Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,14,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(189.798744245\) |
Analytic rank: | \(0\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −7.03559 | −0.0777330 | −0.0388665 | − | 0.999244i | \(-0.512375\pi\) | ||||
−0.0388665 | + | 0.999244i | \(0.512375\pi\) | |||||||
\(3\) | 729.000 | 0.577350 | ||||||||
\(4\) | −8142.50 | −0.993958 | ||||||||
\(5\) | 12466.0 | 0.356798 | 0.178399 | − | 0.983958i | \(-0.442908\pi\) | ||||
0.178399 | + | 0.983958i | \(0.442908\pi\) | |||||||
\(6\) | −5128.95 | −0.0448792 | ||||||||
\(7\) | −179621. | −0.577060 | −0.288530 | − | 0.957471i | \(-0.593166\pi\) | ||||
−0.288530 | + | 0.957471i | \(0.593166\pi\) | |||||||
\(8\) | 114923. | 0.154996 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | −87705.8 | −0.0277350 | ||||||||
\(11\) | −8.91138e6 | −1.51668 | −0.758338 | − | 0.651862i | \(-0.773988\pi\) | ||||
−0.758338 | + | 0.651862i | \(0.773988\pi\) | |||||||
\(12\) | −5.93588e6 | −0.573862 | ||||||||
\(13\) | 2.94142e7 | 1.69015 | 0.845074 | − | 0.534649i | \(-0.179556\pi\) | ||||
0.845074 | + | 0.534649i | \(0.179556\pi\) | |||||||
\(14\) | 1.26374e6 | 0.0448566 | ||||||||
\(15\) | 9.08773e6 | 0.205998 | ||||||||
\(16\) | 6.58948e7 | 0.981909 | ||||||||
\(17\) | −1.63264e7 | −0.164049 | −0.0820245 | − | 0.996630i | \(-0.526139\pi\) | ||||
−0.0820245 | + | 0.996630i | \(0.526139\pi\) | |||||||
\(18\) | −3.73900e6 | −0.0259110 | ||||||||
\(19\) | −1.07100e8 | −0.522264 | −0.261132 | − | 0.965303i | \(-0.584096\pi\) | ||||
−0.261132 | + | 0.965303i | \(0.584096\pi\) | |||||||
\(20\) | −1.01505e8 | −0.354642 | ||||||||
\(21\) | −1.30944e8 | −0.333166 | ||||||||
\(22\) | 6.26968e7 | 0.117896 | ||||||||
\(23\) | 5.82137e8 | 0.819964 | 0.409982 | − | 0.912094i | \(-0.365535\pi\) | ||||
0.409982 | + | 0.912094i | \(0.365535\pi\) | |||||||
\(24\) | 8.37788e7 | 0.0894872 | ||||||||
\(25\) | −1.06530e9 | −0.872695 | ||||||||
\(26\) | −2.06946e8 | −0.131380 | ||||||||
\(27\) | 3.87420e8 | 0.192450 | ||||||||
\(28\) | 1.46257e9 | 0.573573 | ||||||||
\(29\) | −1.37246e9 | −0.428462 | −0.214231 | − | 0.976783i | \(-0.568724\pi\) | ||||
−0.214231 | + | 0.976783i | \(0.568724\pi\) | |||||||
\(30\) | −6.39375e7 | −0.0160128 | ||||||||
\(31\) | −5.70742e9 | −1.15502 | −0.577509 | − | 0.816384i | \(-0.695975\pi\) | ||||
−0.577509 | + | 0.816384i | \(0.695975\pi\) | |||||||
\(32\) | −1.40506e9 | −0.231323 | ||||||||
\(33\) | −6.49640e9 | −0.875653 | ||||||||
\(34\) | 1.14866e8 | 0.0127520 | ||||||||
\(35\) | −2.23916e9 | −0.205894 | ||||||||
\(36\) | −4.32726e9 | −0.331319 | ||||||||
\(37\) | 6.03624e9 | 0.386773 | 0.193386 | − | 0.981123i | \(-0.438053\pi\) | ||||
0.193386 | + | 0.981123i | \(0.438053\pi\) | |||||||
\(38\) | 7.53511e8 | 0.0405972 | ||||||||
\(39\) | 2.14429e10 | 0.975808 | ||||||||
\(40\) | 1.43263e9 | 0.0553024 | ||||||||
\(41\) | −1.15612e10 | −0.380110 | −0.190055 | − | 0.981773i | \(-0.560867\pi\) | ||||
−0.190055 | + | 0.981773i | \(0.560867\pi\) | |||||||
\(42\) | 9.21268e8 | 0.0258980 | ||||||||
\(43\) | −1.85518e9 | −0.0447549 | −0.0223775 | − | 0.999750i | \(-0.507124\pi\) | ||||
−0.0223775 | + | 0.999750i | \(0.507124\pi\) | |||||||
\(44\) | 7.25609e10 | 1.50751 | ||||||||
\(45\) | 6.62495e9 | 0.118933 | ||||||||
\(46\) | −4.09568e9 | −0.0637383 | ||||||||
\(47\) | 4.15668e9 | 0.0562484 | 0.0281242 | − | 0.999604i | \(-0.491047\pi\) | ||||
0.0281242 | + | 0.999604i | \(0.491047\pi\) | |||||||
\(48\) | 4.80373e10 | 0.566906 | ||||||||
\(49\) | −6.46252e10 | −0.667002 | ||||||||
\(50\) | 7.49503e9 | 0.0678372 | ||||||||
\(51\) | −1.19020e10 | −0.0947137 | ||||||||
\(52\) | −2.39505e11 | −1.67994 | ||||||||
\(53\) | 1.45626e11 | 0.902499 | 0.451249 | − | 0.892398i | \(-0.350978\pi\) | ||||
0.451249 | + | 0.892398i | \(0.350978\pi\) | |||||||
\(54\) | −2.72573e9 | −0.0149597 | ||||||||
\(55\) | −1.11089e11 | −0.541147 | ||||||||
\(56\) | −2.06426e10 | −0.0894421 | ||||||||
\(57\) | −7.80758e10 | −0.301529 | ||||||||
\(58\) | 9.65605e9 | 0.0333056 | ||||||||
\(59\) | −4.21805e10 | −0.130189 | ||||||||
\(60\) | −7.39968e10 | −0.204753 | ||||||||
\(61\) | −4.25126e11 | −1.05651 | −0.528255 | − | 0.849086i | \(-0.677154\pi\) | ||||
−0.528255 | + | 0.849086i | \(0.677154\pi\) | |||||||
\(62\) | 4.01551e10 | 0.0897831 | ||||||||
\(63\) | −9.54581e10 | −0.192353 | ||||||||
\(64\) | −5.29925e11 | −0.963928 | ||||||||
\(65\) | 3.66678e11 | 0.603042 | ||||||||
\(66\) | 4.57060e10 | 0.0680672 | ||||||||
\(67\) | 2.63627e11 | 0.356044 | 0.178022 | − | 0.984026i | \(-0.443030\pi\) | ||||
0.178022 | + | 0.984026i | \(0.443030\pi\) | |||||||
\(68\) | 1.32938e11 | 0.163058 | ||||||||
\(69\) | 4.24378e11 | 0.473406 | ||||||||
\(70\) | 1.57538e10 | 0.0160048 | ||||||||
\(71\) | 3.12180e11 | 0.289218 | 0.144609 | − | 0.989489i | \(-0.453808\pi\) | ||||
0.144609 | + | 0.989489i | \(0.453808\pi\) | |||||||
\(72\) | 6.10747e10 | 0.0516655 | ||||||||
\(73\) | −7.30451e11 | −0.564927 | −0.282464 | − | 0.959278i | \(-0.591152\pi\) | ||||
−0.282464 | + | 0.959278i | \(0.591152\pi\) | |||||||
\(74\) | −4.24686e10 | −0.0300650 | ||||||||
\(75\) | −7.76605e11 | −0.503851 | ||||||||
\(76\) | 8.72060e11 | 0.519109 | ||||||||
\(77\) | 1.60067e12 | 0.875212 | ||||||||
\(78\) | −1.50864e11 | −0.0758525 | ||||||||
\(79\) | 2.67532e12 | 1.23823 | 0.619113 | − | 0.785302i | \(-0.287492\pi\) | ||||
0.619113 | + | 0.785302i | \(0.287492\pi\) | |||||||
\(80\) | 8.21446e11 | 0.350344 | ||||||||
\(81\) | 2.82430e11 | 0.111111 | ||||||||
\(82\) | 8.13402e10 | 0.0295471 | ||||||||
\(83\) | −1.18393e12 | −0.397484 | −0.198742 | − | 0.980052i | \(-0.563686\pi\) | ||||
−0.198742 | + | 0.980052i | \(0.563686\pi\) | |||||||
\(84\) | 1.06621e12 | 0.331152 | ||||||||
\(85\) | −2.03526e11 | −0.0585324 | ||||||||
\(86\) | 1.30523e10 | 0.00347894 | ||||||||
\(87\) | −1.00052e12 | −0.247372 | ||||||||
\(88\) | −1.02412e12 | −0.235079 | ||||||||
\(89\) | 3.66061e11 | 0.0780762 | 0.0390381 | − | 0.999238i | \(-0.487571\pi\) | ||||
0.0390381 | + | 0.999238i | \(0.487571\pi\) | |||||||
\(90\) | −4.66105e10 | −0.00924501 | ||||||||
\(91\) | −5.28341e12 | −0.975317 | ||||||||
\(92\) | −4.74005e12 | −0.815009 | ||||||||
\(93\) | −4.16071e12 | −0.666850 | ||||||||
\(94\) | −2.92447e10 | −0.00437236 | ||||||||
\(95\) | −1.33511e12 | −0.186343 | ||||||||
\(96\) | −1.02429e12 | −0.133554 | ||||||||
\(97\) | 1.46548e13 | 1.78634 | 0.893169 | − | 0.449722i | \(-0.148477\pi\) | ||||
0.893169 | + | 0.449722i | \(0.148477\pi\) | |||||||
\(98\) | 4.54676e11 | 0.0518481 | ||||||||
\(99\) | −4.73587e12 | −0.505558 | ||||||||
\(100\) | 8.67422e12 | 0.867422 | ||||||||
\(101\) | −1.06442e13 | −0.997754 | −0.498877 | − | 0.866673i | \(-0.666254\pi\) | ||||
−0.498877 | + | 0.866673i | \(0.666254\pi\) | |||||||
\(102\) | 8.37374e10 | 0.00736239 | ||||||||
\(103\) | 1.23712e13 | 1.02087 | 0.510433 | − | 0.859918i | \(-0.329485\pi\) | ||||
0.510433 | + | 0.859918i | \(0.329485\pi\) | |||||||
\(104\) | 3.38036e12 | 0.261967 | ||||||||
\(105\) | −1.63235e12 | −0.118873 | ||||||||
\(106\) | −1.02457e12 | −0.0701540 | ||||||||
\(107\) | −6.47425e12 | −0.417057 | −0.208528 | − | 0.978016i | \(-0.566867\pi\) | ||||
−0.208528 | + | 0.978016i | \(0.566867\pi\) | |||||||
\(108\) | −3.15457e12 | −0.191287 | ||||||||
\(109\) | 4.60180e12 | 0.262818 | 0.131409 | − | 0.991328i | \(-0.458050\pi\) | ||||
0.131409 | + | 0.991328i | \(0.458050\pi\) | |||||||
\(110\) | 7.81580e11 | 0.0420650 | ||||||||
\(111\) | 4.40042e12 | 0.223303 | ||||||||
\(112\) | −1.18361e13 | −0.566620 | ||||||||
