Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,12,Mod(17,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.17");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.t (of order \(6\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(193.622481501\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Relative dimension: | \(30\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.9 | ||
Character | \(\chi\) | \(=\) | 252.17 |
Dual form | 252.12.t.a.89.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2700.97 | − | 4678.22i | −0.386531 | − | 0.669492i | 0.605449 | − | 0.795884i | \(-0.292994\pi\) |
−0.991980 | + | 0.126392i | \(0.959660\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4004.48 | − | 44286.5i | 0.0900548 | − | 0.995937i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −340633. | − | 196665.i | −0.637716 | − | 0.368186i | 0.146018 | − | 0.989282i | \(-0.453354\pi\) |
−0.783734 | + | 0.621096i | \(0.786688\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.36123e6i | 1.76380i | 0.471434 | + | 0.881901i | \(0.343737\pi\) | ||||
−0.471434 | + | 0.881901i | \(0.656263\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.94565e6 | − | 6.83407e6i | 0.673984 | − | 1.16737i | −0.302781 | − | 0.953060i | \(-0.597915\pi\) |
0.976765 | − | 0.214314i | \(-0.0687517\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.92539e6 | + | 3.42102e6i | −0.549000 | + | 0.316965i | −0.748718 | − | 0.662888i | \(-0.769330\pi\) |
0.199719 | + | 0.979853i | \(0.435997\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.50366e7 | − | 1.44549e7i | 0.811096 | − | 0.468286i | −0.0362405 | − | 0.999343i | \(-0.511538\pi\) |
0.847336 | + | 0.531057i | \(0.178205\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.82359e6 | − | 1.70150e7i | 0.201187 | − | 0.348466i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.75591e7i | 0.430571i | 0.976551 | + | 0.215285i | \(0.0690682\pi\) | ||||
−0.976551 | + | 0.215285i | \(0.930932\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.45313e8 | − | 8.38965e7i | −0.911622 | − | 0.526325i | −0.0306696 | − | 0.999530i | \(-0.509764\pi\) |
−0.880953 | + | 0.473204i | \(0.843097\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.17998e8 | + | 1.00883e8i | −0.701581 | + | 0.324670i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.07000e8 | − | 3.58534e8i | −0.490750 | − | 0.850004i | 0.509193 | − | 0.860652i | \(-0.329944\pi\) |
−0.999943 | + | 0.0106482i | \(0.996611\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.32518e9 | −1.78634 | −0.893170 | − | 0.449720i | \(-0.851524\pi\) | ||||
−0.893170 | + | 0.449720i | \(0.851524\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.71848e8 | −0.178266 | −0.0891329 | − | 0.996020i | \(-0.528410\pi\) | ||||
−0.0891329 | + | 0.996020i | \(0.528410\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.33734e7 | + | 5.78044e7i | 0.0212257 | + | 0.0367640i | 0.876443 | − | 0.481505i | \(-0.159910\pi\) |
−0.855217 | + | 0.518269i | \(0.826576\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.94526e9 | − | 3.54689e8i | −0.983780 | − | 0.179378i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.71761e8 | + | 3.87842e8i | 0.220647 | + | 0.127391i | 0.606250 | − | 0.795274i | \(-0.292673\pi\) |
−0.385603 | + | 0.922665i | \(0.626007\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.12474e9i | 0.569261i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.25190e9 | − | 3.90041e9i | 0.410075 | − | 0.710271i | −0.584822 | − | 0.811161i | \(-0.698836\pi\) |
0.994898 | + | 0.100890i | \(0.0321691\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.99546e8 | + | 3.46148e8i | −0.0908884 | + | 0.0524745i | −0.544755 | − | 0.838595i | \(-0.683377\pi\) |
0.453867 | + | 0.891069i | \(0.350044\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.10463e10 | − | 6.37761e9i | 1.18085 | − | 0.681765i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.47653e8 | − | 4.28948e8i | 0.0224095 | − | 0.0388144i | −0.854603 | − | 0.519282i | \(-0.826200\pi\) |
0.877013 | + | 0.480467i | \(0.159533\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.34975e10i | − | 0.887836i | −0.896067 | − | 0.443918i | \(-0.853588\pi\) | ||
0.896067 | − | 0.443918i | \(-0.146412\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.37824e10 | − | 7.95725e9i | −0.778122 | − | 0.449249i | 0.0576420 | − | 0.998337i | \(-0.481642\pi\) |
−0.835764 | + | 0.549088i | \(0.814975\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00736e10 | + | 1.42979e10i | −0.424119 | + | 0.601968i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.08540e10 | + | 1.87996e10i | 0.396862 | + | 0.687385i | 0.993337 | − | 0.115247i | \(-0.0367658\pi\) |
−0.596475 | + | 0.802632i | \(0.703432\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.48592e10 | −0.692721 | −0.346360 | − | 0.938102i | \(-0.612583\pi\) | ||||
−0.346360 | + | 0.938102i | \(0.612583\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.26283e10 | −1.04206 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.70878e10 | + | 2.95969e10i | 0.324370 | + | 0.561826i | 0.981385 | − | 0.192052i | \(-0.0615143\pi\) |
−0.657014 | + | 0.753878i | \(0.728181\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.04571e11 | + | 9.45550e9i | 1.75664 | + | 0.158839i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.20086e10 | + | 1.84802e10i | 0.424411 | + | 0.245034i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 7.99477e9i | − | 0.0945282i | −0.998882 | − | 0.0472641i | \(-0.984950\pi\) | ||
0.998882 | − | 0.0472641i | \(-0.0150502\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.95490e10 | + | 5.11804e10i | −0.279753 | + | 0.484547i | −0.971323 | − | 0.237762i | \(-0.923586\pi\) |
0.691570 | + | 0.722309i | \(0.256919\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.40418e11 | − | 8.10706e10i | 1.19349 | − | 0.689063i | 0.234395 | − | 0.972141i | \(-0.424689\pi\) |
0.959097 | + | 0.283079i | \(0.0913558\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.58732e10 | − | 5.53524e10i | 0.660825 | − | 0.381528i | −0.131766 | − | 0.991281i | \(-0.542065\pi\) |
