Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,1,Mod(110,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, base_ring=CyclotomicField(156))
chi = DirichletCharacter(H, H._module([78, 130, 113]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3549.110");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.ea (of order \(156\), degree \(48\), 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: | \(1.77118172983\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Coefficient field: | \(\Q(\zeta_{156})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{48} + x^{46} - x^{42} - x^{40} + x^{36} + x^{34} - x^{30} - x^{28} + x^{24} - x^{20} - x^{18} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{156}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{156} - \cdots)\) |
Embedding invariants
Embedding label | 2294.1 | ||
Root | \(0.160411 + 0.987050i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.2294 |
Dual form | 3549.1.ea.a.1298.1 |
$q$-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 \(\left(\mathbb{Z}/3549\mathbb{Z}\right)^\times\).
\(n\) | \(1184\) | \(1522\) | \(3382\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{17}{156}\right)\) |
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 | 0.761712 | − | 0.647915i | \(-0.224359\pi\) | ||||
−0.761712 | + | 0.647915i | \(0.775641\pi\) | |||||||
\(3\) | 0.464723 | + | 0.885456i | 0.464723 | + | 0.885456i | ||||
\(4\) | 0.160411 | − | 0.987050i | 0.160411 | − | 0.987050i | ||||
\(5\) | 0 | 0 | −0.894635 | − | 0.446798i | \(-0.852564\pi\) | ||||
0.894635 | + | 0.446798i | \(0.147436\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.692724 | + | 0.721202i | 0.692724 | + | 0.721202i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.568065 | + | 0.822984i | −0.568065 | + | 0.822984i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.180255 | − | 0.983620i | \(-0.442308\pi\) | ||||
−0.180255 | + | 0.983620i | \(0.557692\pi\) | |||||||
\(12\) | 0.948536 | − | 0.316668i | 0.948536 | − | 0.316668i | ||||
\(13\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.948536 | − | 0.316668i | −0.948536 | − | 0.316668i | ||||
\(17\) | 0 | 0 | 0.692724 | − | 0.721202i | \(-0.256410\pi\) | ||||
−0.692724 | + | 0.721202i | \(0.743590\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.916291 | + | 0.916291i | 0.916291 | + | 0.916291i | 0.996757 | − | 0.0804666i | \(-0.0256410\pi\) |
−0.0804666 | + | 0.996757i | \(0.525641\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.316668 | + | 0.948536i | −0.316668 | + | 0.948536i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.600742 | + | 0.799443i | 0.600742 | + | 0.799443i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.992709 | − | 0.120537i | −0.992709 | − | 0.120537i | ||||
\(28\) | 0.822984 | − | 0.568065i | 0.822984 | − | 0.568065i | ||||
\(29\) | 0 | 0 | −0.428693 | − | 0.903450i | \(-0.641026\pi\) | ||||
0.428693 | + | 0.903450i | \(0.358974\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.761468 | + | 0.306465i | 0.761468 | + | 0.306465i | 0.721202 | − | 0.692724i | \(-0.243590\pi\) |
0.0402659 | + | 0.999189i | \(0.487179\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.721202 | + | 0.692724i | 0.721202 | + | 0.692724i | ||||
\(37\) | 1.85500 | + | 0.746571i | 1.85500 | + | 0.746571i | 0.935016 | + | 0.354605i | \(0.115385\pi\) |
0.919979 | + | 0.391967i | \(0.128205\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.0402659 | − | 0.999189i | 0.0402659 | − | 0.999189i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.735006 | − | 0.678061i | \(-0.237179\pi\) | ||||
−0.735006 | + | 0.678061i | \(0.762821\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.866514 | + | 1.15312i | 0.866514 | + | 1.15312i | 0.987050 | + | 0.160411i | \(0.0512821\pi\) |
−0.120537 | + | 0.992709i | \(0.538462\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.994935 | − | 0.100522i | \(-0.967949\pi\) | ||||
