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 | 1.6 | ||
Root | \(527.645\) 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 | ||||||||
\(5\) | 529.645 | 1.89491 | 0.947457 | − | 0.319883i | \(-0.103644\pi\) | ||||
0.947457 | + | 0.319883i | \(0.103644\pi\) | |||||||
\(6\) | −216.000 | −0.408248 | ||||||||
\(7\) | 343.000 | 0.377964 | ||||||||
\(8\) | 512.000 | 0.353553 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 4237.16 | 1.33991 | ||||||||
\(11\) | 3727.68 | 0.844432 | 0.422216 | − | 0.906495i | \(-0.361252\pi\) | ||||
0.422216 | + | 0.906495i | \(0.361252\pi\) | |||||||
\(12\) | −1728.00 | −0.288675 | ||||||||
\(13\) | −2197.00 | −0.277350 | ||||||||
\(14\) | 2744.00 | 0.267261 | ||||||||
\(15\) | −14300.4 | −1.09403 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | 24121.3 | 1.19078 | 0.595388 | − | 0.803438i | \(-0.296998\pi\) | ||||
0.595388 | + | 0.803438i | \(0.296998\pi\) | |||||||
\(18\) | 5832.00 | 0.235702 | ||||||||
\(19\) | 9818.46 | 0.328402 | 0.164201 | − | 0.986427i | \(-0.447495\pi\) | ||||
0.164201 | + | 0.986427i | \(0.447495\pi\) | |||||||
\(20\) | 33897.3 | 0.947457 | ||||||||
\(21\) | −9261.00 | −0.218218 | ||||||||
\(22\) | 29821.5 | 0.597104 | ||||||||
\(23\) | −36040.5 | −0.617651 | −0.308825 | − | 0.951119i | \(-0.599936\pi\) | ||||
−0.308825 | + | 0.951119i | \(0.599936\pi\) | |||||||
\(24\) | −13824.0 | −0.204124 | ||||||||
\(25\) | 202398. | 2.59070 | ||||||||
\(26\) | −17576.0 | −0.196116 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | 21952.0 | 0.188982 | ||||||||
\(29\) | −159862. | −1.21717 | −0.608587 | − | 0.793487i | \(-0.708263\pi\) | ||||
−0.608587 | + | 0.793487i | \(0.708263\pi\) | |||||||
\(30\) | −114403. | −0.773596 | ||||||||
\(31\) | 222746. | 1.34290 | 0.671452 | − | 0.741048i | \(-0.265671\pi\) | ||||
0.671452 | + | 0.741048i | \(0.265671\pi\) | |||||||
\(32\) | 32768.0 | 0.176777 | ||||||||
\(33\) | −100647. | −0.487533 | ||||||||
\(34\) | 192971. | 0.842006 | ||||||||
\(35\) | 181668. | 0.716210 | ||||||||
\(36\) | 46656.0 | 0.166667 | ||||||||
\(37\) | 219687. | 0.713013 | 0.356507 | − | 0.934293i | \(-0.383968\pi\) | ||||
0.356507 | + | 0.934293i | \(0.383968\pi\) | |||||||
\(38\) | 78547.7 | 0.232215 | ||||||||
\(39\) | 59319.0 | 0.160128 | ||||||||
\(40\) | 271178. | 0.669953 | ||||||||
\(41\) | −29299.4 | −0.0663919 | −0.0331959 | − | 0.999449i | \(-0.510569\pi\) | ||||
−0.0331959 | + | 0.999449i | \(0.510569\pi\) | |||||||
\(42\) | −74088.0 | −0.154303 | ||||||||
\(43\) | −79448.9 | −0.152387 | −0.0761936 | − | 0.997093i | \(-0.524277\pi\) | ||||
−0.0761936 | + | 0.997093i | \(0.524277\pi\) | |||||||
\(44\) | 238572. | 0.422216 | ||||||||
\(45\) | 386111. | 0.631638 | ||||||||
\(46\) | −288324. | −0.436745 | ||||||||
\(47\) | 652464. | 0.916673 | 0.458336 | − | 0.888779i | \(-0.348446\pi\) | ||||
0.458336 | + | 0.888779i | \(0.348446\pi\) | |||||||
\(48\) | −110592. | −0.144338 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | 1.61919e6 | 1.83190 | ||||||||
\(51\) | −651276. | −0.687495 | ||||||||
\(52\) | −140608. | −0.138675 | ||||||||
\(53\) | 586529. | 0.541158 | 0.270579 | − | 0.962698i | \(-0.412785\pi\) | ||||
0.270579 | + | 0.962698i | \(0.412785\pi\) | |||||||
\(54\) | −157464. | −0.136083 | ||||||||
\(55\) | 1.97435e6 | 1.60013 | ||||||||
\(56\) | 175616. | 0.133631 | ||||||||
\(57\) | −265098. | −0.189603 | ||||||||
\(58\) | −1.27890e6 | −0.860672 | ||||||||
\(59\) | −1.11075e6 | −0.704100 | −0.352050 | − | 0.935981i | \(-0.614515\pi\) | ||||
−0.352050 | + | 0.935981i | \(0.614515\pi\) | |||||||
\(60\) | −915226. | −0.547015 | ||||||||
\(61\) | 370461. | 0.208972 | 0.104486 | − | 0.994526i | \(-0.466680\pi\) | ||||
0.104486 | + | 0.994526i | \(0.466680\pi\) | |||||||
\(62\) | 1.78197e6 | 0.949576 | ||||||||
\(63\) | 250047. | 0.125988 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | −1.16363e6 | −0.525555 | ||||||||
\(66\) | −805180. | −0.344738 | ||||||||
\(67\) | −3.54571e6 | −1.44026 | −0.720130 | − | 0.693839i | \(-0.755918\pi\) | ||||
−0.720130 | + | 0.693839i | \(0.755918\pi\) | |||||||
\(68\) | 1.54377e6 | 0.595388 | ||||||||
\(69\) | 973093. | 0.356601 | ||||||||
\(70\) | 1.45334e6 | 0.506437 | ||||||||
\(71\) | 3.51099e6 | 1.16419 | 0.582097 | − | 0.813119i | \(-0.302232\pi\) | ||||
0.582097 | + | 0.813119i | \(0.302232\pi\) | |||||||
\(72\) | 373248. | 0.117851 | ||||||||
\(73\) | −6.04121e6 | −1.81758 | −0.908791 | − | 0.417251i | \(-0.862994\pi\) | ||||
−0.908791 | + | 0.417251i | \(0.862994\pi\) | |||||||
\(74\) | 1.75749e6 | 0.504177 | ||||||||
\(75\) | −5.46476e6 | −1.49574 | ||||||||
\(76\) | 628381. | 0.164201 | ||||||||
\(77\) | 1.27860e6 | 0.319165 | ||||||||
\(78\) | 474552. | 0.113228 | ||||||||
\(79\) | −4.72429e6 | −1.07806 | −0.539028 | − | 0.842288i | \(-0.681208\pi\) | ||||
−0.539028 | + | 0.842288i | \(0.681208\pi\) | |||||||
\(80\) | 2.16942e6 | 0.473729 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −234395. | −0.0469461 | ||||||||
\(83\) | 2.27200e6 | 0.436149 | 0.218075 | − | 0.975932i | \(-0.430022\pi\) | ||||
0.218075 | + | 0.975932i | \(0.430022\pi\) | |||||||
\(84\) | −592704. | −0.109109 | ||||||||
\(85\) | 1.27757e7 | 2.25642 | ||||||||
\(86\) | −635591. | −0.107754 | ||||||||
\(87\) | 4.31628e6 | 0.702735 | ||||||||
\(88\) | 1.90857e6 | 0.298552 | ||||||||
\(89\) | −2.77728e6 | −0.417595 | −0.208797 | − | 0.977959i | \(-0.566955\pi\) | ||||
−0.208797 | + | 0.977959i | \(0.566955\pi\) | |||||||
\(90\) | 3.08889e6 | 0.446636 | ||||||||
\(91\) | −753571. | −0.104828 | ||||||||
\(92\) | −2.30659e6 | −0.308825 | ||||||||
\(93\) | −6.01415e6 | −0.775326 | ||||||||
\(94\) | 5.21971e6 | 0.648185 | ||||||||
\(95\) | 5.20029e6 | 0.622293 | ||||||||
\(96\) | −884736. | −0.102062 | ||||||||
\(97\) | 3.86868e6 | 0.430390 | 0.215195 | − | 0.976571i | \(-0.430961\pi\) | ||||
0.215195 | + | 0.976571i | \(0.430961\pi\) | |||||||
\(98\) | 941192. | 0.101015 | ||||||||
\(99\) | 2.71748e6 | 0.281477 | ||||||||
\(100\) | 1.29535e7 | 1.29535 | ||||||||
\(101\) | −4.17061e6 | −0.402786 | −0.201393 | − | 0.979511i | \(-0.564547\pi\) | ||||
−0.201393 | + | 0.979511i | \(0.564547\pi\) | |||||||
\(102\) | −5.21021e6 | −0.486133 | ||||||||
\(103\) | 5.54746e6 | 0.500223 | 0.250111 | − | 0.968217i | \(-0.419533\pi\) | ||||
0.250111 | + | 0.968217i | \(0.419533\pi\) | |||||||
\(104\) | −1.12486e6 | −0.0980581 | ||||||||
\(105\) | −4.90504e6 | −0.413504 | ||||||||
\(106\) | 4.69223e6 | 0.382657 | ||||||||
\(107\) | −2.37587e7 | −1.87490 | −0.937452 | − | 0.348115i | \(-0.886822\pi\) | ||||
−0.937452 | + | 0.348115i | \(0.886822\pi\) | |||||||
\(108\) | −1.25971e6 | −0.0962250 | ||||||||
\(109\) | 1.37063e7 | 1.01374 | 0.506870 | − | 0.862022i | \(-0.330802\pi\) | ||||
0.506870 | + | 0.862022i | \(0.330802\pi\) | |||||||
\(110\) | 1.57948e7 | 1.13146 | ||||||||
\(111\) | −5.93154e6 | −0.411658 | ||||||||
\(112\) | 1.40493e6 | 0.0944911 | ||||||||
\(113\) | −2.23664e6 | −0.145821 | −0.0729107 | − | 0.997338i | \(-0.523229\pi\) | ||||
−0.0729107 | + | 0.997338i | \(0.523229\pi\) | |||||||
\(114\) | −2.12079e6 | −0.134070 | ||||||||
\(115\) | −1.90886e7 | −1.17040 | ||||||||
\(116\) | −1.02312e7 | −0.608587 | ||||||||
\(117\) | −1.60161e6 | −0.0924500 | ||||||||
\(118\) | −8.88600e6 | −0.497874 | ||||||||
\(119\) | 8.27362e6 | 0.450071 | ||||||||
\(120\) | −7.32181e6 | −0.386798 | ||||||||
