Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,12,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, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
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: | \(135.996742959\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −88.1033 | −1.94683 | −0.973414 | − | 0.229055i | \(-0.926436\pi\) | ||||
−0.973414 | + | 0.229055i | \(0.926436\pi\) | |||||||
\(3\) | 243.000 | 0.577350 | ||||||||
\(4\) | 5714.20 | 2.79014 | ||||||||
\(5\) | 1093.28 | 0.156458 | 0.0782291 | − | 0.996935i | \(-0.475073\pi\) | ||||
0.0782291 | + | 0.996935i | \(0.475073\pi\) | |||||||
\(6\) | −21409.1 | −1.12400 | ||||||||
\(7\) | −20521.5 | −0.461499 | −0.230750 | − | 0.973013i | \(-0.574118\pi\) | ||||
−0.230750 | + | 0.973013i | \(0.574118\pi\) | |||||||
\(8\) | −323004. | −3.48508 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | −96322.0 | −0.304597 | ||||||||
\(11\) | 619162. | 1.15916 | 0.579581 | − | 0.814915i | \(-0.303216\pi\) | ||||
0.579581 | + | 0.814915i | \(0.303216\pi\) | |||||||
\(12\) | 1.38855e6 | 1.61089 | ||||||||
\(13\) | 1.84815e6 | 1.38054 | 0.690268 | − | 0.723553i | \(-0.257492\pi\) | ||||
0.690268 | + | 0.723553i | \(0.257492\pi\) | |||||||
\(14\) | 1.80802e6 | 0.898459 | ||||||||
\(15\) | 265668. | 0.0903312 | ||||||||
\(16\) | 1.67551e7 | 3.99472 | ||||||||
\(17\) | −6.92865e6 | −1.18353 | −0.591765 | − | 0.806110i | \(-0.701569\pi\) | ||||
−0.591765 | + | 0.806110i | \(0.701569\pi\) | |||||||
\(18\) | −5.20241e6 | −0.648942 | ||||||||
\(19\) | −1.82009e7 | −1.68635 | −0.843177 | − | 0.537636i | \(-0.819318\pi\) | ||||
−0.843177 | + | 0.537636i | \(0.819318\pi\) | |||||||
\(20\) | 6.24724e6 | 0.436539 | ||||||||
\(21\) | −4.98674e6 | −0.266447 | ||||||||
\(22\) | −5.45502e7 | −2.25669 | ||||||||
\(23\) | 3.56074e7 | 1.15355 | 0.576776 | − | 0.816903i | \(-0.304311\pi\) | ||||
0.576776 | + | 0.816903i | \(0.304311\pi\) | |||||||
\(24\) | −7.84900e7 | −2.01211 | ||||||||
\(25\) | −4.76329e7 | −0.975521 | ||||||||
\(26\) | −1.62828e8 | −2.68767 | ||||||||
\(27\) | 1.43489e7 | 0.192450 | ||||||||
\(28\) | −1.17264e8 | −1.28765 | ||||||||
\(29\) | 1.95174e8 | 1.76699 | 0.883494 | − | 0.468443i | \(-0.155185\pi\) | ||||
0.883494 | + | 0.468443i | \(0.155185\pi\) | |||||||
\(30\) | −2.34063e7 | −0.175859 | ||||||||
\(31\) | −2.04113e7 | −0.128050 | −0.0640252 | − | 0.997948i | \(-0.520394\pi\) | ||||
−0.0640252 | + | 0.997948i | \(0.520394\pi\) | |||||||
\(32\) | −8.14665e8 | −4.29195 | ||||||||
\(33\) | 1.50456e8 | 0.669243 | ||||||||
\(34\) | 6.10437e8 | 2.30413 | ||||||||
\(35\) | −2.24359e7 | −0.0722053 | ||||||||
\(36\) | 3.37418e8 | 0.930045 | ||||||||
\(37\) | −1.33972e8 | −0.317618 | −0.158809 | − | 0.987309i | \(-0.550765\pi\) | ||||
−0.158809 | + | 0.987309i | \(0.550765\pi\) | |||||||
\(38\) | 1.60356e9 | 3.28304 | ||||||||
\(39\) | 4.49100e8 | 0.797053 | ||||||||
\(40\) | −3.53136e8 | −0.545270 | ||||||||
\(41\) | 5.40984e8 | 0.729245 | 0.364623 | − | 0.931155i | \(-0.381198\pi\) | ||||
0.364623 | + | 0.931155i | \(0.381198\pi\) | |||||||
\(42\) | 4.39348e8 | 0.518726 | ||||||||
\(43\) | 6.33160e8 | 0.656805 | 0.328403 | − | 0.944538i | \(-0.393490\pi\) | ||||
0.328403 | + | 0.944538i | \(0.393490\pi\) | |||||||
\(44\) | 3.53801e9 | 3.23422 | ||||||||
\(45\) | 6.45574e7 | 0.0521527 | ||||||||
\(46\) | −3.13713e9 | −2.24576 | ||||||||
\(47\) | 1.05650e8 | 0.0671938 | 0.0335969 | − | 0.999435i | \(-0.489304\pi\) | ||||
0.0335969 | + | 0.999435i | \(0.489304\pi\) | |||||||
\(48\) | 4.07148e9 | 2.30635 | ||||||||
\(49\) | −1.55619e9 | −0.787019 | ||||||||
\(50\) | 4.19661e9 | 1.89917 | ||||||||
\(51\) | −1.68366e9 | −0.683312 | ||||||||
\(52\) | 1.05607e10 | 3.85188 | ||||||||
\(53\) | 2.39652e9 | 0.787162 | 0.393581 | − | 0.919290i | \(-0.371236\pi\) | ||||
0.393581 | + | 0.919290i | \(0.371236\pi\) | |||||||
\(54\) | −1.26419e9 | −0.374667 | ||||||||
\(55\) | 6.76920e8 | 0.181360 | ||||||||
\(56\) | 6.62855e9 | 1.60836 | ||||||||
\(57\) | −4.42283e9 | −0.973617 | ||||||||
\(58\) | −1.71955e10 | −3.44002 | ||||||||
\(59\) | 7.14924e8 | 0.130189 | ||||||||
\(60\) | 1.51808e9 | 0.252036 | ||||||||
\(61\) | −5.42720e9 | −0.822739 | −0.411369 | − | 0.911469i | \(-0.634949\pi\) | ||||
−0.411369 | + | 0.911469i | \(0.634949\pi\) | |||||||
\(62\) | 1.79830e9 | 0.249292 | ||||||||
\(63\) | −1.21178e9 | −0.153833 | ||||||||
\(64\) | 3.74603e10 | 4.36095 | ||||||||
\(65\) | 2.02055e9 | 0.215996 | ||||||||
\(66\) | −1.32557e10 | −1.30290 | ||||||||
\(67\) | 3.68213e9 | 0.333187 | 0.166593 | − | 0.986026i | \(-0.446723\pi\) | ||||
0.166593 | + | 0.986026i | \(0.446723\pi\) | |||||||
\(68\) | −3.95917e10 | −3.30221 | ||||||||
\(69\) | 8.65259e9 | 0.666003 | ||||||||
\(70\) | 1.97668e9 | 0.140571 | ||||||||
\(71\) | −1.73720e10 | −1.14269 | −0.571345 | − | 0.820710i | \(-0.693578\pi\) | ||||
−0.571345 | + | 0.820710i | \(0.693578\pi\) | |||||||
\(72\) | −1.90731e10 | −1.16169 | ||||||||
\(73\) | 3.22301e10 | 1.81964 | 0.909822 | − | 0.415000i | \(-0.136218\pi\) | ||||
0.909822 | + | 0.415000i | \(0.136218\pi\) | |||||||
\(74\) | 1.18034e10 | 0.618347 | ||||||||
\(75\) | −1.15748e10 | −0.563217 | ||||||||
\(76\) | −1.04004e11 | −4.70516 | ||||||||
\(77\) | −1.27062e10 | −0.534952 | ||||||||
\(78\) | −3.95672e10 | −1.55172 | ||||||||
\(79\) | 3.35728e10 | 1.22755 | 0.613775 | − | 0.789481i | \(-0.289650\pi\) | ||||
0.613775 | + | 0.789481i | \(0.289650\pi\) | |||||||
\(80\) | 1.83181e10 | 0.625007 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | −4.76625e10 | −1.41971 | ||||||||
\(83\) | 4.98543e10 | 1.38923 | 0.694613 | − | 0.719384i | \(-0.255576\pi\) | ||||
0.694613 | + | 0.719384i | \(0.255576\pi\) | |||||||
\(84\) | −2.84952e10 | −0.743422 | ||||||||
\(85\) | −7.57498e9 | −0.185173 | ||||||||
\(86\) | −5.57835e10 | −1.27869 | ||||||||
\(87\) | 4.74273e10 | 1.02017 | ||||||||
\(88\) | −1.99992e11 | −4.03978 | ||||||||
\(89\) | 4.19017e10 | 0.795403 | 0.397701 | − | 0.917515i | \(-0.369808\pi\) | ||||
0.397701 | + | 0.917515i | \(0.369808\pi\) | |||||||
\(90\) | −5.68772e9 | −0.101532 | ||||||||
\(91\) | −3.79268e10 | −0.637117 | ||||||||
\(92\) | 2.03468e11 | 3.21856 | ||||||||
\(93\) | −4.95994e9 | −0.0739300 | ||||||||
\(94\) | −9.30808e9 | −0.130815 | ||||||||
\(95\) | −1.98988e10 | −0.263844 | ||||||||
\(96\) | −1.97964e11 | −2.47796 | ||||||||
\(97\) | 5.06612e10 | 0.599005 | 0.299503 | − | 0.954095i | \(-0.403179\pi\) | ||||
0.299503 | + | 0.954095i | \(0.403179\pi\) | |||||||
\(98\) | 1.37106e11 | 1.53219 | ||||||||
\(99\) | 3.65609e10 | 0.386387 | ||||||||
\(100\) | −2.72184e11 | −2.72184 | ||||||||
\(101\) | −1.58115e10 | −0.149694 | −0.0748472 | − | 0.997195i | \(-0.523847\pi\) | ||||
−0.0748472 | + | 0.997195i | \(0.523847\pi\) | |||||||
\(102\) | 1.48336e11 | 1.33029 | ||||||||
\(103\) | −4.41647e10 | −0.375380 | −0.187690 | − | 0.982228i | \(-0.560100\pi\) | ||||
−0.187690 | + | 0.982228i | \(0.560100\pi\) | |||||||
\(104\) | −5.96959e11 | −4.81129 | ||||||||
\(105\) | −5.45192e9 | −0.0416878 | ||||||||
\(106\) | −2.11142e11 | −1.53247 | ||||||||
\(107\) | −2.25267e11 | −1.55270 | −0.776348 | − | 0.630305i | \(-0.782930\pi\) | ||||
−0.776348 | + | 0.630305i | \(0.782930\pi\) | |||||||
\(108\) | 8.19925e10 | 0.536962 | ||||||||
\(109\) | −2.67814e11 | −1.66720 | −0.833598 | − | 0.552371i | \(-0.813723\pi\) | ||||
−0.833598 | + | 0.552371i | \(0.813723\pi\) | |||||||
\(110\) | −5.96389e10 | −0.353077 | ||||||||
\(111\) | −3.25552e10 | −0.183377 | ||||||||