0.994935 | + | 0.100522i | \(0.0320513\pi\) | |||||||
\(48\) | −0.160411 | − | 0.987050i | −0.160411 | − | 0.987050i | ||||
\(49\) | −0.0402659 | + | 0.999189i | −0.0402659 | + | 0.999189i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.632445 | + | 0.774605i | −0.632445 | + | 0.774605i | ||||
\(53\) | 0 | 0 | −0.278217 | − | 0.960518i | \(-0.589744\pi\) | ||||
0.278217 | + | 0.960518i | \(0.410256\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.385514 | + | 1.23716i | −0.385514 | + | 1.23716i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.446798 | − | 0.894635i | \(-0.352564\pi\) | ||||
−0.446798 | + | 0.894635i | \(0.647436\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.472433 | − | 1.91674i | −0.472433 | − | 1.91674i | −0.391967 | − | 0.919979i | \(-0.628205\pi\) |
−0.0804666 | − | 0.996757i | \(-0.525641\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.987050 | + | 0.160411i | −0.987050 | + | 0.160411i | ||||
\(64\) | −0.464723 | + | 0.885456i | −0.464723 | + | 0.885456i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.646140 | − | 1.43566i | −0.646140 | − | 1.43566i | −0.885456 | − | 0.464723i | \(-0.846154\pi\) |
0.239316 | − | 0.970942i | \(-0.423077\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.975564 | − | 0.219715i | \(-0.0705128\pi\) | ||||
−0.975564 | + | 0.219715i | \(0.929487\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.600666 | − | 1.68543i | −0.600666 | − | 1.68543i | −0.721202 | − | 0.692724i | \(-0.756410\pi\) |
0.120537 | − | 0.992709i | \(-0.461538\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.428693 | + | 0.903450i | −0.428693 | + | 0.903450i | ||||
\(76\) | 1.05141 | − | 0.757442i | 1.05141 | − | 0.757442i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.587824 | + | 0.719954i | 0.587824 | + | 0.719954i | 0.979791 | − | 0.200026i | \(-0.0641026\pi\) |
−0.391967 | + | 0.919979i | \(0.628205\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.354605 | − | 0.935016i | −0.354605 | − | 0.935016i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.297503 | − | 0.954721i | \(-0.596154\pi\) | ||||
0.297503 | + | 0.954721i | \(0.403846\pi\) | |||||||
\(84\) | 0.885456 | + | 0.464723i | 0.885456 | + | 0.464723i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.239316 | − | 0.970942i | −0.239316 | − | 0.970942i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.0825110 | + | 0.816668i | 0.0825110 | + | 0.816668i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.863148 | − | 1.72830i | −0.863148 | − | 1.72830i | −0.663123 | − | 0.748511i | \(-0.730769\pi\) |
−0.200026 | − | 0.979791i | \(-0.564103\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.885456 | − | 0.464723i | 0.885456 | − | 0.464723i | ||||
\(101\) | 0 | 0 | −0.120537 | − | 0.992709i | \(-0.538462\pi\) | ||||
0.120537 | + | 0.992709i | \(0.461538\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.0763874 | + | 1.89553i | −0.0763874 | + | 1.89553i | 0.278217 | + | 0.960518i | \(0.410256\pi\) |
−0.354605 | + | 0.935016i | \(0.615385\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.200026 | − | 0.979791i | \(-0.435897\pi\) | ||||
−0.200026 | + | 0.979791i | \(0.564103\pi\) | |||||||
\(108\) | −0.278217 | + | 0.960518i | −0.278217 | + | 0.960518i | ||||
\(109\) | −0.234430 | + | 1.65196i | −0.234430 | + | 1.65196i | 0.428693 | + | 0.903450i | \(0.358974\pi\) |
−0.663123 | + | 0.748511i | \(0.730769\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.201003 | + | 1.98947i | 0.201003 | + | 1.98947i | ||||
\(112\) | −0.428693 | − | 0.903450i | −0.428693 | − | 0.903450i | ||||
\(113\) | 0 | 0 | −0.0402659 | − | 0.999189i | \(-0.512821\pi\) | ||||
0.0402659 | + | 0.999189i | \(0.487179\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.903450 | − | 0.428693i | 0.903450 | − | 0.428693i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.935016 | − | 0.354605i | −0.935016 | − | 0.354605i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.424644 | − | 0.702447i | 0.424644 | − | 0.702447i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.309882 | − | 0.253011i | 0.309882 | − | 0.253011i | −0.464723 | − | 0.885456i | \(-0.653846\pi\) |