\(113\) | 4.25972e12 | 0.192474 | 0.0962368 | − | 0.995358i | \(-0.469319\pi\) | ||||
0.0962368 | + | 0.995358i | \(0.469319\pi\) | |||||||
\(114\) | 5.49309e11 | 0.0234388 | ||||||||
\(115\) | 7.25694e12 | 0.292562 | ||||||||
\(116\) | 1.11752e13 | 0.425873 | ||||||||
\(117\) | 1.56319e13 | 0.563383 | ||||||||
\(118\) | 2.96765e11 | 0.0101200 | ||||||||
\(119\) | 2.93258e12 | 0.0946660 | ||||||||
\(120\) | 1.04439e12 | 0.0319289 | ||||||||
\(121\) | 4.48900e13 | 1.30030 | ||||||||
\(122\) | 2.99101e12 | 0.0821258 | ||||||||
\(123\) | −8.42815e12 | −0.219457 | ||||||||
\(124\) | 4.64727e13 | 1.14804 | ||||||||
\(125\) | −2.84974e13 | −0.668174 | ||||||||
\(126\) | 6.71604e11 | 0.0149522 | ||||||||
\(127\) | 5.28410e13 | 1.11750 | 0.558749 | − | 0.829337i | \(-0.311282\pi\) | ||||
0.558749 | + | 0.829337i | \(0.311282\pi\) | |||||||
\(128\) | 1.52386e13 | 0.306252 | ||||||||
\(129\) | −1.35243e12 | −0.0258393 | ||||||||
\(130\) | −2.57980e12 | −0.0468763 | ||||||||
\(131\) | 2.73432e13 | 0.472700 | 0.236350 | − | 0.971668i | \(-0.424049\pi\) | ||||
0.236350 | + | 0.971668i | \(0.424049\pi\) | |||||||
\(132\) | 5.28969e13 | 0.870362 | ||||||||
\(133\) | 1.92374e13 | 0.301378 | ||||||||
\(134\) | −1.85477e12 | −0.0276764 | ||||||||
\(135\) | 4.82959e12 | 0.0686659 | ||||||||
\(136\) | −1.87628e12 | −0.0254270 | ||||||||
\(137\) | 1.79816e13 | 0.232351 | 0.116176 | − | 0.993229i | \(-0.462936\pi\) | ||||
0.116176 | + | 0.993229i | \(0.462936\pi\) | |||||||
\(138\) | −2.98575e12 | −0.0367993 | ||||||||
\(139\) | −7.96675e13 | −0.936883 | −0.468441 | − | 0.883495i | \(-0.655184\pi\) | ||||
−0.468441 | + | 0.883495i | \(0.655184\pi\) | |||||||
\(140\) | 1.82324e13 | 0.204650 | ||||||||
\(141\) | 3.03022e12 | 0.0324750 | ||||||||
\(142\) | −2.19637e12 | −0.0224818 | ||||||||
\(143\) | −2.62121e14 | −2.56341 | ||||||||
\(144\) | 3.50192e13 | 0.327303 | ||||||||
\(145\) | −1.71091e13 | −0.152874 | ||||||||
\(146\) | 5.13915e12 | 0.0439135 | ||||||||
\(147\) | −4.71118e13 | −0.385094 | ||||||||
\(148\) | −4.91501e13 | −0.384436 | ||||||||
\(149\) | −1.42990e14 | −1.07052 | −0.535260 | − | 0.844687i | \(-0.679786\pi\) | ||||
−0.535260 | + | 0.844687i | \(0.679786\pi\) | |||||||
\(150\) | 5.46387e12 | 0.0391658 | ||||||||
\(151\) | −6.78139e12 | −0.0465552 | −0.0232776 | − | 0.999729i | \(-0.507410\pi\) | ||||
−0.0232776 | + | 0.999729i | \(0.507410\pi\) | |||||||
\(152\) | −1.23082e13 | −0.0809491 | ||||||||
\(153\) | −8.67654e12 | −0.0546830 | ||||||||
\(154\) | −1.12617e13 | −0.0680329 | ||||||||
\(155\) | −7.11488e13 | −0.412109 | ||||||||
\(156\) | −1.74599e14 | −0.969912 | ||||||||
\(157\) | −2.37938e13 | −0.126799 | −0.0633995 | − | 0.997988i | \(-0.520194\pi\) | ||||
−0.0633995 | + | 0.997988i | \(0.520194\pi\) | |||||||
\(158\) | −1.88225e13 | −0.0962511 | ||||||||
\(159\) | 1.06162e14 | 0.521058 | ||||||||
\(160\) | −1.75155e13 | −0.0825357 | ||||||||
\(161\) | −1.04564e14 | −0.473168 | ||||||||
\(162\) | −1.98706e12 | −0.00863700 | ||||||||
\(163\) | −3.02948e14 | −1.26517 | −0.632586 | − | 0.774491i | \(-0.718006\pi\) | ||||
−0.632586 | + | 0.774491i | \(0.718006\pi\) | |||||||
\(164\) | 9.41374e13 | 0.377813 | ||||||||
\(165\) | −8.09842e13 | −0.312431 | ||||||||
\(166\) | 8.32967e12 | 0.0308976 | ||||||||
\(167\) | 3.90932e14 | 1.39458 | 0.697291 | − | 0.716788i | \(-0.254388\pi\) | ||||
0.697291 | + | 0.716788i | \(0.254388\pi\) | |||||||
\(168\) | −1.50485e13 | −0.0516394 | ||||||||
\(169\) | 5.62319e14 | 1.85660 | ||||||||
\(170\) | 1.43192e12 | 0.00454990 | ||||||||
\(171\) | −5.69172e13 | −0.174088 | ||||||||
\(172\) | 1.51058e13 | 0.0444845 | ||||||||
\(173\) | 3.21297e14 | 0.911185 | 0.455592 | − | 0.890188i | \(-0.349427\pi\) | ||||
0.455592 | + | 0.890188i | \(0.349427\pi\) | |||||||
\(174\) | 7.03926e12 | 0.0192290 | ||||||||
\(175\) | 1.91351e14 | 0.503597 | ||||||||
\(176\) | −5.87214e14 | −1.48924 | ||||||||
\(177\) | −3.07496e13 | −0.0751646 | ||||||||
\(178\) | −2.57546e12 | −0.00606910 | ||||||||
\(179\) | 5.49082e14 | 1.24765 | 0.623825 | − | 0.781564i | \(-0.285578\pi\) | ||||
0.623825 | + | 0.781564i | \(0.285578\pi\) | |||||||
\(180\) | −5.39437e13 | −0.118214 | ||||||||
\(181\) | −1.94033e14 | −0.410172 | −0.205086 | − | 0.978744i | \(-0.565747\pi\) | ||||
−0.205086 | + | 0.978744i | \(0.565747\pi\) | |||||||
\(182\) | 3.71719e13 | 0.0758143 | ||||||||
\(183\) | −3.09917e14 | −0.609977 | ||||||||
\(184\) | 6.69009e13 | 0.127091 | ||||||||
\(185\) | 7.52480e13 | 0.138000 | ||||||||
\(186\) | 2.92731e13 | 0.0518363 | ||||||||
\(187\) | 1.45491e14 | 0.248809 | ||||||||
\(188\) | −3.38458e13 | −0.0559085 | ||||||||
\(189\) | −6.95890e13 | −0.111055 | ||||||||
\(190\) | 9.39328e12 | 0.0144850 | ||||||||
\(191\) | 4.48927e14 | 0.669051 | 0.334525 | − | 0.942387i | \(-0.391424\pi\) | ||||
0.334525 | + | 0.942387i | \(0.391424\pi\) | |||||||
\(192\) | −3.86315e14 | −0.556524 | ||||||||
\(193\) | 5.66130e14 | 0.788485 | 0.394243 | − | 0.919006i | \(-0.371007\pi\) | ||||
0.394243 | + | 0.919006i | \(0.371007\pi\) | |||||||
\(194\) | −1.03105e14 | −0.138857 | ||||||||
\(195\) | 2.67308e14 | 0.348167 | ||||||||
\(196\) | 5.26211e14 | 0.662972 | ||||||||
\(197\) | −1.04131e14 | −0.126925 | −0.0634626 | − | 0.997984i | \(-0.520214\pi\) | ||||
−0.0634626 | + | 0.997984i | \(0.520214\pi\) | |||||||
\(198\) | 3.33197e13 | 0.0392986 | ||||||||
\(199\) | 6.44197e13 | 0.0735315 | 0.0367658 | − | 0.999324i | \(-0.488294\pi\) | ||||
0.0367658 | + | 0.999324i | \(0.488294\pi\) | |||||||
\(200\) | −1.22428e14 | −0.135265 | ||||||||
\(201\) | 1.92184e14 | 0.205562 | ||||||||
\(202\) | 7.48882e13 | 0.0775585 | ||||||||
\(203\) | 2.46523e14 | 0.247248 | ||||||||
\(204\) | 9.69118e13 | 0.0941414 | ||||||||
\(205\) | −1.44123e14 | −0.135623 | ||||||||
\(206\) | −8.70384e13 | −0.0793549 | ||||||||
\(207\) | 3.09372e14 | 0.273321 | ||||||||
\(208\) | 1.93824e15 | 1.65957 | ||||||||
\(209\) | 9.54408e14 | 0.792105 | ||||||||
\(210\) | 1.14845e13 | 0.00924035 | ||||||||
\(211\) | 9.34027e14 | 0.728657 | 0.364329 | − | 0.931270i | \(-0.381298\pi\) | ||||
0.364329 | + | 0.931270i | \(0.381298\pi\) | |||||||
\(212\) | −1.18576e15 | −0.897046 | ||||||||
\(213\) | 2.27579e14 | 0.166980 | ||||||||
\(214\) | 4.55502e13 | 0.0324191 | ||||||||
\(215\) | −2.31267e13 | −0.0159685 | ||||||||
\(216\) | 4.45235e13 | 0.0298291 | ||||||||
\(217\) | 1.02517e15 | 0.666514 | ||||||||
\(218\) | −3.23764e13 | −0.0204297 | ||||||||
\(219\) | −5.32499e14 | −0.326161 | ||||||||
\(220\) | 9.04546e14 | 0.537877 | ||||||||
\(221\) | −4.80229e14 | −0.277267 | ||||||||
\(222\) | −3.09596e13 | −0.0173580 | ||||||||
\(223\) | 1.24475e15 | 0.677799 | 0.338900 | − | 0.940823i | \(-0.389945\pi\) | ||||
0.338900 | + | 0.940823i | \(0.389945\pi\) | |||||||
\(224\) | 2.52378e14 | 0.133487 | ||||||||
\(225\) | −5.66145e14 | −0.290898 | ||||||||
\(226\) | −2.99696e13 | −0.0149616 | ||||||||
\(227\) | 3.20457e15 | 1.55454 | 0.777270 | − | 0.629167i | \(-0.216604\pi\) | ||||
0.777270 | + | 0.629167i | \(0.216604\pi\) | |||||||
\(228\) | 6.35732e14 | 0.299707 | ||||||||
\(229\) | 3.77559e15 | 1.73003 | 0.865016 | − | 0.501744i | \(-0.167308\pi\) | ||||
0.865016 | + | 0.501744i | \(0.167308\pi\) | |||||||
\(230\) | −5.10568e13 | −0.0227417 | ||||||||
\(231\) | 1.16689e15 | 0.505304 | ||||||||
\(232\) | −1.57727e14 | −0.0664100 | ||||||||
\(233\) | 2.48828e15 | 1.01879 | 0.509397 | − | 0.860532i | \(-0.329869\pi\) | ||||
0.509397 | + | 0.860532i | \(0.329869\pi\) | |||||||
\(234\) | −1.09980e14 | −0.0437935 | ||||||||
\(235\) | 5.18172e13 | 0.0200693 | ||||||||