\(112\) | −3.43840e11 | −1.84356 | ||||||||
\(113\) | −2.91433e11 | −1.48802 | −0.744008 | − | 0.668171i | \(-0.767077\pi\) | ||||
−0.744008 | + | 0.668171i | \(0.767077\pi\) | |||||||
\(114\) | 3.89666e11 | 1.89546 | ||||||||
\(115\) | 3.89290e10 | 0.180483 | ||||||||
\(116\) | 1.11526e12 | 4.93013 | ||||||||
\(117\) | 1.09131e11 | 0.460179 | ||||||||
\(118\) | −6.29872e10 | −0.253455 | ||||||||
\(119\) | 1.42187e11 | 0.546198 | ||||||||
\(120\) | −8.58119e10 | −0.314812 | ||||||||
\(121\) | 9.80494e10 | 0.343657 | ||||||||
\(122\) | 4.78155e11 | 1.60173 | ||||||||
\(123\) | 1.31459e11 | 0.421030 | ||||||||
\(124\) | −1.16634e11 | −0.357278 | ||||||||
\(125\) | −1.05459e11 | −0.309086 | ||||||||
\(126\) | 1.06762e11 | 0.299486 | ||||||||
\(127\) | 5.75720e10 | 0.154629 | 0.0773145 | − | 0.997007i | \(-0.475365\pi\) | ||||
0.0773145 | + | 0.997007i | \(0.475365\pi\) | |||||||
\(128\) | −1.63194e12 | −4.19808 | ||||||||
\(129\) | 1.53858e11 | 0.379207 | ||||||||
\(130\) | −1.78017e11 | −0.420507 | ||||||||
\(131\) | 4.17694e11 | 0.945945 | 0.472973 | − | 0.881077i | \(-0.343181\pi\) | ||||
0.472973 | + | 0.881077i | \(0.343181\pi\) | |||||||
\(132\) | 8.59737e11 | 1.86728 | ||||||||
\(133\) | 3.73511e11 | 0.778251 | ||||||||
\(134\) | −3.24408e11 | −0.648657 | ||||||||
\(135\) | 1.56874e10 | 0.0301104 | ||||||||
\(136\) | 2.23798e12 | 4.12470 | ||||||||
\(137\) | −9.85876e10 | −0.174526 | −0.0872628 | − | 0.996185i | \(-0.527812\pi\) | ||||
−0.0872628 | + | 0.996185i | \(0.527812\pi\) | |||||||
\(138\) | −7.62322e11 | −1.29659 | ||||||||
\(139\) | −1.00244e12 | −1.63861 | −0.819305 | − | 0.573358i | \(-0.805640\pi\) | ||||
−0.819305 | + | 0.573358i | \(0.805640\pi\) | |||||||
\(140\) | −1.28203e11 | −0.201463 | ||||||||
\(141\) | 2.56728e10 | 0.0387944 | ||||||||
\(142\) | 1.53053e12 | 2.22462 | ||||||||
\(143\) | 1.14430e12 | 1.60027 | ||||||||
\(144\) | 9.89370e11 | 1.33157 | ||||||||
\(145\) | 2.13381e11 | 0.276460 | ||||||||
\(146\) | −2.83958e12 | −3.54253 | ||||||||
\(147\) | −3.78155e11 | −0.454385 | ||||||||
\(148\) | −7.65543e11 | −0.886197 | ||||||||
\(149\) | 1.24570e12 | 1.38959 | 0.694797 | − | 0.719206i | \(-0.255494\pi\) | ||||
0.694797 | + | 0.719206i | \(0.255494\pi\) | |||||||
\(150\) | 1.01978e12 | 1.09649 | ||||||||
\(151\) | −1.32489e12 | −1.37343 | −0.686713 | − | 0.726929i | \(-0.740947\pi\) | ||||
−0.686713 | + | 0.726929i | \(0.740947\pi\) | |||||||
\(152\) | 5.87898e12 | 5.87709 | ||||||||
\(153\) | −4.09130e11 | −0.394510 | ||||||||
\(154\) | 1.11945e12 | 1.04146 | ||||||||
\(155\) | −2.23154e10 | −0.0200345 | ||||||||
\(156\) | 2.56624e12 | 2.22389 | ||||||||
\(157\) | −1.12257e12 | −0.939215 | −0.469607 | − | 0.882875i | \(-0.655605\pi\) | ||||
−0.469607 | + | 0.882875i | \(0.655605\pi\) | |||||||
\(158\) | −2.95788e12 | −2.38983 | ||||||||
\(159\) | 5.82355e11 | 0.454468 | ||||||||
\(160\) | −8.90661e11 | −0.671510 | ||||||||
\(161\) | −7.30719e11 | −0.532363 | ||||||||
\(162\) | −3.07197e11 | −0.216314 | ||||||||
\(163\) | 4.81822e11 | 0.327985 | 0.163993 | − | 0.986462i | \(-0.447563\pi\) | ||||
0.163993 | + | 0.986462i | \(0.447563\pi\) | |||||||
\(164\) | 3.09129e12 | 2.03469 | ||||||||
\(165\) | 1.64492e11 | 0.104708 | ||||||||
\(166\) | −4.39233e12 | −2.70458 | ||||||||
\(167\) | 1.26248e12 | 0.752112 | 0.376056 | − | 0.926597i | \(-0.377280\pi\) | ||||
0.376056 | + | 0.926597i | \(0.377280\pi\) | |||||||
\(168\) | 1.61074e12 | 0.928589 | ||||||||
\(169\) | 1.62349e12 | 0.905882 | ||||||||
\(170\) | 6.67381e11 | 0.360500 | ||||||||
\(171\) | −1.07475e12 | −0.562118 | ||||||||
\(172\) | 3.61800e12 | 1.83258 | ||||||||
\(173\) | 2.46270e12 | 1.20825 | 0.604126 | − | 0.796889i | \(-0.293522\pi\) | ||||
0.604126 | + | 0.796889i | \(0.293522\pi\) | |||||||
\(174\) | −4.17851e12 | −1.98610 | ||||||||
\(175\) | 9.77500e11 | 0.450202 | ||||||||
\(176\) | 1.03741e13 | 4.63053 | ||||||||
\(177\) | 1.73727e11 | 0.0751646 | ||||||||
\(178\) | −3.69168e12 | −1.54851 | ||||||||
\(179\) | 5.63806e11 | 0.229318 | 0.114659 | − | 0.993405i | \(-0.463422\pi\) | ||||
0.114659 | + | 0.993405i | \(0.463422\pi\) | |||||||
\(180\) | 3.68894e11 | 0.145513 | ||||||||
\(181\) | −3.73001e12 | −1.42718 | −0.713588 | − | 0.700566i | \(-0.752931\pi\) | ||||
−0.713588 | + | 0.700566i | \(0.752931\pi\) | |||||||
\(182\) | 3.34148e12 | 1.24036 | ||||||||
\(183\) | −1.31881e12 | −0.475008 | ||||||||
\(184\) | −1.15013e13 | −4.02022 | ||||||||
\(185\) | −1.46470e11 | −0.0496939 | ||||||||
\(186\) | 4.36988e11 | 0.143929 | ||||||||
\(187\) | −4.28995e12 | −1.37190 | ||||||||
\(188\) | 6.03702e11 | 0.187480 | ||||||||
\(189\) | −2.94462e11 | −0.0888156 | ||||||||
\(190\) | 1.75315e12 | 0.513658 | ||||||||
\(191\) | 1.29232e12 | 0.367864 | 0.183932 | − | 0.982939i | \(-0.441117\pi\) | ||||
0.183932 | + | 0.982939i | \(0.441117\pi\) | |||||||
\(192\) | 9.10286e12 | 2.51780 | ||||||||
\(193\) | 6.90513e12 | 1.85612 | 0.928061 | − | 0.372428i | \(-0.121475\pi\) | ||||
0.928061 | + | 0.372428i | \(0.121475\pi\) | |||||||
\(194\) | −4.46342e12 | −1.16616 | ||||||||
\(195\) | 4.90994e11 | 0.124706 | ||||||||
\(196\) | −8.89239e12 | −2.19589 | ||||||||
\(197\) | 7.78475e12 | 1.86931 | 0.934653 | − | 0.355562i | \(-0.115711\pi\) | ||||
0.934653 | + | 0.355562i | \(0.115711\pi\) | |||||||
\(198\) | −3.22113e12 | −0.752229 | ||||||||
\(199\) | −4.00111e12 | −0.908843 | −0.454421 | − | 0.890787i | \(-0.650154\pi\) | ||||
−0.454421 | + | 0.890787i | \(0.650154\pi\) | |||||||
\(200\) | 1.53856e13 | 3.39977 | ||||||||
\(201\) | 8.94757e11 | 0.192365 | ||||||||
\(202\) | 1.39305e12 | 0.291429 | ||||||||
\(203\) | −4.00528e12 | −0.815463 | ||||||||
\(204\) | −9.62077e12 | −1.90653 | ||||||||
\(205\) | 5.91450e11 | 0.114096 | ||||||||
\(206\) | 3.89106e12 | 0.730799 | ||||||||
\(207\) | 2.10258e12 | 0.384517 | ||||||||
\(208\) | 3.09658e13 | 5.51486 | ||||||||
\(209\) | −1.12693e13 | −1.95476 | ||||||||
\(210\) | 4.80333e11 | 0.0811588 | ||||||||
\(211\) | 1.12159e13 | 1.84620 | 0.923101 | − | 0.384558i | \(-0.125646\pi\) | ||||
0.923101 | + | 0.384558i | \(0.125646\pi\) | |||||||
\(212\) | 1.36942e13 | 2.19629 | ||||||||
\(213\) | −4.22139e12 | −0.659733 | ||||||||
\(214\) | 1.98468e13 | 3.02283 | ||||||||
\(215\) | 6.92224e11 | 0.102763 | ||||||||
\(216\) | −4.63476e12 | −0.670705 | ||||||||
\(217\) | 4.18871e11 | 0.0590952 | ||||||||
\(218\) | 2.35953e13 | 3.24574 | ||||||||
\(219\) | 7.83192e12 | 1.05057 | ||||||||
\(220\) | 3.86805e12 | 0.506020 | ||||||||
\(221\) | −1.28052e13 | −1.63391 | ||||||||
\(222\) | 2.86822e12 | 0.357003 | ||||||||
\(223\) | 1.87818e12 | 0.228065 | 0.114033 | − | 0.993477i | \(-0.463623\pi\) | ||||
0.114033 | + | 0.993477i | \(0.463623\pi\) | |||||||
\(224\) | 1.67182e13 | 1.98073 | ||||||||
\(225\) | −2.81267e12 | −0.325174 | ||||||||
\(226\) | 2.56762e13 | 2.89691 | ||||||||
\(227\) | 6.00593e12 | 0.661360 | 0.330680 | − | 0.943743i | \(-0.392722\pi\) | ||||
0.330680 | + | 0.943743i | \(0.392722\pi\) | |||||||
\(228\) | −2.52729e13 | −2.71652 | ||||||||
\(229\) | −7.32590e12 | −0.768716 | −0.384358 | − | 0.923184i | \(-0.625577\pi\) | ||||
−0.384358 | + | 0.923184i | \(0.625577\pi\) | |||||||
\(230\) | −3.42978e12 | −0.351368 | ||||||||
\(231\) | −3.08760e12 | −0.308855 | ||||||||
\(232\) | −6.30421e13 | −6.15810 | ||||||||
\(233\) | −7.79070e11 | −0.0743223 | −0.0371611 | − | 0.999309i | \(-0.511831\pi\) | ||||
−0.0371611 | + | 0.999309i | \(0.511831\pi\) | |||||||
\(234\) | −9.61482e12 | −0.895889 | ||||||||
