
0.233085 | + | 0.972456i | \(0.425118\pi\) | |||||||
\(572\) | 9.25307e52 | 0.157421 | ||||||||
\(573\) | 1.62597e53 | 0.267360 | ||||||||
\(574\) | −1.68200e53 | −0.267327 | ||||||||
\(575\) | −8.38776e53 | −1.28861 | ||||||||
\(576\) | −1.06523e53 | −0.158199 | ||||||||
\(577\) | 9.15202e53 | 1.31398 | 0.656989 | − | 0.753900i | \(-0.271830\pi\) | ||||
0.656989 | + | 0.753900i | \(0.271830\pi\) | |||||||
\(578\) | −9.61014e53 | −1.33394 | ||||||||
\(579\) | −7.10023e53 | −0.952884 | ||||||||
\(580\) | 1.40097e53 | 0.181795 | ||||||||
\(581\) | 1.07071e53 | 0.134350 | ||||||||
\(582\) | 3.96591e53 | 0.481222 | ||||||||
\(583\) | −1.33239e54 | −1.56349 | ||||||||
\(584\) | 4.41717e53 | 0.501296 | ||||||||
\(585\) | −2.49945e52 | −0.0274350 | ||||||||
\(586\) | −5.19844e53 | −0.551911 | ||||||||
\(587\) | −1.24680e54 | −1.28042 | −0.640212 | − | 0.768199i | \(-0.721153\pi\) | ||||
−0.640212 | + | 0.768199i | \(0.721153\pi\) | |||||||
\(588\) | 4.27170e53 | 0.424368 | ||||||||
\(589\) | −3.74613e53 | −0.360027 | ||||||||
\(590\) | −3.05457e53 | −0.284011 | ||||||||
\(591\) | 5.34304e53 | 0.480654 | ||||||||
\(592\) | 1.55382e54 | 1.35247 | ||||||||
\(593\) | 1.19143e54 | 1.00346 | 0.501730 | − | 0.865024i | \(-0.332697\pi\) | ||||
0.501730 | + | 0.865024i | \(0.332697\pi\) | |||||||
\(594\) | −2.92217e53 | −0.238160 | ||||||||
\(595\) | −1.18899e53 | −0.0937770 | ||||||||
\(596\) | −1.51561e53 | −0.115687 | ||||||||
\(597\) | 1.32782e54 | 0.980935 | ||||||||
\(598\) | 6.15629e53 | 0.440196 | ||||||||
\(599\) | 1.12943e54 | 0.781694 | 0.390847 | − | 0.920456i | \(-0.372182\pi\) | ||||
0.390847 | + | 0.920456i | \(0.372182\pi\) | |||||||
\(600\) | 2.37389e53 | 0.159042 | ||||||||
\(601\) | 1.31522e54 | 0.852997 | 0.426498 | − | 0.904488i | \(-0.359747\pi\) | ||||
0.426498 | + | 0.904488i | \(0.359747\pi\) | |||||||
\(602\) | 4.69957e53 | 0.295071 | ||||||||
\(603\) | 5.54603e53 | 0.337128 | ||||||||
\(604\) | 5.59801e53 | 0.329468 | ||||||||
\(605\) | −8.41753e52 | −0.0479683 | ||||||||
\(606\) | 1.07821e54 | 0.594960 | ||||||||
\(607\) | −1.47634e54 | −0.788872 | −0.394436 | − | 0.918924i | \(-0.629060\pi\) | ||||
−0.394436 | + | 0.918924i | \(0.629060\pi\) | |||||||
\(608\) | −7.82342e53 | −0.404834 | ||||||||
\(609\) | −1.33138e53 | −0.0667211 | ||||||||
\(610\) | −1.05545e54 | −0.512279 | ||||||||
\(611\) | 3.95931e53 | 0.186130 | ||||||||
\(612\) | −7.87181e53 | −0.358444 | ||||||||
\(613\) | −2.90350e54 | −1.28069 | −0.640343 | − | 0.768089i | \(-0.721208\pi\) | ||||
−0.640343 | + | 0.768089i | \(0.721208\pi\) | |||||||
\(614\) | −4.21950e54 | −1.80292 | ||||||||
\(615\) | −5.82406e53 | −0.241080 | ||||||||
\(616\) | −1.32791e53 | −0.0532531 | ||||||||
\(617\) | 4.37494e53 | 0.169985 | 0.0849926 | − | 0.996382i | \(-0.472913\pi\) | ||||
0.0849926 | + | 0.996382i | \(0.472913\pi\) | |||||||
\(618\) | −2.06753e54 | −0.778355 | ||||||||
\(619\) | −1.36826e54 | −0.499114 | −0.249557 | − | 0.968360i | \(-0.580285\pi\) | ||||
−0.249557 | + | 0.968360i | \(0.580285\pi\) | |||||||
\(620\) | 8.84118e53 | 0.312516 | ||||||||
\(621\) | −8.39093e53 | −0.287425 | ||||||||
\(622\) | 2.38908e54 | 0.793082 | ||||||||