\(121\) | −5.59154e6 | −0.286934 | ||||||||
\(122\) | 2.96369e6 | 0.147765 | ||||||||
\(123\) | 791083. | 0.0383314 | ||||||||
\(124\) | 1.42558e7 | 0.671452 | ||||||||
\(125\) | 6.58208e7 | 3.01424 | ||||||||
\(126\) | 2.00038e6 | 0.0890871 | ||||||||
\(127\) | −9.41494e6 | −0.407854 | −0.203927 | − | 0.978986i | \(-0.565370\pi\) | ||||
−0.203927 | + | 0.978986i | \(0.565370\pi\) | |||||||
\(128\) | 2.09715e6 | 0.0883883 | ||||||||
\(129\) | 2.14512e6 | 0.0879808 | ||||||||
\(130\) | −9.30903e6 | −0.371623 | ||||||||
\(131\) | −1.62654e7 | −0.632145 | −0.316072 | − | 0.948735i | \(-0.602364\pi\) | ||||
−0.316072 | + | 0.948735i | \(0.602364\pi\) | |||||||
\(132\) | −6.44144e6 | −0.243767 | ||||||||
\(133\) | 3.36773e6 | 0.124124 | ||||||||
\(134\) | −2.83656e7 | −1.01842 | ||||||||
\(135\) | −1.04250e7 | −0.364676 | ||||||||
\(136\) | 1.23501e7 | 0.421003 | ||||||||
\(137\) | −2.09518e7 | −0.696146 | −0.348073 | − | 0.937467i | \(-0.613164\pi\) | ||||
−0.348073 | + | 0.937467i | \(0.613164\pi\) | |||||||
\(138\) | 7.78474e6 | 0.252155 | ||||||||
\(139\) | −2.42651e7 | −0.766355 | −0.383177 | − | 0.923675i | \(-0.625170\pi\) | ||||
−0.383177 | + | 0.923675i | \(0.625170\pi\) | |||||||
\(140\) | 1.16268e7 | 0.358105 | ||||||||
\(141\) | −1.76165e7 | −0.529241 | ||||||||
\(142\) | 2.80879e7 | 0.823210 | ||||||||
\(143\) | −8.18972e6 | −0.234203 | ||||||||
\(144\) | 2.98598e6 | 0.0833333 | ||||||||
\(145\) | −8.46701e7 | −2.30644 | ||||||||
\(146\) | −4.83297e7 | −1.28522 | ||||||||
\(147\) | −3.17652e6 | −0.0824786 | ||||||||
\(148\) | 1.40599e7 | 0.356507 | ||||||||
\(149\) | 4.42973e7 | 1.09705 | 0.548523 | − | 0.836135i | \(-0.315190\pi\) | ||||
0.548523 | + | 0.836135i | \(0.315190\pi\) | |||||||
\(150\) | −4.37181e7 | −1.05765 | ||||||||
\(151\) | −5.68350e7 | −1.34337 | −0.671687 | − | 0.740835i | \(-0.734430\pi\) | ||||
−0.671687 | + | 0.740835i | \(0.734430\pi\) | |||||||
\(152\) | 5.02705e6 | 0.116108 | ||||||||
\(153\) | 1.75845e7 | 0.396926 | ||||||||
\(154\) | 1.02288e7 | 0.225684 | ||||||||
\(155\) | 1.17976e8 | 2.54469 | ||||||||
\(156\) | 3.79642e6 | 0.0800641 | ||||||||
\(157\) | 7.78930e7 | 1.60639 | 0.803193 | − | 0.595719i | \(-0.203133\pi\) | ||||
0.803193 | + | 0.595719i | \(0.203133\pi\) | |||||||
\(158\) | −3.77943e7 | −0.762301 | ||||||||
\(159\) | −1.58363e7 | −0.312438 | ||||||||
\(160\) | 1.73554e7 | 0.334977 | ||||||||
\(161\) | −1.23619e7 | −0.233450 | ||||||||
\(162\) | 4.25153e6 | 0.0785674 | ||||||||
\(163\) | −5.14450e7 | −0.930436 | −0.465218 | − | 0.885196i | \(-0.654024\pi\) | ||||
−0.465218 | + | 0.885196i | \(0.654024\pi\) | |||||||
\(164\) | −1.87516e6 | −0.0331959 | ||||||||
\(165\) | −5.33074e7 | −0.923834 | ||||||||
\(166\) | 1.81760e7 | 0.308404 | ||||||||
\(167\) | 2.40929e7 | 0.400296 | 0.200148 | − | 0.979766i | \(-0.435858\pi\) | ||||
0.200148 | + | 0.979766i | \(0.435858\pi\) | |||||||
\(168\) | −4.74163e6 | −0.0771517 | ||||||||
\(169\) | 4.82681e6 | 0.0769231 | ||||||||
\(170\) | 1.02206e8 | 1.59553 | ||||||||
\(171\) | 7.15766e6 | 0.109467 | ||||||||
\(172\) | −5.08473e6 | −0.0761936 | ||||||||
\(173\) | 8.78537e7 | 1.29003 | 0.645013 | − | 0.764171i | \(-0.276852\pi\) | ||||
0.645013 | + | 0.764171i | \(0.276852\pi\) | |||||||
\(174\) | 3.45302e7 | 0.496909 | ||||||||
\(175\) | 6.94227e7 | 0.979193 | ||||||||
\(176\) | 1.52686e7 | 0.211108 | ||||||||
\(177\) | 2.99903e7 | 0.406512 | ||||||||
\(178\) | −2.22183e7 | −0.295284 | ||||||||
\(179\) | 7.47061e7 | 0.973578 | 0.486789 | − | 0.873520i | \(-0.338168\pi\) | ||||
0.486789 | + | 0.873520i | \(0.338168\pi\) | |||||||
\(180\) | 2.47111e7 | 0.315819 | ||||||||
\(181\) | 5.00109e7 | 0.626887 | 0.313444 | − | 0.949607i | \(-0.398517\pi\) | ||||
0.313444 | + | 0.949607i | \(0.398517\pi\) | |||||||
\(182\) | −6.02857e6 | −0.0741249 | ||||||||
\(183\) | −1.00024e7 | −0.120650 | ||||||||
\(184\) | −1.84527e7 | −0.218373 | ||||||||
\(185\) | 1.16356e8 | 1.35110 | ||||||||
\(186\) | −4.81132e7 | −0.548238 | ||||||||
\(187\) | 8.99168e7 | 1.00553 | ||||||||
\(188\) | 4.17577e7 | 0.458336 | ||||||||
\(189\) | −6.75127e6 | −0.0727393 | ||||||||
\(190\) | 4.16023e7 | 0.440028 | ||||||||
\(191\) | 1.78752e8 | 1.85624 | 0.928119 | − | 0.372284i | \(-0.121425\pi\) | ||||
0.928119 | + | 0.372284i | \(0.121425\pi\) | |||||||
\(192\) | −7.07789e6 | −0.0721688 | ||||||||
\(193\) | 2.51808e7 | 0.252127 | 0.126063 | − | 0.992022i | \(-0.459766\pi\) | ||||
0.126063 | + | 0.992022i | \(0.459766\pi\) | |||||||
\(194\) | 3.09495e7 | 0.304332 | ||||||||
\(195\) | 3.14180e7 | 0.303429 | ||||||||
\(196\) | 7.52954e6 | 0.0714286 | ||||||||
\(197\) | 1.23584e8 | 1.15168 | 0.575839 | − | 0.817563i | \(-0.304675\pi\) | ||||
0.575839 | + | 0.817563i | \(0.304675\pi\) | |||||||
\(198\) | 2.17399e7 | 0.199035 | ||||||||
\(199\) | 2.90019e7 | 0.260880 | 0.130440 | − | 0.991456i | \(-0.458361\pi\) | ||||
0.130440 | + | 0.991456i | \(0.458361\pi\) | |||||||
\(200\) | 1.03628e8 | 0.915951 | ||||||||
\(201\) | 9.57341e7 | 0.831535 | ||||||||
\(202\) | −3.33649e7 | −0.284813 | ||||||||
\(203\) | −5.48327e7 | −0.460048 | ||||||||
\(204\) | −4.16817e7 | −0.343748 | ||||||||
\(205\) | −1.55183e7 | −0.125807 | ||||||||
\(206\) | 4.43797e7 | 0.353711 | ||||||||
\(207\) | −2.62735e7 | −0.205884 | ||||||||
\(208\) | −8.99891e6 | −0.0693375 | ||||||||
\(209\) | 3.66001e7 | 0.277313 | ||||||||
\(210\) | −3.92403e7 | −0.292392 | ||||||||
\(211\) | −6.62659e7 | −0.485625 | −0.242813 | − | 0.970073i | \(-0.578070\pi\) | ||||
−0.242813 | + | 0.970073i | \(0.578070\pi\) | |||||||
\(212\) | 3.75379e7 | 0.270579 | ||||||||
\(213\) | −9.47968e7 | −0.672148 | ||||||||
\(214\) | −1.90069e8 | −1.32576 | ||||||||
\(215\) | −4.20797e7 | −0.288761 | ||||||||
\(216\) | −1.00777e7 | −0.0680414 | ||||||||
\(217\) | 7.64020e7 | 0.507570 | ||||||||
\(218\) | 1.09650e8 | 0.716823 | ||||||||
\(219\) | 1.63113e8 | 1.04938 | ||||||||
\(220\) | 1.26358e8 | 0.800063 | ||||||||
\(221\) | −5.29946e7 | −0.330262 | ||||||||
\(222\) | −4.74523e7 | −0.291086 | ||||||||
\(223\) | 2.82014e8 | 1.70296 | 0.851479 | − | 0.524389i | \(-0.175706\pi\) | ||||
0.851479 | + | 0.524389i | \(0.175706\pi\) | |||||||
\(224\) | 1.12394e7 | 0.0668153 | ||||||||
\(225\) | 1.47548e8 | 0.863567 | ||||||||
\(226\) | −1.78931e7 | −0.103111 | ||||||||
\(227\) | −1.19805e8 | −0.679805 | −0.339903 | − | 0.940461i | \(-0.610394\pi\) | ||||
−0.339903 | + | 0.940461i | \(0.610394\pi\) | |||||||
\(228\) | −1.69663e7 | −0.0948015 | ||||||||
\(229\) | 1.03961e7 | 0.0572064 | 0.0286032 | − | 0.999591i | \(-0.490894\pi\) | ||||
0.0286032 | + | 0.999591i | \(0.490894\pi\) | |||||||
\(230\) | −1.52709e8 | −0.827595 | ||||||||
\(231\) | −3.45221e7 | −0.184270 | ||||||||
\(232\) | −8.18494e7 | −0.430336 | ||||||||
\(233\) | −1.76469e8 | −0.913952 | −0.456976 | − | 0.889479i | \(-0.651067\pi\) | ||||
−0.456976 | + | 0.889479i | \(0.651067\pi\) | |||||||
\(234\) | −1.28129e7 | −0.0653720 | ||||||||
\(235\) | 3.45574e8 | 1.73702 | ||||||||
\(236\) | −7.10880e7 | −0.352050 | ||||||||
\(237\) | 1.27556e8 | 0.622416 | ||||||||
\(238\) | 6.61890e7 | 0.318248 | ||||||||
\(239\) | 2.48570e8 | 1.17776 | 0.588878 | − | 0.808222i | \(-0.299570\pi\) | ||||
0.588878 | + | 0.808222i | \(0.299570\pi\) | |||||||
\(240\) | −5.85745e7 | −0.273507 | ||||||||
\(241\) | −3.65205e7 | −0.168065 | −0.0840326 | − | 0.996463i | \(-0.526780\pi\) | ||||