0.774605 | + | 0.632445i | \(0.217949\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.618348 | + | 1.30314i | −0.618348 | + | 1.30314i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.903450 | − | 0.428693i | \(-0.141026\pi\) | ||||
−0.903450 | + | 0.428693i | \(0.858974\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.0260942 | + | 1.29557i | −0.0260942 | + | 1.29557i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.373361 | − | 0.927686i | \(-0.621795\pi\) | ||||
0.373361 | + | 0.927686i | \(0.378205\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.628718 | − | 1.88324i | 0.628718 | − | 1.88324i | 0.200026 | − | 0.979791i | \(-0.435897\pi\) |
0.428693 | − | 0.903450i | \(-0.358974\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.799443 | − | 0.600742i | 0.799443 | − | 0.600742i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.903450 | + | 0.428693i | −0.903450 | + | 0.428693i | ||||
\(148\) | 1.03447 | − | 1.71122i | 1.03447 | − | 1.71122i | ||||
\(149\) | 0 | 0 | −0.410413 | − | 0.911900i | \(-0.634615\pi\) | ||||
0.410413 | + | 0.911900i | \(0.365385\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.22719 | + | 0.123988i | −1.22719 | + | 0.123988i | −0.692724 | − | 0.721202i | \(-0.743590\pi\) |
−0.534466 | + | 0.845190i | \(0.679487\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.979791 | − | 0.200026i | −0.979791 | − | 0.200026i | ||||
\(157\) | −1.51790 | − | 0.309882i | −1.51790 | − | 0.309882i | −0.632445 | − | 0.774605i | \(-0.717949\pi\) |
−0.885456 | + | 0.464723i | \(0.846154\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.55875 | − | 1.22120i | 1.55875 | − | 1.22120i | 0.692724 | − | 0.721202i | \(-0.256410\pi\) |
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.941967 | − | 0.335705i | \(-0.891026\pi\) | ||||
0.941967 | + | 0.335705i | \(0.108974\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.27460 | + | 0.233580i | −1.27460 | + | 0.233580i | ||||
\(172\) | 1.27719 | − | 0.670319i | 1.27719 | − | 0.670319i | ||||
\(173\) | 0 | 0 | −0.354605 | − | 0.935016i | \(-0.615385\pi\) | ||||
0.354605 | + | 0.935016i | \(0.384615\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.160411 | + | 0.987050i | −0.160411 | + | 0.987050i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.239316 | − | 0.970942i | \(-0.576923\pi\) | ||||
0.239316 | + | 0.970942i | \(0.423077\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.19678 | + | 1.06026i | 1.19678 | + | 1.06026i | 0.996757 | + | 0.0804666i | \(0.0256410\pi\) |
0.200026 | + | 0.979791i | \(0.435897\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.47764 | − | 1.30907i | 1.47764 | − | 1.30907i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.600742 | − | 0.799443i | −0.600742 | − | 0.799443i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(192\) | −1.00000 | −1.00000 | ||||||||
\(193\) | −1.49919 | − | 0.906291i | −1.49919 | − | 0.906291i | −0.999189 | − | 0.0402659i | \(-0.987179\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.979791 | + | 0.200026i | 0.979791 | + | 0.200026i | ||||
\(197\) | 0 | 0 | 0.927686 | − | 0.373361i | \(-0.121795\pi\) | ||||
−0.927686 | + | 0.373361i | \(0.878205\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.0321908 | + | 0.157681i | 0.0321908 | + | 0.157681i | 0.992709 | − | 0.120537i | \(-0.0384615\pi\) |
−0.960518 | + | 0.278217i | \(0.910256\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.970942 | − | 1.23932i | 0.970942 | − | 1.23932i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.663123 | + | 0.748511i | 0.663123 | + | 0.748511i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.759873 | + | 0.930676i | 0.759873 | + | 0.930676i | 0.999189 | − | 0.0402659i | \(-0.0128205\pi\) |