\(235\) | 1.15505e11 | 0.0105130 | ||||||||
\(236\) | 4.08522e12 | 0.363245 | ||||||||
\(237\) | 8.15820e12 | 0.708726 | ||||||||
\(238\) | −1.25271e13 | −1.06335 | ||||||||
\(239\) | 1.42626e13 | 1.18307 | 0.591536 | − | 0.806278i | \(-0.298522\pi\) | ||||
0.591536 | + | 0.806278i | \(0.298522\pi\) | |||||||
\(240\) | 4.45129e12 | 0.360848 | ||||||||
\(241\) | 1.12584e13 | 0.892038 | 0.446019 | − | 0.895024i | \(-0.352841\pi\) | ||||
0.446019 | + | 0.895024i | \(0.352841\pi\) | |||||||
\(242\) | −8.63848e12 | −0.669041 | ||||||||
\(243\) | 8.47289e11 | 0.0641500 | ||||||||
\(244\) | −3.10121e13 | −2.29555 | ||||||||
\(245\) | −1.70136e12 | −0.123135 | ||||||||
\(246\) | −1.15820e13 | −0.819672 | ||||||||
\(247\) | −3.36380e13 | −2.32807 | ||||||||
\(248\) | 6.59293e12 | 0.446267 | ||||||||
\(249\) | 1.21146e13 | 0.802070 | ||||||||
\(250\) | 9.29132e12 | 0.601738 | ||||||||
\(251\) | 7.93703e12 | 0.502866 | 0.251433 | − | 0.967875i | \(-0.419098\pi\) | ||||
0.251433 | + | 0.967875i | \(0.419098\pi\) | |||||||
\(252\) | −6.92433e12 | −0.429215 | ||||||||
\(253\) | 2.20467e13 | 1.33715 | ||||||||
\(254\) | −5.07228e12 | −0.301036 | ||||||||
\(255\) | −1.84072e12 | −0.106910 | ||||||||
\(256\) | 6.70610e13 | 3.81198 | ||||||||
\(257\) | −1.72639e13 | −0.960523 | −0.480262 | − | 0.877125i | \(-0.659458\pi\) | ||||
−0.480262 | + | 0.877125i | \(0.659458\pi\) | |||||||
\(258\) | −1.35554e13 | −0.738250 | ||||||||
\(259\) | 2.74931e12 | 0.146580 | ||||||||
\(260\) | 1.15458e13 | 0.602659 | ||||||||
\(261\) | 1.15248e13 | 0.588996 | ||||||||
\(262\) | −3.68002e13 | −1.84159 | ||||||||
\(263\) | −1.16164e13 | −0.569265 | −0.284632 | − | 0.958637i | \(-0.591872\pi\) | ||||
−0.284632 | + | 0.958637i | \(0.591872\pi\) | |||||||
\(264\) | −4.85980e13 | −2.33237 | ||||||||
\(265\) | 2.62008e12 | 0.123158 | ||||||||
\(266\) | −3.29076e13 | −1.51512 | ||||||||
\(267\) | 1.01821e13 | 0.459226 | ||||||||
\(268\) | 2.10404e13 | 0.929636 | ||||||||
\(269\) | −1.52243e13 | −0.659020 | −0.329510 | − | 0.944152i | \(-0.606884\pi\) | ||||
−0.329510 | + | 0.944152i | \(0.606884\pi\) | |||||||
\(270\) | −1.38212e12 | −0.0586197 | ||||||||
\(271\) | 3.62900e13 | 1.50819 | 0.754094 | − | 0.656767i | \(-0.228076\pi\) | ||||
0.754094 | + | 0.656767i | \(0.228076\pi\) | |||||||
\(272\) | −1.16090e14 | −4.72787 | ||||||||
\(273\) | −9.21622e12 | −0.367839 | ||||||||
\(274\) | 8.68589e12 | 0.339771 | ||||||||
\(275\) | −2.94924e13 | −1.13079 | ||||||||
\(276\) | 4.94426e13 | 1.85824 | ||||||||
\(277\) | −2.91834e13 | −1.07522 | −0.537610 | − | 0.843193i | \(-0.680673\pi\) | ||||
−0.537610 | + | 0.843193i | \(0.680673\pi\) | |||||||
\(278\) | 8.83180e13 | 3.19009 | ||||||||
\(279\) | −1.20527e12 | −0.0426835 | ||||||||
\(280\) | 7.24689e12 | 0.251642 | ||||||||
\(281\) | −3.08384e12 | −0.105004 | −0.0525022 | − | 0.998621i | \(-0.516720\pi\) | ||||
−0.0525022 | + | 0.998621i | \(0.516720\pi\) | |||||||
\(282\) | −2.26186e12 | −0.0755259 | ||||||||
\(283\) | 4.66033e13 | 1.52613 | 0.763064 | − | 0.646323i | \(-0.223694\pi\) | ||||
0.763064 | + | 0.646323i | \(0.223694\pi\) | |||||||
\(284\) | −9.92670e13 | −3.18826 | ||||||||
\(285\) | −4.83541e12 | −0.152330 | ||||||||
\(286\) | −1.00817e14 | −3.11544 | ||||||||
\(287\) | −1.11018e13 | −0.336546 | ||||||||
\(288\) | −4.81052e13 | −1.43065 | ||||||||
\(289\) | 1.37343e13 | 0.400744 | ||||||||
\(290\) | −1.87996e13 | −0.538219 | ||||||||
\(291\) | 1.23107e13 | 0.345836 | ||||||||
\(292\) | 1.84169e14 | 5.07705 | ||||||||
\(293\) | 2.51439e13 | 0.680238 | 0.340119 | − | 0.940382i | \(-0.389533\pi\) | ||||
0.340119 | + | 0.940382i | \(0.389533\pi\) | |||||||
\(294\) | 3.33167e13 | 0.884610 | ||||||||
\(295\) | 7.81616e11 | 0.0203691 | ||||||||
\(296\) | 4.32735e13 | 1.10692 | ||||||||
\(297\) | 8.88429e12 | 0.223081 | ||||||||
\(298\) | −1.09750e14 | −2.70530 | ||||||||
\(299\) | 6.58077e13 | 1.59252 | ||||||||
\(300\) | −6.61406e13 | −1.57145 | ||||||||
\(301\) | −1.29934e13 | −0.303115 | ||||||||
\(302\) | 1.16727e14 | 2.67382 | ||||||||
\(303\) | −3.84219e12 | −0.0864261 | ||||||||
\(304\) | −3.04958e14 | −6.73651 | ||||||||
\(305\) | −5.93348e12 | −0.128724 | ||||||||
\(306\) | 3.60457e13 | 0.768043 | ||||||||
\(307\) | −6.27605e13 | −1.31349 | −0.656743 | − | 0.754115i | \(-0.728066\pi\) | ||||
−0.656743 | + | 0.754115i | \(0.728066\pi\) | |||||||
\(308\) | −7.26055e13 | −1.49259 | ||||||||
\(309\) | −1.07320e13 | −0.216726 | ||||||||
\(310\) | 1.96606e12 | 0.0390038 | ||||||||
\(311\) | −5.92798e13 | −1.15538 | −0.577689 | − | 0.816257i | \(-0.696045\pi\) | ||||
−0.577689 | + | 0.816257i | \(0.696045\pi\) | |||||||
\(312\) | −1.45061e14 | −2.77780 | ||||||||
\(313\) | 4.70084e13 | 0.884468 | 0.442234 | − | 0.896900i | \(-0.354186\pi\) | ||||
0.442234 | + | 0.896900i | \(0.354186\pi\) | |||||||
\(314\) | 9.89021e13 | 1.82849 | ||||||||
\(315\) | −1.32482e12 | −0.0240684 | ||||||||
\(316\) | 1.91842e14 | 3.42503 | ||||||||
\(317\) | 7.22217e13 | 1.26719 | 0.633595 | − | 0.773665i | \(-0.281579\pi\) | ||||
0.633595 | + | 0.773665i | \(0.281579\pi\) | |||||||
\(318\) | −5.13074e13 | −0.884771 | ||||||||
\(319\) | 1.20844e14 | 2.04823 | ||||||||
\(320\) | 4.09548e13 | 0.682307 | ||||||||
\(321\) | −5.47398e13 | −0.896449 | ||||||||
\(322\) | 6.43787e13 | 1.03642 | ||||||||
\(323\) | 1.26108e14 | 1.99585 | ||||||||
\(324\) | 1.99242e13 | 0.310015 | ||||||||
\(325\) | −8.80325e13 | −1.34674 | ||||||||
\(326\) | −4.24501e13 | −0.638531 | ||||||||
\(327\) | −6.50787e13 | −0.962556 | ||||||||
\(328\) | −1.74740e14 | −2.54148 | ||||||||
\(329\) | −2.16809e12 | −0.0310099 | ||||||||
\(330\) | −1.44923e13 | −0.203849 | ||||||||
\(331\) | 9.66001e13 | 1.33636 | 0.668180 | − | 0.743999i | \(-0.267073\pi\) | ||||
0.668180 | + | 0.743999i | \(0.267073\pi\) | |||||||
\(332\) | 2.84877e14 | 3.87613 | ||||||||
\(333\) | −7.91092e12 | −0.105873 | ||||||||
\(334\) | −1.11228e14 | −1.46423 | ||||||||
\(335\) | 4.02562e12 | 0.0521298 | ||||||||
\(336\) | −8.35531e13 | −1.06438 | ||||||||
\(337\) | 3.74070e13 | 0.468800 | 0.234400 | − | 0.972140i | \(-0.424687\pi\) | ||||
0.234400 | + | 0.972140i | \(0.424687\pi\) | |||||||
\(338\) | −1.43035e14 | −1.76360 | ||||||||
\(339\) | −7.08183e13 | −0.859106 | ||||||||
\(340\) | −4.32850e13 | −0.516658 | ||||||||
\(341\) | −1.26379e13 | −0.148431 | ||||||||
\(342\) | 9.46888e13 | 1.09435 | ||||||||
\(343\) | 7.25133e13 | 0.824708 | ||||||||
\(344\) | −2.04513e14 | −2.28902 | ||||||||
\(345\) | 9.45975e12 | 0.104202 | ||||||||
\(346\) | −2.16972e14 | −2.35226 | ||||||||
\(347\) | −5.26244e13 | −0.561532 | −0.280766 | − | 0.959776i | \(-0.590589\pi\) | ||||
−0.280766 | + | 0.959776i | \(0.590589\pi\) | |||||||
\(348\) | 2.71009e14 | 2.84641 | ||||||||
\(349\) | 6.09941e13 | 0.630592 | 0.315296 | − | 0.948993i | \(-0.397896\pi\) | ||||
0.315296 | + | 0.948993i | \(0.397896\pi\) | |||||||
\(350\) | −8.61210e13 | −0.876465 | ||||||||
\(351\) | 2.65189e13 | 0.265684 | ||||||||
\(352\) | −5.04409e14 | −4.97506 | ||||||||
\(353\) | 2.03250e14 | 1.97365 | 0.986824 | − | 0.161798i | \(-0.0517292\pi\) | ||||
0.986824 | + | 0.161798i | \(0.0517292\pi\) | |||||||
\(354\) | −1.53059e13 | −0.146332 | ||||||||
\(355\) | −1.89925e13 | −0.178783 | ||||||||
\(356\) | 2.39435e14 | 2.21928 | ||||||||
\(357\) | 3.45513e13 | 0.315348 | ||||||||
\(358\) | −4.96732e13 | −0.446443 | ||||||||
\(359\) | 7.30453e13 | 0.646506 | 0.323253 | − | 0.946313i | \(-0.395223\pi\) | ||||
0.323253 | + | 0.946313i | \(0.395223\pi\) | |||||||
