Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,8,Mod(1,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.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: | \(170.562223914\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 367021x^{4} - 17702143x^{3} + 34815194576x^{2} + 1422988371620x - 933871993059968 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-309.150\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.00000 | 0.707107 | ||||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | −307.150 | −1.09889 | −0.549447 | − | 0.835528i | \(-0.685162\pi\) | ||||
−0.549447 | + | 0.835528i | \(0.685162\pi\) | |||||||
\(6\) | −216.000 | −0.408248 | ||||||||
\(7\) | 343.000 | 0.377964 | ||||||||
\(8\) | 512.000 | 0.353553 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | −2457.20 | −0.777036 | ||||||||
\(11\) | −7421.86 | −1.68127 | −0.840636 | − | 0.541600i | \(-0.817819\pi\) | ||||
−0.840636 | + | 0.541600i | \(0.817819\pi\) | |||||||
\(12\) | −1728.00 | −0.288675 | ||||||||
\(13\) | −2197.00 | −0.277350 | ||||||||
\(14\) | 2744.00 | 0.267261 | ||||||||
\(15\) | 8293.06 | 0.634447 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | −5217.71 | −0.257578 | −0.128789 | − | 0.991672i | \(-0.541109\pi\) | ||||
−0.128789 | + | 0.991672i | \(0.541109\pi\) | |||||||
\(18\) | 5832.00 | 0.235702 | ||||||||
\(19\) | −610.200 | −0.0204096 | −0.0102048 | − | 0.999948i | \(-0.503248\pi\) | ||||
−0.0102048 | + | 0.999948i | \(0.503248\pi\) | |||||||
\(20\) | −19657.6 | −0.549447 | ||||||||
\(21\) | −9261.00 | −0.218218 | ||||||||
\(22\) | −59374.9 | −1.18884 | ||||||||
\(23\) | −53724.9 | −0.920721 | −0.460360 | − | 0.887732i | \(-0.652280\pi\) | ||||
−0.460360 | + | 0.887732i | \(0.652280\pi\) | |||||||
\(24\) | −13824.0 | −0.204124 | ||||||||
\(25\) | 16216.4 | 0.207569 | ||||||||
\(26\) | −17576.0 | −0.196116 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | 21952.0 | 0.188982 | ||||||||
\(29\) | 55488.3 | 0.422482 | 0.211241 | − | 0.977434i | \(-0.432250\pi\) | ||||
0.211241 | + | 0.977434i | \(0.432250\pi\) | |||||||
\(30\) | 66344.5 | 0.448622 | ||||||||
\(31\) | −13695.2 | −0.0825664 | −0.0412832 | − | 0.999147i | \(-0.513145\pi\) | ||||
−0.0412832 | + | 0.999147i | \(0.513145\pi\) | |||||||
\(32\) | 32768.0 | 0.176777 | ||||||||
\(33\) | 200390. | 0.970683 | ||||||||
\(34\) | −41741.7 | −0.182135 | ||||||||
\(35\) | −105353. | −0.415343 | ||||||||
\(36\) | 46656.0 | 0.166667 | ||||||||
\(37\) | −143013. | −0.464161 | −0.232080 | − | 0.972697i | \(-0.574553\pi\) | ||||
−0.232080 | + | 0.972697i | \(0.574553\pi\) | |||||||
\(38\) | −4881.60 | −0.0144318 | ||||||||
\(39\) | 59319.0 | 0.160128 | ||||||||
\(40\) | −157261. | −0.388518 | ||||||||
\(41\) | −303729. | −0.688246 | −0.344123 | − | 0.938925i | \(-0.611824\pi\) | ||||
−0.344123 | + | 0.938925i | \(0.611824\pi\) | |||||||
\(42\) | −74088.0 | −0.154303 | ||||||||
\(43\) | −68421.4 | −0.131236 | −0.0656180 | − | 0.997845i | \(-0.520902\pi\) | ||||
−0.0656180 | + | 0.997845i | \(0.520902\pi\) | |||||||
\(44\) | −474999. | −0.840636 | ||||||||
\(45\) | −223913. | −0.366298 | ||||||||
\(46\) | −429799. | −0.651048 | ||||||||
\(47\) | −927094. | −1.30251 | −0.651255 | − | 0.758859i | \(-0.725757\pi\) | ||||
−0.651255 | + | 0.758859i | \(0.725757\pi\) | |||||||
\(48\) | −110592. | −0.144338 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | 129731. | 0.146774 | ||||||||
\(51\) | 140878. | 0.148713 | ||||||||
\(52\) | −140608. | −0.138675 | ||||||||
\(53\) | 1.71806e6 | 1.58515 | 0.792577 | − | 0.609772i | \(-0.208739\pi\) | ||||
0.792577 | + | 0.609772i | \(0.208739\pi\) | |||||||
\(54\) | −157464. | −0.136083 | ||||||||
\(55\) | 2.27963e6 | 1.84754 | ||||||||
\(56\) | 175616. | 0.133631 | ||||||||
\(57\) | 16475.4 | 0.0117835 | ||||||||
\(58\) | 443906. | 0.298740 | ||||||||
\(59\) | −316898. | −0.200880 | −0.100440 | − | 0.994943i | \(-0.532025\pi\) | ||||
−0.100440 | + | 0.994943i | \(0.532025\pi\) | |||||||
\(60\) | 530756. | 0.317224 | ||||||||
\(61\) | 1.21928e6 | 0.687778 | 0.343889 | − | 0.939010i | \(-0.388256\pi\) | ||||
0.343889 | + | 0.939010i | \(0.388256\pi\) | |||||||
\(62\) | −109562. | −0.0583833 | ||||||||
\(63\) | 250047. | 0.125988 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | 674809. | 0.304779 | ||||||||
\(66\) | 1.60312e6 | 0.686377 | ||||||||
\(67\) | −2.28233e6 | −0.927081 | −0.463540 | − | 0.886076i | \(-0.653421\pi\) | ||||
−0.463540 | + | 0.886076i | \(0.653421\pi\) | |||||||
\(68\) | −333934. | −0.128789 | ||||||||
\(69\) | 1.45057e6 | 0.531578 | ||||||||
\(70\) | −842821. | −0.293692 | ||||||||
\(71\) | −2.74579e6 | −0.910466 | −0.455233 | − | 0.890372i | \(-0.650444\pi\) | ||||
−0.455233 | + | 0.890372i | \(0.650444\pi\) | |||||||
\(72\) | 373248. | 0.117851 | ||||||||
\(73\) | −3.47442e6 | −1.04533 | −0.522664 | − | 0.852539i | \(-0.675062\pi\) | ||||
−0.522664 | + | 0.852539i | \(0.675062\pi\) | |||||||
\(74\) | −1.14410e6 | −0.328211 | ||||||||
\(75\) | −437841. | −0.119840 | ||||||||
\(76\) | −39052.8 | −0.0102048 | ||||||||
\(77\) | −2.54570e6 | −0.635461 | ||||||||
\(78\) | 474552. | 0.113228 | ||||||||
\(79\) | 4.82863e6 | 1.10187 | 0.550933 | − | 0.834549i | \(-0.314272\pi\) | ||||
0.550933 | + | 0.834549i | \(0.314272\pi\) | |||||||
\(80\) | −1.25809e6 | −0.274724 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −2.42984e6 | −0.486663 | ||||||||
\(83\) | −2.84197e6 | −0.545564 | −0.272782 | − | 0.962076i | \(-0.587944\pi\) | ||||
−0.272782 | + | 0.962076i | \(0.587944\pi\) | |||||||
\(84\) | −592704. | −0.109109 | ||||||||
\(85\) | 1.60262e6 | 0.283051 | ||||||||
\(86\) | −547372. | −0.0927978 | ||||||||
\(87\) | −1.49818e6 | −0.243920 | ||||||||
\(88\) | −3.79999e6 | −0.594420 | ||||||||
\(89\) | −419990. | −0.0631501 | −0.0315751 | − | 0.999501i | \(-0.510052\pi\) | ||||
−0.0315751 | + | 0.999501i | \(0.510052\pi\) | |||||||
\(90\) | −1.79130e6 | −0.259012 | ||||||||
\(91\) | −753571. | −0.104828 | ||||||||
\(92\) | −3.43839e6 | −0.460360 | ||||||||
\(93\) | 369771. | 0.0476697 | ||||||||
\(94\) | −7.41675e6 | −0.921014 | ||||||||
\(95\) | 187423. | 0.0224280 | ||||||||
\(96\) | −884736. | −0.102062 | ||||||||
\(97\) | −5.79829e6 | −0.645058 | −0.322529 | − | 0.946560i | \(-0.604533\pi\) | ||||
−0.322529 | + | 0.946560i | \(0.604533\pi\) | |||||||
\(98\) | 941192. | 0.101015 | ||||||||
\(99\) | −5.41053e6 | −0.560424 | ||||||||
\(100\) | 1.03785e6 | 0.103785 | ||||||||
\(101\) | 1.36733e7 | 1.32053 | 0.660267 | − | 0.751031i | \(-0.270443\pi\) | ||||
0.660267 | + | 0.751031i | \(0.270443\pi\) | |||||||
\(102\) | 1.12703e6 | 0.105156 | ||||||||
\(103\) | 8.83659e6 | 0.796809 | 0.398405 | − | 0.917210i | \(-0.369564\pi\) | ||||
0.398405 | + | 0.917210i | \(0.369564\pi\) | |||||||
\(104\) | −1.12486e6 | −0.0980581 | ||||||||
\(105\) | 2.84452e6 | 0.239798 | ||||||||
\(106\) | 1.37444e7 | 1.12087 | ||||||||
\(107\) | −8.19534e6 | −0.646731 | −0.323366 | − | 0.946274i | \(-0.604814\pi\) | ||||
−0.323366 | + | 0.946274i | \(0.604814\pi\) | |||||||
\(108\) | −1.25971e6 | −0.0962250 | ||||||||
\(109\) | 7.31130e6 | 0.540757 | 0.270378 | − | 0.962754i | \(-0.412851\pi\) | ||||
0.270378 | + | 0.962754i | \(0.412851\pi\) | |||||||
\(110\) | 1.82370e7 | 1.30641 | ||||||||
\(111\) | 3.86134e6 | 0.267983 | ||||||||
\(112\) | 1.40493e6 | 0.0944911 | ||||||||
\(113\) | −9.07202e6 | −0.591466 | −0.295733 | − | 0.955271i | \(-0.595564\pi\) | ||||