−0.0840326 | + | 0.996463i | \(0.526780\pi\) | |||||||
\(242\) | −4.47323e7 | −0.202893 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | 2.37095e7 | 0.104486 | ||||||||
\(245\) | 6.23122e7 | 0.270702 | ||||||||
\(246\) | 6.32867e6 | 0.0271044 | ||||||||
\(247\) | −2.15712e7 | −0.0910823 | ||||||||
\(248\) | 1.14046e8 | 0.474788 | ||||||||
\(249\) | −6.13440e7 | −0.251811 | ||||||||
\(250\) | 5.26566e8 | 2.13139 | ||||||||
\(251\) | 3.43704e8 | 1.37191 | 0.685957 | − | 0.727643i | \(-0.259384\pi\) | ||||
0.685957 | + | 0.727643i | \(0.259384\pi\) | |||||||
\(252\) | 1.60030e7 | 0.0629941 | ||||||||
\(253\) | −1.34348e8 | −0.521564 | ||||||||
\(254\) | −7.53195e7 | −0.288396 | ||||||||
\(255\) | −3.44945e8 | −1.30274 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | −2.72290e8 | −1.00061 | −0.500306 | − | 0.865849i | \(-0.666779\pi\) | ||||
−0.500306 | + | 0.865849i | \(0.666779\pi\) | |||||||
\(258\) | 1.71610e7 | 0.0622118 | ||||||||
\(259\) | 7.53525e7 | 0.269494 | ||||||||
\(260\) | −7.44723e7 | −0.262777 | ||||||||
\(261\) | −1.16539e8 | −0.405724 | ||||||||
\(262\) | −1.30124e8 | −0.446994 | ||||||||
\(263\) | 3.55067e8 | 1.20355 | 0.601777 | − | 0.798664i | \(-0.294460\pi\) | ||||
0.601777 | + | 0.798664i | \(0.294460\pi\) | |||||||
\(264\) | −5.15315e7 | −0.172369 | ||||||||
\(265\) | 3.10652e8 | 1.02545 | ||||||||
\(266\) | 2.69418e7 | 0.0877691 | ||||||||
\(267\) | 7.49867e7 | 0.241099 | ||||||||
\(268\) | −2.26925e8 | −0.720130 | ||||||||
\(269\) | 2.87140e8 | 0.899417 | 0.449709 | − | 0.893175i | \(-0.351528\pi\) | ||||
0.449709 | + | 0.893175i | \(0.351528\pi\) | |||||||
\(270\) | −8.34000e7 | −0.257865 | ||||||||
\(271\) | −5.05877e8 | −1.54402 | −0.772009 | − | 0.635611i | \(-0.780748\pi\) | ||||
−0.772009 | + | 0.635611i | \(0.780748\pi\) | |||||||
\(272\) | 9.88010e7 | 0.297694 | ||||||||
\(273\) | 2.03464e7 | 0.0605228 | ||||||||
\(274\) | −1.67615e8 | −0.492250 | ||||||||
\(275\) | 7.54478e8 | 2.18767 | ||||||||
\(276\) | 6.22779e7 | 0.178300 | ||||||||
\(277\) | 3.57253e8 | 1.00994 | 0.504971 | − | 0.863136i | \(-0.331503\pi\) | ||||
0.504971 | + | 0.863136i | \(0.331503\pi\) | |||||||
\(278\) | −1.94121e8 | −0.541895 | ||||||||
\(279\) | 1.62382e8 | 0.447635 | ||||||||
\(280\) | 9.30141e7 | 0.253219 | ||||||||
\(281\) | −3.11274e8 | −0.836893 | −0.418447 | − | 0.908241i | \(-0.637425\pi\) | ||||
−0.418447 | + | 0.908241i | \(0.637425\pi\) | |||||||
\(282\) | −1.40932e8 | −0.374230 | ||||||||
\(283\) | −3.45216e8 | −0.905396 | −0.452698 | − | 0.891664i | \(-0.649538\pi\) | ||||
−0.452698 | + | 0.891664i | \(0.649538\pi\) | |||||||
\(284\) | 2.24703e8 | 0.582097 | ||||||||
\(285\) | −1.40408e8 | −0.359281 | ||||||||
\(286\) | −6.55178e7 | −0.165607 | ||||||||
\(287\) | −1.00497e7 | −0.0250938 | ||||||||
\(288\) | 2.38879e7 | 0.0589256 | ||||||||
\(289\) | 1.71501e8 | 0.417949 | ||||||||
\(290\) | −6.77361e8 | −1.63090 | ||||||||
\(291\) | −1.04454e8 | −0.248486 | ||||||||
\(292\) | −3.86638e8 | −0.908791 | ||||||||
\(293\) | −7.03438e8 | −1.63376 | −0.816882 | − | 0.576805i | \(-0.804299\pi\) | ||||
−0.816882 | + | 0.576805i | \(0.804299\pi\) | |||||||
\(294\) | −2.54122e7 | −0.0583212 | ||||||||
\(295\) | −5.88303e8 | −1.33421 | ||||||||
\(296\) | 1.12480e8 | 0.252088 | ||||||||
\(297\) | −7.33720e7 | −0.162511 | ||||||||
\(298\) | 3.54378e8 | 0.775729 | ||||||||
\(299\) | 7.91809e7 | 0.171306 | ||||||||
\(300\) | −3.49745e8 | −0.747871 | ||||||||
\(301\) | −2.72510e7 | −0.0575969 | ||||||||
\(302\) | −4.54680e8 | −0.949909 | ||||||||
\(303\) | 1.12606e8 | 0.232549 | ||||||||
\(304\) | 4.02164e7 | 0.0821005 | ||||||||
\(305\) | 1.96213e8 | 0.395984 | ||||||||
\(306\) | 1.40676e8 | 0.280669 | ||||||||
\(307\) | 3.64374e8 | 0.718726 | 0.359363 | − | 0.933198i | \(-0.382994\pi\) | ||||
0.359363 | + | 0.933198i | \(0.382994\pi\) | |||||||
\(308\) | 8.18301e7 | 0.159583 | ||||||||
\(309\) | −1.49781e8 | −0.288804 | ||||||||
\(310\) | 9.43812e8 | 1.79937 | ||||||||
\(311\) | −1.04616e9 | −1.97214 | −0.986071 | − | 0.166325i | \(-0.946810\pi\) | ||||
−0.986071 | + | 0.166325i | \(0.946810\pi\) | |||||||
\(312\) | 3.03713e7 | 0.0566139 | ||||||||
\(313\) | 5.12995e8 | 0.945601 | 0.472800 | − | 0.881170i | \(-0.343243\pi\) | ||||
0.472800 | + | 0.881170i | \(0.343243\pi\) | |||||||
\(314\) | 6.23144e8 | 1.13589 | ||||||||
\(315\) | 1.32436e8 | 0.238737 | ||||||||
\(316\) | −3.02354e8 | −0.539028 | ||||||||
\(317\) | 9.43433e8 | 1.66343 | 0.831714 | − | 0.555205i | \(-0.187360\pi\) | ||||
0.831714 | + | 0.555205i | \(0.187360\pi\) | |||||||
\(318\) | −1.26690e8 | −0.220927 | ||||||||
\(319\) | −5.95915e8 | −1.02782 | ||||||||
\(320\) | 1.38843e8 | 0.236864 | ||||||||
\(321\) | 6.41484e8 | 1.08248 | ||||||||
\(322\) | −9.88951e7 | −0.165074 | ||||||||
\(323\) | 2.36834e8 | 0.391053 | ||||||||
\(324\) | 3.40122e7 | 0.0555556 | ||||||||
\(325\) | −4.44669e8 | −0.718531 | ||||||||
\(326\) | −4.11560e8 | −0.657917 | ||||||||
\(327\) | −3.70069e8 | −0.585283 | ||||||||
\(328\) | −1.50013e7 | −0.0234731 | ||||||||
\(329\) | 2.23795e8 | 0.346470 | ||||||||
\(330\) | −4.26459e8 | −0.653249 | ||||||||
\(331\) | −6.52039e8 | −0.988270 | −0.494135 | − | 0.869385i | \(-0.664515\pi\) | ||||
−0.494135 | + | 0.869385i | \(0.664515\pi\) | |||||||
\(332\) | 1.45408e8 | 0.218075 | ||||||||
\(333\) | 1.60152e8 | 0.237671 | ||||||||
\(334\) | 1.92743e8 | 0.283052 | ||||||||
\(335\) | −1.87796e9 | −2.72917 | ||||||||
\(336\) | −3.79331e7 | −0.0545545 | ||||||||
\(337\) | −5.31387e8 | −0.756322 | −0.378161 | − | 0.925740i | \(-0.623443\pi\) | ||||
−0.378161 | + | 0.925740i | \(0.623443\pi\) | |||||||
\(338\) | 3.86145e7 | 0.0543928 | ||||||||
\(339\) | 6.03893e7 | 0.0841901 | ||||||||
\(340\) | 8.17648e8 | 1.12821 | ||||||||
\(341\) | 8.30329e8 | 1.13399 | ||||||||
\(342\) | 5.72612e7 | 0.0774051 | ||||||||
\(343\) | 4.03536e7 | 0.0539949 | ||||||||
\(344\) | −4.06779e7 | −0.0538770 | ||||||||
\(345\) | 5.15393e8 | 0.675728 | ||||||||
\(346\) | 7.02830e8 | 0.912187 | ||||||||
\(347\) | −4.68034e8 | −0.601345 | −0.300673 | − | 0.953727i | \(-0.597211\pi\) | ||||
−0.300673 | + | 0.953727i | \(0.597211\pi\) | |||||||
\(348\) | 2.76242e8 | 0.351368 | ||||||||
\(349\) | 5.87418e7 | 0.0739704 | 0.0369852 | − | 0.999316i | \(-0.488225\pi\) | ||||
0.0369852 | + | 0.999316i | \(0.488225\pi\) | |||||||
\(350\) | 5.55381e8 | 0.692394 | ||||||||
\(351\) | 4.32436e7 | 0.0533761 | ||||||||
\(352\) | 1.22149e8 | 0.149276 | ||||||||
\(353\) | 6.26384e8 | 0.757930 | 0.378965 | − | 0.925411i | \(-0.376280\pi\) | ||||
0.378965 | + | 0.925411i | \(0.376280\pi\) | |||||||
\(354\) | 2.39922e8 | 0.287448 | ||||||||
\(355\) | 1.85958e9 | 2.20605 | ||||||||
\(356\) | −1.77746e8 | −0.208797 | ||||||||
\(357\) | −2.23388e8 | −0.259849 | ||||||||
\(358\) | 5.97649e8 | 0.688423 | ||||||||
\(359\) | −6.26958e8 | −0.715167 | −0.357584 | − | 0.933881i | \(-0.616399\pi\) | ||||
−0.357584 | + | 0.933881i | \(0.616399\pi\) | |||||||
\(360\) | 1.97689e8 | 0.223318 | ||||||||
\(361\) | −7.97470e8 | −0.892152 | ||||||||
\(362\) | 4.00087e8 | 0.443276 | ||||||||
\(363\) | 1.50971e8 | 0.165662 | ||||||||
\(364\) | −4.82285e7 | −0.0524142 | ||||||||
\(365\) | −3.19970e9 | −3.44416 | ||||||||
\(366\) | −8.00195e7 | −0.0853124 | ||||||||
\(367\) | −1.88762e8 | −0.199335 | −0.0996676 | − | 0.995021i | \(-0.531778\pi\) | ||||