\(623\) | −1.05325e53 | −0.0338857 | ||||||||
\(624\) | −4.86641e53 | −0.151743 | ||||||||
\(625\) | 2.00926e54 | 0.607261 | ||||||||
\(626\) | 1.40191e54 | 0.410695 | ||||||||
\(627\) | −6.14564e53 | −0.174522 | ||||||||
\(628\) | 2.99993e54 | 0.825843 | ||||||||
\(629\) | 6.06806e54 | 1.61943 | ||||||||
\(630\) | −1.13149e53 | −0.0292760 | ||||||||
\(631\) | −2.93523e54 | −0.736325 | −0.368162 | − | 0.929762i | \(-0.620013\pi\) | ||||
−0.368162 | + | 0.929762i | \(0.620013\pi\) | |||||||
\(632\) | −1.92481e54 | −0.468172 | ||||||||
\(633\) | −3.45808e54 | −0.815573 | ||||||||
\(634\) | 7.06806e53 | 0.161644 | ||||||||
\(635\) | 2.28229e54 | 0.506154 | ||||||||
\(636\) | −3.41568e54 | −0.734621 | ||||||||
\(637\) | 1.03129e54 | 0.215112 | ||||||||
\(638\) | 3.95431e54 | 0.799959 | ||||||||
\(639\) | 1.17513e54 | 0.230578 | ||||||||
\(640\) | −1.20665e54 | −0.229654 | ||||||||
\(641\) | −4.74778e54 | −0.876514 | −0.438257 | − | 0.898850i | \(-0.644404\pi\) | ||||
−0.438257 | + | 0.898850i | \(0.644404\pi\) | |||||||
\(642\) | 4.58394e54 | 0.820929 | ||||||||
\(643\) | 3.92907e54 | 0.682616 | 0.341308 | − | 0.939952i | \(-0.389130\pi\) | ||||
0.341308 | + | 0.939952i | \(0.389130\pi\) | |||||||
\(644\) | 1.20281e54 | 0.202733 | ||||||||
\(645\) | 1.62727e54 | 0.266100 | ||||||||
\(646\) | −3.83588e54 | −0.608598 | ||||||||
\(647\) | 3.76973e54 | 0.580332 | 0.290166 | − | 0.956976i | \(-0.406289\pi\) | ||||
0.290166 | + | 0.956976i | \(0.406289\pi\) | |||||||
\(648\) | 2.37479e53 | 0.0354742 | ||||||||
\(649\) | −3.72104e54 | −0.539377 | ||||||||
\(650\) | −1.80787e54 | −0.254306 | ||||||||
\(651\) | −8.40200e53 | −0.114697 | ||||||||
\(652\) | −4.22609e54 | −0.559900 | ||||||||
\(653\) | 7.52716e54 | 0.967886 | 0.483943 | − | 0.875100i | \(-0.339204\pi\) | ||||
0.483943 | + | 0.875100i | \(0.339204\pi\) | |||||||
\(654\) | 2.50977e54 | 0.313233 | ||||||||
\(655\) | −1.80969e54 | −0.219229 | ||||||||
\(656\) | −1.13394e55 | −1.33341 | ||||||||
\(657\) | 4.58503e54 | 0.523381 | ||||||||
\(658\) | 1.79237e54 | 0.198619 | ||||||||
\(659\) | 1.58833e55 | 1.70874 | 0.854369 | − | 0.519666i | \(-0.173944\pi\) | ||||
0.854369 | + | 0.519666i | \(0.173944\pi\) | |||||||
\(660\) | 1.45042e54 | 0.151491 | ||||||||
\(661\) | −8.67678e54 | −0.879893 | −0.439947 | − | 0.898024i | \(-0.645003\pi\) | ||||
−0.439947 | + | 0.898024i | \(0.645003\pi\) | |||||||
\(662\) | −1.27134e55 | −1.25179 | ||||||||
\(663\) | −1.90045e54 | −0.181695 | ||||||||
\(664\) | 2.58441e54 | 0.239929 | ||||||||
\(665\) | −2.37966e53 | −0.0214532 | ||||||||
\(666\) | 5.77464e54 | 0.505565 | ||||||||
\(667\) | 1.13547e55 | 0.965433 | ||||||||
\(668\) | −7.70091e54 | −0.635918 | ||||||||
\(669\) | −1.11591e55 | −0.894996 | ||||||||
\(670\) | −6.37822e54 | −0.496867 | ||||||||
\(671\) | −1.28574e55 | −0.972889 | ||||||||
\(672\) | −1.75467e54 | −0.128972 | ||||||||
\(673\) | 6.85577e54 | 0.489511 | 0.244756 | − | 0.969585i | \(-0.421292\pi\) | ||||
0.244756 | + | 0.969585i | \(0.421292\pi\) | |||||||
\(674\) | −1.09530e54 | −0.0759742 | ||||||||
\(675\) | 2.46410e54 | 0.166049 | ||||||||
\(676\) | −1.10250e55 | −0.721802 | ||||||||