−0.295733 | + | 0.955271i | \(0.595564\pi\) | |||||||
\(114\) | 131803. | 0.00833219 | ||||||||
\(115\) | 1.65016e7 | 1.01177 | ||||||||
\(116\) | 3.55125e6 | 0.211241 | ||||||||
\(117\) | −1.60161e6 | −0.0924500 | ||||||||
\(118\) | −2.53519e6 | −0.142044 | ||||||||
\(119\) | −1.78968e6 | −0.0973553 | ||||||||
\(120\) | 4.24605e6 | 0.224311 | ||||||||
\(121\) | 3.55968e7 | 1.82668 | ||||||||
\(122\) | 9.75423e6 | 0.486333 | ||||||||
\(123\) | 8.20069e6 | 0.397359 | ||||||||
\(124\) | −876495. | −0.0412832 | ||||||||
\(125\) | 1.90153e7 | 0.870798 | ||||||||
\(126\) | 2.00038e6 | 0.0890871 | ||||||||
\(127\) | 3.47437e7 | 1.50509 | 0.752545 | − | 0.658541i | \(-0.228826\pi\) | ||||
0.752545 | + | 0.658541i | \(0.228826\pi\) | |||||||
\(128\) | 2.09715e6 | 0.0883883 | ||||||||
\(129\) | 1.84738e6 | 0.0757691 | ||||||||
\(130\) | 5.39847e6 | 0.215511 | ||||||||
\(131\) | 928307. | 0.0360780 | 0.0180390 | − | 0.999837i | \(-0.494258\pi\) | ||||
0.0180390 | + | 0.999837i | \(0.494258\pi\) | |||||||
\(132\) | 1.28250e7 | 0.485342 | ||||||||
\(133\) | −209299. | −0.00771411 | ||||||||
\(134\) | −1.82587e7 | −0.655545 | ||||||||
\(135\) | 6.04564e6 | 0.211482 | ||||||||
\(136\) | −2.67147e6 | −0.0910676 | ||||||||
\(137\) | 8.16328e6 | 0.271233 | 0.135617 | − | 0.990761i | \(-0.456698\pi\) | ||||
0.135617 | + | 0.990761i | \(0.456698\pi\) | |||||||
\(138\) | 1.16046e7 | 0.375883 | ||||||||
\(139\) | −1.18165e7 | −0.373196 | −0.186598 | − | 0.982436i | \(-0.559746\pi\) | ||||
−0.186598 | + | 0.982436i | \(0.559746\pi\) | |||||||
\(140\) | −6.74256e6 | −0.207672 | ||||||||
\(141\) | 2.50315e7 | 0.752005 | ||||||||
\(142\) | −2.19664e7 | −0.643797 | ||||||||
\(143\) | 1.63058e7 | 0.466301 | ||||||||
\(144\) | 2.98598e6 | 0.0833333 | ||||||||
\(145\) | −1.70432e7 | −0.464263 | ||||||||
\(146\) | −2.77954e7 | −0.739158 | ||||||||
\(147\) | −3.17652e6 | −0.0824786 | ||||||||
\(148\) | −9.15281e6 | −0.232080 | ||||||||
\(149\) | 2.13672e7 | 0.529170 | 0.264585 | − | 0.964362i | \(-0.414765\pi\) | ||||
0.264585 | + | 0.964362i | \(0.414765\pi\) | |||||||
\(150\) | −3.50273e6 | −0.0847398 | ||||||||
\(151\) | 4.40020e7 | 1.04005 | 0.520023 | − | 0.854152i | \(-0.325923\pi\) | ||||
0.520023 | + | 0.854152i | \(0.325923\pi\) | |||||||
\(152\) | −312422. | −0.00721588 | ||||||||
\(153\) | −3.80371e6 | −0.0858593 | ||||||||
\(154\) | −2.03656e7 | −0.449339 | ||||||||
\(155\) | 4.20650e6 | 0.0907318 | ||||||||
\(156\) | 3.79642e6 | 0.0800641 | ||||||||
\(157\) | 8.55801e7 | 1.76492 | 0.882458 | − | 0.470391i | \(-0.155887\pi\) | ||||
0.882458 | + | 0.470391i | \(0.155887\pi\) | |||||||
\(158\) | 3.86290e7 | 0.779137 | ||||||||
\(159\) | −4.63875e7 | −0.915189 | ||||||||
\(160\) | −1.00647e7 | −0.194259 | ||||||||
\(161\) | −1.84276e7 | −0.348000 | ||||||||
\(162\) | 4.25153e6 | 0.0785674 | ||||||||
\(163\) | 1.02567e8 | 1.85503 | 0.927513 | − | 0.373790i | \(-0.121942\pi\) | ||||
0.927513 | + | 0.373790i | \(0.121942\pi\) | |||||||
\(164\) | −1.94387e7 | −0.344123 | ||||||||
\(165\) | −6.15499e7 | −1.06668 | ||||||||
\(166\) | −2.27357e7 | −0.385772 | ||||||||
\(167\) | −4.69828e7 | −0.780605 | −0.390303 | − | 0.920687i | \(-0.627630\pi\) | ||||
−0.390303 | + | 0.920687i | \(0.627630\pi\) | |||||||
\(168\) | −4.74163e6 | −0.0771517 | ||||||||
\(169\) | 4.82681e6 | 0.0769231 | ||||||||
\(170\) | 1.28210e7 | 0.200147 | ||||||||
\(171\) | −444836. | −0.00680320 | ||||||||
\(172\) | −4.37897e6 | −0.0656180 | ||||||||
\(173\) | 2.45043e7 | 0.359816 | 0.179908 | − | 0.983683i | \(-0.442420\pi\) | ||||
0.179908 | + | 0.983683i | \(0.442420\pi\) | |||||||
\(174\) | −1.19855e7 | −0.172478 | ||||||||
\(175\) | 5.56221e6 | 0.0784538 | ||||||||
\(176\) | −3.03999e7 | −0.420318 | ||||||||
\(177\) | 8.55625e6 | 0.115978 | ||||||||
\(178\) | −3.35992e6 | −0.0446539 | ||||||||
\(179\) | −2.71333e7 | −0.353604 | −0.176802 | − | 0.984246i | \(-0.556575\pi\) | ||||
−0.176802 | + | 0.984246i | \(0.556575\pi\) | |||||||
\(180\) | −1.43304e7 | −0.183149 | ||||||||
\(181\) | −9.04524e7 | −1.13382 | −0.566911 | − | 0.823779i | \(-0.691862\pi\) | ||||
−0.566911 | + | 0.823779i | \(0.691862\pi\) | |||||||
\(182\) | −6.02857e6 | −0.0741249 | ||||||||
\(183\) | −3.29205e7 | −0.397089 | ||||||||
\(184\) | −2.75071e7 | −0.325524 | ||||||||
\(185\) | 4.39264e7 | 0.510064 | ||||||||
\(186\) | 2.95817e6 | 0.0337076 | ||||||||
\(187\) | 3.87251e7 | 0.433059 | ||||||||
\(188\) | −5.93340e7 | −0.651255 | ||||||||
\(189\) | −6.75127e6 | −0.0727393 | ||||||||
\(190\) | 1.49939e6 | 0.0158590 | ||||||||
\(191\) | 1.61288e8 | 1.67489 | 0.837443 | − | 0.546525i | \(-0.184049\pi\) | ||||
0.837443 | + | 0.546525i | \(0.184049\pi\) | |||||||
\(192\) | −7.07789e6 | −0.0721688 | ||||||||
\(193\) | 4.29648e7 | 0.430192 | 0.215096 | − | 0.976593i | \(-0.430994\pi\) | ||||
0.215096 | + | 0.976593i | \(0.430994\pi\) | |||||||
\(194\) | −4.63863e7 | −0.456125 | ||||||||
\(195\) | −1.82199e7 | −0.175964 | ||||||||
\(196\) | 7.52954e6 | 0.0714286 | ||||||||
\(197\) | −1.01679e8 | −0.947548 | −0.473774 | − | 0.880646i | \(-0.657109\pi\) | ||||
−0.473774 | + | 0.880646i | \(0.657109\pi\) | |||||||
\(198\) | −4.32843e7 | −0.396280 | ||||||||
\(199\) | 7.99607e7 | 0.719268 | 0.359634 | − | 0.933093i | \(-0.382901\pi\) | ||||
0.359634 | + | 0.933093i | \(0.382901\pi\) | |||||||
\(200\) | 8.30277e6 | 0.0733868 | ||||||||
\(201\) | 6.16230e7 | 0.535250 | ||||||||
\(202\) | 1.09387e8 | 0.933758 | ||||||||
\(203\) | 1.90325e7 | 0.159683 | ||||||||
\(204\) | 9.01621e6 | 0.0743564 | ||||||||
\(205\) | 9.32906e7 | 0.756309 | ||||||||
\(206\) | 7.06927e7 | 0.563429 | ||||||||
\(207\) | −3.91654e7 | −0.306907 | ||||||||
\(208\) | −8.99891e6 | −0.0693375 | ||||||||
\(209\) | 4.52882e6 | 0.0343141 | ||||||||
\(210\) | 2.27562e7 | 0.169563 | ||||||||
\(211\) | 2.05436e7 | 0.150552 | 0.0752761 | − | 0.997163i | \(-0.476016\pi\) | ||||
0.0752761 | + | 0.997163i | \(0.476016\pi\) | |||||||
\(212\) | 1.09956e8 | 0.792577 | ||||||||
\(213\) | 7.41365e7 | 0.525658 | ||||||||
\(214\) | −6.55627e7 | −0.457308 | ||||||||
\(215\) | 2.10157e7 | 0.144214 | ||||||||
\(216\) | −1.00777e7 | −0.0680414 | ||||||||
\(217\) | −4.69746e6 | −0.0312072 | ||||||||
\(218\) | 5.84904e7 | 0.382373 | ||||||||
\(219\) | 9.38094e7 | 0.603520 | ||||||||
\(220\) | 1.45896e8 | 0.923771 | ||||||||
\(221\) | 1.14633e7 | 0.0714393 | ||||||||
\(222\) | 3.08907e7 | 0.189493 | ||||||||
\(223\) | 660460. | 0.00398822 | 0.00199411 | − | 0.999998i | \(-0.499365\pi\) | ||||
0.00199411 | + | 0.999998i | \(0.499365\pi\) | |||||||
\(224\) | 1.12394e7 | 0.0668153 | ||||||||
\(225\) | 1.18217e7 | 0.0691898 | ||||||||
\(226\) | −7.25762e7 | −0.418229 | ||||||||
\(227\) | −2.60405e8 | −1.47761 | −0.738804 | − | 0.673920i | \(-0.764609\pi\) | ||||
−0.738804 | + | 0.673920i | \(0.764609\pi\) | |||||||
\(228\) | 1.05443e6 | 0.00589175 | ||||||||
\(229\) | 1.41759e8 | 0.780057 | 0.390028 | − | 0.920803i | \(-0.372465\pi\) | ||||
0.390028 | + | 0.920803i | \(0.372465\pi\) | |||||||
\(230\) | 1.32013e8 | 0.715433 | ||||||||
\(231\) | 6.87338e7 | 0.366884 | ||||||||
\(232\) | 2.84100e7 | 0.149370 | ||||||||
\(233\) | 1.36610e7 | 0.0707518 | 0.0353759 | − | 0.999374i | \(-0.488737\pi\) | ||||
0.0353759 | + | 0.999374i | \(0.488737\pi\) | |||||||
\(234\) | −1.28129e7 | −0.0653720 | ||||||||
\(235\) | 2.84757e8 | 1.43132 | ||||||||
\(236\) | −2.02815e7 | −0.100440 | ||||||||
\(237\) | −1.30373e8 | −0.636163 | ||||||||