−0.0996676 | + | 0.995021i | \(0.531778\pi\) | |||||||
\(368\) | −1.47622e8 | −0.154413 | ||||||||
\(369\) | −2.13593e7 | −0.0221306 | ||||||||
\(370\) | 9.30847e8 | 0.955371 | ||||||||
\(371\) | 2.01180e8 | 0.204539 | ||||||||
\(372\) | −3.84906e8 | −0.387663 | ||||||||
\(373\) | −5.38574e8 | −0.537358 | −0.268679 | − | 0.963230i | \(-0.586587\pi\) | ||||
−0.268679 | + | 0.963230i | \(0.586587\pi\) | |||||||
\(374\) | 7.19334e8 | 0.711017 | ||||||||
\(375\) | −1.77716e9 | −1.74027 | ||||||||
\(376\) | 3.34062e8 | 0.324093 | ||||||||
\(377\) | 3.51217e8 | 0.337583 | ||||||||
\(378\) | −5.40102e7 | −0.0514344 | ||||||||
\(379\) | −1.41681e9 | −1.33682 | −0.668411 | − | 0.743792i | \(-0.733025\pi\) | ||||
−0.668411 | + | 0.743792i | \(0.733025\pi\) | |||||||
\(380\) | 3.32819e8 | 0.311147 | ||||||||
\(381\) | 2.54203e8 | 0.235474 | ||||||||
\(382\) | 1.43001e9 | 1.31256 | ||||||||
\(383\) | −2.11756e8 | −0.192593 | −0.0962965 | − | 0.995353i | \(-0.530700\pi\) | ||||
−0.0962965 | + | 0.995353i | \(0.530700\pi\) | |||||||
\(384\) | −5.66231e7 | −0.0510310 | ||||||||
\(385\) | 6.77201e8 | 0.604791 | ||||||||
\(386\) | 2.01447e8 | 0.178281 | ||||||||
\(387\) | −5.79183e7 | −0.0507957 | ||||||||
\(388\) | 2.47596e8 | 0.215195 | ||||||||
\(389\) | 1.97233e9 | 1.69885 | 0.849427 | − | 0.527706i | \(-0.176948\pi\) | ||||
0.849427 | + | 0.527706i | \(0.176948\pi\) | |||||||
\(390\) | 2.51344e8 | 0.214557 | ||||||||
\(391\) | −8.69345e8 | −0.735484 | ||||||||
\(392\) | 6.02363e7 | 0.0505076 | ||||||||
\(393\) | 4.39167e8 | 0.364969 | ||||||||
\(394\) | 9.88674e8 | 0.814360 | ||||||||
\(395\) | −2.50219e9 | −2.04282 | ||||||||
\(396\) | 1.73919e8 | 0.140739 | ||||||||
\(397\) | −1.50693e9 | −1.20872 | −0.604359 | − | 0.796712i | \(-0.706571\pi\) | ||||
−0.604359 | + | 0.796712i | \(0.706571\pi\) | |||||||
\(398\) | 2.32015e8 | 0.184470 | ||||||||
\(399\) | −9.09287e7 | −0.0716632 | ||||||||
\(400\) | 8.29024e8 | 0.647675 | ||||||||
\(401\) | 1.47465e9 | 1.14205 | 0.571023 | − | 0.820934i | \(-0.306547\pi\) | ||||
0.571023 | + | 0.820934i | \(0.306547\pi\) | |||||||
\(402\) | 7.65873e8 | 0.587984 | ||||||||
\(403\) | −4.89374e8 | −0.372455 | ||||||||
\(404\) | −2.66919e8 | −0.201393 | ||||||||
\(405\) | 2.81475e8 | 0.210546 | ||||||||
\(406\) | −4.38662e8 | −0.325303 | ||||||||
\(407\) | 8.18923e8 | 0.602091 | ||||||||
\(408\) | −3.33454e8 | −0.243066 | ||||||||
\(409\) | 6.90014e8 | 0.498685 | 0.249342 | − | 0.968415i | \(-0.419786\pi\) | ||||
0.249342 | + | 0.968415i | \(0.419786\pi\) | |||||||
\(410\) | −1.24146e8 | −0.0889589 | ||||||||
\(411\) | 5.65700e8 | 0.401920 | ||||||||
\(412\) | 3.55037e8 | 0.250111 | ||||||||
\(413\) | −3.80987e8 | −0.266125 | ||||||||
\(414\) | −2.10188e8 | −0.145582 | ||||||||
\(415\) | 1.20335e9 | 0.826465 | ||||||||
\(416\) | −7.19913e7 | −0.0490290 | ||||||||
\(417\) | 6.55157e8 | 0.442455 | ||||||||
\(418\) | 2.92801e8 | 0.196090 | ||||||||
\(419\) | 2.48002e9 | 1.64704 | 0.823522 | − | 0.567284i | \(-0.192006\pi\) | ||||
0.823522 | + | 0.567284i | \(0.192006\pi\) | |||||||
\(420\) | −3.13922e8 | −0.206752 | ||||||||
\(421\) | 6.39837e8 | 0.417909 | 0.208955 | − | 0.977925i | \(-0.432994\pi\) | ||||
0.208955 | + | 0.977925i | \(0.432994\pi\) | |||||||
\(422\) | −5.30127e8 | −0.343389 | ||||||||
\(423\) | 4.75646e8 | 0.305558 | ||||||||
\(424\) | 3.00303e8 | 0.191328 | ||||||||
\(425\) | 4.88212e9 | 3.08495 | ||||||||
\(426\) | −7.58374e8 | −0.475281 | ||||||||
\(427\) | 1.27068e8 | 0.0789840 | ||||||||
\(428\) | −1.52056e9 | −0.937452 | ||||||||
\(429\) | 2.21123e8 | 0.135217 | ||||||||
\(430\) | −3.36638e8 | −0.204185 | ||||||||
\(431\) | −9.03517e8 | −0.543583 | −0.271792 | − | 0.962356i | \(-0.587616\pi\) | ||||
−0.271792 | + | 0.962356i | \(0.587616\pi\) | |||||||
\(432\) | −8.06216e7 | −0.0481125 | ||||||||
\(433\) | 6.85293e8 | 0.405666 | 0.202833 | − | 0.979213i | \(-0.434985\pi\) | ||||
0.202833 | + | 0.979213i | \(0.434985\pi\) | |||||||
\(434\) | 6.11216e8 | 0.358906 | ||||||||
\(435\) | 2.28609e9 | 1.33162 | ||||||||
\(436\) | 8.77202e8 | 0.506870 | ||||||||
\(437\) | −3.53862e8 | −0.202838 | ||||||||
\(438\) | 1.30490e9 | 0.742025 | ||||||||
\(439\) | 6.71521e8 | 0.378821 | 0.189410 | − | 0.981898i | \(-0.439342\pi\) | ||||
0.189410 | + | 0.981898i | \(0.439342\pi\) | |||||||
\(440\) | 1.01087e9 | 0.565730 | ||||||||
\(441\) | 8.57661e7 | 0.0476190 | ||||||||
\(442\) | −4.23957e8 | −0.233531 | ||||||||
\(443\) | −2.23297e9 | −1.22031 | −0.610155 | − | 0.792282i | \(-0.708893\pi\) | ||||
−0.610155 | + | 0.792282i | \(0.708893\pi\) | |||||||
\(444\) | −3.79619e8 | −0.205829 | ||||||||
\(445\) | −1.47097e9 | −0.791307 | ||||||||
\(446\) | 2.25611e9 | 1.20417 | ||||||||
\(447\) | −1.19603e9 | −0.633380 | ||||||||
\(448\) | 8.99154e7 | 0.0472456 | ||||||||
\(449\) | −3.27633e9 | −1.70815 | −0.854075 | − | 0.520150i | \(-0.825876\pi\) | ||||
−0.854075 | + | 0.520150i | \(0.825876\pi\) | |||||||
\(450\) | 1.18039e9 | 0.610634 | ||||||||
\(451\) | −1.09219e8 | −0.0560634 | ||||||||
\(452\) | −1.43145e8 | −0.0729107 | ||||||||
\(453\) | 1.53455e9 | 0.775597 | ||||||||
\(454\) | −9.58440e8 | −0.480695 | ||||||||
\(455\) | −3.99125e8 | −0.198641 | ||||||||
\(456\) | −1.35730e8 | −0.0670348 | ||||||||
\(457\) | 3.24483e9 | 1.59032 | 0.795161 | − | 0.606398i | \(-0.207386\pi\) | ||||
0.795161 | + | 0.606398i | \(0.207386\pi\) | |||||||
\(458\) | 8.31685e7 | 0.0404510 | ||||||||
\(459\) | −4.74780e8 | −0.229165 | ||||||||
\(460\) | −1.22167e9 | −0.585198 | ||||||||
\(461\) | 2.24985e9 | 1.06955 | 0.534775 | − | 0.844994i | \(-0.320396\pi\) | ||||
0.534775 | + | 0.844994i | \(0.320396\pi\) | |||||||
\(462\) | −2.76177e8 | −0.130299 | ||||||||
\(463\) | −1.87496e9 | −0.877929 | −0.438964 | − | 0.898504i | \(-0.644655\pi\) | ||||
−0.438964 | + | 0.898504i | \(0.644655\pi\) | |||||||
\(464\) | −6.54795e8 | −0.304293 | ||||||||
\(465\) | −3.18536e9 | −1.46918 | ||||||||
\(466\) | −1.41175e9 | −0.646262 | ||||||||
\(467\) | −1.48428e9 | −0.674385 | −0.337192 | − | 0.941436i | \(-0.609477\pi\) | ||||
−0.337192 | + | 0.941436i | \(0.609477\pi\) | |||||||
\(468\) | −1.02503e8 | −0.0462250 | ||||||||
\(469\) | −1.21618e9 | −0.544367 | ||||||||
\(470\) | 2.76459e9 | 1.22826 | ||||||||
\(471\) | −2.10311e9 | −0.927447 | ||||||||
\(472\) | −5.68704e8 | −0.248937 | ||||||||
\(473\) | −2.96161e8 | −0.128681 | ||||||||
\(474\) | 1.02045e9 | 0.440115 | ||||||||
\(475\) | 1.98724e9 | 0.850791 | ||||||||
\(476\) | 5.29512e8 | 0.225036 | ||||||||
\(477\) | 4.27580e8 | 0.180386 | ||||||||
\(478\) | 1.98856e9 | 0.832799 | ||||||||
\(479\) | −1.16314e9 | −0.483568 | −0.241784 | − | 0.970330i | \(-0.577733\pi\) | ||||
−0.241784 | + | 0.970330i | \(0.577733\pi\) | |||||||
\(480\) | −4.68596e8 | −0.193399 | ||||||||
\(481\) | −4.82652e8 | −0.197754 | ||||||||
\(482\) | −2.92164e8 | −0.118840 | ||||||||
\(483\) | 3.33771e8 | 0.134782 | ||||||||
\(484\) | −3.57858e8 | −0.143467 | ||||||||
\(485\) | 2.04903e9 | 0.815552 | ||||||||
\(486\) | −1.14791e8 | −0.0453609 | ||||||||
\(487\) | 1.04706e9 | 0.410790 | 0.205395 | − | 0.978679i | \(-0.434152\pi\) | ||||
0.205395 | + | 0.978679i | \(0.434152\pi\) | |||||||
\(488\) | 1.89676e8 | 0.0738827 | ||||||||
\(489\) | 1.38901e9 | 0.537187 | ||||||||
\(490\) | 4.98497e8 | 0.191415 | ||||||||