\(236\) | 3.43455e14 | 0.129402 | ||||||||
\(237\) | 1.95031e15 | 0.714890 | ||||||||
\(238\) | −2.06324e13 | −0.00735868 | ||||||||
\(239\) | 3.56407e15 | 1.23697 | 0.618486 | − | 0.785796i | \(-0.287746\pi\) | ||||
0.618486 | + | 0.785796i | \(0.287746\pi\) | |||||||
\(240\) | 5.98834e14 | 0.202271 | ||||||||
\(241\) | 1.24378e14 | 0.0408914 | 0.0204457 | − | 0.999791i | \(-0.493491\pi\) | ||||
0.0204457 | + | 0.999791i | \(0.493491\pi\) | |||||||
\(242\) | −3.15828e14 | −0.101077 | ||||||||
\(243\) | 2.05891e14 | 0.0641500 | ||||||||
\(244\) | 3.46159e15 | 1.05013 | ||||||||
\(245\) | −8.05619e14 | −0.237985 | ||||||||
\(246\) | 5.92970e13 | 0.0170590 | ||||||||
\(247\) | −3.15025e15 | −0.882705 | ||||||||
\(248\) | −6.55913e14 | −0.179024 | ||||||||
\(249\) | −8.63087e14 | −0.229487 | ||||||||
\(250\) | 2.00496e14 | 0.0519392 | ||||||||
\(251\) | 3.21526e15 | 0.811590 | 0.405795 | − | 0.913964i | \(-0.366995\pi\) | ||||
0.405795 | + | 0.913964i | \(0.366995\pi\) | |||||||
\(252\) | 7.77268e14 | 0.191191 | ||||||||
\(253\) | −5.18765e15 | −1.24362 | ||||||||
\(254\) | −3.71767e14 | −0.0868665 | ||||||||
\(255\) | −1.48370e14 | −0.0337937 | ||||||||
\(256\) | 4.23393e15 | 0.940122 | ||||||||
\(257\) | −2.73468e15 | −0.592026 | −0.296013 | − | 0.955184i | \(-0.595657\pi\) | ||||
−0.296013 | + | 0.955184i | \(0.595657\pi\) | |||||||
\(258\) | 9.51511e12 | 0.00200856 | ||||||||
\(259\) | −1.08424e15 | −0.223191 | ||||||||
\(260\) | −2.98567e15 | −0.599398 | ||||||||
\(261\) | −7.29380e14 | −0.142821 | ||||||||
\(262\) | −1.92376e14 | −0.0367444 | ||||||||
\(263\) | −7.63743e15 | −1.42310 | −0.711549 | − | 0.702636i | \(-0.752006\pi\) | ||||
−0.711549 | + | 0.702636i | \(0.752006\pi\) | |||||||
\(264\) | −7.46585e14 | −0.135723 | ||||||||
\(265\) | 1.81538e15 | 0.322010 | ||||||||
\(266\) | −1.35347e14 | −0.0234270 | ||||||||
\(267\) | 2.66859e14 | 0.0450773 | ||||||||
\(268\) | −2.14658e15 | −0.353893 | ||||||||
\(269\) | −1.61454e15 | −0.259811 | −0.129906 | − | 0.991526i | \(-0.541467\pi\) | ||||
−0.129906 | + | 0.991526i | \(0.541467\pi\) | |||||||
\(270\) | −3.39790e13 | −0.00533761 | ||||||||
\(271\) | 1.26053e16 | 1.93310 | 0.966549 | − | 0.256483i | \(-0.0825637\pi\) | ||||
0.966549 | + | 0.256483i | \(0.0825637\pi\) | |||||||
\(272\) | −1.07583e15 | −0.161081 | ||||||||
\(273\) | −3.85161e15 | −0.563099 | ||||||||
\(274\) | −1.26511e14 | −0.0180614 | ||||||||
\(275\) | 9.49331e15 | 1.32359 | ||||||||
\(276\) | −3.45550e15 | −0.470546 | ||||||||
\(277\) | −3.71246e15 | −0.493791 | −0.246895 | − | 0.969042i | \(-0.579410\pi\) | ||||
−0.246895 | + | 0.969042i | \(0.579410\pi\) | |||||||
\(278\) | 5.60508e14 | 0.0728267 | ||||||||
\(279\) | −3.03316e15 | −0.385006 | ||||||||
\(280\) | −2.57331e14 | −0.0319128 | ||||||||
\(281\) | 1.22310e16 | 1.48208 | 0.741039 | − | 0.671462i | \(-0.234333\pi\) | ||||
0.741039 | + | 0.671462i | \(0.234333\pi\) | |||||||
\(282\) | −2.13194e13 | −0.00252438 | ||||||||
\(283\) | 2.91187e15 | 0.336946 | 0.168473 | − | 0.985706i | \(-0.446116\pi\) | ||||
0.168473 | + | 0.985706i | \(0.446116\pi\) | |||||||
\(284\) | −2.54192e15 | −0.287470 | ||||||||
\(285\) | −9.73294e14 | −0.107585 | ||||||||
\(286\) | 1.84418e15 | 0.199261 | ||||||||
\(287\) | 2.07665e15 | 0.219346 | ||||||||
\(288\) | −7.46705e14 | −0.0771077 | ||||||||
\(289\) | −9.63803e15 | −0.973088 | ||||||||
\(290\) | 1.20373e14 | 0.0118834 | ||||||||
\(291\) | 1.06833e16 | 1.03134 | ||||||||
\(292\) | 5.94770e15 | 0.561514 | ||||||||
\(293\) | 1.09631e16 | 1.01227 | 0.506133 | − | 0.862455i | \(-0.331074\pi\) | ||||
0.506133 | + | 0.862455i | \(0.331074\pi\) | |||||||
\(294\) | 3.31459e14 | 0.0299345 | ||||||||
\(295\) | −5.25823e14 | −0.0464512 | ||||||||
\(296\) | 6.93703e14 | 0.0599483 | ||||||||
\(297\) | −3.45245e15 | −0.291884 | ||||||||
\(298\) | 1.00602e15 | 0.0832148 | ||||||||
\(299\) | 1.71231e16 | 1.38586 | ||||||||
\(300\) | 6.32350e15 | 0.500806 | ||||||||
\(301\) | 3.33230e14 | 0.0258263 | ||||||||
\(302\) | 4.77111e13 | 0.00361888 | ||||||||
\(303\) | −7.75961e15 | −0.576054 | ||||||||
\(304\) | −7.05732e15 | −0.512816 | ||||||||
\(305\) | −5.29963e15 | −0.376961 | ||||||||
\(306\) | 6.10446e13 | 0.00425068 | ||||||||
\(307\) | 1.75297e16 | 1.19502 | 0.597510 | − | 0.801861i | \(-0.296157\pi\) | ||||
0.597510 | + | 0.801861i | \(0.296157\pi\) | |||||||
\(308\) | −1.30335e16 | −0.869924 | ||||||||
\(309\) | 9.01857e15 | 0.589397 | ||||||||
\(310\) | 5.00574e14 | 0.0320344 | ||||||||
\(311\) | 2.05232e16 | 1.28618 | 0.643092 | − | 0.765789i | \(-0.277651\pi\) | ||||
0.643092 | + | 0.765789i | \(0.277651\pi\) | |||||||
\(312\) | 2.46428e15 | 0.151247 | ||||||||
\(313\) | −1.67629e16 | −1.00765 | −0.503826 | − | 0.863805i | \(-0.668075\pi\) | ||||
−0.503826 | + | 0.863805i | \(0.668075\pi\) | |||||||
\(314\) | 1.67403e14 | 0.00985647 | ||||||||
\(315\) | −1.18998e15 | −0.0686313 | ||||||||
\(316\) | −2.17838e16 | −1.23074 | ||||||||
\(317\) | 1.94562e15 | 0.107689 | 0.0538447 | − | 0.998549i | \(-0.482852\pi\) | ||||
0.0538447 | + | 0.998549i | \(0.482852\pi\) | |||||||
\(318\) | −7.46909e14 | −0.0405034 | ||||||||
\(319\) | 1.22305e16 | 0.649837 | ||||||||
\(320\) | −6.60605e15 | −0.343928 | ||||||||
\(321\) | −4.71973e15 | −0.240788 | ||||||||
\(322\) | 7.35672e14 | 0.0367808 | ||||||||
\(323\) | 1.74856e15 | 0.0856769 | ||||||||
\(324\) | −2.29968e15 | −0.110440 | ||||||||
\(325\) | −3.13350e16 | −1.47498 | ||||||||
\(326\) | 2.13142e15 | 0.0983456 | ||||||||
\(327\) | 3.35471e15 | 0.151738 | ||||||||
\(328\) | −1.32865e15 | −0.0589157 | ||||||||
\(329\) | −7.46628e14 | −0.0324587 | ||||||||
\(330\) | 5.69772e14 | 0.0242863 | ||||||||
\(331\) | 3.46353e16 | 1.44756 | 0.723781 | − | 0.690030i | \(-0.242403\pi\) | ||||
0.723781 | + | 0.690030i | \(0.242403\pi\) | |||||||
\(332\) | 9.64018e15 | 0.395082 | ||||||||
\(333\) | 3.20791e15 | 0.128924 | ||||||||
\(334\) | −2.75044e15 | −0.108405 | ||||||||
\(335\) | 3.28638e15 | 0.127036 | ||||||||
\(336\) | −8.62853e15 | −0.327138 | ||||||||
\(337\) | 8.51087e15 | 0.316504 | 0.158252 | − | 0.987399i | \(-0.449414\pi\) | ||||
0.158252 | + | 0.987399i | \(0.449414\pi\) | |||||||
\(338\) | −3.95625e15 | −0.144319 | ||||||||
\(339\) | 3.10533e15 | 0.111125 | ||||||||
\(340\) | 1.65721e15 | 0.0581787 | ||||||||
\(341\) | 5.08610e16 | 1.75179 | ||||||||
\(342\) | 4.00446e14 | 0.0135324 | ||||||||
\(343\) | 2.90114e16 | 0.961960 | ||||||||
\(344\) | −2.13202e14 | −0.00693685 | ||||||||
\(345\) | 5.29031e15 | 0.168911 | ||||||||
\(346\) | −2.26051e15 | −0.0708292 | ||||||||
\(347\) | 5.87073e16 | 1.80530 | 0.902652 | − | 0.430370i | \(-0.141617\pi\) | ||||
0.902652 | + | 0.430370i | \(0.141617\pi\) | |||||||
\(348\) | 8.14675e15 | 0.245878 | ||||||||
\(349\) | −3.61511e16 | −1.07092 | −0.535459 | − | 0.844561i | \(-0.679861\pi\) | ||||
−0.535459 | + | 0.844561i | \(0.679861\pi\) | |||||||
\(350\) | −1.34627e15 | −0.0391461 | ||||||||
\(351\) | 1.13957e16 | 0.325269 | ||||||||
\(352\) | 1.25210e16 | 0.350842 | ||||||||
\(353\) | −1.87312e16 | −0.515264 | −0.257632 | − | 0.966243i | \(-0.582942\pi\) | ||||
−0.257632 | + | 0.966243i | \(0.582942\pi\) | |||||||
\(354\) | 2.16342e14 | 0.00584277 | ||||||||
\(355\) | 3.89164e15 | 0.103192 | ||||||||
\(356\) | −2.98066e15 | −0.0776045 | ||||||||
\(357\) | 2.13785e15 | 0.0546555 | ||||||||
\(358\) | −3.86312e15 | −0.0969836 | ||||||||
\(359\) | −4.30600e16 | −1.06160 | −0.530799 | − | 0.847497i | \(-0.678108\pi\) | ||||
−0.530799 | + | 0.847497i | \(0.678108\pi\) | |||||||
\(360\) | 7.61359e14 | 0.0184341 | ||||||||