0.792591 | + | 0.609753i | \(0.208731\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.87065e10 | + | 1.36324e11i | −0.489965 | + | 0.848644i | −0.999933 | − | 0.0115492i | \(-0.996324\pi\) |
0.509969 | + | 0.860193i | \(0.329657\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.42059e11i | 1.23592i | 0.786211 | + | 0.617958i | \(0.212040\pi\) | ||||
−0.786211 | + | 0.617958i | \(0.787960\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.35246e11 | − | 7.80844e10i | −0.627028 | − | 0.362015i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.86856e11 | − | 2.02106e11i | −1.10194 | − | 0.776373i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.53017e10 | − | 1.13106e11i | −0.228879 | − | 0.396429i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.69899e11 | −1.08412 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.71254e11 | −0.728543 | −0.364271 | − | 0.931293i | \(-0.618682\pi\) | ||||
−0.364271 | + | 0.931293i | \(0.618682\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.23359e11 | + | 3.86870e11i | 0.505839 | + | 0.876138i | 0.999977 | + | 0.00675504i | \(0.00215021\pi\) |
−0.494139 | + | 0.869383i | \(0.664516\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.27777e11 | + | 2.76114e11i | 0.266237 | + | 0.575313i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.71042e11 | + | 2.71956e11i | 0.833866 | + | 0.481433i | 0.855175 | − | 0.518340i | \(-0.173450\pi\) |
−0.0213084 | + | 0.999773i | \(0.506783\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 4.89521e11i | − | 0.800184i | −0.916475 | − | 0.400092i | \(-0.868978\pi\) | ||
0.916475 | − | 0.400092i | \(-0.131022\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.64371e11 | − | 8.04314e11i | 0.649407 | − | 1.12481i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.22492e11 | − | 1.28456e11i | 0.288264 | − | 0.166429i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.02931e12 | − | 5.94275e11i | 1.14822 | − | 0.662923i | 0.199764 | − | 0.979844i | \(-0.435982\pi\) |
0.948452 | + | 0.316921i | \(0.102649\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.46820e11 | + | 1.29353e12i | −0.774181 | + | 1.34092i | 0.161072 | + | 0.986943i | \(0.448505\pi\) |
−0.935253 | + | 0.353979i | \(0.884828\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.06407e11i | 0.813765i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.97874e11 | + | 2.87447e11i | 0.416554 | + | 0.240497i | 0.693602 | − | 0.720359i | \(-0.256023\pi\) |
−0.277048 | + | 0.960856i | \(0.589356\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.39897e11 | − | 1.16667e12i | −0.393341 | − | 0.849972i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.55478e11 | + | 1.65494e12i | 0.650413 | + | 1.12655i | 0.983023 | + | 0.183483i | \(0.0587373\pi\) |
−0.332610 | + | 0.943064i | \(0.607929\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.78403e11 | −0.463728 | −0.231864 | − | 0.972748i | \(-0.574483\pi\) | ||||
−0.231864 | + | 0.972748i | \(0.574483\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.78325e12 | −2.11100 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.70124e12 | + | 2.94663e12i | 0.834664 | + | 1.44568i | 0.894304 | + | 0.447460i | \(0.147671\pi\) |
−0.0596400 | + | 0.998220i | \(0.518995\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.14194e11 | − | 5.03188e11i | −0.328932 | − | 0.231751i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.35774e10 | − | 1.93859e10i | −0.0136570 | − | 0.00788488i | 0.493156 | − | 0.869941i | \(-0.335843\pi\) |
−0.506813 | + | 0.862056i | \(0.669177\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 4.20245e12i | − | 1.60794i | −0.594669 | − | 0.803971i | \(-0.702717\pi\) | ||
0.594669 | − | 0.803971i | \(-0.297283\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.11820e12 | + | 1.93678e12i | −0.379381 | + | 0.657106i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.68804e12 | + | 1.55194e12i | −0.859621 | + | 0.496303i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.50011e12 | + | 1.44344e12i | −0.711666 | + | 0.410881i | −0.811678 | − | 0.584106i | \(-0.801445\pi\) |
0.100011 | + | 0.994986i | \(0.468112\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.17096e12 | − | 3.76022e12i | 0.583563 | − | 1.01076i | −0.411490 | − | 0.911414i | \(-0.634992\pi\) |
0.995053 | − | 0.0993460i | \(-0.0316751\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.21480e12i | 1.73245i | 0.499657 | + | 0.866223i | \(0.333459\pi\) | ||||
−0.499657 | + | 0.866223i | \(0.666541\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.38871e12 | − | 8.01772e11i | −0.315442 | − | 0.182121i | 0.333917 | − | 0.942602i | \(-0.391629\pi\) |
−0.649359 | + | 0.760482i | \(0.724963\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.10622e12 | + | 1.90449e11i | 0.428821 | + | 0.0387750i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.57927e12 | + | 6.19948e12i | 0.690476 | + | 1.19594i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.69118e12 | 0.466808 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.39437e11 | 0.138177 | 0.0690883 | − | 0.997611i | \(-0.477991\pi\) | ||||
0.0690883 | + | 0.997611i | \(0.477991\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.64156e11 | + | 8.03942e11i | 0.0689053 | + | 0.119347i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.29738e12 | + | 6.09944e12i | −0.606283 | + | 0.860520i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.61368e13 | + | 9.31659e12i | 2.05902 | + | 1.18877i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.43605e13i | 1.74378i | 0.489701 | + | 0.871890i | \(0.337106\pi\) | ||||
−0.489701 | + | 0.871890i | \(0.662894\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.38982e11 | + | 2.40724e11i | −0.0153044 | + | 0.0265080i | −0.873576 | − | 0.486687i | \(-0.838205\pi\) |
0.858272 | + | 0.513195i | \(0.171538\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.97705e12 | + | 1.71880e12i | −0.312385 | + | 0.180356i | −0.647993 | − | 0.761646i | \(-0.724392\pi\) |