\(491\) | 2.44817e8 | 0.0933374 | 0.0466687 | − | 0.998910i | \(-0.485139\pi\) | ||||
0.0466687 | + | 0.998910i | \(0.485139\pi\) | |||||||
\(492\) | 5.06293e7 | 0.0191657 | ||||||||
\(493\) | −3.85609e9 | −1.44938 | ||||||||
\(494\) | −1.72569e8 | −0.0644049 | ||||||||
\(495\) | 1.43930e9 | 0.533376 | ||||||||
\(496\) | 9.12370e8 | 0.335726 | ||||||||
\(497\) | 1.20427e9 | 0.440024 | ||||||||
\(498\) | −4.90752e8 | −0.178057 | ||||||||
\(499\) | −1.10896e9 | −0.399543 | −0.199771 | − | 0.979843i | \(-0.564020\pi\) | ||||
−0.199771 | + | 0.979843i | \(0.564020\pi\) | |||||||
\(500\) | 4.21253e9 | 1.50712 | ||||||||
\(501\) | −6.50509e8 | −0.231111 | ||||||||
\(502\) | 2.74963e9 | 0.970089 | ||||||||
\(503\) | −3.69487e9 | −1.29453 | −0.647264 | − | 0.762266i | \(-0.724087\pi\) | ||||
−0.647264 | + | 0.762266i | \(0.724087\pi\) | |||||||
\(504\) | 1.28024e8 | 0.0445435 | ||||||||
\(505\) | −2.20894e9 | −0.763245 | ||||||||
\(506\) | −1.07478e9 | −0.368802 | ||||||||
\(507\) | −1.30324e8 | −0.0444116 | ||||||||
\(508\) | −6.02556e8 | −0.203927 | ||||||||
\(509\) | 2.94308e8 | 0.0989213 | 0.0494606 | − | 0.998776i | \(-0.484250\pi\) | ||||
0.0494606 | + | 0.998776i | \(0.484250\pi\) | |||||||
\(510\) | −2.75956e9 | −0.921180 | ||||||||
\(511\) | −2.07214e9 | −0.686982 | ||||||||
\(512\) | 1.34218e8 | 0.0441942 | ||||||||
\(513\) | −1.93257e8 | −0.0632010 | ||||||||
\(514\) | −2.17832e9 | −0.707539 | ||||||||
\(515\) | 2.93818e9 | 0.947880 | ||||||||
\(516\) | 1.37288e8 | 0.0439904 | ||||||||
\(517\) | 2.43218e9 | 0.774068 | ||||||||
\(518\) | 6.02820e8 | 0.190561 | ||||||||
\(519\) | −2.37205e9 | −0.744797 | ||||||||
\(520\) | −5.95778e8 | −0.185812 | ||||||||
\(521\) | −4.14682e9 | −1.28465 | −0.642323 | − | 0.766434i | \(-0.722029\pi\) | ||||
−0.642323 | + | 0.766434i | \(0.722029\pi\) | |||||||
\(522\) | −9.32316e8 | −0.286891 | ||||||||
\(523\) | −1.27950e9 | −0.391096 | −0.195548 | − | 0.980694i | \(-0.562649\pi\) | ||||
−0.195548 | + | 0.980694i | \(0.562649\pi\) | |||||||
\(524\) | −1.04099e9 | −0.316072 | ||||||||
\(525\) | −1.87441e9 | −0.565337 | ||||||||
\(526\) | 2.84054e9 | 0.851041 | ||||||||
\(527\) | 5.37295e9 | 1.59910 | ||||||||
\(528\) | −4.12252e8 | −0.121883 | ||||||||
\(529\) | −2.10591e9 | −0.618507 | ||||||||
\(530\) | 2.48522e9 | 0.725101 | ||||||||
\(531\) | −8.09737e8 | −0.234700 | ||||||||
\(532\) | 2.15535e8 | 0.0620621 | ||||||||
\(533\) | 6.43707e7 | 0.0184138 | ||||||||
\(534\) | 5.99893e8 | 0.170482 | ||||||||
\(535\) | −1.25837e10 | −3.55278 | ||||||||
\(536\) | −1.81540e9 | −0.509209 | ||||||||
\(537\) | −2.01707e9 | −0.562095 | ||||||||
\(538\) | 2.29712e9 | 0.635984 | ||||||||
\(539\) | 4.38558e8 | 0.120633 | ||||||||
\(540\) | −6.67200e8 | −0.182338 | ||||||||
\(541\) | 1.56702e9 | 0.425486 | 0.212743 | − | 0.977108i | \(-0.431760\pi\) | ||||
0.212743 | + | 0.977108i | \(0.431760\pi\) | |||||||
\(542\) | −4.04702e9 | −1.09179 | ||||||||
\(543\) | −1.35029e9 | −0.361934 | ||||||||
\(544\) | 7.90408e8 | 0.210502 | ||||||||
\(545\) | 7.25946e9 | 1.92095 | ||||||||
\(546\) | 1.62771e8 | 0.0427960 | ||||||||
\(547\) | −1.56165e8 | −0.0407971 | −0.0203986 | − | 0.999792i | \(-0.506494\pi\) | ||||
−0.0203986 | + | 0.999792i | \(0.506494\pi\) | |||||||
\(548\) | −1.34092e9 | −0.348073 | ||||||||
\(549\) | 2.70066e8 | 0.0696573 | ||||||||
\(550\) | 6.03582e9 | 1.54692 | ||||||||
\(551\) | −1.56960e9 | −0.399722 | ||||||||
\(552\) | 4.98224e8 | 0.126077 | ||||||||
\(553\) | −1.62043e9 | −0.407467 | ||||||||
\(554\) | 2.85802e9 | 0.714137 | ||||||||
\(555\) | −3.14161e9 | −0.780057 | ||||||||
\(556\) | −1.55296e9 | −0.383177 | ||||||||
\(557\) | 3.69047e9 | 0.904875 | 0.452438 | − | 0.891796i | \(-0.350554\pi\) | ||||
0.452438 | + | 0.891796i | \(0.350554\pi\) | |||||||
\(558\) | 1.29906e9 | 0.316525 | ||||||||
\(559\) | 1.74549e8 | 0.0422646 | ||||||||
\(560\) | 7.44113e8 | 0.179053 | ||||||||
\(561\) | −2.42775e9 | −0.580543 | ||||||||
\(562\) | −2.49019e9 | −0.591773 | ||||||||
\(563\) | −4.93440e9 | −1.16535 | −0.582673 | − | 0.812706i | \(-0.697993\pi\) | ||||
−0.582673 | + | 0.812706i | \(0.697993\pi\) | |||||||
\(564\) | −1.12746e9 | −0.264621 | ||||||||
\(565\) | −1.18462e9 | −0.276319 | ||||||||
\(566\) | −2.76173e9 | −0.640212 | ||||||||
\(567\) | 1.82284e8 | 0.0419961 | ||||||||
\(568\) | 1.79763e9 | 0.411605 | ||||||||
\(569\) | −7.09618e9 | −1.61485 | −0.807424 | − | 0.589972i | \(-0.799139\pi\) | ||||
−0.807424 | + | 0.589972i | \(0.799139\pi\) | |||||||
\(570\) | −1.12326e9 | −0.254050 | ||||||||
\(571\) | 4.29669e9 | 0.965845 | 0.482922 | − | 0.875663i | \(-0.339575\pi\) | ||||
0.482922 | + | 0.875663i | \(0.339575\pi\) | |||||||
\(572\) | −5.24142e8 | −0.117102 | ||||||||
\(573\) | −4.82630e9 | −1.07170 | ||||||||
\(574\) | −8.03975e7 | −0.0177440 | ||||||||
\(575\) | −7.29454e9 | −1.60015 | ||||||||
\(576\) | 1.91103e8 | 0.0416667 | ||||||||
\(577\) | 7.52264e9 | 1.63025 | 0.815126 | − | 0.579284i | \(-0.196668\pi\) | ||||
0.815126 | + | 0.579284i | \(0.196668\pi\) | |||||||
\(578\) | 1.37201e9 | 0.295535 | ||||||||
\(579\) | −6.79882e8 | −0.145566 | ||||||||
\(580\) | −5.41889e9 | −1.15322 | ||||||||
\(581\) | 7.79296e8 | 0.164849 | ||||||||
\(582\) | −8.35635e8 | −0.175706 | ||||||||
\(583\) | 2.18640e9 | 0.456971 | ||||||||
\(584\) | −3.09310e9 | −0.642612 | ||||||||
\(585\) | −8.48286e8 | −0.175185 | ||||||||
\(586\) | −5.62750e9 | −1.15525 | ||||||||
\(587\) | −6.87873e9 | −1.40370 | −0.701851 | − | 0.712324i | \(-0.747643\pi\) | ||||
−0.701851 | + | 0.712324i | \(0.747643\pi\) | |||||||
\(588\) | −2.03297e8 | −0.0412393 | ||||||||
\(589\) | 2.18703e9 | 0.441012 | ||||||||
\(590\) | −4.70642e9 | −0.943429 | ||||||||
\(591\) | −3.33677e9 | −0.664922 | ||||||||
\(592\) | 8.99837e8 | 0.178253 | ||||||||
\(593\) | 7.09887e9 | 1.39797 | 0.698985 | − | 0.715137i | \(-0.253636\pi\) | ||||
0.698985 | + | 0.715137i | \(0.253636\pi\) | |||||||
\(594\) | −5.86976e8 | −0.114913 | ||||||||
\(595\) | 4.38208e9 | 0.852847 | ||||||||
\(596\) | 2.83503e9 | 0.548523 | ||||||||
\(597\) | −7.83051e8 | −0.150619 | ||||||||
\(598\) | 6.33447e8 | 0.121131 | ||||||||
\(599\) | 6.05066e9 | 1.15029 | 0.575147 | − | 0.818050i | \(-0.304945\pi\) | ||||
0.575147 | + | 0.818050i | \(0.304945\pi\) | |||||||
\(600\) | −2.79796e9 | −0.528824 | ||||||||
\(601\) | −2.45316e9 | −0.460962 | −0.230481 | − | 0.973077i | \(-0.574030\pi\) | ||||
−0.230481 | + | 0.973077i | \(0.574030\pi\) | |||||||
\(602\) | −2.18008e8 | −0.0407272 | ||||||||
\(603\) | −2.58482e9 | −0.480087 | ||||||||
\(604\) | −3.63744e9 | −0.671687 | ||||||||
\(605\) | −2.96153e9 | −0.543716 | ||||||||
\(606\) | 9.00851e8 | 0.164437 | ||||||||
\(607\) | −9.44990e9 | −1.71501 | −0.857506 | − | 0.514475i | \(-0.827987\pi\) | ||||
−0.857506 | + | 0.514475i | \(0.827987\pi\) | |||||||
\(608\) | 3.21731e8 | 0.0580538 | ||||||||
\(609\) | 1.48048e9 | 0.265609 | ||||||||
\(610\) | 1.56970e9 | 0.280003 | ||||||||
\(611\) | −1.43346e9 | −0.254239 | ||||||||
\(612\) | 1.12541e9 | 0.198463 | ||||||||
\(613\) | 3.84994e9 | 0.675060 | 0.337530 | − | 0.941315i | \(-0.390409\pi\) | ||||
0.337530 | + | 0.941315i | \(0.390409\pi\) | |||||||
\(614\) | 2.91500e9 | 0.508216 | ||||||||
\(615\) | 4.18993e8 | 0.0726347 | ||||||||
\(616\) | 6.54641e8 | 0.112842 | ||||||||
\(617\) | 7.81668e9 | 1.33975 | 0.669876 | − | 0.742473i | \(-0.266347\pi\) | ||||