−0.239316 | + | 0.970942i | \(0.576923\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.306465 | + | 0.761468i | 0.306465 | + | 0.761468i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.21323 | − | 1.31512i | 1.21323 | − | 1.31512i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.26520 | − | 0.631868i | −1.26520 | − | 0.631868i | −0.316668 | − | 0.948536i | \(-0.602564\pi\) |
−0.948536 | + | 0.316668i | \(0.897436\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.999189 | + | 0.0402659i | −0.999189 | + | 0.0402659i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.584522 | − | 0.811378i | \(-0.698718\pi\) | ||||
0.584522 | + | 0.811378i | \(0.301282\pi\) | |||||||
\(228\) | 1.15930 | + | 0.578975i | 1.15930 | + | 0.578975i | ||||
\(229\) | −1.02301 | + | 0.411726i | −1.02301 | + | 0.411726i | −0.822984 | − | 0.568065i | \(-0.807692\pi\) |
−0.200026 | + | 0.979791i | \(0.564103\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.534466 | − | 0.845190i | \(-0.679487\pi\) | ||||
0.534466 | + | 0.845190i | \(0.320513\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.364312 | + | 0.855072i | −0.364312 | + | 0.855072i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.52152 | − | 1.00560i | −1.52152 | − | 1.00560i | −0.987050 | − | 0.160411i | \(-0.948718\pi\) |
−0.534466 | − | 0.845190i | \(-0.679487\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.663123 | − | 0.748511i | 0.663123 | − | 0.748511i | ||||
\(244\) | −1.96770 | + | 0.158849i | −1.96770 | + | 0.158849i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.335386 | − | 1.25168i | −0.335386 | − | 1.25168i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.919979 | − | 0.391967i | \(-0.128205\pi\) | ||||
−0.919979 | + | 0.391967i | \(0.871795\pi\) | |||||||
\(252\) | 1.00000i | 1.00000i | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.799443 | + | 0.600742i | 0.799443 | + | 0.600742i | ||||
\(257\) | 0 | 0 | 0.632445 | − | 0.774605i | \(-0.282051\pi\) | ||||
−0.632445 | + | 0.774605i | \(0.717949\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.746571 | + | 1.85500i | 0.746571 | + | 1.85500i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.568065 | − | 0.822984i | \(-0.692308\pi\) | ||||
0.568065 | + | 0.822984i | \(0.307692\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.52072 | + | 0.407476i | −1.52072 | + | 0.407476i | ||||
\(269\) | 0 | 0 | −0.999189 | − | 0.0402659i | \(-0.987179\pi\) | ||||
0.999189 | + | 0.0402659i | \(0.0128205\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.117515 | − | 0.163123i | 0.117515 | − | 0.163123i | −0.748511 | − | 0.663123i | \(-0.769231\pi\) |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.748511 | − | 0.663123i | 0.748511 | − | 0.663123i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.02673 | − | 0.297395i | −1.02673 | − | 0.297395i | −0.278217 | − | 0.960518i | \(-0.589744\pi\) |
−0.748511 | + | 0.663123i | \(0.769231\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.684779 | + | 0.452584i | −0.684779 | + | 0.452584i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.954721 | − | 0.297503i | \(-0.903846\pi\) | ||||
0.954721 | + | 0.297503i | \(0.0961538\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.0763402 | + | 0.628718i | −0.0763402 | + | 0.628718i | 0.903450 | + | 0.428693i | \(0.141026\pi\) |
−0.979791 | + | 0.200026i | \(0.935897\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.0402659 | − | 0.999189i | −0.0402659 | − | 0.999189i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.12921 | − | 1.56746i | 1.12921 | − | 1.56746i | ||||
\(292\) | −1.75996 | + | 0.322525i | −1.75996 | + | 0.322525i | ||||
\(293\) | 0 | 0 | −0.999797 | − | 0.0201371i | \(-0.993590\pi\) | ||||
0.999797 | + | 0.0201371i | \(0.00641026\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.822984 | + | 0.568065i | 0.822984 | + | 0.568065i | ||||