0.335608 | + | 0.942002i | \(0.391058\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.31378e12 | + | 3.06791e12i | −0.506927 | + | 0.292675i | −0.731570 | − | 0.681767i | \(-0.761212\pi\) |
0.224642 | + | 0.974441i | \(0.427879\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.80281e11 | − | 3.12256e11i | 0.0164088 | − | 0.0284209i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.81277e12i | 0.233317i | 0.993172 | + | 0.116658i | \(0.0372183\pi\) | ||||
−0.993172 | + | 0.116658i | \(0.962782\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.88784e12 | − | 4.55405e12i | −0.624977 | − | 0.360831i | 0.153827 | − | 0.988098i | \(-0.450840\pi\) |
−0.778804 | + | 0.627267i | \(0.784174\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.59477e12 | + | 1.00583e13i | 0.260170 | + | 0.727968i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.07783e12 | − | 1.39912e13i | −0.559064 | − | 0.968327i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.15275e13 | 1.36392 | 0.681958 | − | 0.731391i | \(-0.261129\pi\) | ||||
0.681958 | + | 0.731391i | \(0.261129\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.13711e13 | −0.689665 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.04237e12 | + | 7.00158e12i | 0.224907 | + | 0.389551i | 0.956292 | − | 0.292415i | \(-0.0944587\pi\) |
−0.731384 | + | 0.681965i | \(0.761125\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.67071e13 | + | 7.73154e12i | −0.890745 | + | 0.412209i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.02297e13 | + | 5.90609e12i | 0.501308 | + | 0.289430i | 0.729253 | − | 0.684244i | \(-0.239868\pi\) |
−0.227946 | + | 0.973674i | \(0.573201\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 4.19019e12i | − | 0.196962i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.75322e13 | + | 3.03667e13i | −0.758927 | + | 1.31450i | 0.184471 | + | 0.982838i | \(0.440943\pi\) |
−0.943398 | + | 0.331662i | \(0.892391\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.65747e13 | + | 2.11164e13i | −1.52002 | + | 0.877585i | −0.520301 | + | 0.853983i | \(0.674180\pi\) |
−0.999721 | + | 0.0236019i | \(0.992487\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.69248e12 | + | 3.86391e12i | −0.256601 | + | 0.148148i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.50774e13 | + | 2.61148e13i | −0.555505 | + | 0.962162i | 0.442359 | + | 0.896838i | \(0.354142\pi\) |
−0.997864 | + | 0.0653245i | \(0.979192\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 3.28392e13i | − | 1.11817i | −0.829110 | − | 0.559085i | \(-0.811153\pi\) | ||
0.829110 | − | 0.559085i | \(-0.188847\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.05883e12 | + | 6.11313e11i | 0.0346736 | + | 0.0200188i | 0.517237 | − | 0.855842i | \(-0.326961\pi\) |
−0.482563 | + | 0.875861i | \(0.660294\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.30666e12 | + | 5.86876e13i | −0.160868 | + | 1.77908i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.40004e13 | − | 2.42494e13i | −0.408509 | − | 0.707559i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.60561e13 | 1.51653 | 0.758265 | − | 0.651946i | \(-0.226047\pi\) | ||||
0.758265 | + | 0.651946i | \(0.226047\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.43293e13 | −0.634028 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.41313e13 | + | 5.91172e13i | 0.825965 | + | 1.43061i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.88162e11 | + | 7.61054e12i | −0.0160537 | + | 0.177541i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.23871e12 | + | 1.86987e12i | 0.0702624 | + | 0.0405660i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.45597e13i | 1.56043i | 0.625514 | + | 0.780213i | \(0.284889\pi\) | ||||
−0.625514 | + | 0.780213i | \(0.715111\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.62262e13 | + | 8.00661e13i | −0.900961 | + | 1.56051i | −0.0747115 | + | 0.997205i | \(0.523804\pi\) |
−0.826249 | + | 0.563305i | \(0.809530\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.45348e13 | − | 8.39167e12i | 0.273474 | − | 0.157890i | −0.356992 | − | 0.934108i | \(-0.616198\pi\) |
0.630465 | + | 0.776218i | \(0.282864\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.78507e13 | − | 1.60796e13i | 0.488664 | − | 0.282130i | −0.235356 | − | 0.971909i | \(-0.575626\pi\) |
0.724020 | + | 0.689779i | \(0.242292\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.35320e12 | − | 1.62002e13i | 0.158530 | − | 0.274582i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.39927e13i | 0.854518i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.01762e13 | + | 2.31958e13i | 0.614626 | + | 0.354854i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.69360e12 | − | 1.24651e12i | 0.0385261 | − | 0.0178287i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.76964e13 | − | 9.99331e13i | −0.798169 | − | 1.38247i | −0.920808 | − | 0.390017i | \(-0.872469\pi\) |
0.122639 | − | 0.992451i | \(-0.460864\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.67561e12 | −0.0346479 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.19794e13 | −0.526105 | −0.263052 | − | 0.964782i | \(-0.584729\pi\) | ||||
−0.263052 | + | 0.964782i | \(0.584729\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.29990e13 | + | 5.71559e13i | 0.387571 | + | 0.671293i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.34976e13 | + | 8.47281e13i | −0.267243 | + | 0.963629i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.70933e13 | + | 4.45099e13i | 0.822630 | + | 0.474946i | 0.851323 | − | 0.524642i | \(-0.175801\pi\) |
−0.0286923 | + | 0.999588i | \(0.509134\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.61283e12i | 0.0476901i | 0.999716 | + | 0.0238450i | \(0.00759083\pi\) | ||||
−0.999716 | + | 0.0238450i | \(0.992409\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.43037e13 | + | 2.47748e13i | −0.138895 | + | 0.240574i | −0.927079 | − | 0.374867i | \(-0.877689\pi\) |
0.788183 | + | 0.615441i | \(0.211022\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.31443e13 | + | 3.64564e13i | −0.594399 | + | 0.343176i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.50462e14 | − | 8.68692e13i | 1.33170 | − | 0.768859i | 0.346142 | − | 0.938182i | \(-0.387492\pi\) |