0.669876 | + | 0.742473i | \(0.266347\pi\) | |||||||
\(618\) | −1.19825e9 | −0.204215 | ||||||||
\(619\) | 4.99558e9 | 0.846582 | 0.423291 | − | 0.905994i | \(-0.360875\pi\) | ||||
0.423291 | + | 0.905994i | \(0.360875\pi\) | |||||||
\(620\) | 7.55049e9 | 1.27234 | ||||||||
\(621\) | 7.09385e8 | 0.118867 | ||||||||
\(622\) | −8.36931e9 | −1.39452 | ||||||||
\(623\) | −9.52608e8 | −0.157836 | ||||||||
\(624\) | 2.42971e8 | 0.0400320 | ||||||||
\(625\) | 1.90492e10 | 3.12103 | ||||||||
\(626\) | 4.10396e9 | 0.668641 | ||||||||
\(627\) | −9.88203e8 | −0.160107 | ||||||||
\(628\) | 4.98515e9 | 0.803193 | ||||||||
\(629\) | 5.29914e9 | 0.849040 | ||||||||
\(630\) | 1.05949e9 | 0.168812 | ||||||||
\(631\) | 3.39241e9 | 0.537533 | 0.268767 | − | 0.963205i | \(-0.413384\pi\) | ||||
0.268767 | + | 0.963205i | \(0.413384\pi\) | |||||||
\(632\) | −2.41883e9 | −0.381150 | ||||||||
\(633\) | 1.78918e9 | 0.280376 | ||||||||
\(634\) | 7.54747e9 | 1.17622 | ||||||||
\(635\) | −4.98657e9 | −0.772848 | ||||||||
\(636\) | −1.01352e9 | −0.156219 | ||||||||
\(637\) | −2.58475e8 | −0.0396214 | ||||||||
\(638\) | −4.76732e9 | −0.726779 | ||||||||
\(639\) | 2.55951e9 | 0.388065 | ||||||||
\(640\) | 1.11075e9 | 0.167488 | ||||||||
\(641\) | 8.25496e9 | 1.23798 | 0.618988 | − | 0.785401i | \(-0.287543\pi\) | ||||
0.618988 | + | 0.785401i | \(0.287543\pi\) | |||||||
\(642\) | 5.13187e9 | 0.765426 | ||||||||
\(643\) | −3.80038e9 | −0.563753 | −0.281876 | − | 0.959451i | \(-0.590957\pi\) | ||||
−0.281876 | + | 0.959451i | \(0.590957\pi\) | |||||||
\(644\) | −7.91161e8 | −0.116725 | ||||||||
\(645\) | 1.13615e9 | 0.166716 | ||||||||
\(646\) | 1.89468e9 | 0.276516 | ||||||||
\(647\) | −6.58053e9 | −0.955204 | −0.477602 | − | 0.878576i | \(-0.658494\pi\) | ||||
−0.477602 | + | 0.878576i | \(0.658494\pi\) | |||||||
\(648\) | 2.72098e8 | 0.0392837 | ||||||||
\(649\) | −4.14053e9 | −0.594565 | ||||||||
\(650\) | −3.55736e9 | −0.508078 | ||||||||
\(651\) | −2.06286e9 | −0.293046 | ||||||||
\(652\) | −3.29248e9 | −0.465218 | ||||||||
\(653\) | −6.68693e9 | −0.939790 | −0.469895 | − | 0.882722i | \(-0.655708\pi\) | ||||
−0.469895 | + | 0.882722i | \(0.655708\pi\) | |||||||
\(654\) | −2.96056e9 | −0.413858 | ||||||||
\(655\) | −8.61491e9 | −1.19786 | ||||||||
\(656\) | −1.20010e8 | −0.0165980 | ||||||||
\(657\) | −4.40404e9 | −0.605861 | ||||||||
\(658\) | 1.79036e9 | 0.244991 | ||||||||
\(659\) | 8.02087e8 | 0.109175 | 0.0545874 | − | 0.998509i | \(-0.482616\pi\) | ||||
0.0545874 | + | 0.998509i | \(0.482616\pi\) | |||||||
\(660\) | −3.41167e9 | −0.461917 | ||||||||
\(661\) | 7.97403e9 | 1.07392 | 0.536961 | − | 0.843607i | \(-0.319572\pi\) | ||||
0.536961 | + | 0.843607i | \(0.319572\pi\) | |||||||
\(662\) | −5.21631e9 | −0.698812 | ||||||||
\(663\) | 1.43085e9 | 0.190677 | ||||||||
\(664\) | 1.16326e9 | 0.154202 | ||||||||
\(665\) | 1.78370e9 | 0.235205 | ||||||||
\(666\) | 1.28121e9 | 0.168059 | ||||||||
\(667\) | 5.76151e9 | 0.751788 | ||||||||
\(668\) | 1.54195e9 | 0.200148 | ||||||||
\(669\) | −7.61438e9 | −0.983203 | ||||||||
\(670\) | −1.50237e10 | −1.92981 | ||||||||
\(671\) | 1.38096e9 | 0.176463 | ||||||||
\(672\) | −3.03464e8 | −0.0385758 | ||||||||
\(673\) | −1.27130e10 | −1.60766 | −0.803831 | − | 0.594857i | \(-0.797209\pi\) | ||||
−0.803831 | + | 0.594857i | \(0.797209\pi\) | |||||||
\(674\) | −4.25110e9 | −0.534800 | ||||||||
\(675\) | −3.98381e9 | −0.498580 | ||||||||
\(676\) | 3.08916e8 | 0.0384615 | ||||||||
\(677\) | −5.15085e9 | −0.637997 | −0.318999 | − | 0.947755i | \(-0.603347\pi\) | ||||
−0.318999 | + | 0.947755i | \(0.603347\pi\) | |||||||
\(678\) | 4.83114e8 | 0.0595314 | ||||||||
\(679\) | 1.32696e9 | 0.162672 | ||||||||
\(680\) | 6.54118e9 | 0.797765 | ||||||||
\(681\) | 3.23474e9 | 0.392486 | ||||||||
\(682\) | 6.64263e9 | 0.801853 | ||||||||
\(683\) | −1.06047e10 | −1.27358 | −0.636790 | − | 0.771037i | \(-0.719738\pi\) | ||||
−0.636790 | + | 0.771037i | \(0.719738\pi\) | |||||||
\(684\) | 4.58090e8 | 0.0547337 | ||||||||
\(685\) | −1.10970e10 | −1.31914 | ||||||||
\(686\) | 3.22829e8 | 0.0381802 | ||||||||
\(687\) | −2.80694e8 | −0.0330281 | ||||||||
\(688\) | −3.25423e8 | −0.0380968 | ||||||||
\(689\) | −1.28860e9 | −0.150090 | ||||||||
\(690\) | 4.12315e9 | 0.477812 | ||||||||
\(691\) | −8.18703e9 | −0.943959 | −0.471979 | − | 0.881610i | \(-0.656460\pi\) | ||||
−0.471979 | + | 0.881610i | \(0.656460\pi\) | |||||||
\(692\) | 5.62264e9 | 0.645013 | ||||||||
\(693\) | 9.32096e8 | 0.106388 | ||||||||
\(694\) | −3.74427e9 | −0.425215 | ||||||||
\(695\) | −1.28519e10 | −1.45218 | ||||||||
\(696\) | 2.20993e9 | 0.248454 | ||||||||
\(697\) | −7.06741e8 | −0.0790579 | ||||||||
\(698\) | 4.69934e8 | 0.0523050 | ||||||||
\(699\) | 4.76467e9 | 0.527670 | ||||||||
\(700\) | 4.44305e9 | 0.489596 | ||||||||
\(701\) | −1.01784e10 | −1.11601 | −0.558005 | − | 0.829838i | \(-0.688433\pi\) | ||||
−0.558005 | + | 0.829838i | \(0.688433\pi\) | |||||||
\(702\) | 3.45948e8 | 0.0377426 | ||||||||
\(703\) | 2.15698e9 | 0.234155 | ||||||||
\(704\) | 9.77190e8 | 0.105554 | ||||||||
\(705\) | −9.33050e9 | −1.00287 | ||||||||
\(706\) | 5.01107e9 | 0.535937 | ||||||||
\(707\) | −1.43052e9 | −0.152239 | ||||||||
\(708\) | 1.91938e9 | 0.203256 | ||||||||
\(709\) | 6.47872e9 | 0.682696 | 0.341348 | − | 0.939937i | \(-0.389117\pi\) | ||||
0.341348 | + | 0.939937i | \(0.389117\pi\) | |||||||
\(710\) | 1.48766e10 | 1.55991 | ||||||||
\(711\) | −3.44400e9 | −0.359352 | ||||||||
\(712\) | −1.42197e9 | −0.147642 | ||||||||
\(713\) | −8.02789e9 | −0.829446 | ||||||||
\(714\) | −1.78710e9 | −0.183741 | ||||||||
\(715\) | −4.33764e9 | −0.443795 | ||||||||
\(716\) | 4.78119e9 | 0.486789 | ||||||||
\(717\) | −6.71138e9 | −0.679978 | ||||||||
\(718\) | −5.01566e9 | −0.505700 | ||||||||
\(719\) | 2.52939e9 | 0.253784 | 0.126892 | − | 0.991917i | \(-0.459500\pi\) | ||||
0.126892 | + | 0.991917i | \(0.459500\pi\) | |||||||
\(720\) | 1.58151e9 | 0.157910 | ||||||||
\(721\) | 1.90278e9 | 0.189067 | ||||||||
\(722\) | −6.37976e9 | −0.630847 | ||||||||
\(723\) | 9.86055e8 | 0.0970325 | ||||||||
\(724\) | 3.20070e9 | 0.313444 | ||||||||
\(725\) | −3.23558e10 | −3.15333 | ||||||||
\(726\) | 1.20777e9 | 0.117140 | ||||||||
\(727\) | −1.55617e10 | −1.50205 | −0.751027 | − | 0.660272i | \(-0.770441\pi\) | ||||
−0.751027 | + | 0.660272i | \(0.770441\pi\) | |||||||
\(728\) | −3.85828e8 | −0.0370625 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −2.55976e10 | −2.43539 | ||||||||
\(731\) | −1.91642e9 | −0.181459 | ||||||||
\(732\) | −6.40156e8 | −0.0603250 | ||||||||
\(733\) | −9.41674e9 | −0.883155 | −0.441577 | − | 0.897223i | \(-0.645581\pi\) | ||||
−0.441577 | + | 0.897223i | \(0.645581\pi\) | |||||||
\(734\) | −1.51010e9 | −0.140951 | ||||||||
\(735\) | −1.68243e9 | −0.156290 | ||||||||
\(736\) | −1.18097e9 | −0.109186 | ||||||||
\(737\) | −1.32173e10 | −1.21620 | ||||||||
\(738\) | −1.70874e8 | −0.0156487 | ||||||||
\(739\) | 2.34008e8 | 0.0213292 | 0.0106646 | − | 0.999943i | \(-0.496605\pi\) | ||||
0.0106646 | + | 0.999943i | \(0.496605\pi\) | |||||||
\(740\) | 7.44677e9 | 0.675550 | ||||||||
\(741\) | 5.82421e8 | 0.0525864 | ||||||||
\(742\) | 1.60944e9 | 0.144631 | ||||||||
\(743\) | 1.99362e10 | 1.78312 | 0.891561 | − | 0.452901i | \(-0.149611\pi\) | ||||
0.891561 | + | 0.452901i | \(0.149611\pi\) | |||||||
\(744\) | −3.07925e9 | −0.274119 | ||||||||