\(301\) | −0.231378 | + | 1.42373i | −0.231378 | + | 1.42373i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.578975 | − | 1.15930i | −0.578975 | − | 1.15930i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.638104 | − | 0.814480i | −0.638104 | − | 0.814480i | 0.354605 | − | 0.935016i | \(-0.384615\pi\) |
−0.992709 | + | 0.120537i | \(0.961538\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.71391 | + | 0.813261i | −1.71391 | + | 0.813261i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.919979 | − | 0.391967i | \(-0.128205\pi\) | ||||
−0.919979 | + | 0.391967i | \(0.871795\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.662573 | + | 1.55512i | −0.662573 | + | 1.55512i | 0.160411 | + | 0.987050i | \(0.448718\pi\) |
−0.822984 | + | 0.568065i | \(0.807692\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.804924 | − | 0.464723i | 0.804924 | − | 0.464723i | ||||
\(317\) | 0 | 0 | −0.482459 | − | 0.875918i | \(-0.660256\pi\) | ||||
0.482459 | + | 0.875918i | \(0.339744\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.979791 | + | 0.200026i | −0.979791 | + | 0.200026i | ||||
\(325\) | −0.120537 | − | 0.992709i | −0.120537 | − | 0.992709i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.57168 | + | 0.560127i | −1.57168 | + | 0.560127i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.58779 | − | 0.959854i | 1.58779 | − | 0.959854i | 0.600742 | − | 0.799443i | \(-0.294872\pi\) |
0.987050 | − | 0.160411i | \(-0.0512821\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.66817 | + | 1.10253i | −1.66817 | + | 1.10253i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.600742 | − | 0.799443i | 0.600742 | − | 0.799443i | ||||
\(337\) | − | 0.556435i | − | 0.556435i | −0.960518 | − | 0.278217i | \(-0.910256\pi\) | ||
0.960518 | − | 0.278217i | \(-0.0897436\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.748511 | + | 0.663123i | −0.748511 | + | 0.663123i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.428693 | − | 0.903450i | \(-0.641026\pi\) | ||||
0.428693 | + | 0.903450i | \(0.358974\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.335386 | + | 0.394291i | −0.335386 | + | 0.394291i | −0.903450 | − | 0.428693i | \(-0.858974\pi\) |
0.568065 | + | 0.822984i | \(0.307692\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.799443 | + | 0.600742i | 0.799443 | + | 0.600742i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.517338 | − | 0.855781i | \(-0.673077\pi\) | ||||
0.517338 | + | 0.855781i | \(0.326923\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.875918 | − | 0.482459i | \(-0.160256\pi\) | ||||
−0.875918 | + | 0.482459i | \(0.839744\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.679177i | 0.679177i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.120537 | − | 0.992709i | −0.120537 | − | 0.992709i | ||||
\(364\) | −0.996757 | + | 0.0804666i | −0.996757 | + | 0.0804666i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.64463 | − | 1.13521i | −1.64463 | − | 1.13521i | −0.845190 | − | 0.534466i | \(-0.820513\pi\) |
−0.799443 | − | 0.600742i | \(-0.794872\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.819328 | + | 0.0495602i | 0.819328 | + | 0.0495602i | ||||
\(373\) | 1.06230 | + | 1.53901i | 1.06230 | + | 1.53901i | 0.822984 | + | 0.568065i | \(0.192308\pi\) |
0.239316 | + | 0.970942i | \(0.423077\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.33391 | − | 1.44593i | −1.33391 | − | 1.44593i | −0.799443 | − | 0.600742i | \(-0.794872\pi\) |
−0.534466 | − | 0.845190i | \(-0.679487\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.368039 | + | 0.156807i | 0.368039 | + | 0.156807i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.855781 | − | 0.517338i | \(-0.826923\pi\) | ||||
0.855781 | + | 0.517338i | \(0.173077\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.44124 | + | 0.0580798i | −1.44124 | + | 0.0580798i | ||||