0.985561 | + | 0.169323i | \(0.0541583\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.48383e13 | + | 6.03417e13i | −0.299066 | + | 0.517998i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.59692e13i | 0.694596i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.40860e14 | + | 8.13257e13i | 1.10440 | + | 0.637624i | 0.937372 | − | 0.348329i | \(-0.113251\pi\) |
0.167025 | + | 0.985953i | \(0.446584\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.98662e13 | − | 2.81968e13i | 0.146743 | − | 0.208278i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.59376e13 | + | 6.22457e13i | 0.257721 | + | 0.446386i | 0.965631 | − | 0.259917i | \(-0.0836951\pi\) |
−0.707910 | + | 0.706303i | \(0.750362\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.12298e14 | −0.759442 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.59423e14 | −1.04721 | −0.523606 | − | 0.851960i | \(-0.675414\pi\) | ||||
−0.523606 | + | 0.851960i | \(0.675414\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.04799e14 | − | 1.81517e14i | −0.649776 | − | 1.12545i | −0.983176 | − | 0.182660i | \(-0.941529\pi\) |
0.333400 | − | 0.942785i | \(-0.391804\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.40973e13 | + | 8.50849e12i | 0.566948 | + | 0.0512647i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.32253e14 | + | 1.34091e14i | 1.32202 | + | 0.763268i | 0.984051 | − | 0.177889i | \(-0.0569269\pi\) |
0.337969 | + | 0.941157i | \(0.390260\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 2.28136e14i | − | 1.26247i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.86325e13 | − | 1.01554e14i | 0.306799 | − | 0.531392i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.02107e14 | + | 1.16687e14i | −1.02857 | + | 0.593846i | −0.916575 | − | 0.399863i | \(-0.869058\pi\) |
−0.111996 | + | 0.993709i | \(0.535724\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.69993e14 | + | 1.55880e14i | −1.30034 | + | 0.750753i | −0.980463 | − | 0.196705i | \(-0.936976\pi\) |
−0.319880 | + | 0.947458i | \(0.603643\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.98099e14 | − | 3.43117e14i | 0.928334 | − | 1.60792i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.62838e14i | 0.722749i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.03199e14 | − | 5.95817e13i | −0.445857 | − | 0.257415i | 0.260222 | − | 0.965549i | \(-0.416204\pi\) |
−0.706079 | + | 0.708133i | \(0.749538\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.63718e14 | − | 1.15348e14i | −0.670456 | − | 0.472372i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.71440e13 | + | 1.16297e14i | 0.267758 | + | 0.463771i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.45115e14 | −0.927241 | −0.463620 | − | 0.886034i | \(-0.653450\pi\) | ||||
−0.463620 | + | 0.886034i | \(0.653450\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.58067e14 | −1.68802 | −0.844009 | − | 0.536329i | \(-0.819811\pi\) | ||||
−0.844009 | + | 0.536329i | \(0.819811\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.75209e13 | − | 1.34270e14i | −0.271194 | − | 0.469721i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.29288e13 | + | 2.79379e13i | 0.0440763 | + | 0.0952447i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.16894e14 | − | 6.74886e13i | −0.378587 | − | 0.218577i | 0.298616 | − | 0.954373i | \(-0.403475\pi\) |
−0.677203 | + | 0.735796i | \(0.736808\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2.84613e14i | − | 0.898610i | −0.893378 | − | 0.449305i | \(-0.851672\pi\) | ||
0.893378 | − | 0.449305i | \(-0.148328\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.89010e13 | + | 1.71302e14i | −0.296861 | + | 0.514178i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.05389e13 | + | 4.64991e13i | −0.235749 | + | 0.136110i | −0.613222 | − | 0.789911i | \(-0.710127\pi\) |
0.377472 | + | 0.926021i | \(0.376793\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.75581e14 | − | 2.74577e14i | 1.32435 | − | 0.764616i | 0.339934 | − | 0.940449i | \(-0.389595\pi\) |
0.984420 | + | 0.175833i | \(0.0562619\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.23072e13 | − | 1.59881e14i | 0.250759 | − | 0.434327i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 7.15312e14i | − | 1.84987i | −0.380129 | − | 0.924934i | \(-0.624120\pi\) | ||
0.380129 | − | 0.924934i | \(-0.375880\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.51401e14 | + | 2.60616e14i | 1.13918 | + | 0.657705i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.38207e14 | − | 5.14743e14i | −0.572653 | − | 1.23745i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.63739e14 | + | 4.56810e14i | 0.618922 | + | 1.07200i | 0.989683 | + | 0.143276i | \(0.0457637\pi\) |
−0.370761 | + | 0.928728i | \(0.620903\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.01854e14 | 0.675215 | 0.337607 | − | 0.941287i | \(-0.390382\pi\) | ||||
0.337607 | + | 0.941287i | \(0.390382\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.27040e14 | 1.80647 | 0.903236 | − | 0.429144i | \(-0.141185\pi\) | ||||
0.903236 | + | 0.429144i | \(0.141185\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.81459e14 | + | 3.14297e14i | 0.378039 | + | 0.654783i | 0.990777 | − | 0.135503i | \(-0.0432651\pi\) |
−0.612738 | + | 0.790286i | \(0.709932\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.80049e13 | − | 1.26854e13i | −0.0366386 | − | 0.0258139i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.85372e13 | + | 3.37965e13i | 0.113683 | + | 0.0656349i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.34427e14i | 0.255077i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.87101e14 | − | 4.97273e14i | 0.520222 | − | 0.901052i | −0.479501 | − | 0.877541i | \(-0.659182\pi\) |
0.999724 | − | 0.0235104i | \(-0.00748428\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.46582e14 | − | 4.88774e14i | 1.49924 | − | 0.865586i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.74013e13 | + | 2.15936e13i | −0.0632859 | + | 0.0365381i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.04344e14 | − | 5.27139e14i | 0.503449 | − | 0.871998i | −0.496544 | − | 0.868012i | \(-0.665398\pi\) |