\(360\) | −2.08523e13 | −0.181757 | ||||||||
\(361\) | 2.14784e14 | 1.84379 | ||||||||
\(362\) | 3.28626e14 | 2.77846 | ||||||||
\(363\) | 2.38260e13 | 0.198411 | ||||||||
\(364\) | −2.16721e14 | −1.77764 | ||||||||
\(365\) | 3.52367e13 | 0.284698 | ||||||||
\(366\) | 1.16192e14 | 0.924759 | ||||||||
\(367\) | 1.07824e14 | 0.845379 | 0.422690 | − | 0.906275i | \(-0.361086\pi\) | ||||
0.422690 | + | 0.906275i | \(0.361086\pi\) | |||||||
\(368\) | 5.96604e14 | 4.60811 | ||||||||
\(369\) | 3.19446e13 | 0.243082 | ||||||||
\(370\) | 1.29045e13 | 0.0967454 | ||||||||
\(371\) | −4.91804e13 | −0.363275 | ||||||||
\(372\) | −2.83421e13 | −0.206275 | ||||||||
\(373\) | 1.82945e14 | 1.31197 | 0.655984 | − | 0.754775i | \(-0.272254\pi\) | ||||
0.655984 | + | 0.754775i | \(0.272254\pi\) | |||||||
\(374\) | 3.77959e14 | 2.67086 | ||||||||
\(375\) | −2.56266e13 | −0.178451 | ||||||||
\(376\) | −3.41252e13 | −0.234176 | ||||||||
\(377\) | 3.60711e14 | 2.43939 | ||||||||
\(378\) | 2.59431e13 | 0.172909 | ||||||||
\(379\) | 1.05180e14 | 0.690903 | 0.345451 | − | 0.938437i | \(-0.387726\pi\) | ||||
0.345451 | + | 0.938437i | \(0.387726\pi\) | |||||||
\(380\) | −1.13706e14 | −0.736160 | ||||||||
\(381\) | 1.39900e13 | 0.0892751 | ||||||||
\(382\) | −1.13858e14 | −0.716167 | ||||||||
\(383\) | −8.06324e13 | −0.499938 | −0.249969 | − | 0.968254i | \(-0.580420\pi\) | ||||
−0.249969 | + | 0.968254i | \(0.580420\pi\) | |||||||
\(384\) | −3.96563e14 | −2.42376 | ||||||||
\(385\) | −1.38914e13 | −0.0836977 | ||||||||
\(386\) | −6.08365e14 | −3.61355 | ||||||||
\(387\) | 3.73874e13 | 0.218935 | ||||||||
\(388\) | 2.89488e14 | 1.67131 | ||||||||
\(389\) | 1.77980e14 | 1.01309 | 0.506546 | − | 0.862213i | \(-0.330922\pi\) | ||||
0.506546 | + | 0.862213i | \(0.330922\pi\) | |||||||
\(390\) | −4.32582e13 | −0.242780 | ||||||||
\(391\) | −2.46711e14 | −1.36526 | ||||||||
\(392\) | 5.02657e14 | 2.74283 | ||||||||
\(393\) | 1.01500e14 | 0.546142 | ||||||||
\(394\) | −6.85862e14 | −3.63921 | ||||||||
\(395\) | 3.67047e13 | 0.192060 | ||||||||
\(396\) | 2.08916e14 | 1.07807 | ||||||||
\(397\) | −1.80915e13 | −0.0920717 | −0.0460359 | − | 0.998940i | \(-0.514659\pi\) | ||||
−0.0460359 | + | 0.998940i | \(0.514659\pi\) | |||||||
\(398\) | 3.52511e14 | 1.76936 | ||||||||
\(399\) | 9.07632e13 | 0.449323 | ||||||||
\(400\) | −7.98092e14 | −3.89693 | ||||||||
\(401\) | −2.06313e14 | −0.993649 | −0.496825 | − | 0.867851i | \(-0.665501\pi\) | ||||
−0.496825 | + | 0.867851i | \(0.665501\pi\) | |||||||
\(402\) | −7.88311e13 | −0.374502 | ||||||||
\(403\) | −3.77231e13 | −0.176778 | ||||||||
\(404\) | −9.03500e13 | −0.417668 | ||||||||
\(405\) | 3.81205e12 | 0.0173842 | ||||||||
\(406\) | 3.52878e14 | 1.58757 | ||||||||
\(407\) | −8.29504e13 | −0.368171 | ||||||||
\(408\) | 5.43830e14 | 2.38140 | ||||||||
\(409\) | −2.21304e14 | −0.956118 | −0.478059 | − | 0.878328i | \(-0.658660\pi\) | ||||
−0.478059 | + | 0.878328i | \(0.658660\pi\) | |||||||
\(410\) | −5.21087e13 | −0.222126 | ||||||||
\(411\) | −2.39568e13 | −0.100762 | ||||||||
\(412\) | −2.52366e14 | −1.04736 | ||||||||
\(413\) | −1.46714e13 | −0.0600821 | ||||||||
\(414\) | −1.85244e14 | −0.748588 | ||||||||
\(415\) | 5.45049e13 | 0.217356 | ||||||||
\(416\) | −1.50562e15 | −5.92519 | ||||||||
\(417\) | −2.43592e14 | −0.946052 | ||||||||
\(418\) | 9.92865e14 | 3.80558 | ||||||||
\(419\) | 6.95620e13 | 0.263145 | 0.131572 | − | 0.991307i | \(-0.457997\pi\) | ||||
0.131572 | + | 0.991307i | \(0.457997\pi\) | |||||||
\(420\) | −3.11534e13 | −0.116314 | ||||||||
\(421\) | −2.67808e14 | −0.986896 | −0.493448 | − | 0.869775i | \(-0.664264\pi\) | ||||
−0.493448 | + | 0.869775i | \(0.664264\pi\) | |||||||
\(422\) | −9.88155e14 | −3.59424 | ||||||||
\(423\) | 6.23850e12 | 0.0223979 | ||||||||
\(424\) | −7.74087e14 | −2.74333 | ||||||||
\(425\) | 3.30031e14 | 1.15456 | ||||||||
\(426\) | 3.71919e14 | 1.28439 | ||||||||
\(427\) | 1.11375e14 | 0.379693 | ||||||||
\(428\) | −1.28722e15 | −4.33223 | ||||||||
\(429\) | 2.78065e14 | 0.923914 | ||||||||
\(430\) | −6.09872e13 | −0.200061 | ||||||||
\(431\) | 9.63333e13 | 0.311998 | 0.155999 | − | 0.987757i | \(-0.450140\pi\) | ||||
0.155999 | + | 0.987757i | \(0.450140\pi\) | |||||||
\(432\) | 2.40417e14 | 0.768784 | ||||||||
\(433\) | 2.29331e14 | 0.724070 | 0.362035 | − | 0.932165i | \(-0.382082\pi\) | ||||
0.362035 | + | 0.932165i | \(0.382082\pi\) | |||||||
\(434\) | −3.69040e13 | −0.115048 | ||||||||
\(435\) | 5.18516e13 | 0.159614 | ||||||||
\(436\) | −1.53034e15 | −4.65170 | ||||||||
\(437\) | −6.48088e14 | −1.94530 | ||||||||
\(438\) | −6.90018e14 | −2.04528 | ||||||||
\(439\) | 3.63338e14 | 1.06355 | 0.531773 | − | 0.846887i | \(-0.321526\pi\) | ||||
0.531773 | + | 0.846887i | \(0.321526\pi\) | |||||||
\(440\) | −2.18648e14 | −0.632056 | ||||||||
\(441\) | −9.18916e13 | −0.262340 | ||||||||
\(442\) | 1.12818e15 | 3.18093 | ||||||||
\(443\) | 1.99410e14 | 0.555298 | 0.277649 | − | 0.960683i | \(-0.410445\pi\) | ||||
0.277649 | + | 0.960683i | \(0.410445\pi\) | |||||||
\(444\) | −1.86027e14 | −0.511646 | ||||||||
\(445\) | 4.58105e13 | 0.124447 | ||||||||
\(446\) | −1.65474e14 | −0.444004 | ||||||||
\(447\) | 3.02704e14 | 0.802282 | ||||||||
\(448\) | −7.68744e14 | −2.01258 | ||||||||
\(449\) | −3.12549e14 | −0.808283 | −0.404141 | − | 0.914697i | \(-0.632430\pi\) | ||||
−0.404141 | + | 0.914697i | \(0.632430\pi\) | |||||||
\(450\) | 2.47806e14 | 0.633057 | ||||||||
\(451\) | 3.34957e14 | 0.845314 | ||||||||
\(452\) | −1.66531e15 | −4.15177 | ||||||||
\(453\) | −3.21947e14 | −0.792947 | ||||||||
\(454\) | −5.29142e14 | −1.28755 | ||||||||
\(455\) | −4.14648e13 | −0.0996821 | ||||||||
\(456\) | 1.42859e15 | 3.39314 | ||||||||
\(457\) | −9.29028e13 | −0.218017 | −0.109008 | − | 0.994041i | \(-0.534768\pi\) | ||||
−0.109008 | + | 0.994041i | \(0.534768\pi\) | |||||||
\(458\) | 6.45436e14 | 1.49656 | ||||||||
\(459\) | −9.94185e13 | −0.227771 | ||||||||
\(460\) | 2.22448e14 | 0.503571 | ||||||||
\(461\) | 9.54233e13 | 0.213452 | 0.106726 | − | 0.994288i | \(-0.465963\pi\) | ||||
0.106726 | + | 0.994288i | \(0.465963\pi\) | |||||||
\(462\) | 2.72027e14 | 0.601287 | ||||||||
\(463\) | 8.09112e13 | 0.176731 | 0.0883656 | − | 0.996088i | \(-0.471836\pi\) | ||||
0.0883656 | + | 0.996088i | \(0.471836\pi\) | |||||||
\(464\) | 3.27016e15 | 7.05862 | ||||||||
\(465\) | −5.42263e12 | −0.0115670 | ||||||||
\(466\) | 6.86387e13 | 0.144693 | ||||||||
\(467\) | 4.40005e14 | 0.916674 | 0.458337 | − | 0.888778i | \(-0.348445\pi\) | ||||
0.458337 | + | 0.888778i | \(0.348445\pi\) | |||||||
\(468\) | 6.23597e14 | 1.28396 | ||||||||
\(469\) | −7.55630e13 | −0.153765 | ||||||||
\(470\) | −1.01764e13 | −0.0204670 | ||||||||
\(471\) | −2.72784e14 | −0.542256 | ||||||||
\(472\) | −2.30924e14 | −0.453719 | ||||||||
\(473\) | 3.92028e14 | 0.761344 | ||||||||
\(474\) | −7.18764e14 | −1.37977 | ||||||||
\(475\) | 8.66962e14 | 1.64507 | ||||||||
\(476\) | 8.12482e14 | 1.52397 | ||||||||
\(477\) | 1.41512e14 | 0.262387 | ||||||||
\(478\) | −1.25659e15 | −2.30324 | ||||||||
\(479\) | −2.58001e14 | −0.467495 | −0.233747 | − | 0.972297i | \(-0.575099\pi\) | ||||
−0.233747 | + | 0.972297i | \(0.575099\pi\) | |||||||
\(480\) | −2.16431e14 | −0.387696 | ||||||||
\(481\) | −2.47600e14 | −0.438483 | ||||||||
\(482\) | −9.91903e14 | −1.73664 | ||||||||
\(483\) | −1.77565e14 | −0.307360 | ||||||||
\(484\) | 5.60274e14 | 0.958850 | ||||||||
\(485\) | 5.53871e13 | 0.0937193 | ||||||||
\(486\) | −7.46490e13 | −0.124889 | ||||||||