\(745\) | 2.34618e10 | 2.07881 | ||||||||
\(746\) | −4.30859e9 | −0.379970 | ||||||||
\(747\) | 1.65629e9 | 0.145383 | ||||||||
\(748\) | 5.75467e9 | 0.502765 | ||||||||
\(749\) | −8.14923e9 | −0.708647 | ||||||||
\(750\) | −1.42173e10 | −1.23056 | ||||||||
\(751\) | 1.01576e10 | 0.875091 | 0.437545 | − | 0.899196i | \(-0.355848\pi\) | ||||
0.437545 | + | 0.899196i | \(0.355848\pi\) | |||||||
\(752\) | 2.67249e9 | 0.229168 | ||||||||
\(753\) | −9.28001e9 | −0.792074 | ||||||||
\(754\) | 2.80974e9 | 0.238707 | ||||||||
\(755\) | −3.01024e10 | −2.54558 | ||||||||
\(756\) | −4.32081e8 | −0.0363696 | ||||||||
\(757\) | −4.40537e9 | −0.369102 | −0.184551 | − | 0.982823i | \(-0.559083\pi\) | ||||
−0.184551 | + | 0.982823i | \(0.559083\pi\) | |||||||
\(758\) | −1.13345e10 | −0.945276 | ||||||||
\(759\) | 3.62738e9 | 0.301125 | ||||||||
\(760\) | 2.66255e9 | 0.220014 | ||||||||
\(761\) | −2.28127e9 | −0.187642 | −0.0938210 | − | 0.995589i | \(-0.529908\pi\) | ||||
−0.0938210 | + | 0.995589i | \(0.529908\pi\) | |||||||
\(762\) | 2.03363e9 | 0.166506 | ||||||||
\(763\) | 4.70125e9 | 0.383158 | ||||||||
\(764\) | 1.14401e10 | 0.928119 | ||||||||
\(765\) | 9.31352e9 | 0.752140 | ||||||||
\(766\) | −1.69405e9 | −0.136184 | ||||||||
\(767\) | 2.44032e9 | 0.195282 | ||||||||
\(768\) | −4.52985e8 | −0.0360844 | ||||||||
\(769\) | −1.11493e10 | −0.884112 | −0.442056 | − | 0.896987i | \(-0.645751\pi\) | ||||
−0.442056 | + | 0.896987i | \(0.645751\pi\) | |||||||
\(770\) | 5.41761e9 | 0.427652 | ||||||||
\(771\) | 7.35182e9 | 0.577703 | ||||||||
\(772\) | 1.61157e9 | 0.126063 | ||||||||
\(773\) | −2.11163e10 | −1.64433 | −0.822167 | − | 0.569247i | \(-0.807235\pi\) | ||||
−0.822167 | + | 0.569247i | \(0.807235\pi\) | |||||||
\(774\) | −4.63346e8 | −0.0359180 | ||||||||
\(775\) | 4.50835e10 | 3.47906 | ||||||||
\(776\) | 1.98076e9 | 0.152166 | ||||||||
\(777\) | −2.03452e9 | −0.155592 | ||||||||
\(778\) | 1.57786e10 | 1.20127 | ||||||||
\(779\) | −2.87675e8 | −0.0218032 | ||||||||
\(780\) | 2.01075e9 | 0.151715 | ||||||||
\(781\) | 1.30879e10 | 0.983084 | ||||||||
\(782\) | −6.95476e9 | −0.520066 | ||||||||
\(783\) | 3.14657e9 | 0.234245 | ||||||||
\(784\) | 4.81890e8 | 0.0357143 | ||||||||
\(785\) | 4.12556e10 | 3.04396 | ||||||||
\(786\) | 3.51334e9 | 0.258072 | ||||||||
\(787\) | −6.54202e9 | −0.478410 | −0.239205 | − | 0.970969i | \(-0.576887\pi\) | ||||
−0.239205 | + | 0.970969i | \(0.576887\pi\) | |||||||
\(788\) | 7.90939e9 | 0.575839 | ||||||||
\(789\) | −9.58681e9 | −0.694872 | ||||||||
\(790\) | −2.00175e10 | −1.44449 | ||||||||
\(791\) | −7.67167e8 | −0.0551153 | ||||||||
\(792\) | 1.39135e9 | 0.0995173 | ||||||||
\(793\) | −8.13903e8 | −0.0579584 | ||||||||
\(794\) | −1.20554e10 | −0.854693 | ||||||||
\(795\) | −8.38761e9 | −0.592043 | ||||||||
\(796\) | 1.85612e9 | 0.130440 | ||||||||
\(797\) | 9.86813e9 | 0.690447 | 0.345224 | − | 0.938520i | \(-0.387803\pi\) | ||||
0.345224 | + | 0.938520i | \(0.387803\pi\) | |||||||
\(798\) | −7.27430e8 | −0.0506735 | ||||||||
\(799\) | 1.57383e10 | 1.09155 | ||||||||
\(800\) | 6.63219e9 | 0.457975 | ||||||||
\(801\) | −2.02464e9 | −0.139198 | ||||||||
\(802\) | 1.17972e10 | 0.807549 | ||||||||
\(803\) | −2.25197e10 | −1.53483 | ||||||||
\(804\) | 6.12698e9 | 0.415767 | ||||||||
\(805\) | −6.54741e9 | −0.442368 | ||||||||
\(806\) | −3.91499e9 | −0.263365 | ||||||||
\(807\) | −7.75279e9 | −0.519279 | ||||||||
\(808\) | −2.13535e9 | −0.142406 | ||||||||
\(809\) | −2.46408e10 | −1.63619 | −0.818097 | − | 0.575081i | \(-0.804971\pi\) | ||||
−0.818097 | + | 0.575081i | \(0.804971\pi\) | |||||||
\(810\) | 2.25180e9 | 0.148879 | ||||||||
\(811\) | 2.37028e9 | 0.156037 | 0.0780184 | − | 0.996952i | \(-0.475141\pi\) | ||||
0.0780184 | + | 0.996952i | \(0.475141\pi\) | |||||||
\(812\) | −3.50929e9 | −0.230024 | ||||||||
\(813\) | 1.36587e10 | 0.891439 | ||||||||
\(814\) | 6.55138e9 | 0.425743 | ||||||||
\(815\) | −2.72476e10 | −1.76310 | ||||||||
\(816\) | −2.66763e9 | −0.171874 | ||||||||
\(817\) | −7.80066e8 | −0.0500442 | ||||||||
\(818\) | 5.52011e9 | 0.352623 | ||||||||
\(819\) | −5.49353e8 | −0.0349428 | ||||||||
\(820\) | −9.93169e8 | −0.0629035 | ||||||||
\(821\) | −1.17171e10 | −0.738956 | −0.369478 | − | 0.929239i | \(-0.620464\pi\) | ||||
−0.369478 | + | 0.929239i | \(0.620464\pi\) | |||||||
\(822\) | 4.52560e9 | 0.284200 | ||||||||
\(823\) | 1.94300e10 | 1.21499 | 0.607496 | − | 0.794323i | \(-0.292174\pi\) | ||||
0.607496 | + | 0.794323i | \(0.292174\pi\) | |||||||
\(824\) | 2.84030e9 | 0.176856 | ||||||||
\(825\) | −2.03709e10 | −1.26305 | ||||||||
\(826\) | −3.04790e9 | −0.188179 | ||||||||
\(827\) | −1.04477e10 | −0.642319 | −0.321159 | − | 0.947025i | \(-0.604073\pi\) | ||||
−0.321159 | + | 0.947025i | \(0.604073\pi\) | |||||||
\(828\) | −1.68150e9 | −0.102942 | ||||||||
\(829\) | 8.73946e9 | 0.532775 | 0.266387 | − | 0.963866i | \(-0.414170\pi\) | ||||
0.266387 | + | 0.963866i | \(0.414170\pi\) | |||||||
\(830\) | 9.62682e9 | 0.584399 | ||||||||
\(831\) | −9.64582e9 | −0.583090 | ||||||||
\(832\) | −5.75930e8 | −0.0346688 | ||||||||
\(833\) | 2.83785e9 | 0.170111 | ||||||||
\(834\) | 5.24126e9 | 0.312863 | ||||||||
\(835\) | 1.27607e10 | 0.758527 | ||||||||
\(836\) | 2.34241e9 | 0.138657 | ||||||||
\(837\) | −4.38432e9 | −0.258442 | ||||||||
\(838\) | 1.98401e10 | 1.16464 | ||||||||
\(839\) | 9.85221e9 | 0.575926 | 0.287963 | − | 0.957642i | \(-0.407022\pi\) | ||||
0.287963 | + | 0.957642i | \(0.407022\pi\) | |||||||
\(840\) | −2.51138e9 | −0.146196 | ||||||||
\(841\) | 8.30601e9 | 0.481511 | ||||||||
\(842\) | 5.11870e9 | 0.295506 | ||||||||
\(843\) | 8.40439e9 | 0.483181 | ||||||||
\(844\) | −4.24102e9 | −0.242813 | ||||||||
\(845\) | 2.55649e9 | 0.145763 | ||||||||
\(846\) | 3.80517e9 | 0.216062 | ||||||||
\(847\) | −1.91790e9 | −0.108451 | ||||||||
\(848\) | 2.40242e9 | 0.135290 | ||||||||
\(849\) | 9.32084e9 | 0.522731 | ||||||||
\(850\) | 3.90570e10 | 2.18139 | ||||||||
\(851\) | −7.91761e9 | −0.440393 | ||||||||
\(852\) | −6.06699e9 | −0.336074 | ||||||||
\(853\) | −2.69371e10 | −1.48604 | −0.743019 | − | 0.669270i | \(-0.766607\pi\) | ||||
−0.743019 | + | 0.669270i | \(0.766607\pi\) | |||||||
\(854\) | 1.01654e9 | 0.0558501 | ||||||||
\(855\) | 3.79101e9 | 0.207431 | ||||||||
\(856\) | −1.21644e10 | −0.662879 | ||||||||
\(857\) | −2.42559e10 | −1.31639 | −0.658194 | − | 0.752848i | \(-0.728680\pi\) | ||||
−0.658194 | + | 0.752848i | \(0.728680\pi\) | |||||||
\(858\) | 1.76898e9 | 0.0956131 | ||||||||
\(859\) | −1.59346e10 | −0.857761 | −0.428880 | − | 0.903361i | \(-0.641092\pi\) | ||||
−0.428880 | + | 0.903361i | \(0.641092\pi\) | |||||||
\(860\) | −2.69310e9 | −0.144380 | ||||||||
\(861\) | 2.71342e8 | 0.0144879 | ||||||||
\(862\) | −7.22814e9 | −0.384371 | ||||||||
\(863\) | 1.82541e10 | 0.966767 | 0.483384 | − | 0.875409i | \(-0.339408\pi\) | ||||
0.483384 | + | 0.875409i | \(0.339408\pi\) | |||||||
\(864\) | −6.44973e8 | −0.0340207 | ||||||||
\(865\) | 4.65312e10 | 2.44449 | ||||||||
\(866\) | 5.48234e9 | 0.286849 | ||||||||
\(867\) | −4.63052e9 | −0.241303 | ||||||||
\(868\) | 4.88973e9 | 0.253785 | ||||||||
\(869\) | −1.76107e10 | −0.910345 | ||||||||
\(870\) | 1.82887e10 | 0.941600 | ||||||||
\(871\) | 7.78992e9 | 0.399456 | ||||||||
\(872\) | 7.01761e9 | 0.358411 | ||||||||
\(873\) | 2.82027e9 | 0.143463 | ||||||||