0.999992 | − | 0.00398663i | \(-0.00126899\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.23677e14i | 0.353730i | 0.984235 | + | 0.176865i | \(0.0565957\pi\) | ||||
−0.984235 | + | 0.176865i | \(0.943404\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.25022e14 | + | 1.87652e14i | 0.502637 | + | 0.290198i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.97757e14 | − | 5.40505e13i | −0.884229 | − | 0.0799539i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.07164e14 | − | 5.32023e14i | −0.444444 | − | 0.769800i | 0.553569 | − | 0.832803i | \(-0.313265\pi\) |
−0.998013 | + | 0.0630035i | \(0.979932\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.47466e14 | −0.758112 | −0.379056 | − | 0.925374i | \(-0.623751\pi\) | ||||
−0.379056 | + | 0.925374i | \(0.623751\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.19244e14 | 0.432534 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.35621e14 | − | 1.10093e15i | −0.824614 | − | 1.42827i | −0.902214 | − | 0.431289i | \(-0.858059\pi\) |
0.0776001 | − | 0.996985i | \(-0.475274\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.07590e14 | + | 5.78507e14i | −0.517498 | + | 0.734504i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.58532e14 | − | 4.37939e14i | −0.922644 | − | 0.532689i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 2.62535e13i | − | 0.0312600i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.23767e14 | + | 1.08040e15i | −0.711893 | + | 1.23304i | 0.252253 | + | 0.967661i | \(0.418829\pi\) |
−0.964146 | + | 0.265374i | \(0.914505\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.95535e14 | − | 5.17038e14i | 1.00075 | − | 0.577780i | 0.0922764 | − | 0.995733i | \(-0.470586\pi\) |
0.908469 | + | 0.417953i | \(0.137252\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.14671e15 | + | 6.62053e14i | −1.22884 | + | 0.709470i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.85175e13 | + | 1.01355e14i | −0.0614157 | + | 0.106375i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 3.12906e15i | − | 3.15075i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.17901e14 | − | 2.99010e14i | −0.510859 | − | 0.294945i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.92864e14 | + | 5.03382e14i | 0.561328 | + | 0.476606i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.22170e14 | − | 1.07763e15i | −0.577197 | − | 0.999734i | −0.995799 | − | 0.0915645i | \(-0.970813\pi\) |
0.418602 | − | 0.908170i | \(-0.362520\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.50336e14 | 0.757547 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.78552e14 | −0.243207 | −0.121603 | − | 0.992579i | \(-0.538804\pi\) | ||||
−0.121603 | + | 0.992579i | \(0.538804\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.62701e14 | − | 2.81806e14i | −0.136476 | − | 0.236383i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.76033e14 | − | 4.05401e14i | 0.720332 | − | 0.333347i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.78466e14 | − | 5.07183e14i | −0.694259 | − | 0.400831i | 0.110947 | − | 0.993826i | \(-0.464612\pi\) |
−0.805206 | + | 0.592996i | \(0.797945\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 4.05773e14i | − | 0.314426i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.14888e15 | − | 1.98992e15i | 0.856012 | − | 1.48266i | −0.0196912 | − | 0.999806i | \(-0.506268\pi\) |
0.875703 | − | 0.482850i | \(-0.160398\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.13240e15 | − | 6.53793e14i | 0.827436 | − | 0.477720i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.53352e14 | − | 3.19478e14i | 0.388941 | − | 0.224555i | −0.292760 | − | 0.956186i | \(-0.594574\pi\) |
0.681701 | + | 0.731631i | \(0.261240\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.06657e14 | + | 7.04350e14i | −0.280369 | + | 0.485613i | −0.971475 | − | 0.237140i | \(-0.923790\pi\) |
0.691107 | + | 0.722752i | \(0.257123\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 5.67995e14i | − | 0.376853i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.83403e14 | − | 1.05888e14i | −0.119382 | − | 0.0689253i | 0.439120 | − | 0.898429i | \(-0.355290\pi\) |
−0.558502 | + | 0.829503i | \(0.688624\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.95483e13 | + | 1.10093e15i | −0.0623828 | + | 0.689906i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.52550e14 | − | 2.64224e14i | −0.0938067 | − | 0.162478i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.12299e15 | 0.665066 | 0.332533 | − | 0.943092i | \(-0.392097\pi\) | ||||
0.332533 | + | 0.943092i | \(0.392097\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.14805e15 | 0.667307 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.64461e14 | − | 1.15088e15i | −0.372108 | − | 0.644510i | 0.617782 | − | 0.786350i | \(-0.288031\pi\) |
−0.989890 | + | 0.141840i | \(0.954698\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.70704e14 | + | 1.88786e15i | −0.0938429 | + | 1.03783i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.42460e15 | − | 1.39984e15i | −1.28467 | − | 0.741705i | −0.306972 | − | 0.951719i | \(-0.599316\pi\) |
−0.977698 | + | 0.210014i | \(0.932649\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.11706e15i | 0.581121i | 0.956857 | + | 0.290560i | \(0.0938417\pi\) | ||||
−0.956857 | + | 0.290560i | \(0.906158\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.52756e14 | + | 6.10991e14i | −0.176938 | + | 0.306465i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.84629e15 | + | 1.06595e15i | −0.909413 | + | 0.525050i | −0.880242 | − | 0.474525i | \(-0.842620\pi\) |
−0.0291707 | + | 0.999574i | \(0.509287\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.36490e14 | + | 7.88023e13i | −0.0648445 | + | 0.0374380i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.32483e14 | − | 1.61511e15i | 0.435119 | − | 0.753649i | −0.562186 | − | 0.827011i | \(-0.690040\pi\) |