\(677\) | −2.36538e55 | −1.50460 | −0.752301 | − | 0.658819i | \(-0.771056\pi\) | ||||
−0.752301 | + | 0.658819i | \(0.771056\pi\) | |||||||
\(678\) | 2.06740e55 | 1.27775 | ||||||||
\(679\) | 1.87070e54 | 0.112343 | ||||||||
\(680\) | −2.86990e54 | −0.167472 | ||||||||
\(681\) | −1.02650e55 | −0.582091 | ||||||||
\(682\) | 2.49547e55 | 1.37517 | ||||||||
\(683\) | 6.41764e53 | 0.0343694 | 0.0171847 | − | 0.999852i | \(-0.494530\pi\) | ||||
0.0171847 | + | 0.999852i | \(0.494530\pi\) | |||||||
\(684\) | −1.57548e54 | −0.0820007 | ||||||||
\(685\) | 1.04943e55 | 0.530868 | ||||||||
\(686\) | 9.49142e54 | 0.466671 | ||||||||
\(687\) | −6.08630e54 | −0.290869 | ||||||||
\(688\) | 3.16827e55 | 1.47180 | ||||||||
\(689\) | −8.24630e54 | −0.372378 | ||||||||
\(690\) | 9.65001e54 | 0.423614 | ||||||||
\(691\) | 8.58416e54 | 0.366333 | 0.183166 | − | 0.983082i | \(-0.441365\pi\) | ||||
0.183166 | + | 0.983082i | \(0.441365\pi\) | |||||||
\(692\) | 5.28803e54 | 0.219394 | ||||||||
\(693\) | −1.37837e54 | −0.0555992 | ||||||||
\(694\) | 2.84635e55 | 1.11630 | ||||||||
\(695\) | 9.98251e54 | 0.380659 | ||||||||
\(696\) | −3.21359e54 | −0.119154 | ||||||||
\(697\) | −4.42831e55 | −1.59661 | ||||||||
\(698\) | 4.57894e55 | 1.60540 | ||||||||
\(699\) | −5.72576e54 | −0.195222 | ||||||||
\(700\) | −3.53221e54 | −0.117121 | ||||||||
\(701\) | −2.73445e55 | −0.881797 | −0.440899 | − | 0.897557i | \(-0.645340\pi\) | ||||
−0.440899 | + | 0.897557i | \(0.645340\pi\) | |||||||
\(702\) | −1.80856e54 | −0.0567229 | ||||||||
\(703\) | 1.21447e55 | 0.370474 | ||||||||
\(704\) | 1.49236e55 | 0.442799 | ||||||||
\(705\) | 6.20623e54 | 0.179118 | ||||||||
\(706\) | −9.18076e55 | −2.57743 | ||||||||
\(707\) | 5.08587e54 | 0.138895 | ||||||||
\(708\) | −9.53913e54 | −0.253431 | ||||||||
\(709\) | −4.45024e55 | −1.15022 | −0.575112 | − | 0.818075i | \(-0.695041\pi\) | ||||
−0.575112 | + | 0.818075i | \(0.695041\pi\) | |||||||
\(710\) | −1.35146e55 | −0.339832 | ||||||||
\(711\) | −1.99796e55 | −0.488798 | ||||||||
\(712\) | −2.54228e54 | −0.0605151 | ||||||||
\(713\) | 7.16569e55 | 1.65963 | ||||||||
\(714\) | −8.60329e54 | −0.193887 | ||||||||
\(715\) | 3.50168e54 | 0.0767907 | ||||||||
\(716\) | −4.55460e55 | −0.971955 | ||||||||
\(717\) | 1.61139e55 | 0.334639 | ||||||||
\(718\) | −8.26196e55 | −1.66977 | ||||||||
\(719\) | −7.96989e54 | −0.156761 | −0.0783807 | − | 0.996924i | \(-0.524975\pi\) | ||||
−0.0783807 | + | 0.996924i | \(0.524975\pi\) | |||||||
\(720\) | −7.62811e54 | −0.146027 | ||||||||
\(721\) | −9.75246e54 | −0.181709 | ||||||||
\(722\) | 6.54611e55 | 1.18716 | ||||||||
\(723\) | 3.11648e55 | 0.550132 | ||||||||
\(724\) | 3.15434e55 | 0.542009 | ||||||||
\(725\) | −3.33445e55 | −0.557742 | ||||||||
\(726\) | −6.09076e54 | −0.0991762 | ||||||||
\(727\) | 1.16079e56 | 1.84006 | 0.920031 | − | 0.391845i | \(-0.128163\pi\) | ||||
0.920031 | + | 0.391845i | \(0.128163\pi\) | |||||||
\(728\) | −8.21855e53 | −0.0126833 | ||||||||
\(729\) | 2.46503e54 | 0.0370370 | ||||||||
\(730\) | −5.27303e55 | −0.771373 | ||||||||
\(731\) | 1.23729e56 | 1.76231 | ||||||||
\(732\) | −3.29607e55 | −0.457121 | ||||||||