\(238\) | −1.43174e7 | −0.0688406 | ||||||||
\(239\) | −7.19950e7 | −0.341122 | −0.170561 | − | 0.985347i | \(-0.554558\pi\) | ||||
−0.170561 | + | 0.985347i | \(0.554558\pi\) | |||||||
\(240\) | 3.39684e7 | 0.158612 | ||||||||
\(241\) | 3.34392e8 | 1.53885 | 0.769425 | − | 0.638737i | \(-0.220543\pi\) | ||||
0.769425 | + | 0.638737i | \(0.220543\pi\) | |||||||
\(242\) | 2.84774e8 | 1.29166 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | 7.80338e7 | 0.343889 | ||||||||
\(245\) | −3.61359e7 | −0.156985 | ||||||||
\(246\) | 6.56056e7 | 0.280975 | ||||||||
\(247\) | 1.34061e6 | 0.00566061 | ||||||||
\(248\) | −7.01196e6 | −0.0291916 | ||||||||
\(249\) | 7.67331e7 | 0.314981 | ||||||||
\(250\) | 1.52122e8 | 0.615747 | ||||||||
\(251\) | −8.40775e6 | −0.0335600 | −0.0167800 | − | 0.999859i | \(-0.505341\pi\) | ||||
−0.0167800 | + | 0.999859i | \(0.505341\pi\) | |||||||
\(252\) | 1.60030e7 | 0.0629941 | ||||||||
\(253\) | 3.98738e8 | 1.54798 | ||||||||
\(254\) | 2.77949e8 | 1.06426 | ||||||||
\(255\) | −4.32708e7 | −0.163420 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | 1.07446e8 | 0.394842 | 0.197421 | − | 0.980319i | \(-0.436743\pi\) | ||||
0.197421 | + | 0.980319i | \(0.436743\pi\) | |||||||
\(258\) | 1.47790e7 | 0.0535768 | ||||||||
\(259\) | −4.90534e7 | −0.175436 | ||||||||
\(260\) | 4.31878e7 | 0.152389 | ||||||||
\(261\) | 4.04509e7 | 0.140827 | ||||||||
\(262\) | 7.42646e6 | 0.0255110 | ||||||||
\(263\) | 6.92726e7 | 0.234810 | 0.117405 | − | 0.993084i | \(-0.462542\pi\) | ||||
0.117405 | + | 0.993084i | \(0.462542\pi\) | |||||||
\(264\) | 1.02600e8 | 0.343188 | ||||||||
\(265\) | −5.27701e8 | −1.74192 | ||||||||
\(266\) | −1.67439e6 | −0.00545470 | ||||||||
\(267\) | 1.13397e7 | 0.0364597 | ||||||||
\(268\) | −1.46069e8 | −0.463540 | ||||||||
\(269\) | 1.25605e8 | 0.393435 | 0.196718 | − | 0.980460i | \(-0.436972\pi\) | ||||
0.196718 | + | 0.980460i | \(0.436972\pi\) | |||||||
\(270\) | 4.83651e7 | 0.149541 | ||||||||
\(271\) | −3.20934e8 | −0.979543 | −0.489771 | − | 0.871851i | \(-0.662920\pi\) | ||||
−0.489771 | + | 0.871851i | \(0.662920\pi\) | |||||||
\(272\) | −2.13717e7 | −0.0643945 | ||||||||
\(273\) | 2.03464e7 | 0.0605228 | ||||||||
\(274\) | 6.53062e7 | 0.191791 | ||||||||
\(275\) | −1.20355e8 | −0.348981 | ||||||||
\(276\) | 9.28366e7 | 0.265789 | ||||||||
\(277\) | 6.25623e7 | 0.176861 | 0.0884307 | − | 0.996082i | \(-0.471815\pi\) | ||||
0.0884307 | + | 0.996082i | \(0.471815\pi\) | |||||||
\(278\) | −9.45321e7 | −0.263890 | ||||||||
\(279\) | −9.98382e6 | −0.0275221 | ||||||||
\(280\) | −5.39405e7 | −0.146846 | ||||||||
\(281\) | 5.22648e8 | 1.40520 | 0.702599 | − | 0.711586i | \(-0.252023\pi\) | ||||
0.702599 | + | 0.711586i | \(0.252023\pi\) | |||||||
\(282\) | 2.00252e8 | 0.531748 | ||||||||
\(283\) | −1.06892e8 | −0.280346 | −0.140173 | − | 0.990127i | \(-0.544766\pi\) | ||||
−0.140173 | + | 0.990127i | \(0.544766\pi\) | |||||||
\(284\) | −1.75731e8 | −0.455233 | ||||||||
\(285\) | −5.06042e6 | −0.0129488 | ||||||||
\(286\) | 1.30447e8 | 0.329725 | ||||||||
\(287\) | −1.04179e8 | −0.260132 | ||||||||
\(288\) | 2.38879e7 | 0.0589256 | ||||||||
\(289\) | −3.83114e8 | −0.933654 | ||||||||
\(290\) | −1.36346e8 | −0.328284 | ||||||||
\(291\) | 1.56554e8 | 0.372425 | ||||||||
\(292\) | −2.22363e8 | −0.522664 | ||||||||
\(293\) | −2.66459e8 | −0.618862 | −0.309431 | − | 0.950922i | \(-0.600139\pi\) | ||||
−0.309431 | + | 0.950922i | \(0.600139\pi\) | |||||||
\(294\) | −2.54122e7 | −0.0583212 | ||||||||
\(295\) | 9.73354e7 | 0.220746 | ||||||||
\(296\) | −7.32225e7 | −0.164106 | ||||||||
\(297\) | 1.46084e8 | 0.323561 | ||||||||
\(298\) | 1.70937e8 | 0.374180 | ||||||||
\(299\) | 1.18034e8 | 0.255362 | ||||||||
\(300\) | −2.80219e7 | −0.0599201 | ||||||||
\(301\) | −2.34686e7 | −0.0496025 | ||||||||
\(302\) | 3.52016e8 | 0.735424 | ||||||||
\(303\) | −3.69180e8 | −0.762410 | ||||||||
\(304\) | −2.49938e6 | −0.00510240 | ||||||||
\(305\) | −3.74502e8 | −0.755796 | ||||||||
\(306\) | −3.04297e7 | −0.0607117 | ||||||||
\(307\) | 5.30742e8 | 1.04688 | 0.523442 | − | 0.852061i | \(-0.324648\pi\) | ||||
0.523442 | + | 0.852061i | \(0.324648\pi\) | |||||||
\(308\) | −1.62925e8 | −0.317731 | ||||||||
\(309\) | −2.38588e8 | −0.460038 | ||||||||
\(310\) | 3.36520e7 | 0.0641571 | ||||||||
\(311\) | −3.44691e8 | −0.649784 | −0.324892 | − | 0.945751i | \(-0.605328\pi\) | ||||
−0.324892 | + | 0.945751i | \(0.605328\pi\) | |||||||
\(312\) | 3.03713e7 | 0.0566139 | ||||||||
\(313\) | 1.35845e8 | 0.250402 | 0.125201 | − | 0.992131i | \(-0.460042\pi\) | ||||
0.125201 | + | 0.992131i | \(0.460042\pi\) | |||||||
\(314\) | 6.84641e8 | 1.24798 | ||||||||
\(315\) | −7.68020e7 | −0.138448 | ||||||||
\(316\) | 3.09032e8 | 0.550933 | ||||||||
\(317\) | 1.85065e8 | 0.326301 | 0.163150 | − | 0.986601i | \(-0.447834\pi\) | ||||
0.163150 | + | 0.986601i | \(0.447834\pi\) | |||||||
\(318\) | −3.71100e8 | −0.647137 | ||||||||
\(319\) | −4.11826e8 | −0.710307 | ||||||||
\(320\) | −8.05176e7 | −0.137362 | ||||||||
\(321\) | 2.21274e8 | 0.373390 | ||||||||
\(322\) | −1.47421e8 | −0.246073 | ||||||||
\(323\) | 3.18385e6 | 0.00525707 | ||||||||
\(324\) | 3.40122e7 | 0.0555556 | ||||||||
\(325\) | −3.56273e7 | −0.0575694 | ||||||||
\(326\) | 8.20534e8 | 1.31170 | ||||||||
\(327\) | −1.97405e8 | −0.312206 | ||||||||
\(328\) | −1.55509e8 | −0.243332 | ||||||||
\(329\) | −3.17993e8 | −0.492303 | ||||||||
\(330\) | −4.92399e8 | −0.754256 | ||||||||
\(331\) | −9.81458e7 | −0.148756 | −0.0743779 | − | 0.997230i | \(-0.523697\pi\) | ||||
−0.0743779 | + | 0.997230i | \(0.523697\pi\) | |||||||
\(332\) | −1.81886e8 | −0.272782 | ||||||||
\(333\) | −1.04256e8 | −0.154720 | ||||||||
\(334\) | −3.75863e8 | −0.551971 | ||||||||
\(335\) | 7.01020e8 | 1.01876 | ||||||||
\(336\) | −3.79331e7 | −0.0545545 | ||||||||
\(337\) | 9.10127e8 | 1.29538 | 0.647690 | − | 0.761904i | \(-0.275735\pi\) | ||||
0.647690 | + | 0.761904i | \(0.275735\pi\) | |||||||
\(338\) | 3.86145e7 | 0.0543928 | ||||||||
\(339\) | 2.44945e8 | 0.341483 | ||||||||
\(340\) | 1.02568e8 | 0.141526 | ||||||||
\(341\) | 1.01644e8 | 0.138817 | ||||||||
\(342\) | −3.55869e6 | −0.00481059 | ||||||||
\(343\) | 4.03536e7 | 0.0539949 | ||||||||
\(344\) | −3.50318e7 | −0.0463989 | ||||||||
\(345\) | −4.45544e8 | −0.584149 | ||||||||
\(346\) | 1.96034e8 | 0.254428 | ||||||||
\(347\) | 2.62561e8 | 0.337348 | 0.168674 | − | 0.985672i | \(-0.446052\pi\) | ||||
0.168674 | + | 0.985672i | \(0.446052\pi\) | |||||||
\(348\) | −9.58837e7 | −0.121960 | ||||||||
\(349\) | −5.47050e8 | −0.688871 | −0.344435 | − | 0.938810i | \(-0.611930\pi\) | ||||
−0.344435 | + | 0.938810i | \(0.611930\pi\) | |||||||
\(350\) | 4.44977e7 | 0.0554752 | ||||||||
\(351\) | 4.32436e7 | 0.0533761 | ||||||||
\(352\) | −2.43199e8 | −0.297210 | ||||||||
\(353\) | 2.61210e8 | 0.316067 | 0.158033 | − | 0.987434i | \(-0.449485\pi\) | ||||
0.158033 | + | 0.987434i | \(0.449485\pi\) | |||||||
\(354\) | 6.84500e7 | 0.0820091 | ||||||||
\(355\) | 8.43372e8 | 1.00051 | ||||||||
\(356\) | −2.68794e7 | −0.0315751 | ||||||||
\(357\) | 4.83212e7 | 0.0562081 | ||||||||
\(358\) | −2.17066e8 | −0.250036 | ||||||||
\(359\) | 1.25452e9 | 1.43103 | 0.715513 | − | 0.698600i | \(-0.246193\pi\) | ||||
0.715513 | + | 0.698600i | \(0.246193\pi\) | |||||||
\(360\) | −1.14643e8 | −0.129506 | ||||||||
\(361\) | −8.93499e8 | −0.999583 | ||||||||
\(362\) | −7.23619e8 | −0.801733 | ||||||||