\(487\) | 1.06913e15 | 1.76856 | 0.884279 | − | 0.466958i | \(-0.154650\pi\) | ||||
0.884279 | + | 0.466958i | \(0.154650\pi\) | |||||||
\(488\) | 1.75301e15 | 2.86731 | ||||||||
\(489\) | 1.17083e14 | 0.189362 | ||||||||
\(490\) | 1.49896e14 | 0.239723 | ||||||||
\(491\) | −3.04828e14 | −0.482066 | −0.241033 | − | 0.970517i | \(-0.577486\pi\) | ||||
−0.241033 | + | 0.970517i | \(0.577486\pi\) | |||||||
\(492\) | 7.51184e14 | 1.17473 | ||||||||
\(493\) | −1.35229e15 | −2.09128 | ||||||||
\(494\) | 2.96362e15 | 4.53236 | ||||||||
\(495\) | 3.99714e13 | 0.0604535 | ||||||||
\(496\) | −3.41993e14 | −0.511526 | ||||||||
\(497\) | 3.56500e14 | 0.527351 | ||||||||
\(498\) | −1.06734e15 | −1.56149 | ||||||||
\(499\) | 1.75672e12 | 0.00254185 | 0.00127092 | − | 0.999999i | \(-0.499595\pi\) | ||||
0.00127092 | + | 0.999999i | \(0.499595\pi\) | |||||||
\(500\) | −6.02615e14 | −0.862393 | ||||||||
\(501\) | 3.06782e14 | 0.434232 | ||||||||
\(502\) | −6.99279e14 | −0.978993 | ||||||||
\(503\) | −7.62058e14 | −1.05527 | −0.527636 | − | 0.849471i | \(-0.676921\pi\) | ||||
−0.527636 | + | 0.849471i | \(0.676921\pi\) | |||||||
\(504\) | 3.91409e14 | 0.536121 | ||||||||
\(505\) | −1.72865e13 | −0.0234209 | ||||||||
\(506\) | −1.94239e15 | −2.60321 | ||||||||
\(507\) | 3.94507e14 | 0.523011 | ||||||||
\(508\) | 3.28978e14 | 0.431436 | ||||||||
\(509\) | 6.14338e14 | 0.797003 | 0.398501 | − | 0.917168i | \(-0.369530\pi\) | ||||
0.398501 | + | 0.917168i | \(0.369530\pi\) | |||||||
\(510\) | 1.62174e14 | 0.208135 | ||||||||
\(511\) | −6.61412e14 | −0.839764 | ||||||||
\(512\) | −2.56608e15 | −3.22318 | ||||||||
\(513\) | −2.61163e14 | −0.324539 | ||||||||
\(514\) | 1.52101e15 | 1.86997 | ||||||||
\(515\) | −4.82846e13 | −0.0587312 | ||||||||
\(516\) | 8.79174e14 | 1.05804 | ||||||||
\(517\) | 6.54141e13 | 0.0778885 | ||||||||
\(518\) | −2.42224e14 | −0.285367 | ||||||||
\(519\) | 5.98435e14 | 0.697584 | ||||||||
\(520\) | −6.52646e14 | −0.752765 | ||||||||
\(521\) | 6.95169e14 | 0.793383 | 0.396692 | − | 0.917952i | \(-0.370158\pi\) | ||||
0.396692 | + | 0.917952i | \(0.370158\pi\) | |||||||
\(522\) | −1.01538e15 | −1.14667 | ||||||||
\(523\) | 8.61346e14 | 0.962539 | 0.481270 | − | 0.876573i | \(-0.340176\pi\) | ||||
0.481270 | + | 0.876573i | \(0.340176\pi\) | |||||||
\(524\) | 2.38679e15 | 2.63932 | ||||||||
\(525\) | 2.37532e14 | 0.259924 | ||||||||
\(526\) | 1.02344e15 | 1.10826 | ||||||||
\(527\) | 1.41423e14 | 0.151552 | ||||||||
\(528\) | 2.52091e15 | 2.67344 | ||||||||
\(529\) | 3.15076e14 | 0.330681 | ||||||||
\(530\) | −2.30838e14 | −0.239767 | ||||||||
\(531\) | 4.22156e13 | 0.0433963 | ||||||||
\(532\) | 2.13432e15 | 2.17143 | ||||||||
\(533\) | 9.99819e14 | 1.00675 | ||||||||
\(534\) | −8.97079e14 | −0.894033 | ||||||||
\(535\) | −2.46281e14 | −0.242932 | ||||||||
\(536\) | −1.18934e15 | −1.16118 | ||||||||
\(537\) | 1.37005e14 | 0.132397 | ||||||||
\(538\) | 1.34131e15 | 1.28300 | ||||||||
\(539\) | −9.63535e14 | −0.912282 | ||||||||
\(540\) | 8.96411e13 | 0.0840121 | ||||||||
\(541\) | −2.12299e15 | −1.96953 | −0.984766 | − | 0.173886i | \(-0.944368\pi\) | ||||
−0.984766 | + | 0.173886i | \(0.944368\pi\) | |||||||
\(542\) | −3.19727e15 | −2.93618 | ||||||||
\(543\) | −9.06391e14 | −0.823980 | ||||||||
\(544\) | 5.64453e15 | 5.07965 | ||||||||
\(545\) | −2.92796e14 | −0.260847 | ||||||||
\(546\) | 8.11980e14 | 0.716120 | ||||||||
\(547\) | −7.34491e14 | −0.641293 | −0.320646 | − | 0.947199i | \(-0.603900\pi\) | ||||
−0.320646 | + | 0.947199i | \(0.603900\pi\) | |||||||
\(548\) | −5.63349e14 | −0.486950 | ||||||||
\(549\) | −3.20471e14 | −0.274246 | ||||||||
\(550\) | 2.59838e15 | 2.20145 | ||||||||
\(551\) | −3.55235e15 | −2.97977 | ||||||||
\(552\) | −2.79482e15 | −2.32108 | ||||||||
\(553\) | −6.88966e14 | −0.566513 | ||||||||
\(554\) | 2.57116e15 | 2.09327 | ||||||||
\(555\) | −3.55921e13 | −0.0286908 | ||||||||
\(556\) | −5.72812e15 | −4.57194 | ||||||||
\(557\) | 8.26995e14 | 0.653581 | 0.326790 | − | 0.945097i | \(-0.394033\pi\) | ||||
0.326790 | + | 0.945097i | \(0.394033\pi\) | |||||||
\(558\) | 1.06188e14 | 0.0830974 | ||||||||
\(559\) | 1.17017e15 | 0.906744 | ||||||||
\(560\) | −3.75915e14 | −0.288440 | ||||||||
\(561\) | −1.04246e15 | −0.792069 | ||||||||
\(562\) | 2.71697e14 | 0.204425 | ||||||||
\(563\) | 1.57630e15 | 1.17447 | 0.587236 | − | 0.809416i | \(-0.300216\pi\) | ||||
0.587236 | + | 0.809416i | \(0.300216\pi\) | |||||||
\(564\) | 1.46700e14 | 0.108242 | ||||||||
\(565\) | −3.18619e14 | −0.232812 | ||||||||
\(566\) | −4.10590e15 | −2.97111 | ||||||||
\(567\) | −7.15542e13 | −0.0512777 | ||||||||
\(568\) | 5.61123e15 | 3.98237 | ||||||||
\(569\) | −1.61475e14 | −0.113498 | −0.0567491 | − | 0.998388i | \(-0.518074\pi\) | ||||
−0.0567491 | + | 0.998388i | \(0.518074\pi\) | |||||||
\(570\) | 4.26016e14 | 0.296561 | ||||||||
\(571\) | 1.21281e15 | 0.836167 | 0.418083 | − | 0.908409i | \(-0.362702\pi\) | ||||
0.418083 | + | 0.908409i | \(0.362702\pi\) | |||||||
\(572\) | 6.53876e15 | 4.46496 | ||||||||
\(573\) | 3.14034e14 | 0.212386 | ||||||||
\(574\) | 9.78109e14 | 0.655197 | ||||||||
\(575\) | −1.69608e15 | −1.12531 | ||||||||
\(576\) | 2.21199e15 | 1.45365 | ||||||||
\(577\) | 9.98453e14 | 0.649921 | 0.324961 | − | 0.945728i | \(-0.394649\pi\) | ||||
0.324961 | + | 0.945728i | \(0.394649\pi\) | |||||||
\(578\) | −1.21003e15 | −0.780180 | ||||||||
\(579\) | 1.67795e15 | 1.07163 | ||||||||
\(580\) | 1.21930e15 | 0.771360 | ||||||||
\(581\) | −1.02309e15 | −0.641127 | ||||||||
\(582\) | −1.08461e15 | −0.673283 | ||||||||
\(583\) | 1.48384e15 | 0.912449 | ||||||||
\(584\) | −1.04105e16 | −6.34161 | ||||||||
\(585\) | 1.19311e14 | 0.0719988 | ||||||||
\(586\) | −2.21526e15 | −1.32430 | ||||||||
\(587\) | 1.48736e15 | 0.880857 | 0.440428 | − | 0.897788i | \(-0.354827\pi\) | ||||
0.440428 | + | 0.897788i | \(0.354827\pi\) | |||||||
\(588\) | −2.16085e15 | −1.26780 | ||||||||
\(589\) | 3.71505e14 | 0.215939 | ||||||||
\(590\) | −6.88630e13 | −0.0396552 | ||||||||
\(591\) | 1.89169e15 | 1.07924 | ||||||||
\(592\) | −2.24471e15 | −1.26879 | ||||||||
\(593\) | −2.02826e15 | −1.13585 | −0.567927 | − | 0.823079i | \(-0.692255\pi\) | ||||
−0.567927 | + | 0.823079i | \(0.692255\pi\) | |||||||
\(594\) | −7.82736e14 | −0.434300 | ||||||||
\(595\) | 1.55450e14 | 0.0854572 | ||||||||
\(596\) | 7.11816e15 | 3.87715 | ||||||||
\(597\) | −9.72270e14 | −0.524721 | ||||||||
\(598\) | −5.79787e15 | −3.10036 | ||||||||
\(599\) | −2.43769e15 | −1.29161 | −0.645804 | − | 0.763503i | \(-0.723478\pi\) | ||||
−0.645804 | + | 0.763503i | \(0.723478\pi\) | |||||||
\(600\) | 3.73870e15 | 1.96286 | ||||||||
\(601\) | 3.49824e15 | 1.81987 | 0.909935 | − | 0.414751i | \(-0.136131\pi\) | ||||
0.909935 | + | 0.414751i | \(0.136131\pi\) | |||||||
\(602\) | 1.14476e15 | 0.590113 | ||||||||
\(603\) | 2.17426e14 | 0.111062 | ||||||||
\(604\) | −7.57065e15 | −3.83204 | ||||||||
\(605\) | 1.07196e14 | 0.0537680 | ||||||||
\(606\) | 3.38510e14 | 0.168257 | ||||||||
\(607\) | 3.57626e14 | 0.176153 | 0.0880766 | − | 0.996114i | \(-0.471928\pi\) | ||||
0.0880766 | + | 0.996114i | \(0.471928\pi\) | |||||||
\(608\) | 1.48277e16 | 7.23774 | ||||||||
\(609\) | −9.73282e14 | −0.470808 | ||||||||
\(610\) | 5.22759e14 | 0.250604 | ||||||||
\(611\) | 1.95256e14 | 0.0927636 | ||||||||
\(612\) | −2.33785e15 | −1.10074 | ||||||||
\(613\) | 8.75613e14 | 0.408582 | 0.204291 | − | 0.978910i | \(-0.434511\pi\) | ||||
0.204291 | + | 0.978910i | \(0.434511\pi\) | |||||||