\(733\) | 3.74430e55 | 0.505642 | 0.252821 | − | 0.967513i | \(-0.418642\pi\) | ||||
0.252821 | + | 0.967513i | \(0.418642\pi\) | |||||||
\(734\) | 5.42454e55 | 0.713328 | ||||||||
\(735\) | 1.61656e55 | 0.207008 | ||||||||
\(736\) | 1.49648e56 | 1.86618 | ||||||||
\(737\) | −7.76987e55 | −0.943621 | ||||||||
\(738\) | −4.21418e55 | −0.498441 | ||||||||
\(739\) | −8.25189e54 | −0.0950576 | −0.0475288 | − | 0.998870i | \(-0.515135\pi\) | ||||
−0.0475288 | + | 0.998870i | \(0.515135\pi\) | |||||||
\(740\) | −2.86625e55 | −0.321585 | ||||||||
\(741\) | −3.80359e54 | −0.0415660 | ||||||||
\(742\) | −3.73308e55 | −0.397366 | ||||||||
\(743\) | −4.93877e55 | −0.512079 | −0.256040 | − | 0.966666i | \(-0.582418\pi\) | ||||
−0.256040 | + | 0.966666i | \(0.582418\pi\) | |||||||
\(744\) | −2.02802e55 | −0.204833 | ||||||||
\(745\) | −5.73557e54 | −0.0564325 | ||||||||
\(746\) | −2.61133e56 | −2.50296 | ||||||||
\(747\) | 2.68262e55 | 0.250500 | ||||||||
\(748\) | 1.10282e56 | 1.00329 | ||||||||
\(749\) | 2.16222e55 | 0.191648 | ||||||||
\(750\) | −6.11827e55 | −0.528365 | ||||||||
\(751\) | −1.08242e56 | −0.910790 | −0.455395 | − | 0.890290i | \(-0.650502\pi\) | ||||
−0.455395 | + | 0.890290i | \(0.650502\pi\) | |||||||
\(752\) | 1.20835e56 | 0.990703 | ||||||||
\(753\) | 4.26770e55 | 0.340951 | ||||||||
\(754\) | 2.44736e55 | 0.190527 | ||||||||
\(755\) | 2.11848e55 | 0.160716 | ||||||||
\(756\) | −3.53355e54 | −0.0261238 | ||||||||
\(757\) | 4.75165e55 | 0.342353 | 0.171177 | − | 0.985240i | \(-0.445243\pi\) | ||||
0.171177 | + | 0.985240i | \(0.445243\pi\) | |||||||
\(758\) | −2.92990e55 | −0.205733 | ||||||||
\(759\) | 1.17555e56 | 0.804503 | ||||||||
\(760\) | −5.74386e54 | −0.0383124 | ||||||||
\(761\) | −1.65472e56 | −1.07578 | −0.537890 | − | 0.843015i | \(-0.680778\pi\) | ||||
−0.537890 | + | 0.843015i | \(0.680778\pi\) | |||||||
\(762\) | 1.65142e56 | 1.04649 | ||||||||
\(763\) | 1.18384e55 | 0.0731251 | ||||||||
\(764\) | −5.83966e55 | −0.351615 | ||||||||
\(765\) | −2.97896e55 | −0.174851 | ||||||||
\(766\) | −1.47718e56 | −0.845225 | ||||||||
\(767\) | −2.30298e55 | −0.128464 | ||||||||
\(768\) | −1.37697e56 | −0.748826 | ||||||||
\(769\) | −5.44232e55 | −0.288550 | −0.144275 | − | 0.989538i | \(-0.546085\pi\) | ||||
−0.144275 | + | 0.989538i | \(0.546085\pi\) | |||||||
\(770\) | 1.58520e55 | 0.0819436 | ||||||||
\(771\) | 1.24921e56 | 0.629614 | ||||||||
\(772\) | 2.55005e56 | 1.25317 | ||||||||
\(773\) | −2.68720e56 | −1.28766 | −0.643829 | − | 0.765169i | \(-0.722655\pi\) | ||||
−0.643829 | + | 0.765169i | \(0.722655\pi\) | |||||||
\(774\) | 1.17746e56 | 0.550170 | ||||||||
\(775\) | −2.10429e56 | −0.958789 | ||||||||
\(776\) | 4.51538e55 | 0.200628 | ||||||||
\(777\) | 2.72387e55 | 0.118026 | ||||||||
\(778\) | −3.64620e56 | −1.54077 | ||||||||
\(779\) | −8.86288e55 | −0.365253 | ||||||||
\(780\) | 8.97679e54 | 0.0360808 | ||||||||
\(781\) | −1.64633e56 | −0.645388 | ||||||||
\(782\) | 7.33736e56 | 2.80549 | ||||||||
\(783\) | −3.33571e55 | −0.124404 | ||||||||
\(784\) | 3.14742e56 | 1.14496 | ||||||||
\(785\) | 1.13527e56 | 0.402849 | ||||||||
\(786\) | −1.30946e56 | −0.453264 | ||||||||