\(874\) | −2.83090e9 | −0.143428 | ||||||||
\(875\) | 2.25765e10 | 1.13928 | ||||||||
\(876\) | 1.04392e10 | 0.524691 | ||||||||
\(877\) | 2.98698e10 | 1.49532 | 0.747660 | − | 0.664082i | \(-0.231177\pi\) | ||||
0.747660 | + | 0.664082i | \(0.231177\pi\) | |||||||
\(878\) | 5.37217e9 | 0.267867 | ||||||||
\(879\) | 1.89928e10 | 0.943254 | ||||||||
\(880\) | 8.08693e9 | 0.400032 | ||||||||
\(881\) | −3.44603e10 | −1.69787 | −0.848933 | − | 0.528501i | \(-0.822754\pi\) | ||||
−0.848933 | + | 0.528501i | \(0.822754\pi\) | |||||||
\(882\) | 6.86129e8 | 0.0336718 | ||||||||
\(883\) | 2.69143e10 | 1.31559 | 0.657794 | − | 0.753197i | \(-0.271490\pi\) | ||||
0.657794 | + | 0.753197i | \(0.271490\pi\) | |||||||
\(884\) | −3.39165e9 | −0.165131 | ||||||||
\(885\) | 1.58842e10 | 0.770306 | ||||||||
\(886\) | −1.78638e10 | −0.862889 | ||||||||
\(887\) | −3.92756e10 | −1.88969 | −0.944844 | − | 0.327522i | \(-0.893787\pi\) | ||||
−0.944844 | + | 0.327522i | \(0.893787\pi\) | |||||||
\(888\) | −3.03695e9 | −0.145543 | ||||||||
\(889\) | −3.22932e9 | −0.154154 | ||||||||
\(890\) | −1.17678e10 | −0.559538 | ||||||||
\(891\) | 1.98104e9 | 0.0938258 | ||||||||
\(892\) | 1.80489e10 | 0.851479 | ||||||||
\(893\) | 6.40619e9 | 0.301037 | ||||||||
\(894\) | −9.56821e9 | −0.447867 | ||||||||
\(895\) | 3.95677e10 | 1.84485 | ||||||||
\(896\) | 7.19323e8 | 0.0334077 | ||||||||
\(897\) | −2.13789e9 | −0.0989033 | ||||||||
\(898\) | −2.62107e10 | −1.20784 | ||||||||
\(899\) | −3.56087e10 | −1.63455 | ||||||||
\(900\) | 9.44310e9 | 0.431783 | ||||||||
\(901\) | 1.41479e10 | 0.644398 | ||||||||
\(902\) | −8.73751e8 | −0.0396428 | ||||||||
\(903\) | 7.35777e8 | 0.0332536 | ||||||||
\(904\) | −1.14516e9 | −0.0515557 | ||||||||
\(905\) | 2.64880e10 | 1.18790 | ||||||||
\(906\) | 1.22764e10 | 0.548430 | ||||||||
\(907\) | 7.28341e9 | 0.324123 | 0.162061 | − | 0.986781i | \(-0.448186\pi\) | ||||
0.162061 | + | 0.986781i | \(0.448186\pi\) | |||||||
\(908\) | −7.66752e9 | −0.339903 | ||||||||
\(909\) | −3.04037e9 | −0.134262 | ||||||||
\(910\) | −3.19300e9 | −0.140460 | ||||||||
\(911\) | 3.07735e10 | 1.34854 | 0.674269 | − | 0.738486i | \(-0.264459\pi\) | ||||
0.674269 | + | 0.738486i | \(0.264459\pi\) | |||||||
\(912\) | −1.08584e9 | −0.0474007 | ||||||||
\(913\) | 8.46930e9 | 0.368298 | ||||||||
\(914\) | 2.59586e10 | 1.12453 | ||||||||
\(915\) | −5.29774e9 | −0.228621 | ||||||||
\(916\) | 6.65348e8 | 0.0286032 | ||||||||
\(917\) | −5.57905e9 | −0.238928 | ||||||||
\(918\) | −3.79824e9 | −0.162044 | ||||||||
\(919\) | 1.31495e10 | 0.558863 | 0.279431 | − | 0.960166i | \(-0.409854\pi\) | ||||
0.279431 | + | 0.960166i | \(0.409854\pi\) | |||||||
\(920\) | −9.77339e9 | −0.413797 | ||||||||
\(921\) | −9.83811e9 | −0.414957 | ||||||||
\(922\) | 1.79988e10 | 0.756286 | ||||||||
\(923\) | −7.71365e9 | −0.322890 | ||||||||
\(924\) | −2.20941e9 | −0.0921351 | ||||||||
\(925\) | 4.44642e10 | 1.84720 | ||||||||
\(926\) | −1.49997e10 | −0.620790 | ||||||||
\(927\) | 4.04410e9 | 0.166741 | ||||||||
\(928\) | −5.23836e9 | −0.215168 | ||||||||
\(929\) | 5.08773e9 | 0.208195 | 0.104097 | − | 0.994567i | \(-0.466805\pi\) | ||||
0.104097 | + | 0.994567i | \(0.466805\pi\) | |||||||
\(930\) | −2.54829e10 | −1.03886 | ||||||||
\(931\) | 1.15513e9 | 0.0469146 | ||||||||
\(932\) | −1.12940e10 | −0.456976 | ||||||||
\(933\) | 2.82464e10 | 1.13862 | ||||||||
\(934\) | −1.18743e10 | −0.476862 | ||||||||
\(935\) | 4.76239e10 | 1.90539 | ||||||||
\(936\) | −8.20026e8 | −0.0326860 | ||||||||
\(937\) | −2.49041e10 | −0.988968 | −0.494484 | − | 0.869187i | \(-0.664643\pi\) | ||||
−0.494484 | + | 0.869187i | \(0.664643\pi\) | |||||||
\(938\) | −9.72942e9 | −0.384926 | ||||||||
\(939\) | −1.38509e10 | −0.545943 | ||||||||
\(940\) | 2.21168e10 | 0.868508 | ||||||||
\(941\) | −4.73818e9 | −0.185374 | −0.0926868 | − | 0.995695i | \(-0.529546\pi\) | ||||
−0.0926868 | + | 0.995695i | \(0.529546\pi\) | |||||||
\(942\) | −1.68249e10 | −0.655804 | ||||||||
\(943\) | 1.05596e9 | 0.0410070 | ||||||||
\(944\) | −4.54963e9 | −0.176025 | ||||||||
\(945\) | −3.57577e9 | −0.137835 | ||||||||
\(946\) | −2.36928e9 | −0.0909910 | ||||||||
\(947\) | 3.83034e10 | 1.46559 | 0.732794 | − | 0.680450i | \(-0.238216\pi\) | ||||
0.732794 | + | 0.680450i | \(0.238216\pi\) | |||||||
\(948\) | 8.16357e9 | 0.311208 | ||||||||
\(949\) | 1.32725e10 | 0.504107 | ||||||||
\(950\) | 1.58979e10 | 0.601600 | ||||||||
\(951\) | −2.54727e10 | −0.960380 | ||||||||
\(952\) | 4.23609e9 | 0.159124 | ||||||||
\(953\) | 2.03440e10 | 0.761397 | 0.380698 | − | 0.924699i | \(-0.375684\pi\) | ||||
0.380698 | + | 0.924699i | \(0.375684\pi\) | |||||||
\(954\) | 3.42064e9 | 0.127552 | ||||||||
\(955\) | 9.46749e10 | 3.51741 | ||||||||
\(956\) | 1.59085e10 | 0.588878 | ||||||||
\(957\) | 1.60897e10 | 0.593412 | ||||||||
\(958\) | −9.30512e9 | −0.341934 | ||||||||
\(959\) | −7.18648e9 | −0.263118 | ||||||||
\(960\) | −3.74877e9 | −0.136754 | ||||||||
\(961\) | 2.21034e10 | 0.803391 | ||||||||
\(962\) | −3.86121e9 | −0.139833 | ||||||||
\(963\) | −1.73201e10 | −0.624968 | ||||||||
\(964\) | −2.33732e9 | −0.0840326 | ||||||||
\(965\) | 1.33369e10 | 0.477759 | ||||||||
\(966\) | 2.67017e9 | 0.0953056 | ||||||||
\(967\) | 1.63326e10 | 0.580848 | 0.290424 | − | 0.956898i | \(-0.406204\pi\) | ||||
0.290424 | + | 0.956898i | \(0.406204\pi\) | |||||||
\(968\) | −2.86287e9 | −0.101447 | ||||||||
\(969\) | −6.39453e9 | −0.225775 | ||||||||
\(970\) | 1.63922e10 | 0.576682 | ||||||||
\(971\) | −2.46533e10 | −0.864188 | −0.432094 | − | 0.901829i | \(-0.642225\pi\) | ||||
−0.432094 | + | 0.901829i | \(0.642225\pi\) | |||||||
\(972\) | −9.18330e8 | −0.0320750 | ||||||||
\(973\) | −8.32292e9 | −0.289655 | ||||||||
\(974\) | 8.37648e9 | 0.290473 | ||||||||
\(975\) | 1.20061e10 | 0.414844 | ||||||||
\(976\) | 1.51741e9 | 0.0522430 | ||||||||
\(977\) | 2.98530e10 | 1.02413 | 0.512067 | − | 0.858946i | \(-0.328880\pi\) | ||||
0.512067 | + | 0.858946i | \(0.328880\pi\) | |||||||
\(978\) | 1.11121e10 | 0.379849 | ||||||||
\(979\) | −1.03528e10 | −0.352631 | ||||||||
\(980\) | 3.98798e9 | 0.135351 | ||||||||
\(981\) | 9.99187e9 | 0.337913 | ||||||||
\(982\) | 1.95853e9 | 0.0659995 | ||||||||
\(983\) | −2.65165e10 | −0.890389 | −0.445194 | − | 0.895434i | \(-0.646865\pi\) | ||||
−0.445194 | + | 0.895434i | \(0.646865\pi\) | |||||||
\(984\) | 4.05035e8 | 0.0135522 | ||||||||
\(985\) | 6.54557e10 | 2.18233 | ||||||||
\(986\) | −3.08487e10 | −1.02487 | ||||||||
\(987\) | −6.04247e9 | −0.200034 | ||||||||
\(988\) | −1.38055e9 | −0.0455411 | ||||||||
\(989\) | 2.86338e9 | 0.0941221 | ||||||||
\(990\) | 1.15144e10 | 0.377153 | ||||||||
\(991\) | −3.95353e10 | −1.29041 | −0.645205 | − | 0.764010i | \(-0.723228\pi\) | ||||
−0.645205 | + | 0.764010i | \(0.723228\pi\) | |||||||
\(992\) | 7.29896e9 | 0.237394 | ||||||||
\(993\) | 1.76051e10 | 0.570578 | ||||||||
\(994\) | 9.63416e9 | 0.311144 | ||||||||
\(995\) | 1.53607e10 | 0.494345 | ||||||||
\(996\) | −3.92602e9 | −0.125905 | ||||||||
\(997\) | 2.19110e10 | 0.700211 | 0.350105 | − | 0.936710i | \(-0.386146\pi\) | ||||
0.350105 | + | 0.936710i | \(0.386146\pi\) | |||||||
\(998\) | −8.87167e9 | −0.282520 | ||||||||
\(999\) | −4.32409e9 | −0.137219 |
(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.1.6 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.8.a.q.1.6 | ✓ | 6 | 1.1 | even | 1 | trivial |