\(388\) | −1.84438 | + | 0.574732i | −1.84438 | + | 0.574732i | ||||
\(389\) | 0 | 0 | 0.721202 | − | 0.692724i | \(-0.243590\pi\) | ||||
−0.721202 | + | 0.692724i | \(0.756410\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.61980 | − | 0.0979795i | 1.61980 | − | 0.0979795i | 0.774605 | − | 0.632445i | \(-0.217949\pi\) |
0.845190 | + | 0.534466i | \(0.179487\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.15930 | + | 0.578975i | −1.15930 | + | 0.578975i | ||||
\(400\) | −0.316668 | − | 0.948536i | −0.316668 | − | 0.948536i | ||||
\(401\) | 0 | 0 | −0.446798 | − | 0.894635i | \(-0.647436\pi\) | ||||
0.446798 | + | 0.894635i | \(0.352564\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.506219 | − | 0.646140i | −0.506219 | − | 0.646140i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.38470 | − | 1.27742i | 1.38470 | − | 1.27742i | 0.464723 | − | 0.885456i | \(-0.346154\pi\) |
0.919979 | − | 0.391967i | \(-0.128205\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.85873 | + | 0.379463i | 1.85873 | + | 0.379463i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.95971 | − | 0.318483i | 1.95971 | − | 0.318483i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.160411 | − | 0.987050i | \(-0.448718\pi\) | ||||
−0.160411 | + | 0.987050i | \(0.551282\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.90596 | − | 0.593921i | 1.90596 | − | 0.593921i | 0.935016 | − | 0.354605i | \(-0.115385\pi\) |
0.970942 | − | 0.239316i | \(-0.0769231\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.05509 | − | 1.66849i | 1.05509 | − | 1.66849i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.911900 | − | 0.410413i | \(-0.865385\pi\) | ||||
0.911900 | + | 0.410413i | \(0.134615\pi\) | |||||||
\(432\) | 0.903450 | + | 0.428693i | 0.903450 | + | 0.428693i | ||||
\(433\) | −0.329236 | + | 1.61270i | −0.329236 | + | 1.61270i | 0.391967 | + | 0.919979i | \(0.371795\pi\) |
−0.721202 | + | 0.692724i | \(0.756410\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.59296 | + | 0.496387i | 1.59296 | + | 0.496387i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.59370 | − | 1.19759i | 1.59370 | − | 1.19759i | 0.748511 | − | 0.663123i | \(-0.230769\pi\) |
0.845190 | − | 0.534466i | \(-0.179487\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.799443 | − | 0.600742i | −0.799443 | − | 0.600742i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.845190 | − | 0.534466i | \(-0.179487\pi\) | ||||
−0.845190 | + | 0.534466i | \(0.820513\pi\) | |||||||
\(444\) | 1.99595 | + | 0.120733i | 1.99595 | + | 0.120733i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.960518 | + | 0.278217i | −0.960518 | + | 0.278217i | ||||
\(449\) | 0 | 0 | 0.994935 | − | 0.100522i | \(-0.0320513\pi\) | ||||
−0.994935 | + | 0.100522i | \(0.967949\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.680089 | − | 1.02900i | −0.680089 | − | 1.02900i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.0887571 | − | 0.0818806i | −0.0887571 | − | 0.0818806i | 0.632445 | − | 0.774605i | \(-0.282051\pi\) |
−0.721202 | + | 0.692724i | \(0.756410\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.647915 | − | 0.761712i | \(-0.724359\pi\) | ||||
0.647915 | + | 0.761712i | \(0.275641\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.660411 | + | 0.121025i | −0.660411 | + | 0.121025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.160411 | + | 0.987050i | \(0.551282\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.996757 | − | 0.0804666i | \(-0.0256410\pi\) | ||||
−0.996757 | + | 0.0804666i | \(0.974359\pi\) | |||||||
\(468\) | −0.278217 | − | 0.960518i | −0.278217 | − | 0.960518i | ||||
\(469\) | 0.587808 | − | 1.46052i | 0.587808 | − | 1.46052i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.431017 | − | 1.48804i | −0.431017 | − | 1.48804i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.182067 | + | 1.28298i | −0.182067 | + | 1.28298i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.787183 | − | 0.616719i | \(-0.788462\pi\) | ||||