\(361\) | −3.05826e16 | −0.727240 | ||||||||
\(362\) | 1.36514e15 | 0.0318839 | ||||||||
\(363\) | 3.27248e16 | 0.750731 | ||||||||
\(364\) | 4.30202e16 | 0.969423 | ||||||||
\(365\) | −9.10582e15 | −0.201565 | ||||||||
\(366\) | 2.18045e15 | 0.0474153 | ||||||||
\(367\) | 4.70659e16 | 1.00549 | 0.502744 | − | 0.864436i | \(-0.332324\pi\) | ||||
0.502744 | + | 0.864436i | \(0.332324\pi\) | |||||||
\(368\) | 3.83598e16 | 0.805130 | ||||||||
\(369\) | −6.14412e15 | −0.126703 | ||||||||
\(370\) | −5.29414e14 | −0.0107271 | ||||||||
\(371\) | −2.61576e16 | −0.520796 | ||||||||
\(372\) | 3.38786e16 | 0.662821 | ||||||||
\(373\) | −2.01671e15 | −0.0387736 | −0.0193868 | − | 0.999812i | \(-0.506171\pi\) | ||||
−0.0193868 | + | 0.999812i | \(0.506171\pi\) | |||||||
\(374\) | −1.02362e15 | −0.0193407 | ||||||||
\(375\) | −2.07746e16 | −0.385771 | ||||||||
\(376\) | 4.77697e14 | 0.00871830 | ||||||||
\(377\) | −4.03697e16 | −0.724164 | ||||||||
\(378\) | 4.89600e14 | 0.00863266 | ||||||||
\(379\) | −1.27882e16 | −0.221643 | −0.110822 | − | 0.993840i | \(-0.535348\pi\) | ||||
−0.110822 | + | 0.993840i | \(0.535348\pi\) | |||||||
\(380\) | 1.08711e16 | 0.185217 | ||||||||
\(381\) | 3.85211e16 | 0.645188 | ||||||||
\(382\) | −3.15847e15 | −0.0520073 | ||||||||
\(383\) | 2.55954e16 | 0.414352 | 0.207176 | − | 0.978304i | \(-0.433573\pi\) | ||||
0.207176 | + | 0.978304i | \(0.433573\pi\) | |||||||
\(384\) | 1.11089e16 | 0.176815 | ||||||||
\(385\) | 1.99540e16 | 0.312274 | ||||||||
\(386\) | −3.98306e15 | −0.0612914 | ||||||||
\(387\) | −9.85918e14 | −0.0149183 | ||||||||
\(388\) | −1.19327e17 | −1.77554 | ||||||||
\(389\) | −1.14620e17 | −1.67722 | −0.838608 | − | 0.544735i | \(-0.816630\pi\) | ||||
−0.838608 | + | 0.544735i | \(0.816630\pi\) | |||||||
\(390\) | −1.88067e15 | −0.0270641 | ||||||||
\(391\) | −9.50423e15 | −0.134514 | ||||||||
\(392\) | −7.42691e15 | −0.103383 | ||||||||
\(393\) | 1.99332e16 | 0.272914 | ||||||||
\(394\) | 7.32620e14 | 0.00986628 | ||||||||
\(395\) | 3.33506e16 | 0.441797 | ||||||||
\(396\) | 3.85619e16 | 0.502504 | ||||||||
\(397\) | −7.43340e16 | −0.952904 | −0.476452 | − | 0.879200i | \(-0.658077\pi\) | ||||
−0.476452 | + | 0.879200i | \(0.658077\pi\) | |||||||
\(398\) | −4.53230e14 | −0.00571583 | ||||||||
\(399\) | 1.40241e16 | 0.174000 | ||||||||
\(400\) | −7.01978e16 | −0.856907 | ||||||||
\(401\) | −7.00311e16 | −0.841109 | −0.420555 | − | 0.907267i | \(-0.638164\pi\) | ||||
−0.420555 | + | 0.907267i | \(0.638164\pi\) | |||||||
\(402\) | −1.35213e15 | −0.0159790 | ||||||||
\(403\) | −1.67879e17 | −1.95215 | ||||||||
\(404\) | 8.66703e16 | 0.991725 | ||||||||
\(405\) | 3.52077e15 | 0.0396443 | ||||||||
\(406\) | −1.73443e15 | −0.0192193 | ||||||||
\(407\) | −5.37913e16 | −0.586608 | ||||||||
\(408\) | −1.36781e15 | −0.0146803 | ||||||||
\(409\) | −4.06796e16 | −0.429710 | −0.214855 | − | 0.976646i | \(-0.568928\pi\) | ||||
−0.214855 | + | 0.976646i | \(0.568928\pi\) | |||||||
\(410\) | 1.01399e15 | 0.0105424 | ||||||||
\(411\) | 1.31086e16 | 0.134148 | ||||||||
\(412\) | −1.00732e17 | −1.01470 | ||||||||
\(413\) | 7.57652e15 | 0.0751268 | ||||||||
\(414\) | −2.17661e15 | −0.0212461 | ||||||||
\(415\) | −1.47589e16 | −0.141822 | ||||||||
\(416\) | −4.13286e16 | −0.390971 | ||||||||
\(417\) | −5.80776e16 | −0.540909 | ||||||||
\(418\) | −6.71482e15 | −0.0615728 | ||||||||
\(419\) | 9.40621e16 | 0.849227 | 0.424613 | − | 0.905375i | \(-0.360410\pi\) | ||||
0.424613 | + | 0.905375i | \(0.360410\pi\) | |||||||
\(420\) | 1.32914e16 | 0.118155 | ||||||||
\(421\) | −1.72503e16 | −0.150996 | −0.0754978 | − | 0.997146i | \(-0.524055\pi\) | ||||
−0.0754978 | + | 0.997146i | \(0.524055\pi\) | |||||||
\(422\) | −6.57143e15 | −0.0566408 | ||||||||
\(423\) | 2.20903e15 | 0.0187495 | ||||||||
\(424\) | 1.67358e16 | 0.139884 | ||||||||
\(425\) | 1.73926e16 | 0.143165 | ||||||||
\(426\) | −1.60115e15 | −0.0129799 | ||||||||
\(427\) | 7.63617e16 | 0.609669 | ||||||||
\(428\) | 5.27166e16 | 0.414537 | ||||||||
\(429\) | −1.91086e17 | −1.47998 | ||||||||
\(430\) | 1.62710e14 | 0.00124128 | ||||||||
\(431\) | −1.23734e17 | −0.929795 | −0.464898 | − | 0.885364i | \(-0.653909\pi\) | ||||
−0.464898 | + | 0.885364i | \(0.653909\pi\) | |||||||
\(432\) | 2.55290e16 | 0.188969 | ||||||||
\(433\) | −3.00092e16 | −0.218818 | −0.109409 | − | 0.993997i | \(-0.534896\pi\) | ||||
−0.109409 | + | 0.993997i | \(0.534896\pi\) | |||||||
\(434\) | −7.21271e15 | −0.0518102 | ||||||||
\(435\) | −1.24725e16 | −0.0882621 | ||||||||
\(436\) | −3.74702e16 | −0.261230 | ||||||||
\(437\) | −6.23468e16 | −0.428238 | ||||||||
\(438\) | 3.74644e15 | 0.0253535 | ||||||||
\(439\) | 1.25024e17 | 0.833630 | 0.416815 | − | 0.908991i | \(-0.363146\pi\) | ||||
0.416815 | + | 0.908991i | \(0.363146\pi\) | |||||||
\(440\) | −1.27667e16 | −0.0838759 | ||||||||
\(441\) | −3.43445e16 | −0.222334 | ||||||||
\(442\) | 3.37869e15 | 0.0215528 | ||||||||
\(443\) | −2.66955e17 | −1.67808 | −0.839041 | − | 0.544068i | \(-0.816883\pi\) | ||||
−0.839041 | + | 0.544068i | \(0.816883\pi\) | |||||||
\(444\) | −3.58304e16 | −0.221954 | ||||||||
\(445\) | 4.56333e15 | 0.0278575 | ||||||||
\(446\) | −8.75757e15 | −0.0526874 | ||||||||
\(447\) | −1.04240e17 | −0.618065 | ||||||||
\(448\) | 9.51858e16 | 0.556244 | ||||||||
\(449\) | 2.78758e17 | 1.60556 | 0.802778 | − | 0.596278i | \(-0.203354\pi\) | ||||
0.802778 | + | 0.596278i | \(0.203354\pi\) | |||||||
\(450\) | 3.98316e15 | 0.0226124 | ||||||||
\(451\) | 1.03027e17 | 0.576504 | ||||||||
\(452\) | −3.46848e16 | −0.191311 | ||||||||
\(453\) | −4.94363e15 | −0.0268787 | ||||||||
\(454\) | −2.25461e16 | −0.120839 | ||||||||
\(455\) | −6.58632e16 | −0.347991 | ||||||||
\(456\) | −8.97269e15 | −0.0467360 | ||||||||
\(457\) | 8.18878e16 | 0.420498 | 0.210249 | − | 0.977648i | \(-0.432573\pi\) | ||||
0.210249 | + | 0.977648i | \(0.432573\pi\) | |||||||
\(458\) | −2.65635e16 | −0.134481 | ||||||||
\(459\) | −6.32520e15 | −0.0315712 | ||||||||
\(460\) | −5.90896e16 | −0.290794 | ||||||||
\(461\) | −2.00345e17 | −0.972128 | −0.486064 | − | 0.873923i | \(-0.661568\pi\) | ||||
−0.486064 | + | 0.873923i | \(0.661568\pi\) | |||||||
\(462\) | −8.20977e15 | −0.0392788 | ||||||||
\(463\) | −8.54155e16 | −0.402958 | −0.201479 | − | 0.979493i | \(-0.564575\pi\) | ||||
−0.201479 | + | 0.979493i | \(0.564575\pi\) | |||||||
\(464\) | −9.04378e16 | −0.420710 | ||||||||
\(465\) | −5.18675e16 | −0.237931 | ||||||||
\(466\) | −1.75065e16 | −0.0791939 | ||||||||
\(467\) | 9.72001e16 | 0.433618 | 0.216809 | − | 0.976214i | \(-0.430435\pi\) | ||||
0.216809 | + | 0.976214i | \(0.430435\pi\) | |||||||
\(468\) | −1.27283e17 | −0.559979 | ||||||||
\(469\) | −4.73530e16 | −0.205459 | ||||||||
\(470\) | −3.64565e14 | −0.00156005 | ||||||||
\(471\) | −1.73457e16 | −0.0732074 | ||||||||
\(472\) | −4.84751e15 | −0.0201788 | ||||||||
\(473\) | 1.65322e16 | 0.0678787 | ||||||||
\(474\) | −1.37216e16 | −0.0555706 | ||||||||
\(475\) | 1.14094e17 | 0.455777 | ||||||||
\(476\) | −2.38785e16 | −0.0940940 | ||||||||
\(477\) | 7.73918e16 | 0.300833 | ||||||||
\(478\) | −2.50753e16 | −0.0961536 | ||||||||
\(479\) | −2.68070e17 | −1.01407 | −0.507035 | − | 0.861925i | \(-0.669258\pi\) | ||||
−0.507035 | + | 0.861925i | \(0.669258\pi\) | |||||||
\(480\) | −1.27688e16 | −0.0476520 | ||||||||
\(481\) | 1.77551e17 | 0.653703 | ||||||||
\(482\) | −8.75071e14 | −0.00317861 | ||||||||
\(483\) | −7.62274e16 | −0.273184 | ||||||||
\(484\) | −3.65517e17 | −1.29245 | ||||||||
\(485\) | 1.82687e17 | 0.637362 | ||||||||
\(486\) | −1.44857e15 | −0.00498658 | ||||||||