\(363\) | −9.61113e8 | −1.05463 | ||||||||
\(364\) | −4.82285e7 | −0.0524142 | ||||||||
\(365\) | 1.06717e9 | 1.14870 | ||||||||
\(366\) | −2.63364e8 | −0.280784 | ||||||||
\(367\) | −1.59118e9 | −1.68030 | −0.840150 | − | 0.542354i | \(-0.817533\pi\) | ||||
−0.840150 | + | 0.542354i | \(0.817533\pi\) | |||||||
\(368\) | −2.20057e8 | −0.230180 | ||||||||
\(369\) | −2.21419e8 | −0.229415 | ||||||||
\(370\) | 3.51411e8 | 0.360670 | ||||||||
\(371\) | 5.89293e8 | 0.599132 | ||||||||
\(372\) | 2.36654e7 | 0.0238349 | ||||||||
\(373\) | −8.48507e8 | −0.846592 | −0.423296 | − | 0.905991i | \(-0.639127\pi\) | ||||
−0.423296 | + | 0.905991i | \(0.639127\pi\) | |||||||
\(374\) | 3.09801e8 | 0.306219 | ||||||||
\(375\) | −5.13412e8 | −0.502755 | ||||||||
\(376\) | −4.74672e8 | −0.460507 | ||||||||
\(377\) | −1.21908e8 | −0.117175 | ||||||||
\(378\) | −5.40102e7 | −0.0514344 | ||||||||
\(379\) | 9.05904e8 | 0.854762 | 0.427381 | − | 0.904072i | \(-0.359436\pi\) | ||||
0.427381 | + | 0.904072i | \(0.359436\pi\) | |||||||
\(380\) | 1.19951e7 | 0.0112140 | ||||||||
\(381\) | −9.38079e8 | −0.868964 | ||||||||
\(382\) | 1.29030e9 | 1.18432 | ||||||||
\(383\) | 2.52031e8 | 0.229223 | 0.114612 | − | 0.993410i | \(-0.463438\pi\) | ||||
0.114612 | + | 0.993410i | \(0.463438\pi\) | |||||||
\(384\) | −5.66231e7 | −0.0510310 | ||||||||
\(385\) | 7.81912e8 | 0.698305 | ||||||||
\(386\) | 3.43718e8 | 0.304192 | ||||||||
\(387\) | −4.98792e7 | −0.0437453 | ||||||||
\(388\) | −3.71091e8 | −0.322529 | ||||||||
\(389\) | 1.22239e9 | 1.05290 | 0.526449 | − | 0.850207i | \(-0.323523\pi\) | ||||
0.526449 | + | 0.850207i | \(0.323523\pi\) | |||||||
\(390\) | −1.45759e8 | −0.124425 | ||||||||
\(391\) | 2.80321e8 | 0.237157 | ||||||||
\(392\) | 6.02363e7 | 0.0505076 | ||||||||
\(393\) | −2.50643e7 | −0.0208296 | ||||||||
\(394\) | −8.13435e8 | −0.670018 | ||||||||
\(395\) | −1.48312e9 | −1.21084 | ||||||||
\(396\) | −3.46274e8 | −0.280212 | ||||||||
\(397\) | −2.28816e9 | −1.83536 | −0.917678 | − | 0.397325i | \(-0.869939\pi\) | ||||
−0.917678 | + | 0.397325i | \(0.869939\pi\) | |||||||
\(398\) | 6.39686e8 | 0.508600 | ||||||||
\(399\) | 5.65106e6 | 0.00445374 | ||||||||
\(400\) | 6.64222e7 | 0.0518923 | ||||||||
\(401\) | −7.96685e8 | −0.616994 | −0.308497 | − | 0.951225i | \(-0.599826\pi\) | ||||
−0.308497 | + | 0.951225i | \(0.599826\pi\) | |||||||
\(402\) | 4.92984e8 | 0.378479 | ||||||||
\(403\) | 3.00884e7 | 0.0228998 | ||||||||
\(404\) | 8.75093e8 | 0.660267 | ||||||||
\(405\) | −1.63232e8 | −0.122099 | ||||||||
\(406\) | 1.52260e8 | 0.112913 | ||||||||
\(407\) | 1.06142e9 | 0.780381 | ||||||||
\(408\) | 7.21296e7 | 0.0525779 | ||||||||
\(409\) | −1.31730e9 | −0.952039 | −0.476019 | − | 0.879435i | \(-0.657921\pi\) | ||||
−0.476019 | + | 0.879435i | \(0.657921\pi\) | |||||||
\(410\) | 7.46325e8 | 0.534791 | ||||||||
\(411\) | −2.20408e8 | −0.156596 | ||||||||
\(412\) | 5.65542e8 | 0.398405 | ||||||||
\(413\) | −1.08696e8 | −0.0759257 | ||||||||
\(414\) | −3.13323e8 | −0.217016 | ||||||||
\(415\) | 8.72911e8 | 0.599517 | ||||||||
\(416\) | −7.19913e7 | −0.0490290 | ||||||||
\(417\) | 3.19046e8 | 0.215465 | ||||||||
\(418\) | 3.62305e7 | 0.0242637 | ||||||||
\(419\) | −4.85663e8 | −0.322541 | −0.161271 | − | 0.986910i | \(-0.551559\pi\) | ||||
−0.161271 | + | 0.986910i | \(0.551559\pi\) | |||||||
\(420\) | 1.82049e8 | 0.119899 | ||||||||
\(421\) | 1.18576e9 | 0.774482 | 0.387241 | − | 0.921979i | \(-0.373428\pi\) | ||||
0.387241 | + | 0.921979i | \(0.373428\pi\) | |||||||
\(422\) | 1.64349e8 | 0.106457 | ||||||||
\(423\) | −6.75852e8 | −0.434170 | ||||||||
\(424\) | 8.79644e8 | 0.560437 | ||||||||
\(425\) | −8.46122e7 | −0.0534653 | ||||||||
\(426\) | 5.93092e8 | 0.371696 | ||||||||
\(427\) | 4.18213e8 | 0.259956 | ||||||||
\(428\) | −5.24502e8 | −0.323366 | ||||||||
\(429\) | −4.40257e8 | −0.269219 | ||||||||
\(430\) | 1.68125e8 | 0.101975 | ||||||||
\(431\) | 1.24407e9 | 0.748472 | 0.374236 | − | 0.927334i | \(-0.377905\pi\) | ||||
0.374236 | + | 0.927334i | \(0.377905\pi\) | |||||||
\(432\) | −8.06216e7 | −0.0481125 | ||||||||
\(433\) | −2.23177e9 | −1.32112 | −0.660560 | − | 0.750773i | \(-0.729681\pi\) | ||||
−0.660560 | + | 0.750773i | \(0.729681\pi\) | |||||||
\(434\) | −3.75797e7 | −0.0220668 | ||||||||
\(435\) | 4.60168e8 | 0.268042 | ||||||||
\(436\) | 4.67923e8 | 0.270378 | ||||||||
\(437\) | 3.27829e7 | 0.0187915 | ||||||||
\(438\) | 7.50475e8 | 0.426753 | ||||||||
\(439\) | 8.05249e8 | 0.454260 | 0.227130 | − | 0.973864i | \(-0.427066\pi\) | ||||
0.227130 | + | 0.973864i | \(0.427066\pi\) | |||||||
\(440\) | 1.16717e9 | 0.653205 | ||||||||
\(441\) | 8.57661e7 | 0.0476190 | ||||||||
\(442\) | 9.17065e7 | 0.0505152 | ||||||||
\(443\) | 2.79456e9 | 1.52722 | 0.763608 | − | 0.645680i | \(-0.223426\pi\) | ||||
0.763608 | + | 0.645680i | \(0.223426\pi\) | |||||||
\(444\) | 2.47126e8 | 0.133992 | ||||||||
\(445\) | 1.29000e8 | 0.0693953 | ||||||||
\(446\) | 5.28368e6 | 0.00282010 | ||||||||
\(447\) | −5.76914e8 | −0.305516 | ||||||||
\(448\) | 8.99154e7 | 0.0472456 | ||||||||
\(449\) | −7.24424e8 | −0.377686 | −0.188843 | − | 0.982007i | \(-0.560474\pi\) | ||||
−0.188843 | + | 0.982007i | \(0.560474\pi\) | |||||||
\(450\) | 9.45738e7 | 0.0489245 | ||||||||
\(451\) | 2.25424e9 | 1.15713 | ||||||||
\(452\) | −5.80609e8 | −0.295733 | ||||||||
\(453\) | −1.18805e9 | −0.600471 | ||||||||
\(454\) | −2.08324e9 | −1.04483 | ||||||||
\(455\) | 2.31460e8 | 0.115195 | ||||||||
\(456\) | 8.43540e6 | 0.00416609 | ||||||||
\(457\) | −1.03355e9 | −0.506551 | −0.253275 | − | 0.967394i | \(-0.581508\pi\) | ||||
−0.253275 | + | 0.967394i | \(0.581508\pi\) | |||||||
\(458\) | 1.13407e9 | 0.551583 | ||||||||
\(459\) | 1.02700e8 | 0.0495709 | ||||||||
\(460\) | 1.05610e9 | 0.505887 | ||||||||
\(461\) | −7.46265e8 | −0.354764 | −0.177382 | − | 0.984142i | \(-0.556763\pi\) | ||||
−0.177382 | + | 0.984142i | \(0.556763\pi\) | |||||||
\(462\) | 5.49871e8 | 0.259426 | ||||||||
\(463\) | 3.01290e9 | 1.41075 | 0.705377 | − | 0.708832i | \(-0.250778\pi\) | ||||
0.705377 | + | 0.708832i | \(0.250778\pi\) | |||||||
\(464\) | 2.27280e8 | 0.105620 | ||||||||
\(465\) | −1.13575e8 | −0.0523840 | ||||||||
\(466\) | 1.09288e8 | 0.0500290 | ||||||||
\(467\) | −2.46352e9 | −1.11930 | −0.559650 | − | 0.828729i | \(-0.689064\pi\) | ||||
−0.559650 | + | 0.828729i | \(0.689064\pi\) | |||||||
\(468\) | −1.02503e8 | −0.0462250 | ||||||||
\(469\) | −7.82841e8 | −0.350404 | ||||||||
\(470\) | 2.27806e9 | 1.01210 | ||||||||
\(471\) | −2.31066e9 | −1.01897 | ||||||||
\(472\) | −1.62252e8 | −0.0710220 | ||||||||
\(473\) | 5.07814e8 | 0.220643 | ||||||||
\(474\) | −1.04298e9 | −0.449835 | ||||||||
\(475\) | −9.89522e6 | −0.00423641 | ||||||||
\(476\) | −1.14539e8 | −0.0486777 | ||||||||
\(477\) | 1.25246e9 | 0.528385 | ||||||||
\(478\) | −5.75960e8 | −0.241210 | ||||||||
\(479\) | 1.83805e7 | 0.00764158 | 0.00382079 | − | 0.999993i | \(-0.498784\pi\) | ||||
0.00382079 | + | 0.999993i | \(0.498784\pi\) | |||||||
\(480\) | 2.71747e8 | 0.112155 | ||||||||
\(481\) | 3.14199e8 | 0.128735 | ||||||||
\(482\) | 2.67514e9 | 1.08813 | ||||||||
\(483\) | 4.97546e8 | 0.200918 | ||||||||
\(484\) | 2.27819e9 | 0.913339 | ||||||||
\(485\) | 1.78095e9 | 0.708851 | ||||||||
\(486\) | −1.14791e8 | −0.0453609 | ||||||||
\(487\) | 4.42038e8 | 0.173424 | 0.0867118 | − | 0.996233i | \(-0.472364\pi\) | ||||
0.0867118 | + | 0.996233i | \(0.472364\pi\) | |||||||