\(614\) | 5.52941e15 | 2.55713 | ||||||||
\(615\) | 1.43722e14 | 0.0658736 | ||||||||
\(616\) | 4.10414e15 | 1.86435 | ||||||||
\(617\) | 3.35302e15 | 1.50962 | 0.754809 | − | 0.655944i | \(-0.227729\pi\) | ||||
0.754809 | + | 0.655944i | \(0.227729\pi\) | |||||||
\(618\) | 9.45527e14 | 0.421927 | ||||||||
\(619\) | 2.89676e15 | 1.28119 | 0.640595 | − | 0.767879i | \(-0.278688\pi\) | ||||
0.640595 | + | 0.767879i | \(0.278688\pi\) | |||||||
\(620\) | −1.27514e14 | −0.0558991 | ||||||||
\(621\) | 5.10927e14 | 0.222001 | ||||||||
\(622\) | 5.22274e15 | 2.24932 | ||||||||
\(623\) | −8.59889e14 | −0.367078 | ||||||||
\(624\) | 7.52470e15 | 3.18401 | ||||||||
\(625\) | 2.21053e15 | 0.927162 | ||||||||
\(626\) | −4.14160e15 | −1.72191 | ||||||||
\(627\) | −2.73844e15 | −1.12858 | ||||||||
\(628\) | −6.41458e15 | −2.62054 | ||||||||
\(629\) | 9.28245e14 | 0.375910 | ||||||||
\(630\) | 1.16721e14 | 0.0468571 | ||||||||
\(631\) | −8.50201e14 | −0.338345 | −0.169173 | − | 0.985586i | \(-0.554110\pi\) | ||||
−0.169173 | + | 0.985586i | \(0.554110\pi\) | |||||||
\(632\) | −1.08442e16 | −4.27811 | ||||||||
\(633\) | 2.72545e15 | 1.06591 | ||||||||
\(634\) | −6.36297e15 | −2.46700 | ||||||||
\(635\) | 6.29426e13 | 0.0241930 | ||||||||
\(636\) | 3.32769e15 | 1.26803 | ||||||||
\(637\) | −2.87607e15 | −1.08651 | ||||||||
\(638\) | −1.06468e16 | −3.98754 | ||||||||
\(639\) | −1.02580e15 | −0.380897 | ||||||||
\(640\) | −1.78418e15 | −0.656824 | ||||||||
\(641\) | 2.26152e15 | 0.825432 | 0.412716 | − | 0.910860i | \(-0.364580\pi\) | ||||
0.412716 | + | 0.910860i | \(0.364580\pi\) | |||||||
\(642\) | 4.82276e15 | 1.74523 | ||||||||
\(643\) | 2.45342e15 | 0.880261 | 0.440130 | − | 0.897934i | \(-0.354932\pi\) | ||||
0.440130 | + | 0.897934i | \(0.354932\pi\) | |||||||
\(644\) | −4.17547e15 | −1.48536 | ||||||||
\(645\) | 1.68210e14 | 0.0593300 | ||||||||
\(646\) | −1.11105e16 | −3.88558 | ||||||||
\(647\) | −3.49515e15 | −1.21197 | −0.605986 | − | 0.795475i | \(-0.707221\pi\) | ||||
−0.605986 | + | 0.795475i | \(0.707221\pi\) | |||||||
\(648\) | −1.12625e15 | −0.387232 | ||||||||
\(649\) | 4.42654e14 | 0.150910 | ||||||||
\(650\) | 7.75596e15 | 2.62187 | ||||||||
\(651\) | 1.01786e14 | 0.0341186 | ||||||||
\(652\) | 2.75322e15 | 0.915124 | ||||||||
\(653\) | −2.53333e15 | −0.834967 | −0.417483 | − | 0.908685i | \(-0.637088\pi\) | ||||
−0.417483 | + | 0.908685i | \(0.637088\pi\) | |||||||
\(654\) | 5.73365e15 | 1.87393 | ||||||||
\(655\) | 4.56658e14 | 0.148001 | ||||||||
\(656\) | 9.06423e15 | 2.91313 | ||||||||
\(657\) | 1.90316e15 | 0.606548 | ||||||||
\(658\) | 1.91016e14 | 0.0603709 | ||||||||
\(659\) | −4.97965e14 | −0.156074 | −0.0780368 | − | 0.996950i | \(-0.524865\pi\) | ||||
−0.0780368 | + | 0.996950i | \(0.524865\pi\) | |||||||
\(660\) | 9.39937e14 | 0.292151 | ||||||||
\(661\) | −2.54752e15 | −0.785253 | −0.392626 | − | 0.919698i | \(-0.628433\pi\) | ||||
−0.392626 | + | 0.919698i | \(0.628433\pi\) | |||||||
\(662\) | −8.51079e15 | −2.60166 | ||||||||
\(663\) | −3.11165e15 | −0.943337 | ||||||||
\(664\) | −1.61031e16 | −4.84157 | ||||||||
\(665\) | 4.08354e14 | 0.121764 | ||||||||
\(666\) | 6.96978e14 | 0.206116 | ||||||||
\(667\) | 6.94964e15 | 2.03831 | ||||||||
\(668\) | 7.21404e15 | 2.09849 | ||||||||
\(669\) | 4.56397e14 | 0.131674 | ||||||||
\(670\) | −3.54670e14 | −0.101488 | ||||||||
\(671\) | −3.36032e15 | −0.953688 | ||||||||
\(672\) | 4.06252e15 | 1.14357 | ||||||||
\(673\) | −5.08841e15 | −1.42069 | −0.710345 | − | 0.703853i | \(-0.751461\pi\) | ||||
−0.710345 | + | 0.703853i | \(0.751461\pi\) | |||||||
\(674\) | −3.29568e15 | −0.912673 | ||||||||
\(675\) | −6.83479e14 | −0.187739 | ||||||||
\(676\) | 9.27692e15 | 2.52753 | ||||||||
\(677\) | 3.00230e15 | 0.811366 | 0.405683 | − | 0.914014i | \(-0.367034\pi\) | ||||
0.405683 | + | 0.914014i | \(0.367034\pi\) | |||||||
\(678\) | 6.23932e15 | 1.67253 | ||||||||
\(679\) | −1.03965e15 | −0.276440 | ||||||||
\(680\) | 2.44675e15 | 0.645343 | ||||||||
\(681\) | 1.45944e15 | 0.381836 | ||||||||
\(682\) | 1.11344e15 | 0.288970 | ||||||||
\(683\) | −4.11320e14 | −0.105893 | −0.0529464 | − | 0.998597i | \(-0.516861\pi\) | ||||
−0.0529464 | + | 0.998597i | \(0.516861\pi\) | |||||||
\(684\) | −6.14132e15 | −1.56839 | ||||||||
\(685\) | −1.07784e14 | −0.0273060 | ||||||||
\(686\) | −6.38866e15 | −1.60556 | ||||||||
\(687\) | −1.78019e15 | −0.443818 | ||||||||
\(688\) | 1.06086e16 | 2.62375 | ||||||||
\(689\) | 4.42913e15 | 1.08671 | ||||||||
\(690\) | −8.33435e14 | −0.202863 | ||||||||
\(691\) | −1.49559e14 | −0.0361146 | −0.0180573 | − | 0.999837i | \(-0.505748\pi\) | ||||
−0.0180573 | + | 0.999837i | \(0.505748\pi\) | |||||||
\(692\) | 1.40723e16 | 3.37118 | ||||||||
\(693\) | −7.50286e14 | −0.178317 | ||||||||
\(694\) | 4.63638e15 | 1.09321 | ||||||||
\(695\) | −1.09595e15 | −0.256374 | ||||||||
\(696\) | −1.53192e16 | −3.55538 | ||||||||
\(697\) | −3.74829e15 | −0.863084 | ||||||||
\(698\) | −5.37379e15 | −1.22765 | ||||||||
\(699\) | −1.89314e14 | −0.0429100 | ||||||||
\(700\) | 5.58563e15 | 1.25612 | ||||||||
\(701\) | 7.18063e14 | 0.160219 | 0.0801094 | − | 0.996786i | \(-0.474473\pi\) | ||||
0.0801094 | + | 0.996786i | \(0.474473\pi\) | |||||||
\(702\) | −2.33640e15 | −0.517242 | ||||||||
\(703\) | 2.43842e15 | 0.535616 | ||||||||
\(704\) | 2.31940e16 | 5.05505 | ||||||||
\(705\) | 2.80677e13 | 0.00606970 | ||||||||
\(706\) | −1.79070e16 | −3.84235 | ||||||||
\(707\) | 3.24476e14 | 0.0690838 | ||||||||
\(708\) | 9.92708e14 | 0.209719 | ||||||||
\(709\) | 3.52396e15 | 0.738716 | 0.369358 | − | 0.929287i | \(-0.379578\pi\) | ||||
0.369358 | + | 0.929287i | \(0.379578\pi\) | |||||||
\(710\) | 1.67331e15 | 0.348060 | ||||||||
\(711\) | 1.98244e15 | 0.409183 | ||||||||
\(712\) | −1.35344e16 | −2.77205 | ||||||||
\(713\) | −7.26793e14 | −0.147713 | ||||||||
\(714\) | −3.04409e15 | −0.613927 | ||||||||
\(715\) | 1.25105e15 | 0.250375 | ||||||||
\(716\) | 3.22170e15 | 0.639828 | ||||||||
\(717\) | 3.46582e15 | 0.683047 | ||||||||
\(718\) | −6.43553e15 | −1.25864 | ||||||||
\(719\) | 4.02584e15 | 0.781353 | 0.390677 | − | 0.920528i | \(-0.372241\pi\) | ||||
0.390677 | + | 0.920528i | \(0.372241\pi\) | |||||||
\(720\) | 1.08166e15 | 0.208336 | ||||||||
\(721\) | 9.06328e14 | 0.173237 | ||||||||
\(722\) | −1.89232e16 | −3.58954 | ||||||||
\(723\) | 2.73579e15 | 0.515018 | ||||||||
\(724\) | −2.13140e16 | −3.98201 | ||||||||
\(725\) | −9.29671e15 | −1.72373 | ||||||||
\(726\) | −2.09915e15 | −0.386271 | ||||||||
\(727\) | −2.36147e15 | −0.431264 | −0.215632 | − | 0.976475i | \(-0.569181\pi\) | ||||
−0.215632 | + | 0.976475i | \(0.569181\pi\) | |||||||
\(728\) | 1.22505e16 | 2.22040 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | −3.10447e15 | −0.554258 | ||||||||
\(731\) | −4.38694e15 | −0.777349 | ||||||||
\(732\) | −7.53594e15 | −1.32534 | ||||||||
\(733\) | −4.82143e15 | −0.841597 | −0.420798 | − | 0.907154i | \(-0.638250\pi\) | ||||
−0.420798 | + | 0.907154i | \(0.638250\pi\) | |||||||
\(734\) | −9.49964e15 | −1.64581 | ||||||||
\(735\) | −4.13431e14 | −0.0710923 | ||||||||
\(736\) | −2.90081e16 | −4.95098 | ||||||||
\(737\) | 2.27983e15 | 0.386217 | ||||||||
\(738\) | −2.81442e15 | −0.473238 | ||||||||
\(739\) | −3.95517e15 | −0.660117 | −0.330058 | − | 0.943960i | \(-0.607068\pi\) | ||||
−0.330058 | + | 0.943960i | \(0.607068\pi\) | |||||||
\(740\) | −8.36956e14 | −0.138653 | ||||||||
\(741\) | −8.17403e15 | −1.34411 | ||||||||
\(742\) | 4.33295e15 | 0.707233 | ||||||||