0.997305 | + | 0.0733621i | \(0.0233729\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.84138e15i | 0.829038i | 0.910041 | + | 0.414519i | \(0.136050\pi\) | ||||
−0.910041 | + | 0.414519i | \(0.863950\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.70065e14 | + | 2.13657e14i | 0.163674 | + | 0.0944971i | 0.579599 | − | 0.814902i | \(-0.303209\pi\) |
−0.415926 | + | 0.909399i | \(0.636542\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.37917e15 | − | 6.38238e14i | 0.588754 | − | 0.272457i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.19420e14 | + | 8.99662e14i | 0.217860 | + | 0.377345i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.26700e15 | −1.32303 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.90101e15 | 0.756524 | 0.378262 | − | 0.925699i | \(-0.376522\pi\) | ||||
0.378262 | + | 0.925699i | \(0.376522\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.32648e14 | + | 1.26898e15i | 0.281605 | + | 0.487753i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.37501e14 | − | 4.59320e15i | 0.316387 | − | 1.73519i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.82632e15 | + | 1.63178e15i | 1.03158 | + | 0.595582i | 0.917436 | − | 0.397882i | \(-0.130255\pi\) |
0.114142 | + | 0.993464i | \(0.463588\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.88521e15i | 1.03518i | 0.855628 | + | 0.517592i | \(0.173171\pi\) | ||||
−0.855628 | + | 0.517592i | \(0.826829\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.53543e14 | − | 1.13197e15i | 0.226621 | − | 0.392520i | −0.730183 | − | 0.683251i | \(-0.760565\pi\) |
0.956805 | + | 0.290732i | \(0.0938987\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.53415e15 | + | 8.85740e14i | −0.523023 | + | 0.301968i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.43899e15 | − | 8.30799e14i | 0.474279 | − | 0.273825i | −0.243750 | − | 0.969838i | \(-0.578378\pi\) |
0.718029 | + | 0.696013i | \(0.245044\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.20657e15 | − | 2.08985e15i | 0.391045 | − | 0.677310i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.70468e15i | 1.16113i | 0.814213 | + | 0.580566i | \(0.197169\pi\) | ||||
−0.814213 | + | 0.580566i | \(0.802831\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.81563e15 | − | 1.04825e15i | −0.559654 | − | 0.323116i | 0.193353 | − | 0.981129i | \(-0.438064\pi\) |
−0.753006 | + | 0.658013i | \(0.771397\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.46599e14 | − | 1.34354e15i | 0.282259 | − | 0.400620i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.87461e14 | + | 1.19072e15i | 0.201630 | + | 0.349234i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.72301e14 | 0.0772814 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.70894e14 | 0.215235 | 0.107617 | − | 0.994192i | \(-0.465678\pi\) | ||||
0.107617 | + | 0.994192i | \(0.465678\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.62878e15 | + | 2.82114e15i | 0.440176 | + | 0.762407i | 0.997702 | − | 0.0677526i | \(-0.0215828\pi\) |
−0.557527 | + | 0.830159i | \(0.688250\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.54060e14 | − | 3.20149e13i | −0.0941441 | − | 0.00851272i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.96071e15 | + | 1.13201e15i | 0.504776 | + | 0.291432i | 0.730684 | − | 0.682716i | \(-0.239201\pi\) |
−0.225908 | + | 0.974149i | \(0.572535\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 2.93818e15i | − | 0.744355i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.15784e14 | + | 1.58618e15i | −0.224692 | + | 0.389178i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.07062e15 | + | 2.35017e15i | −0.982949 | + | 0.567506i | −0.903159 | − | 0.429306i | \(-0.858758\pi\) |
−0.0797900 | + | 0.996812i | \(0.525425\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.29009e15 | + | 1.32218e15i | −0.535717 | + | 0.309296i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.22870e15 | + | 9.05638e15i | −1.20396 | + | 2.08533i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.94415e15i | 1.10317i | 0.834118 | + | 0.551586i | \(0.185977\pi\) | ||||
−0.834118 | + | 0.551586i | \(0.814023\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.45311e15 | + | 1.41630e15i | 0.538843 | + | 0.311101i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.14827e15 | + | 1.51357e15i | 0.457385 | + | 0.322253i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.39341e15 | + | 2.41346e15i | 0.292096 | + | 0.505925i | 0.974305 | − | 0.225232i | \(-0.0723139\pi\) |
−0.682209 | + | 0.731157i | \(0.738981\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.85086e15 | −0.985884 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.01701e15 | −1.00406 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.58865e13 | − | 6.21573e13i | −0.00696502 | − | 0.0120638i | 0.862522 | − | 0.506020i | \(-0.168884\pi\) |
−0.869487 | + | 0.493956i | \(0.835550\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.02803e15 | − | 6.54328e15i | −0.578783 | − | 1.25070i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.09216e14 | + | 4.67201e14i | 0.150039 | + | 0.0866253i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 8.98933e15i | − | 1.64168i | −0.571160 | − | 0.820839i | \(-0.693506\pi\) | ||
0.571160 | − | 0.820839i | \(-0.306494\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.78052e14 | + | 1.17442e15i | −0.120148 | + | 0.208103i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.18189e15 | − | 6.82366e14i | 0.206303 | − | 0.119109i | −0.393289 | − | 0.919415i | \(-0.628663\pi\) |
0.599592 | + | 0.800306i | \(0.295329\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.68718e14 | + | 9.74093e13i | −0.0285818 | + | 0.0165017i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.91302e15 | + | 8.50959e15i | −0.819981 | + | 1.42025i | 0.0857143 | + | 0.996320i | \(0.472683\pi\) |
−0.905695 | + | 0.423929i | \(0.860651\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.69770e15i | 1.40918i | 0.709615 | + | 0.704589i | \(0.248869\pi\) | ||||