\(488\) | 6.24271e8 | 0.243166 | ||||||||
\(489\) | −2.76930e9 | −1.07100 | ||||||||
\(490\) | −2.89087e8 | −0.111005 | ||||||||
\(491\) | 2.35072e9 | 0.896223 | 0.448112 | − | 0.893978i | \(-0.352097\pi\) | ||||
0.448112 | + | 0.893978i | \(0.352097\pi\) | |||||||
\(492\) | 5.24844e8 | 0.198679 | ||||||||
\(493\) | −2.89522e8 | −0.108822 | ||||||||
\(494\) | 1.07249e7 | 0.00400265 | ||||||||
\(495\) | 1.66185e9 | 0.615847 | ||||||||
\(496\) | −5.60957e7 | −0.0206416 | ||||||||
\(497\) | −9.41808e8 | −0.344124 | ||||||||
\(498\) | 6.13865e8 | 0.222725 | ||||||||
\(499\) | 1.15163e9 | 0.414917 | 0.207459 | − | 0.978244i | \(-0.433481\pi\) | ||||
0.207459 | + | 0.978244i | \(0.433481\pi\) | |||||||
\(500\) | 1.21698e9 | 0.435399 | ||||||||
\(501\) | 1.26854e9 | 0.450683 | ||||||||
\(502\) | −6.72620e7 | −0.0237305 | ||||||||
\(503\) | −3.31726e9 | −1.16223 | −0.581114 | − | 0.813822i | \(-0.697383\pi\) | ||||
−0.581114 | + | 0.813822i | \(0.697383\pi\) | |||||||
\(504\) | 1.28024e8 | 0.0445435 | ||||||||
\(505\) | −4.19977e9 | −1.45113 | ||||||||
\(506\) | 3.18991e9 | 1.09459 | ||||||||
\(507\) | −1.30324e8 | −0.0444116 | ||||||||
\(508\) | 2.22359e9 | 0.752545 | ||||||||
\(509\) | −4.32515e9 | −1.45375 | −0.726873 | − | 0.686772i | \(-0.759027\pi\) | ||||
−0.726873 | + | 0.686772i | \(0.759027\pi\) | |||||||
\(510\) | −3.46166e8 | −0.115555 | ||||||||
\(511\) | −1.19173e9 | −0.395097 | ||||||||
\(512\) | 1.34218e8 | 0.0441942 | ||||||||
\(513\) | 1.20106e7 | 0.00392783 | ||||||||
\(514\) | 8.59566e8 | 0.279195 | ||||||||
\(515\) | −2.71416e9 | −0.875609 | ||||||||
\(516\) | 1.18232e8 | 0.0378845 | ||||||||
\(517\) | 6.88076e9 | 2.18988 | ||||||||
\(518\) | −3.92427e8 | −0.124052 | ||||||||
\(519\) | −6.61615e8 | −0.207740 | ||||||||
\(520\) | 3.45502e8 | 0.107755 | ||||||||
\(521\) | 1.40342e9 | 0.434766 | 0.217383 | − | 0.976086i | \(-0.430248\pi\) | ||||
0.217383 | + | 0.976086i | \(0.430248\pi\) | |||||||
\(522\) | 3.23608e8 | 0.0995800 | ||||||||
\(523\) | 3.52019e9 | 1.07599 | 0.537997 | − | 0.842947i | \(-0.319181\pi\) | ||||
0.537997 | + | 0.842947i | \(0.319181\pi\) | |||||||
\(524\) | 5.94117e7 | 0.0180390 | ||||||||
\(525\) | −1.50180e8 | −0.0452953 | ||||||||
\(526\) | 5.54181e8 | 0.166036 | ||||||||
\(527\) | 7.14578e7 | 0.0212673 | ||||||||
\(528\) | 8.20798e8 | 0.242671 | ||||||||
\(529\) | −5.18464e8 | −0.152273 | ||||||||
\(530\) | −4.22161e9 | −1.23172 | ||||||||
\(531\) | −2.31019e8 | −0.0669602 | ||||||||
\(532\) | −1.33951e7 | −0.00385705 | ||||||||
\(533\) | 6.67294e8 | 0.190885 | ||||||||
\(534\) | 9.07179e7 | 0.0257809 | ||||||||
\(535\) | 2.51720e9 | 0.710689 | ||||||||
\(536\) | −1.16856e9 | −0.327773 | ||||||||
\(537\) | 7.32599e8 | 0.204153 | ||||||||
\(538\) | 1.00484e9 | 0.278201 | ||||||||
\(539\) | −8.73174e8 | −0.240182 | ||||||||
\(540\) | 3.86921e8 | 0.105741 | ||||||||
\(541\) | −2.84184e9 | −0.771629 | −0.385814 | − | 0.922576i | \(-0.626080\pi\) | ||||
−0.385814 | + | 0.922576i | \(0.626080\pi\) | |||||||
\(542\) | −2.56747e9 | −0.692641 | ||||||||
\(543\) | 2.44221e9 | 0.654612 | ||||||||
\(544\) | −1.70974e8 | −0.0455338 | ||||||||
\(545\) | −2.24567e9 | −0.594235 | ||||||||
\(546\) | 1.62771e8 | 0.0427960 | ||||||||
\(547\) | −1.55988e9 | −0.407507 | −0.203754 | − | 0.979022i | \(-0.565314\pi\) | ||||
−0.203754 | + | 0.979022i | \(0.565314\pi\) | |||||||
\(548\) | 5.22450e8 | 0.135617 | ||||||||
\(549\) | 8.88854e8 | 0.229259 | ||||||||
\(550\) | −9.62843e8 | −0.246767 | ||||||||
\(551\) | −3.38589e7 | −0.00862269 | ||||||||
\(552\) | 7.42693e8 | 0.187941 | ||||||||
\(553\) | 1.65622e9 | 0.416466 | ||||||||
\(554\) | 5.00498e8 | 0.125060 | ||||||||
\(555\) | −1.18601e9 | −0.294486 | ||||||||
\(556\) | −7.56256e8 | −0.186598 | ||||||||
\(557\) | 1.60240e9 | 0.392897 | 0.196448 | − | 0.980514i | \(-0.437059\pi\) | ||||
0.196448 | + | 0.980514i | \(0.437059\pi\) | |||||||
\(558\) | −7.98706e7 | −0.0194611 | ||||||||
\(559\) | 1.50322e8 | 0.0363983 | ||||||||
\(560\) | −4.31524e8 | −0.103836 | ||||||||
\(561\) | −1.04558e9 | −0.250027 | ||||||||
\(562\) | 4.18119e9 | 0.993625 | ||||||||
\(563\) | −6.56271e9 | −1.54990 | −0.774950 | − | 0.632023i | \(-0.782225\pi\) | ||||
−0.774950 | + | 0.632023i | \(0.782225\pi\) | |||||||
\(564\) | 1.60202e9 | 0.376002 | ||||||||
\(565\) | 2.78647e9 | 0.649958 | ||||||||
\(566\) | −8.55139e8 | −0.198235 | ||||||||
\(567\) | 1.82284e8 | 0.0419961 | ||||||||
\(568\) | −1.40585e9 | −0.321898 | ||||||||
\(569\) | −4.75022e9 | −1.08099 | −0.540493 | − | 0.841348i | \(-0.681762\pi\) | ||||
−0.540493 | + | 0.841348i | \(0.681762\pi\) | |||||||
\(570\) | −4.04834e7 | −0.00915619 | ||||||||
\(571\) | 4.04874e9 | 0.910108 | 0.455054 | − | 0.890464i | \(-0.349620\pi\) | ||||
0.455054 | + | 0.890464i | \(0.349620\pi\) | |||||||
\(572\) | 1.04357e9 | 0.233151 | ||||||||
\(573\) | −4.35478e9 | −0.966996 | ||||||||
\(574\) | −8.33434e8 | −0.183941 | ||||||||
\(575\) | −8.71221e8 | −0.191113 | ||||||||
\(576\) | 1.91103e8 | 0.0416667 | ||||||||
\(577\) | 2.39361e9 | 0.518726 | 0.259363 | − | 0.965780i | \(-0.416487\pi\) | ||||
0.259363 | + | 0.965780i | \(0.416487\pi\) | |||||||
\(578\) | −3.06491e9 | −0.660193 | ||||||||
\(579\) | −1.16005e9 | −0.248371 | ||||||||
\(580\) | −1.09077e9 | −0.232132 | ||||||||
\(581\) | −9.74794e8 | −0.206204 | ||||||||
\(582\) | 1.25243e9 | 0.263344 | ||||||||
\(583\) | −1.27512e10 | −2.66508 | ||||||||
\(584\) | −1.77890e9 | −0.369579 | ||||||||
\(585\) | 4.91936e8 | 0.101593 | ||||||||
\(586\) | −2.13167e9 | −0.437601 | ||||||||
\(587\) | −2.96727e9 | −0.605513 | −0.302757 | − | 0.953068i | \(-0.597907\pi\) | ||||
−0.302757 | + | 0.953068i | \(0.597907\pi\) | |||||||
\(588\) | −2.03297e8 | −0.0412393 | ||||||||
\(589\) | 8.35683e6 | 0.00168515 | ||||||||
\(590\) | 7.78683e8 | 0.156091 | ||||||||
\(591\) | 2.74534e9 | 0.547067 | ||||||||
\(592\) | −5.85780e8 | −0.116040 | ||||||||
\(593\) | −6.32481e8 | −0.124554 | −0.0622768 | − | 0.998059i | \(-0.519836\pi\) | ||||
−0.0622768 | + | 0.998059i | \(0.519836\pi\) | |||||||
\(594\) | 1.16868e9 | 0.228792 | ||||||||
\(595\) | 5.49699e8 | 0.106983 | ||||||||
\(596\) | 1.36750e9 | 0.264585 | ||||||||
\(597\) | −2.15894e9 | −0.415270 | ||||||||
\(598\) | 9.44268e8 | 0.180568 | ||||||||
\(599\) | −4.58618e9 | −0.871882 | −0.435941 | − | 0.899975i | \(-0.643584\pi\) | ||||
−0.435941 | + | 0.899975i | \(0.643584\pi\) | |||||||
\(600\) | −2.24175e8 | −0.0423699 | ||||||||
\(601\) | −6.49684e9 | −1.22079 | −0.610395 | − | 0.792097i | \(-0.708989\pi\) | ||||
−0.610395 | + | 0.792097i | \(0.708989\pi\) | |||||||
\(602\) | −1.87748e8 | −0.0350743 | ||||||||
\(603\) | −1.66382e9 | −0.309027 | ||||||||
\(604\) | 2.81612e9 | 0.520023 | ||||||||
\(605\) | −1.09336e10 | −2.00733 | ||||||||
\(606\) | −2.95344e9 | −0.539105 | ||||||||
\(607\) | 3.47548e9 | 0.630747 | 0.315373 | − | 0.948968i | \(-0.397870\pi\) | ||||
0.315373 | + | 0.948968i | \(0.397870\pi\) | |||||||
\(608\) | −1.99950e7 | −0.00360794 | ||||||||
\(609\) | −5.13877e8 | −0.0921931 | ||||||||
\(610\) | −2.99602e9 | −0.534428 | ||||||||
\(611\) | 2.03683e9 | 0.361252 | ||||||||
\(612\) | −2.43438e8 | −0.0429297 | ||||||||
\(613\) | −7.66711e8 | −0.134437 | −0.0672187 | − | 0.997738i | \(-0.521413\pi\) | ||||
−0.0672187 | + | 0.997738i | \(0.521413\pi\) | |||||||
\(614\) | 4.24593e9 | 0.740259 | ||||||||
\(615\) | −2.51885e9 | −0.436655 | ||||||||