\(743\) | 5.89583e15 | 0.955227 | 0.477614 | − | 0.878570i | \(-0.341502\pi\) | ||||
0.477614 | + | 0.878570i | \(0.341502\pi\) | |||||||
\(744\) | 1.60208e15 | 0.257652 | ||||||||
\(745\) | 1.36190e15 | 0.217413 | ||||||||
\(746\) | −1.61181e16 | −2.55417 | ||||||||
\(747\) | 2.94385e15 | 0.463075 | ||||||||
\(748\) | −2.45136e16 | −3.82780 | ||||||||
\(749\) | 4.62282e15 | 0.716568 | ||||||||
\(750\) | 2.25779e15 | 0.347413 | ||||||||
\(751\) | −3.65010e15 | −0.557551 | −0.278776 | − | 0.960356i | \(-0.589929\pi\) | ||||
−0.278776 | + | 0.960356i | \(0.589929\pi\) | |||||||
\(752\) | 1.77017e15 | 0.268421 | ||||||||
\(753\) | 1.92870e15 | 0.290330 | ||||||||
\(754\) | −3.17798e16 | −4.74907 | ||||||||
\(755\) | −1.44848e15 | −0.214884 | ||||||||
\(756\) | −1.68261e15 | −0.247807 | ||||||||
\(757\) | 5.88657e15 | 0.860666 | 0.430333 | − | 0.902670i | \(-0.358396\pi\) | ||||
0.430333 | + | 0.902670i | \(0.358396\pi\) | |||||||
\(758\) | −9.26669e15 | −1.34507 | ||||||||
\(759\) | 5.35735e15 | 0.772006 | ||||||||
\(760\) | 6.42740e15 | 0.919518 | ||||||||
\(761\) | 3.76203e14 | 0.0534327 | 0.0267164 | − | 0.999643i | \(-0.491495\pi\) | ||||
0.0267164 | + | 0.999643i | \(0.491495\pi\) | |||||||
\(762\) | −1.23257e15 | −0.173803 | ||||||||
\(763\) | 5.49595e15 | 0.769410 | ||||||||
\(764\) | 7.38458e15 | 1.02639 | ||||||||
\(765\) | −4.47295e14 | −0.0617243 | ||||||||
\(766\) | 7.10398e15 | 0.973293 | ||||||||
\(767\) | 1.32129e15 | 0.179731 | ||||||||
\(768\) | 1.62958e16 | 2.20085 | ||||||||
\(769\) | −4.85108e15 | −0.650494 | −0.325247 | − | 0.945629i | \(-0.605447\pi\) | ||||
−0.325247 | + | 0.945629i | \(0.605447\pi\) | |||||||
\(770\) | 1.22388e15 | 0.162945 | ||||||||
\(771\) | −4.19514e15 | −0.554558 | ||||||||
\(772\) | 3.94573e16 | 5.17883 | ||||||||
\(773\) | −3.67949e15 | −0.479513 | −0.239757 | − | 0.970833i | \(-0.577068\pi\) | ||||
−0.239757 | + | 0.970833i | \(0.577068\pi\) | |||||||
\(774\) | −3.29396e15 | −0.426229 | ||||||||
\(775\) | 9.72248e14 | 0.124916 | ||||||||
\(776\) | −1.63638e16 | −2.08758 | ||||||||
\(777\) | 6.68083e14 | 0.0846282 | ||||||||
\(778\) | −1.56806e16 | −1.97231 | ||||||||
\(779\) | −9.84642e15 | −1.22977 | ||||||||
\(780\) | 2.80564e15 | 0.347945 | ||||||||
\(781\) | −1.07561e16 | −1.32456 | ||||||||
\(782\) | 2.17361e16 | 2.65793 | ||||||||
\(783\) | 2.80054e15 | 0.340057 | ||||||||
\(784\) | −2.60741e16 | −3.14392 | ||||||||
\(785\) | −1.22729e15 | −0.146948 | ||||||||
\(786\) | −8.94245e15 | −1.06324 | ||||||||
\(787\) | 6.11674e15 | 0.722203 | 0.361101 | − | 0.932527i | \(-0.382401\pi\) | ||||
0.361101 | + | 0.932527i | \(0.382401\pi\) | |||||||
\(788\) | 4.44836e16 | 5.21561 | ||||||||
\(789\) | −2.82278e15 | −0.328665 | ||||||||
\(790\) | −3.23380e15 | −0.373908 | ||||||||
\(791\) | 5.98066e15 | 0.686718 | ||||||||
\(792\) | −1.18093e16 | −1.34659 | ||||||||
\(793\) | −1.00303e16 | −1.13582 | ||||||||
\(794\) | 1.59392e15 | 0.179248 | ||||||||
\(795\) | 6.36680e14 | 0.0711053 | ||||||||
\(796\) | −2.28631e16 | −2.53579 | ||||||||
\(797\) | −6.01045e15 | −0.662043 | −0.331021 | − | 0.943623i | \(-0.607393\pi\) | ||||
−0.331021 | + | 0.943623i | \(0.607393\pi\) | |||||||
\(798\) | −7.99654e15 | −0.874755 | ||||||||
\(799\) | −7.32008e14 | −0.0795259 | ||||||||
\(800\) | 3.88048e16 | 4.18688 | ||||||||
\(801\) | 2.47426e15 | 0.265134 | ||||||||
\(802\) | 1.81769e16 | 1.93446 | ||||||||
\(803\) | 1.99557e16 | 2.10926 | ||||||||
\(804\) | 5.11282e15 | 0.536726 | ||||||||
\(805\) | −7.98883e14 | −0.0832925 | ||||||||
\(806\) | 3.32353e15 | 0.344157 | ||||||||
\(807\) | −3.69950e15 | −0.380486 | ||||||||
\(808\) | 5.10718e15 | 0.521697 | ||||||||
\(809\) | 6.30966e15 | 0.640161 | 0.320080 | − | 0.947390i | \(-0.396290\pi\) | ||||
0.320080 | + | 0.947390i | \(0.396290\pi\) | |||||||
\(810\) | −3.35854e14 | −0.0338441 | ||||||||
\(811\) | 7.52302e15 | 0.752970 | 0.376485 | − | 0.926423i | \(-0.377133\pi\) | ||||
0.376485 | + | 0.926423i | \(0.377133\pi\) | |||||||
\(812\) | −2.28869e16 | −2.27525 | ||||||||
\(813\) | 8.81846e15 | 0.870752 | ||||||||
\(814\) | 7.30820e15 | 0.716764 | ||||||||
\(815\) | 5.26768e14 | 0.0513160 | ||||||||
\(816\) | −2.82099e16 | −2.72964 | ||||||||
\(817\) | −1.15241e16 | −1.10761 | ||||||||
\(818\) | 1.94976e16 | 1.86140 | ||||||||
\(819\) | −2.23954e15 | −0.212372 | ||||||||
\(820\) | 3.37966e15 | 0.318344 | ||||||||
\(821\) | 1.66550e16 | 1.55832 | 0.779160 | − | 0.626825i | \(-0.215646\pi\) | ||||
0.779160 | + | 0.626825i | \(0.215646\pi\) | |||||||
\(822\) | 2.11067e15 | 0.196167 | ||||||||
\(823\) | −1.22782e16 | −1.13354 | −0.566768 | − | 0.823877i | \(-0.691806\pi\) | ||||
−0.566768 | + | 0.823877i | \(0.691806\pi\) | |||||||
\(824\) | 1.42654e16 | 1.30823 | ||||||||
\(825\) | −7.16666e15 | −0.652860 | ||||||||
\(826\) | 1.29260e15 | 0.116969 | ||||||||
\(827\) | −2.18763e16 | −1.96650 | −0.983248 | − | 0.182270i | \(-0.941655\pi\) | ||||
−0.983248 | + | 0.182270i | \(0.941655\pi\) | |||||||
\(828\) | 1.20146e16 | 1.07285 | ||||||||
\(829\) | 1.22692e16 | 1.08835 | 0.544173 | − | 0.838973i | \(-0.316843\pi\) | ||||
0.544173 | + | 0.838973i | \(0.316843\pi\) | |||||||
\(830\) | −4.80206e15 | −0.423154 | ||||||||
\(831\) | −7.09157e15 | −0.620779 | ||||||||
\(832\) | 6.92322e16 | 6.02046 | ||||||||
\(833\) | 1.07823e16 | 0.931460 | ||||||||
\(834\) | 2.14613e16 | 1.84180 | ||||||||
\(835\) | 1.38025e15 | 0.117674 | ||||||||
\(836\) | −6.43951e16 | −5.45404 | ||||||||
\(837\) | −2.92880e14 | −0.0246433 | ||||||||
\(838\) | −6.12864e15 | −0.512297 | ||||||||
\(839\) | −2.00159e15 | −0.166220 | −0.0831102 | − | 0.996540i | \(-0.526485\pi\) | ||||
−0.0831102 | + | 0.996540i | \(0.526485\pi\) | |||||||
\(840\) | 1.76099e15 | 0.145285 | ||||||||
\(841\) | 2.58925e16 | 2.12224 | ||||||||
\(842\) | 2.35948e16 | 1.92132 | ||||||||
\(843\) | −7.49373e14 | −0.0606243 | ||||||||
\(844\) | 6.40896e16 | 5.15115 | ||||||||
\(845\) | 1.77493e15 | 0.141733 | ||||||||
\(846\) | −5.49633e14 | −0.0436049 | ||||||||
\(847\) | −2.01213e15 | −0.158598 | ||||||||
\(848\) | 4.01539e16 | 3.14449 | ||||||||
\(849\) | 1.13246e16 | 0.881111 | ||||||||
\(850\) | −2.90769e16 | −2.24773 | ||||||||
\(851\) | −4.77040e15 | −0.366388 | ||||||||
\(852\) | −2.41219e16 | −1.84074 | ||||||||
\(853\) | 1.90656e16 | 1.44555 | 0.722773 | − | 0.691086i | \(-0.242867\pi\) | ||||
0.722773 | + | 0.691086i | \(0.242867\pi\) | |||||||
\(854\) | −9.81247e15 | −0.739197 | ||||||||
\(855\) | −1.17500e15 | −0.0879480 | ||||||||
\(856\) | 7.27621e16 | 5.41128 | ||||||||
\(857\) | −1.44564e16 | −1.06823 | −0.534117 | − | 0.845411i | \(-0.679356\pi\) | ||||
−0.534117 | + | 0.845411i | \(0.679356\pi\) | |||||||
\(858\) | −2.44985e16 | −1.79870 | ||||||||
\(859\) | −1.39840e16 | −1.02017 | −0.510083 | − | 0.860125i | \(-0.670385\pi\) | ||||
−0.510083 | + | 0.860125i | \(0.670385\pi\) | |||||||
\(860\) | 3.95550e15 | 0.286722 | ||||||||
\(861\) | −2.69775e15 | −0.194305 | ||||||||
\(862\) | −8.48728e15 | −0.607405 | ||||||||
\(863\) | −2.45715e16 | −1.74732 | −0.873660 | − | 0.486538i | \(-0.838260\pi\) | ||||
−0.873660 | + | 0.486538i | \(0.838260\pi\) | |||||||
\(864\) | −1.16896e16 | −0.825985 | ||||||||
\(865\) | 2.69243e15 | 0.189041 | ||||||||
\(866\) | −2.02049e16 | −1.40964 | ||||||||
\(867\) | 3.33743e15 | 0.231370 | ||||||||
\(868\) | 2.39351e15 | 0.164884 | ||||||||
\(869\) | 2.07870e16 | 1.42293 | ||||||||
\(870\) | −4.56830e15 | −0.310741 | ||||||||
\(871\) | 6.80512e15 | 0.459976 | ||||||||
\(872\) | 8.65049e16 | 5.81032 | ||||||||