\(487\) | 2.93239e17 | 0.996054 | 0.498027 | − | 0.867161i | \(-0.334058\pi\) | ||||
0.498027 | + | 0.867161i | \(0.334058\pi\) | |||||||
\(488\) | −4.88567e16 | −0.163755 | ||||||||
\(489\) | −2.20849e17 | −0.730447 | ||||||||
\(490\) | 5.66801e15 | 0.0184993 | ||||||||
\(491\) | 2.35700e17 | 0.759154 | 0.379577 | − | 0.925160i | \(-0.376070\pi\) | ||||
0.379577 | + | 0.925160i | \(0.376070\pi\) | |||||||
\(492\) | 6.86262e16 | 0.218131 | ||||||||
\(493\) | 2.24073e16 | 0.0702887 | ||||||||
\(494\) | 2.21639e16 | 0.0686153 | ||||||||
\(495\) | −5.90375e16 | −0.180382 | ||||||||
\(496\) | −3.76089e17 | −1.13412 | ||||||||
\(497\) | −5.60741e16 | −0.166896 | ||||||||
\(498\) | 6.07233e15 | 0.0178388 | ||||||||
\(499\) | 2.95486e17 | 0.856807 | 0.428404 | − | 0.903587i | \(-0.359076\pi\) | ||||
0.428404 | + | 0.903587i | \(0.359076\pi\) | |||||||
\(500\) | 2.32040e17 | 0.664137 | ||||||||
\(501\) | 2.84990e17 | 0.805163 | ||||||||
\(502\) | −2.26213e16 | −0.0630874 | ||||||||
\(503\) | 6.45285e15 | 0.0177648 | 0.00888238 | − | 0.999961i | \(-0.497173\pi\) | ||||
0.00888238 | + | 0.999961i | \(0.497173\pi\) | |||||||
\(504\) | −1.09703e16 | −0.0298140 | ||||||||
\(505\) | −1.32691e17 | −0.355997 | ||||||||
\(506\) | 3.64982e16 | 0.0966703 | ||||||||
\(507\) | 4.09931e17 | 1.07191 | ||||||||
\(508\) | −4.30258e17 | −1.11075 | ||||||||
\(509\) | −2.90108e17 | −0.739425 | −0.369713 | − | 0.929146i | \(-0.620544\pi\) | ||||
−0.369713 | + | 0.929146i | \(0.620544\pi\) | |||||||
\(510\) | 1.04387e15 | 0.00262689 | ||||||||
\(511\) | 1.31205e17 | 0.325997 | ||||||||
\(512\) | −1.54623e17 | −0.379331 | ||||||||
\(513\) | −4.14927e16 | −0.100510 | ||||||||
\(514\) | 1.92401e16 | 0.0460200 | ||||||||
\(515\) | 1.54219e17 | 0.364243 | ||||||||
\(516\) | 1.10121e16 | 0.0256831 | ||||||||
\(517\) | −3.70418e16 | −0.0853106 | ||||||||
\(518\) | 7.62826e15 | 0.0173493 | ||||||||
\(519\) | 2.34225e17 | 0.526073 | ||||||||
\(520\) | 4.21397e16 | 0.0934694 | ||||||||
\(521\) | −4.12174e17 | −0.902891 | −0.451445 | − | 0.892299i | \(-0.649091\pi\) | ||||
−0.451445 | + | 0.892299i | \(0.649091\pi\) | |||||||
\(522\) | 5.13162e15 | 0.0111019 | ||||||||
\(523\) | −2.59656e17 | −0.554802 | −0.277401 | − | 0.960754i | \(-0.589473\pi\) | ||||
−0.277401 | + | 0.960754i | \(0.589473\pi\) | |||||||
\(524\) | −2.22642e17 | −0.469844 | ||||||||
\(525\) | 1.39495e17 | 0.290752 | ||||||||
\(526\) | 5.37338e16 | 0.110622 | ||||||||
\(527\) | 9.31819e16 | 0.189480 | ||||||||
\(528\) | −4.28079e17 | −0.859812 | ||||||||
\(529\) | −1.65152e17 | −0.327660 | ||||||||
\(530\) | −1.27723e16 | −0.0250308 | ||||||||
\(531\) | −2.24165e16 | −0.0433963 | ||||||||
\(532\) | −1.56641e17 | −0.299557 | ||||||||
\(533\) | −3.40065e17 | −0.642443 | ||||||||
\(534\) | −1.87751e15 | −0.00350400 | ||||||||
\(535\) | −8.07082e16 | −0.148805 | ||||||||
\(536\) | 3.02968e16 | 0.0551855 | ||||||||
\(537\) | 4.00281e17 | 0.720331 | ||||||||
\(538\) | 1.13592e16 | 0.0201959 | ||||||||
\(539\) | 5.75900e17 | 1.01163 | ||||||||
\(540\) | −3.93250e16 | −0.0682510 | ||||||||
\(541\) | −3.59080e17 | −0.615757 | −0.307878 | − | 0.951426i | \(-0.599619\pi\) | ||||
−0.307878 | + | 0.951426i | \(0.599619\pi\) | |||||||
\(542\) | −8.86859e16 | −0.150266 | ||||||||
\(543\) | −1.41450e17 | −0.236813 | ||||||||
\(544\) | 2.29396e16 | 0.0379483 | ||||||||
\(545\) | 5.73661e16 | 0.0937731 | ||||||||
\(546\) | 2.70983e16 | 0.0437714 | ||||||||
\(547\) | −6.59660e17 | −1.05294 | −0.526469 | − | 0.850194i | \(-0.676484\pi\) | ||||
−0.526469 | + | 0.850194i | \(0.676484\pi\) | |||||||
\(548\) | −1.46415e17 | −0.230947 | ||||||||
\(549\) | −2.25929e17 | −0.352170 | ||||||||
\(550\) | −6.67910e16 | −0.102887 | ||||||||
\(551\) | 1.46990e17 | 0.223770 | ||||||||
\(552\) | 4.87708e16 | 0.0733763 | ||||||||
\(553\) | −4.80545e17 | −0.714530 | ||||||||
\(554\) | 2.61193e16 | 0.0383839 | ||||||||
\(555\) | 5.48558e16 | 0.0796742 | ||||||||
\(556\) | 6.48693e17 | 0.931222 | ||||||||
\(557\) | 2.33181e17 | 0.330853 | 0.165426 | − | 0.986222i | \(-0.447100\pi\) | ||||
0.165426 | + | 0.986222i | \(0.447100\pi\) | |||||||
\(558\) | 2.13401e16 | 0.0299277 | ||||||||
\(559\) | −5.45686e16 | −0.0756425 | ||||||||
\(560\) | −1.47549e17 | −0.202169 | ||||||||
\(561\) | 1.06063e17 | 0.143650 | ||||||||
\(562\) | −8.60523e16 | −0.115206 | ||||||||
\(563\) | −9.44765e17 | −1.25031 | −0.625157 | − | 0.780499i | \(-0.714965\pi\) | ||||
−0.625157 | + | 0.780499i | \(0.714965\pi\) | |||||||
\(564\) | −2.46736e16 | −0.0322788 | ||||||||
\(565\) | 5.31017e16 | 0.0686742 | ||||||||
\(566\) | −2.04867e16 | −0.0261918 | ||||||||
\(567\) | −5.07304e16 | −0.0641177 | ||||||||
\(568\) | 3.58766e16 | 0.0448277 | ||||||||
\(569\) | 9.68935e17 | 1.19692 | 0.598460 | − | 0.801153i | \(-0.295780\pi\) | ||||
0.598460 | + | 0.801153i | \(0.295780\pi\) | |||||||
\(570\) | 6.84770e15 | 0.00836292 | ||||||||
\(571\) | 5.42831e17 | 0.655436 | 0.327718 | − | 0.944776i | \(-0.393720\pi\) | ||||
0.327718 | + | 0.944776i | \(0.393720\pi\) | |||||||
\(572\) | 2.13432e18 | 2.54792 | ||||||||
\(573\) | 3.27268e17 | 0.386276 | ||||||||
\(574\) | −1.46104e16 | −0.0170504 | ||||||||
\(575\) | −6.20152e17 | −0.715578 | ||||||||
\(576\) | −2.81624e17 | −0.321309 | ||||||||
\(577\) | −7.74916e17 | −0.874203 | −0.437101 | − | 0.899412i | \(-0.643995\pi\) | ||||
−0.437101 | + | 0.899412i | \(0.643995\pi\) | |||||||
\(578\) | 6.78092e16 | 0.0756411 | ||||||||
\(579\) | 4.12709e17 | 0.455232 | ||||||||
\(580\) | 1.39311e17 | 0.151951 | ||||||||
\(581\) | 2.12660e17 | 0.229372 | ||||||||
\(582\) | −7.51637e16 | −0.0801694 | ||||||||
\(583\) | −1.29773e18 | −1.36880 | ||||||||
\(584\) | −8.39455e16 | −0.0875617 | ||||||||
\(585\) | 1.94868e17 | 0.201014 | ||||||||
\(586\) | −7.71321e16 | −0.0786866 | ||||||||
\(587\) | −1.28751e17 | −0.129898 | −0.0649491 | − | 0.997889i | \(-0.520688\pi\) | ||||
−0.0649491 | + | 0.997889i | \(0.520688\pi\) | |||||||
\(588\) | 3.83608e17 | 0.382767 | ||||||||
\(589\) | 6.11264e17 | 0.603225 | ||||||||
\(590\) | 3.69948e15 | 0.00361079 | ||||||||
\(591\) | −7.59112e16 | −0.0732803 | ||||||||
\(592\) | 3.97757e17 | 0.379776 | ||||||||
\(593\) | 2.83120e17 | 0.267372 | 0.133686 | − | 0.991024i | \(-0.457319\pi\) | ||||
0.133686 | + | 0.991024i | \(0.457319\pi\) | |||||||
\(594\) | 2.42900e16 | 0.0226891 | ||||||||
\(595\) | 3.65576e16 | 0.0337767 | ||||||||
\(596\) | 1.16430e18 | 1.06405 | ||||||||
\(597\) | 4.69619e16 | 0.0424534 | ||||||||
\(598\) | −1.20471e17 | −0.107727 | ||||||||
\(599\) | −3.18328e17 | −0.281579 | −0.140789 | − | 0.990040i | \(-0.544964\pi\) | ||||
−0.140789 | + | 0.990040i | \(0.544964\pi\) | |||||||
\(600\) | −8.92497e16 | −0.0780950 | ||||||||
\(601\) | 3.31331e17 | 0.286799 | 0.143399 | − | 0.989665i | \(-0.454197\pi\) | ||||
0.143399 | + | 0.989665i | \(0.454197\pi\) | |||||||
\(602\) | −2.34447e15 | −0.00200755 | ||||||||
\(603\) | 1.40102e17 | 0.118681 | ||||||||
\(604\) | 5.52174e16 | 0.0462739 | ||||||||
\(605\) | 5.59600e17 | 0.463946 | ||||||||
\(606\) | 5.45935e16 | 0.0447784 | ||||||||
\(607\) | 5.29921e17 | 0.430016 | 0.215008 | − | 0.976612i | \(-0.431022\pi\) | ||||
0.215008 | + | 0.976612i | \(0.431022\pi\) | |||||||
\(608\) | 1.50481e17 | 0.120812 | ||||||||
\(609\) | 1.79715e17 | 0.142749 | ||||||||
\(610\) | 3.72860e16 | 0.0293023 | ||||||||
\(611\) | 1.22265e17 | 0.0950682 | ||||||||
\(612\) | 7.06487e16 | 0.0543526 | ||||||||
\(613\) | −2.12461e18 | −1.61728 | −0.808640 | − | 0.588303i | \(-0.799796\pi\) | ||||
−0.808640 | + | 0.588303i | \(0.799796\pi\) | |||||||