\(616\) | −1.30340e9 | −0.224670 | ||||||||
\(617\) | −1.19940e9 | −0.205573 | −0.102787 | − | 0.994703i | \(-0.532776\pi\) | ||||
−0.102787 | + | 0.994703i | \(0.532776\pi\) | |||||||
\(618\) | −1.90870e9 | −0.325296 | ||||||||
\(619\) | −9.43634e9 | −1.59914 | −0.799569 | − | 0.600574i | \(-0.794939\pi\) | ||||
−0.799569 | + | 0.600574i | \(0.794939\pi\) | |||||||
\(620\) | 2.69216e8 | 0.0453659 | ||||||||
\(621\) | 1.05747e9 | 0.177193 | ||||||||
\(622\) | −2.75753e9 | −0.459467 | ||||||||
\(623\) | −1.44057e8 | −0.0238685 | ||||||||
\(624\) | 2.42971e8 | 0.0400320 | ||||||||
\(625\) | −7.10745e9 | −1.16448 | ||||||||
\(626\) | 1.08676e9 | 0.177061 | ||||||||
\(627\) | −1.22278e8 | −0.0198113 | ||||||||
\(628\) | 5.47713e9 | 0.882458 | ||||||||
\(629\) | 7.46199e8 | 0.119558 | ||||||||
\(630\) | −6.14416e8 | −0.0978973 | ||||||||
\(631\) | −3.35561e9 | −0.531703 | −0.265851 | − | 0.964014i | \(-0.585653\pi\) | ||||
−0.265851 | + | 0.964014i | \(0.585653\pi\) | |||||||
\(632\) | 2.47226e9 | 0.389569 | ||||||||
\(633\) | −5.54676e8 | −0.0869214 | ||||||||
\(634\) | 1.48052e9 | 0.230729 | ||||||||
\(635\) | −1.06715e10 | −1.65394 | ||||||||
\(636\) | −2.96880e9 | −0.457595 | ||||||||
\(637\) | −2.58475e8 | −0.0396214 | ||||||||
\(638\) | −3.29461e9 | −0.502263 | ||||||||
\(639\) | −2.00168e9 | −0.303489 | ||||||||
\(640\) | −6.44141e8 | −0.0971295 | ||||||||
\(641\) | −7.13903e9 | −1.07062 | −0.535311 | − | 0.844655i | \(-0.679805\pi\) | ||||
−0.535311 | + | 0.844655i | \(0.679805\pi\) | |||||||
\(642\) | 1.77019e9 | 0.264027 | ||||||||
\(643\) | −1.31859e9 | −0.195601 | −0.0978006 | − | 0.995206i | \(-0.531181\pi\) | ||||
−0.0978006 | + | 0.995206i | \(0.531181\pi\) | |||||||
\(644\) | −1.17937e9 | −0.174000 | ||||||||
\(645\) | −5.67423e8 | −0.0832622 | ||||||||
\(646\) | 2.54708e7 | 0.00371731 | ||||||||
\(647\) | 1.11425e10 | 1.61741 | 0.808703 | − | 0.588217i | \(-0.200170\pi\) | ||||
0.808703 | + | 0.588217i | \(0.200170\pi\) | |||||||
\(648\) | 2.72098e8 | 0.0392837 | ||||||||
\(649\) | 2.35197e9 | 0.337735 | ||||||||
\(650\) | −2.85019e8 | −0.0407077 | ||||||||
\(651\) | 1.26832e8 | 0.0180175 | ||||||||
\(652\) | 6.56427e9 | 0.927513 | ||||||||
\(653\) | −5.38939e8 | −0.0757432 | −0.0378716 | − | 0.999283i | \(-0.512058\pi\) | ||||
−0.0378716 | + | 0.999283i | \(0.512058\pi\) | |||||||
\(654\) | −1.57924e9 | −0.220763 | ||||||||
\(655\) | −2.85130e8 | −0.0396459 | ||||||||
\(656\) | −1.24408e9 | −0.172061 | ||||||||
\(657\) | −2.53285e9 | −0.348443 | ||||||||
\(658\) | −2.54395e9 | −0.348111 | ||||||||
\(659\) | −9.61970e9 | −1.30937 | −0.654685 | − | 0.755902i | \(-0.727199\pi\) | ||||
−0.654685 | + | 0.755902i | \(0.727199\pi\) | |||||||
\(660\) | −3.93919e9 | −0.533339 | ||||||||
\(661\) | −3.90947e9 | −0.526517 | −0.263258 | − | 0.964725i | \(-0.584797\pi\) | ||||
−0.263258 | + | 0.964725i | \(0.584797\pi\) | |||||||
\(662\) | −7.85166e8 | −0.105186 | ||||||||
\(663\) | −3.09509e8 | −0.0412455 | ||||||||
\(664\) | −1.45509e9 | −0.192886 | ||||||||
\(665\) | 6.42861e7 | 0.00847699 | ||||||||
\(666\) | −8.34050e8 | −0.109404 | ||||||||
\(667\) | −2.98110e9 | −0.388988 | ||||||||
\(668\) | −3.00690e9 | −0.390303 | ||||||||
\(669\) | −1.78324e7 | −0.00230260 | ||||||||
\(670\) | 5.60816e9 | 0.720375 | ||||||||
\(671\) | −9.04931e9 | −1.15634 | ||||||||
\(672\) | −3.03464e8 | −0.0385758 | ||||||||
\(673\) | −1.11640e10 | −1.41178 | −0.705889 | − | 0.708322i | \(-0.749452\pi\) | ||||
−0.705889 | + | 0.708322i | \(0.749452\pi\) | |||||||
\(674\) | 7.28101e9 | 0.915972 | ||||||||
\(675\) | −3.19186e8 | −0.0399467 | ||||||||
\(676\) | 3.08916e8 | 0.0384615 | ||||||||
\(677\) | 1.02373e10 | 1.26801 | 0.634007 | − | 0.773327i | \(-0.281409\pi\) | ||||
0.634007 | + | 0.773327i | \(0.281409\pi\) | |||||||
\(678\) | 1.95956e9 | 0.241465 | ||||||||
\(679\) | −1.98881e9 | −0.243809 | ||||||||
\(680\) | 8.20542e8 | 0.100074 | ||||||||
\(681\) | 7.03094e9 | 0.853097 | ||||||||
\(682\) | 8.13152e8 | 0.0981582 | ||||||||
\(683\) | −5.61057e9 | −0.673806 | −0.336903 | − | 0.941539i | \(-0.609379\pi\) | ||||
−0.336903 | + | 0.941539i | \(0.609379\pi\) | |||||||
\(684\) | −2.84695e7 | −0.00340160 | ||||||||
\(685\) | −2.50735e9 | −0.298057 | ||||||||
\(686\) | 3.22829e8 | 0.0381802 | ||||||||
\(687\) | −3.82749e9 | −0.450366 | ||||||||
\(688\) | −2.80254e8 | −0.0328090 | ||||||||
\(689\) | −3.77457e9 | −0.439643 | ||||||||
\(690\) | −3.56435e9 | −0.413055 | ||||||||
\(691\) | 1.11068e10 | 1.28061 | 0.640305 | − | 0.768121i | \(-0.278808\pi\) | ||||
0.640305 | + | 0.768121i | \(0.278808\pi\) | |||||||
\(692\) | 1.56827e9 | 0.179908 | ||||||||
\(693\) | −1.85581e9 | −0.211820 | ||||||||
\(694\) | 2.10049e9 | 0.238541 | ||||||||
\(695\) | 3.62944e9 | 0.410103 | ||||||||
\(696\) | −7.67070e8 | −0.0862388 | ||||||||
\(697\) | 1.58477e9 | 0.177277 | ||||||||
\(698\) | −4.37640e9 | −0.487105 | ||||||||
\(699\) | −3.68847e8 | −0.0408485 | ||||||||
\(700\) | 3.55981e8 | 0.0392269 | ||||||||
\(701\) | 3.53649e8 | 0.0387757 | 0.0193879 | − | 0.999812i | \(-0.493828\pi\) | ||||
0.0193879 | + | 0.999812i | \(0.493828\pi\) | |||||||
\(702\) | 3.45948e8 | 0.0377426 | ||||||||
\(703\) | 8.72663e7 | 0.00947334 | ||||||||
\(704\) | −1.94560e9 | −0.210159 | ||||||||
\(705\) | −7.68845e9 | −0.826374 | ||||||||
\(706\) | 2.08968e9 | 0.223493 | ||||||||
\(707\) | 4.68995e9 | 0.499115 | ||||||||
\(708\) | 5.47600e8 | 0.0579892 | ||||||||
\(709\) | 1.32419e10 | 1.39537 | 0.697683 | − | 0.716406i | \(-0.254214\pi\) | ||||
0.697683 | + | 0.716406i | \(0.254214\pi\) | |||||||
\(710\) | 6.74697e9 | 0.707465 | ||||||||
\(711\) | 3.52007e9 | 0.367289 | ||||||||
\(712\) | −2.15035e8 | −0.0223269 | ||||||||
\(713\) | 7.35775e8 | 0.0760206 | ||||||||
\(714\) | 3.86570e8 | 0.0397452 | ||||||||
\(715\) | −5.00834e9 | −0.512416 | ||||||||
\(716\) | −1.73653e9 | −0.176802 | ||||||||
\(717\) | 1.94387e9 | 0.196947 | ||||||||
\(718\) | 1.00362e10 | 1.01189 | ||||||||
\(719\) | −1.19576e10 | −1.19975 | −0.599877 | − | 0.800092i | \(-0.704784\pi\) | ||||
−0.599877 | + | 0.800092i | \(0.704784\pi\) | |||||||
\(720\) | −9.17146e8 | −0.0915745 | ||||||||
\(721\) | 3.03095e9 | 0.301166 | ||||||||
\(722\) | −7.14800e9 | −0.706812 | ||||||||
\(723\) | −9.02859e9 | −0.888456 | ||||||||
\(724\) | −5.78895e9 | −0.566911 | ||||||||
\(725\) | 8.99817e8 | 0.0876943 | ||||||||
\(726\) | −7.68891e9 | −0.745738 | ||||||||
\(727\) | −1.41066e10 | −1.36161 | −0.680805 | − | 0.732465i | \(-0.738370\pi\) | ||||
−0.680805 | + | 0.732465i | \(0.738370\pi\) | |||||||
\(728\) | −3.85828e8 | −0.0370625 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 8.53736e9 | 0.812257 | ||||||||
\(731\) | 3.57003e8 | 0.0338035 | ||||||||
\(732\) | −2.10691e9 | −0.198545 | ||||||||
\(733\) | 1.16573e10 | 1.09328 | 0.546642 | − | 0.837366i | \(-0.315906\pi\) | ||||
0.546642 | + | 0.837366i | \(0.315906\pi\) | |||||||
\(734\) | −1.27294e10 | −1.18815 | ||||||||
\(735\) | 9.75670e8 | 0.0906353 | ||||||||
\(736\) | −1.76046e9 | −0.162762 | ||||||||
\(737\) | 1.69392e10 | 1.55868 | ||||||||
\(738\) | −1.77135e9 | −0.162221 | ||||||||
\(739\) | −2.02090e9 | −0.184200 | −0.0920998 | − | 0.995750i | \(-0.529358\pi\) | ||||
−0.0920998 | + | 0.995750i | \(0.529358\pi\) | |||||||
\(740\) | 2.81129e9 | 0.255032 | ||||||||
\(741\) | −3.61965e7 | −0.00326815 | ||||||||
\(742\) | 4.71434e9 | 0.423650 | ||||||||
\(743\) | −1.27579e10 | −1.14108 | −0.570542 | − | 0.821268i | \(-0.693267\pi\) | ||||