\(787\) | 4.30176e56 | 1.45257 | 0.726287 | − | 0.687391i | \(-0.241244\pi\) | ||||
0.726287 | + | 0.687391i | \(0.241244\pi\) | |||||||
\(788\) | −1.91895e56 | −0.632126 | ||||||||
\(789\) | −4.98438e55 | −0.160181 | ||||||||
\(790\) | 2.29776e56 | 0.720404 | ||||||||
\(791\) | 9.75185e55 | 0.298295 | ||||||||
\(792\) | −3.32703e55 | −0.0992923 | ||||||||
\(793\) | −7.95754e55 | −0.231714 | ||||||||
\(794\) | 6.35057e56 | 1.80432 | ||||||||
\(795\) | −1.29261e56 | −0.358351 | ||||||||
\(796\) | −4.76887e56 | −1.29006 | ||||||||
\(797\) | 3.00522e56 | 0.793303 | 0.396652 | − | 0.917969i | \(-0.370172\pi\) | ||||
0.396652 | + | 0.917969i | \(0.370172\pi\) | |||||||
\(798\) | −1.72187e55 | −0.0443552 | ||||||||
\(799\) | 4.71889e56 | 1.18625 | ||||||||
\(800\) | −4.39461e56 | −1.07812 | ||||||||
\(801\) | −2.63889e55 | −0.0631811 | ||||||||
\(802\) | −4.37262e56 | −1.02174 | ||||||||
\(803\) | −6.42354e56 | −1.46495 | ||||||||
\(804\) | −1.99186e56 | −0.443369 | ||||||||
\(805\) | 4.55186e55 | 0.0988939 | ||||||||
\(806\) | 1.54447e56 | 0.327526 | ||||||||
\(807\) | −4.12178e56 | −0.853200 | ||||||||
\(808\) | 1.22760e56 | 0.248047 | ||||||||
\(809\) | −4.70856e56 | −0.928736 | −0.464368 | − | 0.885642i | \(-0.653718\pi\) | ||||
−0.464368 | + | 0.885642i | \(0.653718\pi\) | |||||||
\(810\) | −2.83492e55 | −0.0545862 | ||||||||
\(811\) | 3.36981e56 | 0.633430 | 0.316715 | − | 0.948521i | \(-0.397420\pi\) | ||||
0.316715 | + | 0.948521i | \(0.397420\pi\) | |||||||
\(812\) | 4.78164e55 | 0.0877474 | ||||||||
\(813\) | 2.04294e56 | 0.366008 | ||||||||
\(814\) | −8.09015e56 | −1.41508 | ||||||||
\(815\) | −1.59930e56 | −0.273121 | ||||||||
\(816\) | −5.80002e56 | −0.967099 | ||||||||
\(817\) | 2.47633e56 | 0.403160 | ||||||||
\(818\) | 6.18237e56 | 0.982801 | ||||||||
\(819\) | −8.53087e54 | −0.0132421 | ||||||||
\(820\) | 2.09171e56 | 0.317053 | ||||||||
\(821\) | −1.61083e56 | −0.238428 | −0.119214 | − | 0.992869i | \(-0.538037\pi\) | ||||
−0.119214 | + | 0.992869i | \(0.538037\pi\) | |||||||
\(822\) | 7.59347e56 | 1.09759 | ||||||||
\(823\) | −1.33570e57 | −1.88543 | −0.942716 | − | 0.333597i | \(-0.891738\pi\) | ||||
−0.942716 | + | 0.333597i | \(0.891738\pi\) | |||||||
\(824\) | −2.35399e56 | −0.324507 | ||||||||
\(825\) | −3.45216e56 | −0.464770 | ||||||||
\(826\) | −1.04255e56 | −0.137084 | ||||||||
\(827\) | 1.43015e57 | 1.83664 | 0.918320 | − | 0.395840i | \(-0.129546\pi\) | ||||
0.918320 | + | 0.395840i | \(0.129546\pi\) | |||||||
\(828\) | 3.01361e56 | 0.378003 | ||||||||
\(829\) | 1.29097e57 | 1.58162 | 0.790809 | − | 0.612062i | \(-0.209660\pi\) | ||||
0.790809 | + | 0.612062i | \(0.209660\pi\) | |||||||
\(830\) | −3.08515e56 | −0.369193 | ||||||||
\(831\) | 5.31599e56 | 0.621390 | ||||||||
\(832\) | 9.23635e55 | 0.105462 | ||||||||
\(833\) | 1.22915e57 | 1.37096 | ||||||||
\(834\) | 7.22316e56 | 0.787026 | ||||||||
\(835\) | −2.91429e56 | −0.310203 | ||||||||
\(836\) | 2.20721e56 | 0.229520 | ||||||||
\(837\) | −2.10509e56 | −0.213857 | ||||||||
\(838\) | 3.68517e55 | 0.0365762 | ||||||||
\(839\) | −6.05135e56 | −0.586805 | −0.293402 | − | 0.955989i | \(-0.594788\pi\) | ||||