−0.709615 | + | 0.704589i | \(0.751131\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.56030e15 | − | 3.21024e15i | −0.887643 | − | 0.512481i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.06744e15 | − | 4.46754e15i | −0.320467 | − | 0.692498i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.22886e15 | + | 2.12846e15i | 0.187709 | + | 0.325121i | 0.944486 | − | 0.328552i | \(-0.106561\pi\) |
−0.756777 | + | 0.653673i | \(0.773227\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.06855e15 | 1.19698 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.16763e15 | −0.609343 | −0.304672 | − | 0.952457i | \(-0.598547\pi\) | ||||
−0.304672 | + | 0.952457i | \(0.598547\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.25729e15 | + | 5.64179e15i | 0.462637 | + | 0.801311i | 0.999091 | − | 0.0426182i | \(-0.0135699\pi\) |
−0.536454 | + | 0.843929i | \(0.680237\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.72211e15 | + | 4.03154e15i | 0.801072 | + | 0.564398i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.20977e15 | + | 5.31726e15i | 1.25278 | + | 0.723292i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.34475e15i | 1.11897i | 0.828841 | + | 0.559485i | \(0.189001\pi\) | ||||
−0.828841 | + | 0.559485i | \(0.810999\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.00958e15 | + | 1.74864e15i | −0.131569 | + | 0.227884i | −0.924282 | − | 0.381711i | \(-0.875335\pi\) |
0.792713 | + | 0.609596i | \(0.208668\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.85499e15 | + | 1.64833e15i | −0.366813 | + | 0.211780i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.85221e15 | − | 4.53348e15i | 0.980700 | − | 0.566207i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.65449e15 | + | 4.59770e15i | −0.326889 | + | 0.566188i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 3.10555e15i | − | 0.371839i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.41249e15 | − | 4.85695e15i | −0.993261 | − | 0.573460i | −0.0870138 | − | 0.996207i | \(-0.527732\pi\) |
−0.906248 | + | 0.422747i | \(0.861066\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.07199e16 | + | 9.69319e14i | 1.23089 | + | 0.111300i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.17336e14 | − | 1.41567e15i | −0.0925546 | − | 0.160309i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.76310e15 | −0.304352 | −0.152176 | − | 0.988353i | \(-0.548628\pi\) | ||||
−0.152176 | + | 0.988353i | \(0.548628\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.26719e14 | 0.0572232 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.12982e15 | + | 5.42101e15i | 0.330814 | + | 0.572987i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.99967e15 | + | 5.67689e15i | −0.417011 | + | 0.591879i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.30508e15 | − | 3.06289e15i | −0.538239 | − | 0.310753i | 0.206126 | − | 0.978526i | \(-0.433914\pi\) |
−0.744365 | + | 0.667773i | \(0.767248\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.61829e15i | 0.662416i | 0.943558 | + | 0.331208i | \(0.107456\pi\) | ||||
−0.943558 | + | 0.331208i | \(0.892544\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.16144e15 | − | 8.93987e15i | 0.502810 | − | 0.870892i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.01827e15 | − | 5.87896e14i | 0.0978678 | − | 0.0565040i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.62451e15 | + | 2.09261e15i | −0.339126 | + | 0.195795i | −0.659886 | − | 0.751366i | \(-0.729395\pi\) |
0.320759 | + | 0.947161i | \(0.396062\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.57169e14 | − | 1.13825e15i | 0.0606705 | − | 0.105084i | −0.834095 | − | 0.551621i | \(-0.814009\pi\) |
0.894765 | + | 0.446537i | \(0.147343\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.09328e15i | 0.547735i | 0.961767 | + | 0.273868i | \(0.0883030\pi\) | ||||
−0.961767 | + | 0.273868i | \(0.911697\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.63913e15 | − | 5.56515e15i | −0.855043 | − | 0.493659i | 0.00730638 | − | 0.999973i | \(-0.497674\pi\) |
−0.862349 | + | 0.506314i | \(0.831008\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.00993e16 | + | 1.18945e16i | −0.872453 | + | 1.02754i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.10244e15 | + | 3.64154e15i | 0.179246 | + | 0.310462i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.85748e15 | 0.403386 | 0.201693 | − | 0.979449i | \(-0.435356\pi\) | ||||
0.201693 | + | 0.979449i | \(0.435356\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.93864e15 | 0.814609 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.02184e16 | + | 1.76989e16i | 0.815967 | + | 1.41330i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.27056e15 | + | 2.43905e15i | −0.415430 | + | 0.192248i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.03651e16 | − | 5.98432e15i | −0.796091 | − | 0.459623i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.57207e15i | 0.270832i | 0.990789 | + | 0.135416i | \(0.0432371\pi\) | ||||
−0.990789 | + | 0.135416i | \(0.956763\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.97203e15 | + | 1.55400e16i | −0.662973 | + | 1.14830i | 0.316857 | + | 0.948473i | \(0.397372\pi\) |
−0.979831 | + | 0.199830i | \(0.935961\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.29801e16 | − | 7.49404e15i | 0.946923 | − | 0.546706i | 0.0547990 | − | 0.998497i | \(-0.482548\pi\) |
0.892124 | + | 0.451791i | \(0.149215\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.90372e15 | + | 5.71792e15i | −0.704270 | + | 0.406610i | −0.808936 | − | 0.587897i | \(-0.799956\pi\) |
0.104666 | + | 0.994507i | \(0.466623\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.18999e15 | − | 1.59175e16i | 0.645247 | − | 1.11760i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 8.53838e15i | − | 0.584476i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.01284e15 | + | 5.84766e14i | 0.0684610 | + | 0.0395260i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.48125e15 | + | 1.63815e16i | −0.0976305 | + | 1.07972i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.35712e16 | − | 2.35061e16i | −0.883328 | − | 1.52997i | −0.847619 | − | 0.530606i | \(-0.821964\pi\) |