−0.570542 | + | 0.821268i | \(0.693267\pi\) | |||||||
\(744\) | 1.89323e8 | 0.0168538 | ||||||||
\(745\) | −6.56293e9 | −0.581502 | ||||||||
\(746\) | −6.78805e9 | −0.598631 | ||||||||
\(747\) | −2.07179e9 | −0.181855 | ||||||||
\(748\) | 2.47841e9 | 0.216529 | ||||||||
\(749\) | −2.81100e9 | −0.244441 | ||||||||
\(750\) | −4.10730e9 | −0.355502 | ||||||||
\(751\) | −1.64992e9 | −0.142143 | −0.0710713 | − | 0.997471i | \(-0.522642\pi\) | ||||
−0.0710713 | + | 0.997471i | \(0.522642\pi\) | |||||||
\(752\) | −3.79738e9 | −0.325628 | ||||||||
\(753\) | 2.27009e8 | 0.0193759 | ||||||||
\(754\) | −9.75262e8 | −0.0828555 | ||||||||
\(755\) | −1.35152e10 | −1.14290 | ||||||||
\(756\) | −4.32081e8 | −0.0363696 | ||||||||
\(757\) | 2.32674e10 | 1.94945 | 0.974725 | − | 0.223406i | \(-0.0717177\pi\) | ||||
0.974725 | + | 0.223406i | \(0.0717177\pi\) | |||||||
\(758\) | 7.24723e9 | 0.604408 | ||||||||
\(759\) | −1.07659e10 | −0.893728 | ||||||||
\(760\) | 9.59607e7 | 0.00792950 | ||||||||
\(761\) | 7.25075e9 | 0.596399 | 0.298199 | − | 0.954504i | \(-0.403614\pi\) | ||||
0.298199 | + | 0.954504i | \(0.403614\pi\) | |||||||
\(762\) | −7.50463e9 | −0.614451 | ||||||||
\(763\) | 2.50778e9 | 0.204387 | ||||||||
\(764\) | 1.03224e10 | 0.837443 | ||||||||
\(765\) | 1.16831e9 | 0.0943504 | ||||||||
\(766\) | 2.01625e9 | 0.162085 | ||||||||
\(767\) | 6.96225e8 | 0.0557142 | ||||||||
\(768\) | −4.52985e8 | −0.0360844 | ||||||||
\(769\) | 6.28292e9 | 0.498218 | 0.249109 | − | 0.968475i | \(-0.419862\pi\) | ||||
0.249109 | + | 0.968475i | \(0.419862\pi\) | |||||||
\(770\) | 6.25529e9 | 0.493776 | ||||||||
\(771\) | −2.90104e9 | −0.227962 | ||||||||
\(772\) | 2.74975e9 | 0.215096 | ||||||||
\(773\) | 1.19758e10 | 0.932560 | 0.466280 | − | 0.884637i | \(-0.345594\pi\) | ||||
0.466280 | + | 0.884637i | \(0.345594\pi\) | |||||||
\(774\) | −3.99034e8 | −0.0309326 | ||||||||
\(775\) | −2.22087e8 | −0.0171383 | ||||||||
\(776\) | −2.96872e9 | −0.228063 | ||||||||
\(777\) | 1.32444e9 | 0.101288 | ||||||||
\(778\) | 9.77913e9 | 0.744512 | ||||||||
\(779\) | 1.85336e8 | 0.0140468 | ||||||||
\(780\) | −1.16607e9 | −0.0879820 | ||||||||
\(781\) | 2.03789e10 | 1.53074 | ||||||||
\(782\) | 2.24257e9 | 0.167696 | ||||||||
\(783\) | −1.09218e9 | −0.0813067 | ||||||||
\(784\) | 4.81890e8 | 0.0357143 | ||||||||
\(785\) | −2.62860e10 | −1.93946 | ||||||||
\(786\) | −2.00514e8 | −0.0147288 | ||||||||
\(787\) | 2.56707e9 | 0.187727 | 0.0938634 | − | 0.995585i | \(-0.470078\pi\) | ||||
0.0938634 | + | 0.995585i | \(0.470078\pi\) | |||||||
\(788\) | −6.50748e9 | −0.473774 | ||||||||
\(789\) | −1.87036e9 | −0.135568 | ||||||||
\(790\) | −1.18649e10 | −0.856190 | ||||||||
\(791\) | −3.11170e9 | −0.223553 | ||||||||
\(792\) | −2.77019e9 | −0.198140 | ||||||||
\(793\) | −2.67876e9 | −0.190755 | ||||||||
\(794\) | −1.83053e10 | −1.29779 | ||||||||
\(795\) | 1.42479e10 | 1.00570 | ||||||||
\(796\) | 5.11749e9 | 0.359634 | ||||||||
\(797\) | 7.83653e9 | 0.548302 | 0.274151 | − | 0.961687i | \(-0.411603\pi\) | ||||
0.274151 | + | 0.961687i | \(0.411603\pi\) | |||||||
\(798\) | 4.52085e7 | 0.00314927 | ||||||||
\(799\) | 4.83731e9 | 0.335498 | ||||||||
\(800\) | 5.31377e8 | 0.0366934 | ||||||||
\(801\) | −3.06173e8 | −0.0210500 | ||||||||
\(802\) | −6.37348e9 | −0.436281 | ||||||||
\(803\) | 2.57867e10 | 1.75748 | ||||||||
\(804\) | 3.94387e9 | 0.267625 | ||||||||
\(805\) | 5.66005e9 | 0.382415 | ||||||||
\(806\) | 2.40707e8 | 0.0161926 | ||||||||
\(807\) | −3.39133e9 | −0.227150 | ||||||||
\(808\) | 7.00074e9 | 0.466879 | ||||||||
\(809\) | 2.34797e10 | 1.55910 | 0.779548 | − | 0.626343i | \(-0.215449\pi\) | ||||
0.779548 | + | 0.626343i | \(0.215449\pi\) | |||||||
\(810\) | −1.30586e9 | −0.0863373 | ||||||||
\(811\) | −8.10949e8 | −0.0533851 | −0.0266926 | − | 0.999644i | \(-0.508498\pi\) | ||||
−0.0266926 | + | 0.999644i | \(0.508498\pi\) | |||||||
\(812\) | 1.21808e9 | 0.0798416 | ||||||||
\(813\) | 8.66522e9 | 0.565539 | ||||||||
\(814\) | 8.49136e9 | 0.551813 | ||||||||
\(815\) | −3.15034e10 | −2.03848 | ||||||||
\(816\) | 5.77037e8 | 0.0371782 | ||||||||
\(817\) | 4.17508e7 | 0.00267847 | ||||||||
\(818\) | −1.05384e10 | −0.673193 | ||||||||
\(819\) | −5.49353e8 | −0.0349428 | ||||||||
\(820\) | 5.97060e9 | 0.378155 | ||||||||
\(821\) | −3.19238e9 | −0.201332 | −0.100666 | − | 0.994920i | \(-0.532097\pi\) | ||||
−0.100666 | + | 0.994920i | \(0.532097\pi\) | |||||||
\(822\) | −1.76327e9 | −0.110730 | ||||||||
\(823\) | 2.55539e9 | 0.159793 | 0.0798966 | − | 0.996803i | \(-0.474541\pi\) | ||||
0.0798966 | + | 0.996803i | \(0.474541\pi\) | |||||||
\(824\) | 4.52433e9 | 0.281715 | ||||||||
\(825\) | 3.24960e9 | 0.201484 | ||||||||
\(826\) | −8.69569e8 | −0.0536876 | ||||||||
\(827\) | −1.25561e10 | −0.771945 | −0.385973 | − | 0.922510i | \(-0.626134\pi\) | ||||
−0.385973 | + | 0.922510i | \(0.626134\pi\) | |||||||
\(828\) | −2.50659e9 | −0.153453 | ||||||||
\(829\) | 1.96008e10 | 1.19490 | 0.597451 | − | 0.801906i | \(-0.296180\pi\) | ||||
0.597451 | + | 0.801906i | \(0.296180\pi\) | |||||||
\(830\) | 6.98329e9 | 0.423923 | ||||||||
\(831\) | −1.68918e9 | −0.102111 | ||||||||
\(832\) | −5.75930e8 | −0.0346688 | ||||||||
\(833\) | −6.13859e8 | −0.0367969 | ||||||||
\(834\) | 2.55237e9 | 0.152357 | ||||||||
\(835\) | 1.44308e10 | 0.857803 | ||||||||
\(836\) | 2.89844e8 | 0.0171571 | ||||||||
\(837\) | 2.69563e8 | 0.0158899 | ||||||||
\(838\) | −3.88530e9 | −0.228071 | ||||||||
\(839\) | −3.31937e10 | −1.94039 | −0.970194 | − | 0.242330i | \(-0.922088\pi\) | ||||
−0.970194 | + | 0.242330i | \(0.922088\pi\) | |||||||
\(840\) | 1.45639e9 | 0.0847816 | ||||||||
\(841\) | −1.41709e10 | −0.821509 | ||||||||
\(842\) | 9.48612e9 | 0.547641 | ||||||||
\(843\) | −1.41115e10 | −0.811291 | ||||||||
\(844\) | 1.31479e9 | 0.0752761 | ||||||||
\(845\) | −1.48256e9 | −0.0845304 | ||||||||
\(846\) | −5.40681e9 | −0.307005 | ||||||||
\(847\) | 1.22097e10 | 0.690419 | ||||||||
\(848\) | 7.03715e9 | 0.396289 | ||||||||
\(849\) | 2.88609e9 | 0.161858 | ||||||||
\(850\) | −6.76898e8 | −0.0378057 | ||||||||
\(851\) | 7.68334e9 | 0.427363 | ||||||||
\(852\) | 4.74473e9 | 0.262829 | ||||||||
\(853\) | 1.76675e10 | 0.974663 | 0.487332 | − | 0.873217i | \(-0.337970\pi\) | ||||
0.487332 | + | 0.873217i | \(0.337970\pi\) | |||||||
\(854\) | 3.34570e9 | 0.183817 | ||||||||
\(855\) | 1.36631e8 | 0.00747600 | ||||||||
\(856\) | −4.19601e9 | −0.228654 | ||||||||
\(857\) | 1.64284e10 | 0.891585 | 0.445792 | − | 0.895136i | \(-0.352922\pi\) | ||||
0.445792 | + | 0.895136i | \(0.352922\pi\) | |||||||
\(858\) | −3.52206e9 | −0.190367 | ||||||||
\(859\) | −2.49779e9 | −0.134456 | −0.0672280 | − | 0.997738i | \(-0.521416\pi\) | ||||
−0.0672280 | + | 0.997738i | \(0.521416\pi\) | |||||||
\(860\) | 1.34500e9 | 0.0721072 | ||||||||
\(861\) | 2.81284e9 | 0.150187 | ||||||||
\(862\) | 9.95259e9 | 0.529250 | ||||||||
\(863\) | −2.24625e10 | −1.18965 | −0.594826 | − | 0.803854i | \(-0.702779\pi\) | ||||
−0.594826 | + | 0.803854i | \(0.702779\pi\) | |||||||
\(864\) | −6.44973e8 | −0.0340207 | ||||||||
\(865\) | −7.52649e9 | −0.395400 | ||||||||
\(866\) | −1.78542e10 | −0.934173 | ||||||||
\(867\) | 1.03441e10 | 0.539045 | ||||||||
\(868\) | −3.00638e8 | −0.0156036 | ||||||||
\(869\) | −3.58374e10 | −1.85254 | ||||||||
\(870\) | 3.68134e9 | 0.189535 | ||||||||
\(871\) | 5.01429e9 | 0.257126 | ||||||||
\(872\) | 3.74339e9 | 0.191186 | ||||||||