\(614\) | −1.23332e17 | −0.0928925 | ||||||||
\(615\) | −1.05065e17 | −0.0783018 | ||||||||
\(616\) | 1.83954e17 | 0.135655 | ||||||||
\(617\) | −1.71451e17 | −0.125108 | −0.0625542 | − | 0.998042i | \(-0.519925\pi\) | ||||
−0.0625542 | + | 0.998042i | \(0.519925\pi\) | |||||||
\(618\) | −6.34510e16 | −0.0458156 | ||||||||
\(619\) | 1.45191e18 | 1.03741 | 0.518704 | − | 0.854954i | \(-0.326415\pi\) | ||||
0.518704 | + | 0.854954i | \(0.326415\pi\) | |||||||
\(620\) | 5.79329e17 | 0.409618 | ||||||||
\(621\) | 2.25532e17 | 0.157802 | ||||||||
\(622\) | −1.44393e17 | −0.0999791 | ||||||||
\(623\) | −6.57524e16 | −0.0450546 | ||||||||
\(624\) | 1.41298e18 | 0.958155 | ||||||||
\(625\) | 9.45168e17 | 0.634291 | ||||||||
\(626\) | 1.17937e17 | 0.0783278 | ||||||||
\(627\) | 6.95763e17 | 0.457322 | ||||||||
\(628\) | 1.93741e17 | 0.126033 | ||||||||
\(629\) | −9.85504e16 | −0.0634496 | ||||||||
\(630\) | 8.37224e15 | 0.00533492 | ||||||||
\(631\) | −1.56293e18 | −0.985708 | −0.492854 | − | 0.870112i | \(-0.664046\pi\) | ||||
−0.492854 | + | 0.870112i | \(0.664046\pi\) | |||||||
\(632\) | 3.07456e17 | 0.191921 | ||||||||
\(633\) | 6.80905e17 | 0.420691 | ||||||||
\(634\) | −1.36886e16 | −0.00837102 | ||||||||
\(635\) | 6.58717e17 | 0.398721 | ||||||||
\(636\) | −8.64421e17 | −0.517909 | ||||||||
\(637\) | −1.90090e18 | −1.12733 | ||||||||
\(638\) | −8.60487e16 | −0.0505138 | ||||||||
\(639\) | 1.65905e17 | 0.0964060 | ||||||||
\(640\) | 1.89964e17 | 0.109270 | ||||||||
\(641\) | −1.11430e18 | −0.634488 | −0.317244 | − | 0.948344i | \(-0.602757\pi\) | ||||
−0.317244 | + | 0.948344i | \(0.602757\pi\) | |||||||
\(642\) | 3.32061e16 | 0.0187172 | ||||||||
\(643\) | −1.82846e18 | −1.02027 | −0.510133 | − | 0.860096i | \(-0.670404\pi\) | ||||
−0.510133 | + | 0.860096i | \(0.670404\pi\) | |||||||
\(644\) | 8.51415e17 | 0.470309 | ||||||||
\(645\) | −1.68594e16 | −0.00921941 | ||||||||
\(646\) | −1.23021e16 | −0.00665993 | ||||||||
\(647\) | 2.98220e18 | 1.59830 | 0.799152 | − | 0.601129i | \(-0.205282\pi\) | ||||
0.799152 | + | 0.601129i | \(0.205282\pi\) | |||||||
\(648\) | 3.24576e16 | 0.0172218 | ||||||||
\(649\) | 3.75887e17 | 0.197454 | ||||||||
\(650\) | 2.20460e17 | 0.114655 | ||||||||
\(651\) | 7.47352e17 | 0.384812 | ||||||||
\(652\) | 2.46676e18 | 1.25753 | ||||||||
\(653\) | 2.52221e18 | 1.27305 | 0.636525 | − | 0.771256i | \(-0.280371\pi\) | ||||
0.636525 | + | 0.771256i | \(0.280371\pi\) | |||||||
\(654\) | −2.36024e16 | −0.0117951 | ||||||||
\(655\) | 3.40861e17 | 0.168659 | ||||||||
\(656\) | −7.61826e17 | −0.373234 | ||||||||
\(657\) | −3.88192e17 | −0.188309 | ||||||||
\(658\) | 5.25297e15 | 0.00252311 | ||||||||
\(659\) | 1.01758e18 | 0.483963 | 0.241982 | − | 0.970281i | \(-0.422203\pi\) | ||||
0.241982 | + | 0.970281i | \(0.422203\pi\) | |||||||
\(660\) | 6.59414e17 | 0.310544 | ||||||||
\(661\) | −6.78275e17 | −0.316298 | −0.158149 | − | 0.987415i | \(-0.550553\pi\) | ||||
−0.158149 | + | 0.987415i | \(0.550553\pi\) | |||||||
\(662\) | −2.43680e17 | −0.112523 | ||||||||
\(663\) | −3.50087e17 | −0.160080 | ||||||||
\(664\) | −1.36061e17 | −0.0616086 | ||||||||
\(665\) | 2.39814e17 | 0.107531 | ||||||||
\(666\) | −2.25695e16 | −0.0100217 | ||||||||
\(667\) | −7.98959e17 | −0.351323 | ||||||||
\(668\) | −3.18317e18 | −1.38616 | ||||||||
\(669\) | 9.07424e17 | 0.391328 | ||||||||
\(670\) | −2.31216e16 | −0.00987489 | ||||||||
\(671\) | 3.78846e18 | 1.60238 | ||||||||
\(672\) | 1.83984e17 | 0.0770689 | ||||||||
\(673\) | 1.41680e18 | 0.587776 | 0.293888 | − | 0.955840i | \(-0.405051\pi\) | ||||
0.293888 | + | 0.955840i | \(0.405051\pi\) | |||||||
\(674\) | −5.98790e16 | −0.0246028 | ||||||||
\(675\) | −4.12720e17 | −0.167950 | ||||||||
\(676\) | −4.57868e18 | −1.84539 | ||||||||
\(677\) | 4.12787e18 | 1.64778 | 0.823890 | − | 0.566749i | \(-0.191799\pi\) | ||||
0.823890 | + | 0.566749i | \(0.191799\pi\) | |||||||
\(678\) | −2.18479e16 | −0.00863806 | ||||||||
\(679\) | −2.63231e18 | −1.03082 | ||||||||
\(680\) | −2.33898e16 | −0.00907231 | ||||||||
\(681\) | 2.33613e18 | 0.897514 | ||||||||
\(682\) | −3.57837e17 | −0.136172 | ||||||||
\(683\) | −4.54626e18 | −1.71364 | −0.856820 | − | 0.515615i | \(-0.827563\pi\) | ||||
−0.856820 | + | 0.515615i | \(0.827563\pi\) | |||||||
\(684\) | 4.63449e17 | 0.173036 | ||||||||
\(685\) | 2.24159e17 | 0.0829025 | ||||||||
\(686\) | −2.04112e17 | −0.0747760 | ||||||||
\(687\) | 2.75241e18 | 0.998835 | ||||||||
\(688\) | −1.22247e17 | −0.0439453 | ||||||||
\(689\) | 4.28348e18 | 1.52536 | ||||||||
\(690\) | −3.72204e16 | −0.0131299 | ||||||||
\(691\) | 1.09870e18 | 0.383946 | 0.191973 | − | 0.981400i | \(-0.438511\pi\) | ||||
0.191973 | + | 0.981400i | \(0.438511\pi\) | |||||||
\(692\) | −2.61616e18 | −0.905679 | ||||||||
\(693\) | 8.50664e17 | 0.291737 | ||||||||
\(694\) | −4.13041e17 | −0.140332 | ||||||||
\(695\) | −9.93137e17 | −0.334278 | ||||||||
\(696\) | −1.14983e17 | −0.0383418 | ||||||||
\(697\) | 1.88754e17 | 0.0623567 | ||||||||
\(698\) | 2.54344e17 | 0.0832457 | ||||||||
\(699\) | 1.81396e18 | 0.588201 | ||||||||
\(700\) | −1.55807e18 | −0.500554 | ||||||||
\(701\) | 7.97555e17 | 0.253859 | 0.126930 | − | 0.991912i | \(-0.459488\pi\) | ||||
0.126930 | + | 0.991912i | \(0.459488\pi\) | |||||||
\(702\) | −8.01752e16 | −0.0252842 | ||||||||
\(703\) | −6.46481e17 | −0.201998 | ||||||||
\(704\) | 4.72236e18 | 1.46197 | ||||||||
\(705\) | 3.77748e16 | 0.0115870 | ||||||||
\(706\) | 1.31785e17 | 0.0400531 | ||||||||
\(707\) | 1.91192e18 | 0.575764 | ||||||||
\(708\) | 2.50379e17 | 0.0747104 | ||||||||
\(709\) | 1.42619e18 | 0.421675 | 0.210838 | − | 0.977521i | \(-0.432381\pi\) | ||||
0.210838 | + | 0.977521i | \(0.432381\pi\) | |||||||
\(710\) | −2.73800e16 | −0.00802146 | ||||||||
\(711\) | 1.42178e18 | 0.412742 | ||||||||
\(712\) | 4.20688e16 | 0.0121015 | ||||||||
\(713\) | −3.32250e18 | −0.947073 | ||||||||
\(714\) | −1.50410e16 | −0.00424853 | ||||||||
\(715\) | −3.26761e18 | −0.914619 | ||||||||
\(716\) | −4.47090e18 | −1.24011 | ||||||||
\(717\) | 2.59821e18 | 0.714166 | ||||||||
\(718\) | 3.02953e17 | 0.0825213 | ||||||||
\(719\) | 2.76714e18 | 0.746954 | 0.373477 | − | 0.927639i | \(-0.378165\pi\) | ||||
0.373477 | + | 0.927639i | \(0.378165\pi\) | |||||||
\(720\) | 4.36550e17 | 0.116781 | ||||||||
\(721\) | −2.22212e18 | −0.589100 | ||||||||
\(722\) | 2.15167e17 | 0.0565306 | ||||||||
\(723\) | 9.06714e16 | 0.0236087 | ||||||||
\(724\) | 1.57992e18 | 0.407693 | ||||||||
\(725\) | 1.46208e18 | 0.373916 | ||||||||
\(726\) | −2.30239e17 | −0.0583566 | ||||||||
\(727\) | −1.88892e18 | −0.474505 | −0.237252 | − | 0.971448i | \(-0.576247\pi\) | ||||
−0.237252 | + | 0.971448i | \(0.576247\pi\) | |||||||
\(728\) | −6.07185e17 | −0.151171 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | 6.40648e16 | 0.0156683 | ||||||||
\(731\) | 3.02885e16 | 0.00734200 | ||||||||
\(732\) | 2.52350e18 | 0.606291 | ||||||||
\(733\) | 2.87686e18 | 0.685082 | 0.342541 | − | 0.939503i | \(-0.388712\pi\) | ||||
0.342541 | + | 0.939503i | \(0.388712\pi\) | |||||||
\(734\) | −3.31136e17 | −0.0781596 | ||||||||
\(735\) | −5.87296e17 | −0.137401 | ||||||||
\(736\) | −8.17936e17 | −0.189677 | ||||||||
\(737\) | −2.34928e18 | −0.540003 | ||||||||
\(738\) | 4.32275e16 | 0.00984904 | ||||||||
\(739\) | −4.90104e16 | −0.0110688 | −0.00553438 | − | 0.999985i | \(-0.501762\pi\) | ||||
−0.00553438 | + | 0.999985i | \(0.501762\pi\) | |||||||
\(740\) | −6.12706e17 | −0.137166 | ||||||||
\(741\) | −2.29654e18 | −0.509630 | ||||||||
\(742\) | 1.84034e17 | 0.0404830 | ||||||||