0.787183 | + | 0.616719i | \(0.211538\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.23319 | − | 1.57405i | −1.23319 | − | 1.57405i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.97979 | − | 0.200026i | −1.97979 | − | 0.200026i | −0.979791 | − | 0.200026i | \(-0.935897\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.80571 | + | 0.812683i | 1.80571 | + | 0.812683i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.979791 | − | 0.200026i | \(-0.0641026\pi\) | ||||
−0.979791 | + | 0.200026i | \(0.935897\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.625233 | − | 0.531826i | −0.625233 | − | 0.531826i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.0179944 | + | 0.893416i | 0.0179944 | + | 0.893416i | 0.903450 | + | 0.428693i | \(0.141026\pi\) |
−0.885456 | + | 0.464723i | \(0.846154\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.774605 | − | 0.632445i | \(-0.782051\pi\) | ||||
0.774605 | + | 0.632445i | \(0.217949\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.534466 | + | 0.845190i | −0.534466 | + | 0.845190i | ||||
\(508\) | −0.200026 | − | 0.346455i | −0.200026 | − | 0.346455i | ||||
\(509\) | 0 | 0 | −0.647915 | − | 0.761712i | \(-0.724359\pi\) | ||||
0.647915 | + | 0.761712i | \(0.275641\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.799443 | − | 1.60074i | 0.799443 | − | 1.60074i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.799163 | − | 1.02006i | −0.799163 | − | 1.02006i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.18708 | + | 0.819379i | 1.18708 | + | 0.819379i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.316668 | − | 0.948536i | \(-0.397436\pi\) | ||||
−0.316668 | + | 0.948536i | \(0.602564\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.572188 | − | 1.71391i | 0.572188 | − | 1.71391i | −0.120537 | − | 0.992709i | \(-0.538462\pi\) |
0.692724 | − | 0.721202i | \(-0.256410\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.948536 | + | 0.316668i | −0.948536 | + | 0.316668i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.27460 | + | 0.233580i | 1.27460 | + | 0.233580i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.411726 | − | 0.622958i | 0.411726 | − | 0.622958i | −0.568065 | − | 0.822984i | \(-0.692308\pi\) |
0.979791 | + | 0.200026i | \(0.0641026\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.382638 | + | 1.55242i | −0.382638 | + | 1.55242i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.718540 | − | 1.04098i | −0.718540 | − | 1.04098i | −0.996757 | − | 0.0804666i | \(-0.974359\pi\) |
0.278217 | − | 0.960518i | \(-0.410256\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.84582 | + | 0.700026i | 1.84582 | + | 0.700026i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.112032 | + | 0.922670i | −0.112032 | + | 0.922670i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.75800 | − | 0.922670i | −1.75800 | − | 0.922670i | ||||
\(557\) | 0 | 0 | −0.297503 | − | 0.954721i | \(-0.596154\pi\) | ||||
0.297503 | + | 0.954721i | \(0.403846\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.173863 | − | 1.43189i | −0.173863 | − | 1.43189i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.845190 | − | 0.534466i | \(-0.179487\pi\) | ||||
−0.845190 | + | 0.534466i | \(0.820513\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.428693 | − | 0.903450i | 0.428693 | − | 0.903450i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.979791 | − | 0.200026i | \(-0.935897\pi\) | ||||
0.979791 | + | 0.200026i | \(0.0641026\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.0804666 | − | 0.00324269i | 0.0804666 | − | 0.00324269i | − | 1.00000i | \(-0.5\pi\) | |
0.0804666 | + | 0.996757i | \(0.474359\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.464723 | − | 0.885456i | −0.464723 | − | 0.885456i | ||||
\(577\) | 0.0727294 | − | 0.271430i | 0.0727294 | − | 0.271430i | −0.919979 | − | 0.391967i | \(-0.871795\pi\) |