−0.293402 | + | 0.955989i | \(0.594788\pi\) | |||||||
\(840\) | −1.28826e55 | −0.0122056 | ||||||||
\(841\) | −6.28852e56 | −0.582138 | ||||||||
\(842\) | 1.65246e56 | 0.149467 | ||||||||
\(843\) | −1.04267e56 | −0.0921527 | ||||||||
\(844\) | 1.24197e57 | 1.07259 | ||||||||
\(845\) | −4.17224e56 | −0.352098 | ||||||||
\(846\) | 4.49071e56 | 0.370333 | ||||||||
\(847\) | −2.87298e55 | −0.0231530 | ||||||||
\(848\) | −2.51670e57 | −1.98204 | ||||||||
\(849\) | 7.00556e56 | 0.539191 | ||||||||
\(850\) | −2.15471e57 | −1.62076 | ||||||||
\(851\) | −2.32307e57 | −1.70779 | ||||||||
\(852\) | −4.22047e56 | −0.303241 | ||||||||
\(853\) | 2.15150e57 | 1.51090 | 0.755450 | − | 0.655206i | \(-0.227418\pi\) | ||||
0.755450 | + | 0.655206i | \(0.227418\pi\) | |||||||
\(854\) | −3.60236e56 | −0.247262 | ||||||||
\(855\) | −5.96214e55 | −0.0400003 | ||||||||
\(856\) | 5.21903e56 | 0.342256 | ||||||||
\(857\) | 8.05117e56 | 0.516099 | 0.258050 | − | 0.966132i | \(-0.416920\pi\) | ||||
0.258050 | + | 0.966132i | \(0.416920\pi\) | |||||||
\(858\) | 2.53375e56 | 0.158768 | ||||||||
\(859\) | −1.57853e57 | −0.966909 | −0.483455 | − | 0.875369i | \(-0.660618\pi\) | ||||
−0.483455 | + | 0.875369i | \(0.660618\pi\) | |||||||
\(860\) | −5.84433e56 | −0.349957 | ||||||||
\(861\) | −1.98781e56 | −0.116362 | ||||||||
\(862\) | 3.04924e57 | 1.74502 | ||||||||
\(863\) | 1.37204e57 | 0.767640 | 0.383820 | − | 0.923408i | \(-0.374608\pi\) | ||||
0.383820 | + | 0.923408i | \(0.374608\pi\) | |||||||
\(864\) | −4.39627e56 | −0.240473 | ||||||||
\(865\) | 2.00117e56 | 0.107021 | ||||||||
\(866\) | −5.02582e57 | −2.62790 | ||||||||
\(867\) | −1.13574e57 | −0.580640 | ||||||||
\(868\) | 3.01758e56 | 0.150843 | ||||||||
\(869\) | 2.79910e57 | 1.36815 | ||||||||
\(870\) | 3.83624e56 | 0.183350 | ||||||||
\(871\) | −4.80884e56 | −0.224743 | ||||||||
\(872\) | 2.85749e56 | 0.130591 | ||||||||
\(873\) | 4.68698e56 | 0.209467 | ||||||||
\(874\) | 1.46851e57 | 0.641806 | ||||||||
\(875\) | −2.88596e56 | −0.123348 | ||||||||
\(876\) | −1.64672e57 | −0.688318 | ||||||||
\(877\) | −5.43028e56 | −0.221988 | −0.110994 | − | 0.993821i | \(-0.535403\pi\) | ||||
−0.110994 | + | 0.993821i | \(0.535403\pi\) | |||||||
\(878\) | 2.54164e57 | 1.01618 | ||||||||
\(879\) | −6.14359e56 | −0.240237 | ||||||||
\(880\) | 1.06868e57 | 0.408730 | ||||||||
\(881\) | 2.33735e57 | 0.874365 | 0.437183 | − | 0.899373i | \(-0.355976\pi\) | ||||
0.437183 | + | 0.899373i | \(0.355976\pi\) | |||||||
\(882\) | 1.16971e57 | 0.427997 | ||||||||
\(883\) | −1.13126e57 | −0.404884 | −0.202442 | − | 0.979294i | \(-0.564888\pi\) | ||||
−0.202442 | + | 0.979294i | \(0.564888\pi\) | |||||||
\(884\) | 6.82548e56 | 0.238954 | ||||||||
\(885\) | −3.60993e56 | −0.123625 | ||||||||
\(886\) | −7.32650e57 | −2.45436 | ||||||||
\(887\) | 6.73827e56 | 0.220820 | 0.110410 | − | 0.993886i | \(-0.464784\pi\) | ||||
0.110410 | + | 0.993886i | \(0.464784\pi\) | |||||||
\(888\) | 6.57471e56 | 0.210777 | ||||||||
\(889\) | 7.78967e56 | 0.244306 | ||||||||
\(890\) | 3.03486e56 | 0.0931180 | ||||||||
\(891\) | −3.45346e56 | −0.103667 | ||||||||
\(892\) | 4.00781e57 | 1.17704 | ||||||||
\(893\) | 9.44445e56 | 0.271377 | ||||||||