\(743\) | 2.87146e18 | 0.626146 | 0.313073 | − | 0.949729i | \(-0.398641\pi\) | ||||
0.313073 | + | 0.949729i | \(0.398641\pi\) | |||||||
\(744\) | −4.78161e17 | −0.103359 | ||||||||
\(745\) | −1.78252e18 | −0.381960 | ||||||||
\(746\) | 1.41887e16 | 0.00301399 | ||||||||
\(747\) | −6.29191e17 | −0.132495 | ||||||||
\(748\) | −1.18466e18 | −0.247306 | ||||||||
\(749\) | 1.16291e18 | 0.240667 | ||||||||
\(750\) | 1.46162e17 | 0.0299871 | ||||||||
\(751\) | 4.30483e18 | 0.875581 | 0.437791 | − | 0.899077i | \(-0.355761\pi\) | ||||
0.437791 | + | 0.899077i | \(0.355761\pi\) | |||||||
\(752\) | 2.73904e17 | 0.0552308 | ||||||||
\(753\) | 2.34392e18 | 0.468572 | ||||||||
\(754\) | 2.84025e17 | 0.0562915 | ||||||||
\(755\) | −8.45369e16 | −0.0166108 | ||||||||
\(756\) | 5.66628e17 | 0.110384 | ||||||||
\(757\) | −1.57319e18 | −0.303849 | −0.151925 | − | 0.988392i | \(-0.548547\pi\) | ||||
−0.151925 | + | 0.988392i | \(0.548547\pi\) | |||||||
\(758\) | 8.99725e16 | 0.0172290 | ||||||||
\(759\) | −3.78180e18 | −0.718004 | ||||||||
\(760\) | −1.53435e17 | −0.0288825 | ||||||||
\(761\) | 4.55145e18 | 0.849472 | 0.424736 | − | 0.905317i | \(-0.360367\pi\) | ||||
0.424736 | + | 0.905317i | \(0.360367\pi\) | |||||||
\(762\) | −2.71018e17 | −0.0501524 | ||||||||
\(763\) | −8.26582e17 | −0.151662 | ||||||||
\(764\) | −3.65539e18 | −0.665008 | ||||||||
\(765\) | −1.08162e17 | −0.0195108 | ||||||||
\(766\) | −1.80079e17 | −0.0322089 | ||||||||
\(767\) | −1.24071e18 | −0.220039 | ||||||||
\(768\) | 3.08654e18 | 0.542780 | ||||||||
\(769\) | 5.31422e18 | 0.926655 | 0.463327 | − | 0.886187i | \(-0.346655\pi\) | ||||
0.463327 | + | 0.886187i | \(0.346655\pi\) | |||||||
\(770\) | −1.40388e17 | −0.0242740 | ||||||||
\(771\) | −1.99358e18 | −0.341806 | ||||||||
\(772\) | −4.60971e18 | −0.783721 | ||||||||
\(773\) | −5.62082e18 | −0.947617 | −0.473809 | − | 0.880628i | \(-0.657121\pi\) | ||||
−0.473809 | + | 0.880628i | \(0.657121\pi\) | |||||||
\(774\) | 6.93652e15 | 0.00115965 | ||||||||
\(775\) | 6.08012e18 | 1.00798 | ||||||||
\(776\) | 1.68417e18 | 0.276876 | ||||||||
\(777\) | −7.90410e17 | −0.128859 | ||||||||
\(778\) | 8.06422e17 | 0.130375 | ||||||||
\(779\) | 1.23821e18 | 0.198518 | ||||||||
\(780\) | −2.17656e18 | −0.346063 | ||||||||
\(781\) | −2.78195e18 | −0.438650 | ||||||||
\(782\) | 6.68679e16 | 0.0104562 | ||||||||
\(783\) | −5.31718e17 | −0.0824575 | ||||||||
\(784\) | −4.25846e18 | −0.654936 | ||||||||
\(785\) | −2.96614e17 | −0.0452417 | ||||||||
\(786\) | −1.40242e17 | −0.0212144 | ||||||||
\(787\) | 4.85685e18 | 0.728651 | 0.364325 | − | 0.931272i | \(-0.381300\pi\) | ||||
0.364325 | + | 0.931272i | \(0.381300\pi\) | |||||||
\(788\) | 8.47883e17 | 0.126158 | ||||||||
\(789\) | −5.56769e18 | −0.821626 | ||||||||
\(790\) | −2.34641e17 | −0.0343422 | ||||||||
\(791\) | −7.65136e17 | −0.111069 | ||||||||
\(792\) | −5.44260e17 | −0.0783597 | ||||||||
\(793\) | −1.25047e19 | −1.78566 | ||||||||
\(794\) | 5.22984e17 | 0.0740722 | ||||||||
\(795\) | 1.32341e18 | 0.185913 | ||||||||
\(796\) | −5.24537e17 | −0.0730872 | ||||||||
\(797\) | 9.06607e18 | 1.25297 | 0.626484 | − | 0.779434i | \(-0.284493\pi\) | ||||
0.626484 | + | 0.779434i | \(0.284493\pi\) | |||||||
\(798\) | −9.86677e16 | −0.0135256 | ||||||||
\(799\) | −6.78638e16 | −0.00922750 | ||||||||
\(800\) | 1.49681e18 | 0.201875 | ||||||||
\(801\) | 1.94540e17 | 0.0260254 | ||||||||
\(802\) | 4.92710e17 | 0.0653820 | ||||||||
\(803\) | 6.50933e18 | 0.856811 | ||||||||
\(804\) | −1.56486e18 | −0.204320 | ||||||||
\(805\) | −1.30350e18 | −0.168826 | ||||||||
\(806\) | 1.18113e18 | 0.151747 | ||||||||
\(807\) | −1.17700e18 | −0.150002 | ||||||||
\(808\) | −1.22326e18 | −0.154648 | ||||||||
\(809\) | 1.42718e18 | 0.178984 | 0.0894918 | − | 0.995988i | \(-0.471476\pi\) | ||||
0.0894918 | + | 0.995988i | \(0.471476\pi\) | |||||||
\(810\) | −2.47707e16 | −0.00308167 | ||||||||
\(811\) | −6.88423e18 | −0.849610 | −0.424805 | − | 0.905285i | \(-0.639657\pi\) | ||||
−0.424805 | + | 0.905285i | \(0.639657\pi\) | |||||||
\(812\) | −2.00731e18 | −0.245754 | ||||||||
\(813\) | 9.18928e18 | 1.11607 | ||||||||
\(814\) | 3.78454e17 | 0.0455989 | ||||||||
\(815\) | −3.77656e18 | −0.451411 | ||||||||
\(816\) | −7.84278e17 | −0.0930003 | ||||||||
\(817\) | 1.98689e17 | 0.0233739 | ||||||||
\(818\) | 2.86205e17 | 0.0334027 | ||||||||
\(819\) | −2.80782e18 | −0.325106 | ||||||||
\(820\) | 1.17352e18 | 0.134803 | ||||||||
\(821\) | −3.82786e18 | −0.436240 | −0.218120 | − | 0.975922i | \(-0.569992\pi\) | ||||
−0.218120 | + | 0.975922i | \(0.569992\pi\) | |||||||
\(822\) | −9.22267e16 | −0.0104277 | ||||||||
\(823\) | −4.05729e18 | −0.455132 | −0.227566 | − | 0.973763i | \(-0.573077\pi\) | ||||
−0.227566 | + | 0.973763i | \(0.573077\pi\) | |||||||
\(824\) | 1.42173e18 | 0.158230 | ||||||||
\(825\) | 6.92062e18 | 0.764178 | ||||||||
\(826\) | −5.33053e16 | −0.00583983 | ||||||||
\(827\) | 3.43912e18 | 0.373819 | 0.186909 | − | 0.982377i | \(-0.440153\pi\) | ||||
0.186909 | + | 0.982377i | \(0.440153\pi\) | |||||||
\(828\) | −2.51906e18 | −0.271670 | ||||||||
\(829\) | −1.20942e19 | −1.29411 | −0.647055 | − | 0.762443i | \(-0.724000\pi\) | ||||
−0.647055 | + | 0.762443i | \(0.724000\pi\) | |||||||
\(830\) | 1.03838e17 | 0.0110242 | ||||||||
\(831\) | −2.70638e18 | −0.285090 | ||||||||
\(832\) | −1.55873e19 | −1.62918 | ||||||||
\(833\) | 1.05510e18 | 0.109421 | ||||||||
\(834\) | 4.08611e17 | 0.0420465 | ||||||||
\(835\) | 4.87337e18 | 0.497585 | ||||||||
\(836\) | −7.77126e18 | −0.787319 | ||||||||
\(837\) | −2.21117e18 | −0.222283 | ||||||||
\(838\) | −6.61783e17 | −0.0660130 | ||||||||
\(839\) | −7.44376e18 | −0.736783 | −0.368391 | − | 0.929671i | \(-0.620091\pi\) | ||||
−0.368391 | + | 0.929671i | \(0.620091\pi\) | |||||||
\(840\) | −1.87594e17 | −0.0184249 | ||||||||
\(841\) | −8.37699e18 | −0.816421 | ||||||||
\(842\) | 1.21366e17 | 0.0117373 | ||||||||
\(843\) | 8.91640e18 | 0.855678 | ||||||||
\(844\) | −7.60531e18 | −0.724254 | ||||||||
\(845\) | 7.00988e18 | 0.662433 | ||||||||
\(846\) | −1.55418e16 | −0.00145745 | ||||||||
\(847\) | −8.06321e18 | −0.750353 | ||||||||
\(848\) | 9.59602e18 | 0.886172 | ||||||||
\(849\) | 2.12275e18 | 0.194536 | ||||||||
\(850\) | −1.22367e17 | −0.0111286 | ||||||||
\(851\) | 3.51392e18 | 0.317139 | ||||||||
\(852\) | −1.85306e18 | −0.165971 | ||||||||
\(853\) | −2.12204e19 | −1.88619 | −0.943093 | − | 0.332529i | \(-0.892098\pi\) | ||||
−0.943093 | + | 0.332529i | \(0.892098\pi\) | |||||||
\(854\) | −5.37250e17 | −0.0473915 | ||||||||
\(855\) | −7.09531e17 | −0.0621143 | ||||||||
\(856\) | −7.44040e17 | −0.0646423 | ||||||||
\(857\) | 1.88453e18 | 0.162490 | 0.0812452 | − | 0.996694i | \(-0.474110\pi\) | ||||
0.0812452 | + | 0.996694i | \(0.474110\pi\) | |||||||
\(858\) | 1.34440e18 | 0.115044 | ||||||||
\(859\) | 7.91055e18 | 0.671817 | 0.335909 | − | 0.941895i | \(-0.390957\pi\) | ||||
0.335909 | + | 0.941895i | \(0.390957\pi\) | |||||||
\(860\) | 1.88309e17 | 0.0158720 | ||||||||
\(861\) | 1.51388e18 | 0.126640 | ||||||||
\(862\) | 8.70543e17 | 0.0722758 | ||||||||
\(863\) | 3.54292e18 | 0.291938 | 0.145969 | − | 0.989289i | \(-0.453370\pi\) | ||||
0.145969 | + | 0.989289i | \(0.453370\pi\) | |||||||
\(864\) | −5.44348e17 | −0.0445182 | ||||||||
\(865\) | 4.00529e18 | 0.325109 | ||||||||
\(866\) | 2.11133e17 | 0.0170094 | ||||||||
\(867\) | −7.02612e18 | −0.561813 | ||||||||
\(868\) | −8.34748e18 | −0.662487 | ||||||||
\(869\) | −2.38408e19 | −1.87799 | ||||||||
\(870\) | 8.77516e16 | 0.00686088 | ||||||||
\(871\) | 7.75437e18 | 0.601768 | ||||||||
\(872\) | 5.28852e17 | 0.0407359 | ||||||||