\(873\) | −4.22695e9 | −0.215019 | ||||||||
\(874\) | 2.62263e8 | 0.0132876 | ||||||||
\(875\) | 6.52224e9 | 0.329131 | ||||||||
\(876\) | 6.00380e9 | 0.301760 | ||||||||
\(877\) | 1.03251e10 | 0.516885 | 0.258443 | − | 0.966027i | \(-0.416791\pi\) | ||||
0.258443 | + | 0.966027i | \(0.416791\pi\) | |||||||
\(878\) | 6.44199e9 | 0.321210 | ||||||||
\(879\) | 7.19439e9 | 0.357300 | ||||||||
\(880\) | 9.33735e9 | 0.461885 | ||||||||
\(881\) | 1.26952e10 | 0.625494 | 0.312747 | − | 0.949836i | \(-0.398751\pi\) | ||||
0.312747 | + | 0.949836i | \(0.398751\pi\) | |||||||
\(882\) | 6.86129e8 | 0.0336718 | ||||||||
\(883\) | 3.26436e10 | 1.59564 | 0.797821 | − | 0.602895i | \(-0.205986\pi\) | ||||
0.797821 | + | 0.602895i | \(0.205986\pi\) | |||||||
\(884\) | 7.33652e8 | 0.0357196 | ||||||||
\(885\) | −2.62806e9 | −0.127448 | ||||||||
\(886\) | 2.23565e10 | 1.07991 | ||||||||
\(887\) | 1.48765e10 | 0.715761 | 0.357880 | − | 0.933767i | \(-0.383500\pi\) | ||||
0.357880 | + | 0.933767i | \(0.383500\pi\) | |||||||
\(888\) | 1.97701e9 | 0.0947464 | ||||||||
\(889\) | 1.19171e10 | 0.568871 | ||||||||
\(890\) | 1.03200e9 | 0.0490699 | ||||||||
\(891\) | −3.94428e9 | −0.186808 | ||||||||
\(892\) | 4.22694e7 | 0.00199411 | ||||||||
\(893\) | 5.65713e8 | 0.0265837 | ||||||||
\(894\) | −4.61531e9 | −0.216033 | ||||||||
\(895\) | 8.33400e9 | 0.388573 | ||||||||
\(896\) | 7.19323e8 | 0.0334077 | ||||||||
\(897\) | −3.18691e9 | −0.147433 | ||||||||
\(898\) | −5.79539e9 | −0.267064 | ||||||||
\(899\) | −7.59925e8 | −0.0348828 | ||||||||
\(900\) | 7.56590e8 | 0.0345949 | ||||||||
\(901\) | −8.96432e9 | −0.408301 | ||||||||
\(902\) | 1.80339e10 | 0.818213 | ||||||||
\(903\) | 6.33651e8 | 0.0286380 | ||||||||
\(904\) | −4.64487e9 | −0.209115 | ||||||||
\(905\) | 2.77825e10 | 1.24595 | ||||||||
\(906\) | −9.50442e9 | −0.424597 | ||||||||
\(907\) | 2.62488e10 | 1.16811 | 0.584055 | − | 0.811714i | \(-0.301465\pi\) | ||||
0.584055 | + | 0.811714i | \(0.301465\pi\) | |||||||
\(908\) | −1.66659e10 | −0.738804 | ||||||||
\(909\) | 9.96785e9 | 0.440178 | ||||||||
\(910\) | 1.85168e9 | 0.0814555 | ||||||||
\(911\) | 1.57989e10 | 0.692329 | 0.346164 | − | 0.938174i | \(-0.387484\pi\) | ||||
0.346164 | + | 0.938174i | \(0.387484\pi\) | |||||||
\(912\) | 6.74832e7 | 0.00294587 | ||||||||
\(913\) | 2.10927e10 | 0.917242 | ||||||||
\(914\) | −8.26836e9 | −0.358185 | ||||||||
\(915\) | 1.01116e10 | 0.436359 | ||||||||
\(916\) | 9.07257e9 | 0.390028 | ||||||||
\(917\) | 3.18409e8 | 0.0136362 | ||||||||
\(918\) | 8.21602e8 | 0.0350519 | ||||||||
\(919\) | 8.27399e9 | 0.351650 | 0.175825 | − | 0.984421i | \(-0.443741\pi\) | ||||
0.175825 | + | 0.984421i | \(0.443741\pi\) | |||||||
\(920\) | 8.44883e9 | 0.357716 | ||||||||
\(921\) | −1.43300e10 | −0.604419 | ||||||||
\(922\) | −5.97012e9 | −0.250856 | ||||||||
\(923\) | 6.03251e9 | 0.252518 | ||||||||
\(924\) | 4.39896e9 | 0.183442 | ||||||||
\(925\) | −2.31914e9 | −0.0963455 | ||||||||
\(926\) | 2.41032e10 | 0.997554 | ||||||||
\(927\) | 6.44187e9 | 0.265603 | ||||||||
\(928\) | 1.81824e9 | 0.0746850 | ||||||||
\(929\) | −1.08563e10 | −0.444249 | −0.222125 | − | 0.975018i | \(-0.571299\pi\) | ||||
−0.222125 | + | 0.975018i | \(0.571299\pi\) | |||||||
\(930\) | −9.08603e8 | −0.0370411 | ||||||||
\(931\) | −7.17894e7 | −0.00291566 | ||||||||
\(932\) | 8.74305e8 | 0.0353759 | ||||||||
\(933\) | 9.30666e9 | 0.375153 | ||||||||
\(934\) | −1.97081e10 | −0.791464 | ||||||||
\(935\) | −1.18944e10 | −0.475886 | ||||||||
\(936\) | −8.20026e8 | −0.0326860 | ||||||||
\(937\) | −3.05749e10 | −1.21416 | −0.607080 | − | 0.794641i | \(-0.707659\pi\) | ||||
−0.607080 | + | 0.794641i | \(0.707659\pi\) | |||||||
\(938\) | −6.26273e9 | −0.247773 | ||||||||
\(939\) | −3.66782e9 | −0.144570 | ||||||||
\(940\) | 1.82245e10 | 0.715661 | ||||||||
\(941\) | 2.70986e10 | 1.06019 | 0.530094 | − | 0.847939i | \(-0.322157\pi\) | ||||
0.530094 | + | 0.847939i | \(0.322157\pi\) | |||||||
\(942\) | −1.84853e10 | −0.720524 | ||||||||
\(943\) | 1.63178e10 | 0.633682 | ||||||||
\(944\) | −1.29802e9 | −0.0502201 | ||||||||
\(945\) | 2.07365e9 | 0.0799328 | ||||||||
\(946\) | 4.06251e9 | 0.156018 | ||||||||
\(947\) | 1.35307e10 | 0.517721 | 0.258860 | − | 0.965915i | \(-0.416653\pi\) | ||||
0.258860 | + | 0.965915i | \(0.416653\pi\) | |||||||
\(948\) | −8.34387e9 | −0.318081 | ||||||||
\(949\) | 7.63330e9 | 0.289922 | ||||||||
\(950\) | −7.91617e7 | −0.00299559 | ||||||||
\(951\) | −4.99677e9 | −0.188390 | ||||||||
\(952\) | −9.16314e8 | −0.0344203 | ||||||||
\(953\) | −4.46129e10 | −1.66969 | −0.834844 | − | 0.550486i | \(-0.814442\pi\) | ||||
−0.834844 | + | 0.550486i | \(0.814442\pi\) | |||||||
\(954\) | 1.00197e10 | 0.373624 | ||||||||
\(955\) | −4.95397e10 | −1.84052 | ||||||||
\(956\) | −4.60768e9 | −0.170561 | ||||||||
\(957\) | 1.11193e10 | 0.410096 | ||||||||
\(958\) | 1.47044e8 | 0.00540341 | ||||||||
\(959\) | 2.80000e9 | 0.102516 | ||||||||
\(960\) | 2.17398e9 | 0.0793059 | ||||||||
\(961\) | −2.73251e10 | −0.993183 | ||||||||
\(962\) | 2.51359e9 | 0.0910294 | ||||||||
\(963\) | −5.97440e9 | −0.215577 | ||||||||
\(964\) | 2.14011e10 | 0.769425 | ||||||||
\(965\) | −1.31967e10 | −0.472736 | ||||||||
\(966\) | 3.98037e9 | 0.142070 | ||||||||
\(967\) | 2.85038e10 | 1.01370 | 0.506851 | − | 0.862034i | \(-0.330809\pi\) | ||||
0.506851 | + | 0.862034i | \(0.330809\pi\) | |||||||
\(968\) | 1.82256e10 | 0.645828 | ||||||||
\(969\) | −8.59639e7 | −0.00303517 | ||||||||
\(970\) | 1.42476e10 | 0.501233 | ||||||||
\(971\) | −2.06546e10 | −0.724018 | −0.362009 | − | 0.932175i | \(-0.617909\pi\) | ||||
−0.362009 | + | 0.932175i | \(0.617909\pi\) | |||||||
\(972\) | −9.18330e8 | −0.0320750 | ||||||||
\(973\) | −4.05306e9 | −0.141055 | ||||||||
\(974\) | 3.53630e9 | 0.122629 | ||||||||
\(975\) | 9.61938e8 | 0.0332377 | ||||||||
\(976\) | 4.99417e9 | 0.171945 | ||||||||
\(977\) | −2.31006e10 | −0.792488 | −0.396244 | − | 0.918145i | \(-0.629687\pi\) | ||||
−0.396244 | + | 0.918145i | \(0.629687\pi\) | |||||||
\(978\) | −2.21544e10 | −0.757311 | ||||||||
\(979\) | 3.11711e9 | 0.106173 | ||||||||
\(980\) | −2.31270e9 | −0.0784925 | ||||||||
\(981\) | 5.32994e9 | 0.180252 | ||||||||
\(982\) | 1.88058e10 | 0.633726 | ||||||||
\(983\) | −1.78640e10 | −0.599848 | −0.299924 | − | 0.953963i | \(-0.596961\pi\) | ||||
−0.299924 | + | 0.953963i | \(0.596961\pi\) | |||||||
\(984\) | 4.19876e9 | 0.140488 | ||||||||
\(985\) | 3.12309e10 | 1.04126 | ||||||||
\(986\) | −2.31617e9 | −0.0769488 | ||||||||
\(987\) | 8.58582e9 | 0.284231 | ||||||||
\(988\) | 8.57990e7 | 0.00283030 | ||||||||
\(989\) | 3.67593e9 | 0.120832 | ||||||||
\(990\) | 1.32948e10 | 0.435470 | ||||||||
\(991\) | −3.85854e10 | −1.25940 | −0.629702 | − | 0.776837i | \(-0.716823\pi\) | ||||
−0.629702 | + | 0.776837i | \(0.716823\pi\) | |||||||
\(992\) | −4.48765e8 | −0.0145958 | ||||||||
\(993\) | 2.64994e9 | 0.0858842 | ||||||||
\(994\) | −7.53446e9 | −0.243332 | ||||||||
\(995\) | −2.45600e10 | −0.790400 | ||||||||
\(996\) | 4.91092e9 | 0.157491 | ||||||||
\(997\) | 4.66291e10 | 1.49013 | 0.745065 | − | 0.666992i | \(-0.232418\pi\) | ||||
0.745065 | + | 0.666992i | \(0.232418\pi\) | |||||||
\(998\) | 9.21305e9 | 0.293391 | ||||||||
\(999\) | 2.81492e9 | 0.0893278 |
(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 | 546.8.a.q.1.2 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.8.a.q.1.2 | ✓ | 6 | 1.1 | even | 1 | trivial |