\(894\) | −4.15015e56 | −0.116676 | ||||||||
\(895\) | −1.72362e57 | −0.474123 | ||||||||
\(896\) | −4.11843e56 | −0.110847 | ||||||||
\(897\) | 7.27560e56 | 0.191609 | ||||||||
\(898\) | 5.05817e57 | 1.30348 | ||||||||
\(899\) | 2.84863e57 | 0.718328 | ||||||||
\(900\) | −8.84983e56 | −0.218377 | ||||||||
\(901\) | −9.82833e57 | −2.37327 | ||||||||
\(902\) | 5.90398e57 | 1.39514 | ||||||||
\(903\) | 5.55402e56 | 0.128439 | ||||||||
\(904\) | 2.35384e57 | 0.532712 | ||||||||
\(905\) | 1.19371e57 | 0.264394 | ||||||||
\(906\) | 1.53289e57 | 0.332285 | ||||||||
\(907\) | −4.11384e57 | −0.872782 | −0.436391 | − | 0.899757i | \(-0.643744\pi\) | ||||
−0.436391 | + | 0.899757i | \(0.643744\pi\) | |||||||
\(908\) | 3.68668e57 | 0.765529 | ||||||||
\(909\) | 1.27425e57 | 0.258975 | ||||||||
\(910\) | 9.81094e55 | 0.0195166 | ||||||||
\(911\) | −6.39052e57 | −1.24431 | −0.622154 | − | 0.782895i | \(-0.713742\pi\) | ||||
−0.622154 | + | 0.782895i | \(0.713742\pi\) | |||||||
\(912\) | −1.16082e57 | −0.221242 | ||||||||
\(913\) | −3.75830e57 | −0.701150 | ||||||||
\(914\) | −6.98370e57 | −1.27537 | ||||||||
\(915\) | −1.24735e57 | −0.222985 | ||||||||
\(916\) | 2.18590e57 | 0.382533 | ||||||||
\(917\) | −6.17664e56 | −0.105816 | ||||||||
\(918\) | −2.15552e57 | −0.361510 | ||||||||
\(919\) | 5.76262e55 | 0.00946166 | 0.00473083 | − | 0.999989i | \(-0.498494\pi\) | ||||
0.00473083 | + | 0.999989i | \(0.498494\pi\) | |||||||
\(920\) | 1.09870e57 | 0.176610 | ||||||||
\(921\) | −4.98667e57 | −0.784779 | ||||||||
\(922\) | −1.12419e58 | −1.73215 | ||||||||
\(923\) | −1.01893e57 | −0.153713 | ||||||||
\(924\) | 4.95043e56 | 0.0731206 | ||||||||
\(925\) | 6.82197e57 | 0.986612 | ||||||||
\(926\) | −6.25643e57 | −0.885956 | ||||||||
\(927\) | −2.44344e57 | −0.338803 | ||||||||
\(928\) | 5.94908e57 | 0.807727 | ||||||||
\(929\) | −1.93034e57 | −0.256642 | −0.128321 | − | 0.991733i | \(-0.540959\pi\) | ||||
−0.128321 | + | 0.991733i | \(0.540959\pi\) | |||||||
\(930\) | 2.42096e57 | 0.315189 | ||||||||
\(931\) | 2.46003e57 | 0.313633 | ||||||||
\(932\) | 2.05641e57 | 0.256744 | ||||||||
\(933\) | 2.82345e57 | 0.345214 | ||||||||
\(934\) | 1.58883e58 | 1.90245 | ||||||||
\(935\) | 4.17347e57 | 0.489408 | ||||||||
\(936\) | −2.05913e56 | −0.0236485 | ||||||||
\(937\) | 1.77370e58 | 1.99507 | 0.997537 | − | 0.0701384i | \(-0.0223441\pi\) | ||||
0.997537 | + | 0.0701384i | \(0.0223441\pi\) | |||||||
\(938\) | −2.17695e57 | −0.239824 | ||||||||
\(939\) | 1.65680e57 | 0.178768 | ||||||||
\(940\) | −2.22897e57 | −0.235565 | ||||||||
\(941\) | −1.24048e57 | −0.128408 | −0.0642038 | − | 0.997937i | \(-0.520451\pi\) | ||||
−0.0642038 | + | 0.997937i | \(0.520451\pi\) | |||||||
\(942\) | 8.21464e57 | 0.832905 | ||||||||
\(943\) | 1.69531e58 | 1.68373 | ||||||||
\(944\) | −7.02851e57 | −0.683769 | ||||||||
\(945\) | −1.33722e56 | −0.0127433 | ||||||||
\(946\) | −1.64960e58 | −1.53993 | ||||||||
\(947\) | −1.13841e57 | −0.104106 | −0.0520530 | − | 0.998644i | \(-0.516576\pi\) | ||||
−0.0520530 | + | 0.998644i | \(0.516576\pi\) | |||||||
\(948\) | 7.17568e57 | 0.642837 | ||||||||
\(949\) | −3.97558e57 | −0.348907 | ||||||||