\(873\) | 2.99149e15 | 0.199668 | ||||||||
\(874\) | 5.70987e16 | 3.78716 | ||||||||
\(875\) | 2.16419e15 | 0.142643 | ||||||||
\(876\) | 4.47531e16 | 2.93124 | ||||||||
\(877\) | 5.40079e15 | 0.351528 | 0.175764 | − | 0.984432i | \(-0.443760\pi\) | ||||
0.175764 | + | 0.984432i | \(0.443760\pi\) | |||||||
\(878\) | −3.20113e16 | −2.07054 | ||||||||
\(879\) | 6.10997e15 | 0.392735 | ||||||||
\(880\) | 1.13418e16 | 0.724484 | ||||||||
\(881\) | −2.10009e16 | −1.33312 | −0.666562 | − | 0.745449i | \(-0.732235\pi\) | ||||
−0.666562 | + | 0.745449i | \(0.732235\pi\) | |||||||
\(882\) | 8.09596e15 | 0.510730 | ||||||||
\(883\) | −1.28931e16 | −0.808303 | −0.404152 | − | 0.914692i | \(-0.632433\pi\) | ||||
−0.404152 | + | 0.914692i | \(0.632433\pi\) | |||||||
\(884\) | −7.31712e16 | −4.55882 | ||||||||
\(885\) | 1.89933e14 | 0.0117601 | ||||||||
\(886\) | −1.75687e16 | −1.08107 | ||||||||
\(887\) | −5.76541e13 | −0.00352574 | −0.00176287 | − | 0.999998i | \(-0.500561\pi\) | ||||
−0.00176287 | + | 0.999998i | \(0.500561\pi\) | |||||||
\(888\) | 1.05155e16 | 0.639083 | ||||||||
\(889\) | −1.18147e15 | −0.0713611 | ||||||||
\(890\) | −4.03606e15 | −0.242277 | ||||||||
\(891\) | 2.15888e15 | 0.128796 | ||||||||
\(892\) | 1.07323e16 | 0.636333 | ||||||||
\(893\) | −1.92292e15 | −0.113313 | ||||||||
\(894\) | −2.66693e16 | −1.56190 | ||||||||
\(895\) | 6.16401e14 | 0.0358787 | ||||||||
\(896\) | 3.34900e16 | 1.93741 | ||||||||
\(897\) | 1.59913e16 | 0.919442 | ||||||||
\(898\) | 2.75366e16 | 1.57359 | ||||||||
\(899\) | −3.98376e15 | −0.226264 | ||||||||
\(900\) | −1.60722e16 | −0.907278 | ||||||||
\(901\) | −1.66047e16 | −0.931631 | ||||||||
\(902\) | −2.95108e16 | −1.64568 | ||||||||
\(903\) | −3.15740e15 | −0.175004 | ||||||||
\(904\) | 9.41341e16 | 5.18586 | ||||||||
\(905\) | −4.07796e15 | −0.223293 | ||||||||
\(906\) | 2.83646e16 | 1.54373 | ||||||||
\(907\) | −2.25546e16 | −1.22010 | −0.610049 | − | 0.792364i | \(-0.708850\pi\) | ||||
−0.610049 | + | 0.792364i | \(0.708850\pi\) | |||||||
\(908\) | 3.43191e16 | 1.84528 | ||||||||
\(909\) | −9.33653e14 | −0.0498981 | ||||||||
\(910\) | 3.65319e15 | 0.194064 | ||||||||
\(911\) | 1.05516e16 | 0.557143 | 0.278571 | − | 0.960416i | \(-0.410139\pi\) | ||||
0.278571 | + | 0.960416i | \(0.410139\pi\) | |||||||
\(912\) | −7.41048e16 | −3.88933 | ||||||||
\(913\) | 3.08679e16 | 1.61034 | ||||||||
\(914\) | 8.18505e15 | 0.424441 | ||||||||
\(915\) | −1.44184e15 | −0.0743190 | ||||||||
\(916\) | −4.18616e16 | −2.14482 | ||||||||
\(917\) | −8.57173e15 | −0.436553 | ||||||||
\(918\) | 8.75910e15 | 0.443430 | ||||||||
\(919\) | 5.16429e15 | 0.259881 | 0.129941 | − | 0.991522i | \(-0.458521\pi\) | ||||
0.129941 | + | 0.991522i | \(0.458521\pi\) | |||||||
\(920\) | −1.25742e16 | −0.628997 | ||||||||
\(921\) | −1.52508e16 | −0.758341 | ||||||||
\(922\) | −8.40711e15 | −0.415553 | ||||||||
\(923\) | −3.21060e16 | −1.57753 | ||||||||
\(924\) | −1.76431e16 | −0.861747 | ||||||||
\(925\) | 6.38147e15 | 0.309843 | ||||||||
\(926\) | −7.12855e15 | −0.344065 | ||||||||
\(927\) | −2.60788e15 | −0.125127 | ||||||||
\(928\) | −1.59002e17 | −7.58381 | ||||||||
\(929\) | −1.35039e16 | −0.640286 | −0.320143 | − | 0.947369i | \(-0.603731\pi\) | ||||
−0.320143 | + | 0.947369i | \(0.603731\pi\) | |||||||
\(930\) | 4.77752e14 | 0.0225189 | ||||||||
\(931\) | 2.83242e16 | 1.32719 | ||||||||
\(932\) | −4.45176e15 | −0.207369 | ||||||||
\(933\) | −1.44050e16 | −0.667058 | ||||||||
\(934\) | −3.87659e16 | −1.78461 | ||||||||
\(935\) | −4.69014e15 | −0.214646 | ||||||||
\(936\) | −3.52498e16 | −1.60376 | ||||||||
\(937\) | 4.28349e16 | 1.93745 | 0.968724 | − | 0.248142i | \(-0.0798198\pi\) | ||||
0.968724 | + | 0.248142i | \(0.0798198\pi\) | |||||||
\(938\) | 6.65735e15 | 0.299355 | ||||||||
\(939\) | 1.14230e16 | 0.510648 | ||||||||
\(940\) | 6.60018e14 | 0.0293328 | ||||||||
\(941\) | 2.49613e16 | 1.10287 | 0.551435 | − | 0.834218i | \(-0.314081\pi\) | ||||
0.551435 | + | 0.834218i | \(0.314081\pi\) | |||||||
\(942\) | 2.40332e16 | 1.05568 | ||||||||
\(943\) | 1.92630e16 | 0.841222 | ||||||||
\(944\) | 1.19786e16 | 0.520068 | ||||||||
\(945\) | −3.21931e14 | −0.0138959 | ||||||||
\(946\) | −3.45390e16 | −1.48221 | ||||||||
\(947\) | −1.25777e15 | −0.0536630 | −0.0268315 | − | 0.999640i | \(-0.508542\pi\) | ||||
−0.0268315 | + | 0.999640i | \(0.508542\pi\) | |||||||
\(948\) | 4.66175e16 | 1.97744 | ||||||||
\(949\) | 5.95660e16 | 2.51208 | ||||||||
\(950\) | −7.63823e16 | −3.20267 | ||||||||
\(951\) | 1.75499e16 | 0.731613 | ||||||||
\(952\) | −4.59269e16 | −1.90355 | ||||||||
\(953\) | 1.31585e16 | 0.542246 | 0.271123 | − | 0.962545i | \(-0.412605\pi\) | ||||
0.271123 | + | 0.962545i | \(0.412605\pi\) | |||||||
\(954\) | −1.24677e16 | −0.510823 | ||||||||
\(955\) | 1.41287e15 | 0.0575553 | ||||||||
\(956\) | 8.14995e16 | 3.30093 | ||||||||
\(957\) | 2.93652e16 | 1.18254 | ||||||||
\(958\) | 2.27308e16 | 0.910132 | ||||||||
\(959\) | 2.02317e15 | 0.0805434 | ||||||||
\(960\) | 9.95201e15 | 0.393930 | ||||||||
\(961\) | −2.49919e16 | −0.983603 | ||||||||
\(962\) | 2.18144e16 | 0.853651 | ||||||||
\(963\) | −1.33018e16 | −0.517565 | ||||||||
\(964\) | 6.43328e16 | 2.48891 | ||||||||
\(965\) | 7.54927e15 | 0.290405 | ||||||||
\(966\) | 1.56440e16 | 0.598377 | ||||||||
\(967\) | −2.13925e16 | −0.813609 | −0.406804 | − | 0.913515i | \(-0.633357\pi\) | ||||
−0.406804 | + | 0.913515i | \(0.633357\pi\) | |||||||
\(968\) | −3.16704e16 | −1.19767 | ||||||||
\(969\) | 3.06442e16 | 1.15231 | ||||||||
\(970\) | −4.87979e15 | −0.182455 | ||||||||
\(971\) | −3.57391e16 | −1.32873 | −0.664366 | − | 0.747407i | \(-0.731299\pi\) | ||||
−0.664366 | + | 0.747407i | \(0.731299\pi\) | |||||||
\(972\) | 4.84157e15 | 0.178987 | ||||||||
\(973\) | 2.05716e16 | 0.756217 | ||||||||
\(974\) | −9.41935e16 | −3.44308 | ||||||||
\(975\) | −2.13919e16 | −0.777542 | ||||||||
\(976\) | −9.09332e16 | −3.28661 | ||||||||
\(977\) | −2.16860e16 | −0.779400 | −0.389700 | − | 0.920942i | \(-0.627421\pi\) | ||||
−0.389700 | + | 0.920942i | \(0.627421\pi\) | |||||||
\(978\) | −1.03154e16 | −0.368656 | ||||||||
\(979\) | 2.59439e16 | 0.922001 | ||||||||
\(980\) | −9.72192e15 | −0.343565 | ||||||||
\(981\) | −1.58141e16 | −0.555732 | ||||||||
\(982\) | 2.68563e16 | 0.938499 | ||||||||
\(983\) | 4.70805e16 | 1.63605 | 0.818025 | − | 0.575183i | \(-0.195069\pi\) | ||||
0.818025 | + | 0.575183i | \(0.195069\pi\) | |||||||
\(984\) | −4.24619e16 | −1.46732 | ||||||||
\(985\) | 8.51094e15 | 0.292468 | ||||||||
\(986\) | 1.19142e17 | 4.07137 | ||||||||
\(987\) | −5.26846e14 | −0.0179036 | ||||||||
\(988\) | −1.92214e17 | −6.49564 | ||||||||
\(989\) | 2.25452e16 | 0.757659 | ||||||||
\(990\) | −3.52162e15 | −0.117692 | ||||||||
\(991\) | 2.59802e14 | 0.00863452 | 0.00431726 | − | 0.999991i | \(-0.498626\pi\) | ||||
0.00431726 | + | 0.999991i | \(0.498626\pi\) | |||||||
\(992\) | 1.66284e16 | 0.549586 | ||||||||
\(993\) | 2.34738e16 | 0.771548 | ||||||||
\(994\) | −3.14088e16 | −1.02666 | ||||||||
\(995\) | −4.37435e15 | −0.142196 | ||||||||
\(996\) | 6.92252e16 | 2.23788 | ||||||||
\(997\) | −1.73914e16 | −0.559128 | −0.279564 | − | 0.960127i | \(-0.590190\pi\) | ||||
−0.279564 | + | 0.960127i | \(0.590190\pi\) | |||||||
\(998\) | −1.54773e14 | −0.00494854 | ||||||||
\(999\) | −1.92235e15 | −0.0611256 |
(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 | 177.12.a.d.1.1 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.12.a.d.1.1 | ✓ | 28 | 1.1 | even | 1 | trivial |