\(873\) | 7.78816e18 | 0.595446 | ||||||||
\(874\) | 4.38647e17 | 0.0332882 | ||||||||
\(875\) | 5.11874e18 | 0.385576 | ||||||||
\(876\) | 4.33587e18 | 0.324190 | ||||||||
\(877\) | −1.44911e19 | −1.07548 | −0.537741 | − | 0.843110i | \(-0.680722\pi\) | ||||
−0.537741 | + | 0.843110i | \(0.680722\pi\) | |||||||
\(878\) | −8.79616e17 | −0.0648006 | ||||||||
\(879\) | 7.99212e18 | 0.584432 | ||||||||
\(880\) | −7.32022e18 | −0.531357 | ||||||||
\(881\) | −4.15928e18 | −0.299692 | −0.149846 | − | 0.988709i | \(-0.547878\pi\) | ||||
−0.149846 | + | 0.988709i | \(0.547878\pi\) | |||||||
\(882\) | 2.41634e17 | 0.0172827 | ||||||||
\(883\) | 7.17085e18 | 0.509127 | 0.254564 | − | 0.967056i | \(-0.418068\pi\) | ||||
0.254564 | + | 0.967056i | \(0.418068\pi\) | |||||||
\(884\) | 3.91026e18 | 0.275592 | ||||||||
\(885\) | −3.83325e17 | −0.0268186 | ||||||||
\(886\) | 1.87818e18 | 0.130442 | ||||||||
\(887\) | −6.89321e18 | −0.475246 | −0.237623 | − | 0.971357i | \(-0.576368\pi\) | ||||
−0.237623 | + | 0.971357i | \(0.576368\pi\) | |||||||
\(888\) | 5.05709e17 | 0.0346112 | ||||||||
\(889\) | −9.49137e18 | −0.644863 | ||||||||
\(890\) | −3.21057e16 | −0.00216545 | ||||||||
\(891\) | −2.51684e18 | −0.168519 | ||||||||
\(892\) | −1.01354e19 | −0.673704 | ||||||||
\(893\) | −4.45180e17 | −0.0293765 | ||||||||
\(894\) | 7.33388e17 | 0.0480441 | ||||||||
\(895\) | 6.84487e18 | 0.445159 | ||||||||
\(896\) | −2.73717e18 | −0.176726 | ||||||||
\(897\) | 1.24827e19 | 0.800127 | ||||||||
\(898\) | −1.96122e18 | −0.124805 | ||||||||
\(899\) | 7.83319e18 | 0.494881 | ||||||||
\(900\) | 4.60983e18 | 0.289141 | ||||||||
\(901\) | −2.37756e18 | −0.148054 | ||||||||
\(902\) | −7.24854e17 | −0.0448134 | ||||||||
\(903\) | 2.42924e17 | 0.0149108 | ||||||||
\(904\) | 4.89539e17 | 0.0298327 | ||||||||
\(905\) | −2.41882e18 | −0.146349 | ||||||||
\(906\) | 3.47814e16 | 0.00208936 | ||||||||
\(907\) | 2.30526e19 | 1.37490 | 0.687452 | − | 0.726230i | \(-0.258729\pi\) | ||||
0.687452 | + | 0.726230i | \(0.258729\pi\) | |||||||
\(908\) | −2.60932e19 | −1.54515 | ||||||||
\(909\) | −5.65676e18 | −0.332585 | ||||||||
\(910\) | 4.63386e17 | 0.0270504 | ||||||||
\(911\) | 1.67243e18 | 0.0969344 | 0.0484672 | − | 0.998825i | \(-0.484566\pi\) | ||||
0.0484672 | + | 0.998825i | \(0.484566\pi\) | |||||||
\(912\) | −5.14479e18 | −0.296075 | ||||||||
\(913\) | 1.05505e19 | 0.602854 | ||||||||
\(914\) | −5.76129e17 | −0.0326866 | ||||||||
\(915\) | −3.86343e18 | −0.217639 | ||||||||
\(916\) | −3.07427e19 | −1.71958 | ||||||||
\(917\) | −4.91142e18 | −0.272776 | ||||||||
\(918\) | 4.45015e16 | 0.00245413 | ||||||||
\(919\) | −1.51946e18 | −0.0832027 | −0.0416013 | − | 0.999134i | \(-0.513246\pi\) | ||||
−0.0416013 | + | 0.999134i | \(0.513246\pi\) | |||||||
\(920\) | 8.33988e17 | 0.0453460 | ||||||||
\(921\) | 1.27792e19 | 0.689945 | ||||||||
\(922\) | 1.40955e18 | 0.0755664 | ||||||||
\(923\) | 9.18251e18 | 0.488821 | ||||||||
\(924\) | −9.50142e18 | −0.502251 | ||||||||
\(925\) | −6.43042e18 | −0.337534 | ||||||||
\(926\) | 6.00948e17 | 0.0313232 | ||||||||
\(927\) | 6.57454e18 | 0.340288 | ||||||||
\(928\) | 1.92838e18 | 0.0991131 | ||||||||
\(929\) | 2.11638e19 | 1.08017 | 0.540084 | − | 0.841611i | \(-0.318392\pi\) | ||||
0.540084 | + | 0.841611i | \(0.318392\pi\) | |||||||
\(930\) | 3.64918e17 | 0.0184951 | ||||||||
\(931\) | 6.92135e18 | 0.348351 | ||||||||
\(932\) | −2.02608e19 | −1.01264 | ||||||||
\(933\) | 1.49614e19 | 0.742579 | ||||||||
\(934\) | −6.83860e17 | −0.0337064 | ||||||||
\(935\) | 1.81370e18 | 0.0887746 | ||||||||
\(936\) | 1.79646e18 | 0.0873223 | ||||||||
\(937\) | −1.20261e19 | −0.580519 | −0.290259 | − | 0.956948i | \(-0.593742\pi\) | ||||
−0.290259 | + | 0.956948i | \(0.593742\pi\) | |||||||
\(938\) | 3.33157e17 | 0.0159709 | ||||||||
\(939\) | −1.22201e19 | −0.581768 | ||||||||
\(940\) | −4.21922e17 | −0.0199481 | ||||||||
\(941\) | −3.92961e19 | −1.84509 | −0.922544 | − | 0.385893i | \(-0.873894\pi\) | ||||
−0.922544 | + | 0.385893i | \(0.873894\pi\) | |||||||
\(942\) | 1.22037e17 | 0.00569064 | ||||||||
\(943\) | −6.73023e18 | −0.311677 | ||||||||
\(944\) | −2.77948e18 | −0.127834 | ||||||||
\(945\) | −8.67498e17 | −0.0396243 | ||||||||
\(946\) | −1.16314e17 | −0.00527642 | ||||||||
\(947\) | −1.46194e19 | −0.658648 | −0.329324 | − | 0.944217i | \(-0.606821\pi\) | ||||
−0.329324 | + | 0.944217i | \(0.606821\pi\) | |||||||
\(948\) | −1.58804e19 | −0.710570 | ||||||||
\(949\) | −2.14856e19 | −0.954811 | ||||||||
\(950\) | −8.02716e17 | −0.0354290 | ||||||||
\(951\) | 1.41836e18 | 0.0621745 | ||||||||
\(952\) | 3.37020e17 | 0.0146729 | ||||||||
\(953\) | 1.43682e19 | 0.621298 | 0.310649 | − | 0.950525i | \(-0.399454\pi\) | ||||
0.310649 | + | 0.950525i | \(0.399454\pi\) | |||||||
\(954\) | −5.44497e17 | −0.0233847 | ||||||||
\(955\) | 5.59633e18 | 0.238716 | ||||||||
\(956\) | −2.90204e19 | −1.22950 | ||||||||
\(957\) | 8.91603e18 | 0.375184 | ||||||||
\(958\) | 1.88603e18 | 0.0788267 | ||||||||
\(959\) | −3.22988e18 | −0.134080 | ||||||||
\(960\) | −4.81581e18 | −0.198567 | ||||||||
\(961\) | 8.15710e18 | 0.334067 | ||||||||
\(962\) | −1.24918e18 | −0.0508143 | ||||||||
\(963\) | −3.44068e18 | −0.139019 | ||||||||
\(964\) | −1.01275e18 | −0.0406443 | ||||||||
\(965\) | 7.05739e18 | 0.281330 | ||||||||
\(966\) | 5.36305e17 | 0.0212354 | ||||||||
\(967\) | −4.32204e19 | −1.69987 | −0.849936 | − | 0.526886i | \(-0.823360\pi\) | ||||
−0.849936 | + | 0.526886i | \(0.823360\pi\) | |||||||
\(968\) | 5.15889e18 | 0.201542 | ||||||||
\(969\) | 1.27470e18 | 0.0494656 | ||||||||
\(970\) | −1.28531e18 | −0.0495441 | ||||||||
\(971\) | 3.91080e19 | 1.49741 | 0.748705 | − | 0.662903i | \(-0.230676\pi\) | ||||
0.748705 | + | 0.662903i | \(0.230676\pi\) | |||||||
\(972\) | −1.67647e18 | −0.0637624 | ||||||||
\(973\) | 1.43100e19 | 0.540637 | ||||||||
\(974\) | −2.06311e18 | −0.0774263 | ||||||||
\(975\) | −2.28432e19 | −0.851583 | ||||||||
\(976\) | −2.80136e19 | −1.03740 | ||||||||
\(977\) | −5.18308e18 | −0.190666 | −0.0953329 | − | 0.995445i | \(-0.530392\pi\) | ||||
−0.0953329 | + | 0.995445i | \(0.530392\pi\) | |||||||
\(978\) | 1.55381e18 | 0.0567799 | ||||||||
\(979\) | −3.26211e18 | −0.118416 | ||||||||
\(980\) | 6.55975e18 | 0.236547 | ||||||||
\(981\) | 2.44559e18 | 0.0876061 | ||||||||
\(982\) | −1.65829e18 | −0.0590113 | ||||||||
\(983\) | 4.57127e19 | 1.61599 | 0.807996 | − | 0.589188i | \(-0.200552\pi\) | ||||
0.807996 | + | 0.589188i | \(0.200552\pi\) | |||||||
\(984\) | −9.68587e17 | −0.0340150 | ||||||||
\(985\) | −1.29809e18 | −0.0452867 | ||||||||
\(986\) | −1.57649e17 | −0.00546375 | ||||||||
\(987\) | −5.44292e17 | −0.0187400 | ||||||||
\(988\) | 2.56509e19 | 0.877371 | ||||||||
\(989\) | −1.07997e18 | −0.0366974 | ||||||||
\(990\) | 4.15364e17 | 0.0140217 | ||||||||
\(991\) | −2.18298e19 | −0.732100 | −0.366050 | − | 0.930595i | \(-0.619290\pi\) | ||||
−0.366050 | + | 0.930595i | \(0.619290\pi\) | |||||||
\(992\) | 8.01925e18 | 0.267182 | ||||||||
\(993\) | 2.52491e19 | 0.835750 | ||||||||
\(994\) | 3.94514e17 | 0.0129733 | ||||||||
\(995\) | 8.03057e17 | 0.0262359 | ||||||||
\(996\) | 7.02769e18 | 0.228101 | ||||||||
\(997\) | 5.24614e19 | 1.69169 | 0.845846 | − | 0.533427i | \(-0.179096\pi\) | ||||
0.845846 | + | 0.533427i | \(0.179096\pi\) | |||||||
\(998\) | −2.07892e18 | −0.0666022 | ||||||||
\(999\) | 2.33856e18 | 0.0744344 |
(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 | 177.14.a.c.1.14 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.14.a.c.1.14 | ✓ | 31 | 1.1 | even | 1 | trivial |