\(950\) | −4.31246e57 | −0.370779 | ||||||||
\(951\) | 8.35314e56 | 0.0703606 | ||||||||
\(952\) | −9.79526e56 | −0.0808342 | ||||||||
\(953\) | −3.13047e57 | −0.253103 | −0.126552 | − | 0.991960i | \(-0.540391\pi\) | ||||
−0.126552 | + | 0.991960i | \(0.540391\pi\) | |||||||
\(954\) | −9.35309e57 | −0.740903 | ||||||||
\(955\) | −2.20993e57 | −0.171519 | ||||||||
\(956\) | −5.78731e57 | −0.440097 | ||||||||
\(957\) | 4.67327e57 | 0.348207 | ||||||||
\(958\) | −2.71954e58 | −1.98549 | ||||||||
\(959\) | 3.58180e57 | 0.256235 | ||||||||
\(960\) | 1.44780e57 | 0.101489 | ||||||||
\(961\) | 3.41891e57 | 0.234845 | ||||||||
\(962\) | −5.00706e57 | −0.337031 | ||||||||
\(963\) | 5.41737e57 | 0.357335 | ||||||||
\(964\) | −1.11928e58 | −0.723499 | ||||||||
\(965\) | 9.65026e57 | 0.611303 | ||||||||
\(966\) | 3.29364e57 | 0.204467 | ||||||||
\(967\) | −3.53898e57 | −0.215309 | −0.107655 | − | 0.994188i | \(-0.534334\pi\) | ||||
−0.107655 | + | 0.994188i | \(0.534334\pi\) | |||||||
\(968\) | −6.93463e56 | −0.0413479 | ||||||||
\(969\) | −4.53330e57 | −0.264911 | ||||||||
\(970\) | −5.39027e57 | −0.308718 | ||||||||
\(971\) | −1.69979e58 | −0.954155 | −0.477078 | − | 0.878861i | \(-0.658304\pi\) | ||||
−0.477078 | + | 0.878861i | \(0.658304\pi\) | |||||||
\(972\) | −8.85318e56 | −0.0487088 | ||||||||
\(973\) | 3.40713e57 | 0.183733 | ||||||||
\(974\) | 4.25291e58 | 2.24795 | ||||||||
\(975\) | −2.13657e57 | −0.110695 | ||||||||
\(976\) | −2.42857e58 | −1.23333 | ||||||||
\(977\) | −9.44722e57 | −0.470284 | −0.235142 | − | 0.971961i | \(-0.575555\pi\) | ||||
−0.235142 | + | 0.971961i | \(0.575555\pi\) | |||||||
\(978\) | −1.15722e58 | −0.564688 | ||||||||
\(979\) | 3.69703e57 | 0.176844 | ||||||||
\(980\) | −5.80587e57 | −0.272245 | ||||||||
\(981\) | 2.96608e57 | 0.136344 | ||||||||
\(982\) | 4.27563e58 | 1.92675 | ||||||||
\(983\) | 2.21582e58 | 0.978904 | 0.489452 | − | 0.872030i | \(-0.337197\pi\) | ||||
0.489452 | + | 0.872030i | \(0.337197\pi\) | |||||||
\(984\) | −4.79805e57 | −0.207807 | ||||||||
\(985\) | −7.26198e57 | −0.308353 | ||||||||
\(986\) | 2.91688e58 | 1.21428 | ||||||||
\(987\) | 2.11825e57 | 0.0864554 | ||||||||
\(988\) | 1.36606e57 | 0.0546650 | ||||||||
\(989\) | −4.73678e58 | −1.85847 | ||||||||
\(990\) | 3.97166e57 | 0.152787 | ||||||||
\(991\) | 1.83857e58 | 0.693496 | 0.346748 | − | 0.937958i | \(-0.387286\pi\) | ||||
0.346748 | + | 0.937958i | \(0.387286\pi\) | |||||||
\(992\) | 3.75433e58 | 1.38853 | ||||||||
\(993\) | −1.50249e58 | −0.544880 | ||||||||
\(994\) | −4.61265e57 | −0.164027 | ||||||||
\(995\) | −1.80471e58 | −0.629298 | ||||||||
\(996\) | −9.63464e57 | −0.329442 | ||||||||
\(997\) | −1.92411e57 | −0.0645172 | −0.0322586 | − | 0.999480i | \(-0.510270\pi\) | ||||
−0.0322586 | + | 0.999480i | \(0.510270\pi\) | |||||||
\(998\) | 3.84492e58 | 1.26428 | ||||||||
\(999\) | 6.82456e57 | 0.220063 |
(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 | 3.40.a.b.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 9.40.a.c.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.40.a.b.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
9.40.a.c.1.3 | 3 | 3.2 | odd | 2 |