−0.0357088 | − | 0.999362i | \(-0.511369\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.01673e16 | −0.645415 | −0.322708 | − | 0.946499i | \(-0.604593\pi\) | ||||
−0.322708 | + | 0.946499i | \(0.604593\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.68150e15 | 0.356188 | 0.178094 | − | 0.984013i | \(-0.443007\pi\) | ||||
0.178094 | + | 0.984013i | \(0.443007\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.16448e15 | + | 5.48105e15i | 0.193519 | + | 0.335184i | 0.946414 | − | 0.322956i | \(-0.104677\pi\) |
−0.752895 | + | 0.658140i | \(0.771343\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.08623e15 | + | 1.20129e16i | −0.0656088 | + | 0.725582i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.95501e14 | − | 2.28343e14i | −0.0233058 | − | 0.0134556i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.09443e14i | 0.0121910i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.99004e15 | − | 6.91095e15i | 0.226620 | − | 0.392518i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.30107e15 | − | 3.06058e15i | 0.297425 | − | 0.171718i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.96600e16 | + | 1.13507e16i | −1.07650 | + | 0.621520i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.38089e15 | + | 1.45161e16i | −0.453367 | + | 0.785255i | −0.998593 | − | 0.0530343i | \(-0.983111\pi\) |
0.545225 | + | 0.838290i | \(0.316444\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 3.45702e16i | − | 1.82537i | −0.408663 | − | 0.912685i | \(-0.634005\pi\) | ||
0.408663 | − | 0.912685i | \(-0.365995\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.46789e15 | + | 4.88894e15i | 0.441759 | + | 0.255050i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.80275e16 | − | 8.34258e15i | 0.918131 | − | 0.424883i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.22072e16 | + | 2.11435e16i | 0.614300 | + | 1.06400i | 0.990507 | + | 0.137463i | \(0.0438947\pi\) |
−0.376207 | + | 0.926536i | \(0.622772\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.18707e16 | 1.56597 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.13392e15 | −0.394930 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.85208e16 | − | 3.20790e16i | −0.878159 | − | 1.52102i | −0.853359 | − | 0.521323i | \(-0.825439\pi\) |
−0.0247998 | − | 0.999692i | \(-0.507895\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.27398e16 | − | 4.55310e15i | 0.596951 | − | 0.213346i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.45206e16 | + | 8.38350e15i | 0.664541 | + | 0.383673i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 7.23185e15i | − | 0.327101i | −0.986535 | − | 0.163551i | \(-0.947705\pi\) | ||
0.986535 | − | 0.163551i | \(-0.0522947\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.75183e16 | − | 3.03425e16i | 0.774013 | − | 1.34063i | −0.161334 | − | 0.986900i | \(-0.551580\pi\) |
0.935347 | − | 0.353731i | \(-0.115087\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.31780e16 | + | 1.91553e16i | −1.44889 | + | 0.836518i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.49218e15 | − | 2.01621e15i | 0.148995 | − | 0.0860223i | −0.423649 | − | 0.905826i | \(-0.639251\pi\) |
0.572644 | + | 0.819804i | \(0.305918\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.87889e16 | − | 3.25433e16i | 0.792387 | − | 1.37245i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 3.25006e16i | − | 1.33931i | −0.742673 | − | 0.669654i | \(-0.766442\pi\) | ||
0.742673 | − | 0.669654i | \(-0.233558\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.35055e16 | + | 7.79739e15i | 0.550163 | + | 0.317637i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.39303e16 | − | 1.97717e16i | 0.554570 | − | 0.787123i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.37300e15 | + | 2.37810e15i | 0.0540370 | + | 0.0935948i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.34548e16 | −0.902261 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.04765e15 | 0.115910 | 0.0579548 | − | 0.998319i | \(-0.481542\pi\) | ||||
0.0579548 | + | 0.998319i | \(0.481542\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.08078e16 | − | 1.87197e16i | −0.401821 | − | 0.695974i | 0.592125 | − | 0.805846i | \(-0.298289\pi\) |
−0.993946 | + | 0.109872i | \(0.964956\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.16792e16 | − | 1.96028e15i | −0.796933 | − | 0.0720604i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.84288e16 | − | 1.64134e16i | −1.02174 | − | 0.589900i | −0.107130 | − | 0.994245i | \(-0.534166\pi\) |
−0.914606 | + | 0.404345i | \(0.867499\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.34423e16i | − | 0.477714i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.47053e16 | + | 4.27909e16i | −0.858512 | + | 1.48699i | 0.0148358 | + | 0.999890i | \(0.495277\pi\) |
−0.873348 | + | 0.487097i | \(0.838056\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.37524e16 | − | 1.94869e16i | 1.15986 | − | 0.669645i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.30249e15 | + | 2.48404e15i | −0.144591 | + | 0.0834794i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.07374e15 | + | 5.32387e15i | −0.102155 | + | 0.176938i | −0.912572 | − | 0.408915i | \(-0.865907\pi\) |
0.810417 | + | 0.585853i | \(0.199241\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.66225e15i | 0.281581i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.48816e16 | + | 8.59188e15i | 0.478438 | + | 0.276226i | 0.719765 | − | 0.694218i | \(-0.244249\pi\) |
−0.241328 | + | 0.970444i | \(0.577583\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 252.12.t.a.17.9 | ✓ | 60 | |
3.2 | odd | 2 | inner | 252.12.t.a.17.22 | yes | 60 | |
7.5 | odd | 6 | inner | 252.12.t.a.89.22 | yes | 60 | |
21.5 | even | 6 | inner | 252.12.t.a.89.9 | yes | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.12.t.a.17.9 | ✓ | 60 | 1.1 | even | 1 | trivial | |
252.12.t.a.17.22 | yes | 60 | 3.2 | odd | 2 | inner | |
252.12.t.a.89.9 | yes | 60 | 21.5 | even | 6 | inner | |
252.12.t.a.89.22 | yes | 60 | 7.5 | odd | 6 | inner |