0.992709 | + | 0.120537i | \(0.0384615\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.105773 | − | 1.74864i | 0.105773 | − | 1.74864i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(588\) | 0.278217 | + | 0.960518i | 0.278217 | + | 0.960518i | ||||
\(589\) | 0.416916 | + | 0.978537i | 0.416916 | + | 0.978537i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.52312 | − | 1.29557i | −1.52312 | − | 1.29557i | ||||
\(593\) | 0 | 0 | 0.219715 | − | 0.975564i | \(-0.429487\pi\) | ||||
−0.219715 | + | 0.975564i | \(0.570513\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.124660 | + | 0.101781i | −0.124660 | + | 0.101781i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.632445 | − | 0.774605i | \(-0.282051\pi\) | ||||
−0.632445 | + | 0.774605i | \(0.717949\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.111482 | + | 1.38096i | 0.111482 | + | 1.38096i | 0.774605 | + | 0.632445i | \(0.217949\pi\) |
−0.663123 | + | 0.748511i | \(0.730769\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.54858 | + | 0.283788i | 1.54858 | + | 0.283788i | ||||
\(604\) | −0.0744731 | + | 1.23119i | −0.0744731 | + | 1.23119i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.892750 | − | 1.70099i | −0.892750 | − | 1.70099i | −0.692724 | − | 0.721202i | \(-0.743590\pi\) |
−0.200026 | − | 0.979791i | \(-0.564103\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.0582603 | − | 0.963158i | 0.0582603 | − | 0.963158i | −0.845190 | − | 0.534466i | \(-0.820513\pi\) |
0.903450 | − | 0.428693i | \(-0.141026\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.551377 | − | 0.834256i | \(-0.685897\pi\) | ||||
0.551377 | + | 0.834256i | \(0.314103\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.0392900 | + | 0.00884883i | −0.0392900 | + | 0.00884883i | −0.239316 | − | 0.970942i | \(-0.576923\pi\) |
0.200026 | + | 0.979791i | \(0.435897\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −0.354605 | + | 0.935016i | −0.354605 | + | 0.935016i | ||||
\(625\) | −0.278217 | + | 0.960518i | −0.278217 | + | 0.960518i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.549357 | + | 1.44854i | −0.549357 | + | 1.44854i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.000811002 | 0.0402659i | −0.000811002 | 0.0402659i | 0.999189 | + | 0.0402659i | \(0.0128205\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.470942 | + | 1.10534i | −0.470942 | + | 1.10534i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.534466 | − | 0.845190i | 0.534466 | − | 0.845190i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.0804666 | − | 0.996757i | \(-0.525641\pi\) | ||||
0.0804666 | + | 0.996757i | \(0.474359\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.654274 | + | 0.709221i | −0.654274 | + | 0.709221i | −0.970942 | − | 0.239316i | \(-0.923077\pi\) |
0.316668 | + | 0.948536i | \(0.397436\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.568065 | − | 0.822984i | \(-0.307692\pi\) | ||||
−0.568065 | + | 0.822984i | \(0.692308\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.531826 | + | 0.625233i | −0.531826 | + | 0.625233i | ||||
\(652\) | −0.955347 | − | 1.73446i | −0.955347 | − | 1.73446i | ||||
\(653\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.72830 | + | 0.463097i | 1.72830 | + | 0.463097i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.278217 | − | 0.960518i | \(-0.589744\pi\) | ||||
0.278217 | + | 0.960518i | \(0.410256\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.308518 | + | 0.186505i | −0.308518 | + | 0.186505i | −0.663123 | − | 0.748511i | \(-0.730769\pi\) |
0.354605 | + | 0.935016i | \(0.384615\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.0284781 | − | 1.41393i | −0.0284781 | − | 1.41393i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.80544 | + | 0.0727566i | 1.80544 | + | 0.0727566i | 0.919979 | − | 0.391967i | \(-0.128205\pi\) |
0.885456 | + | 0.464723i | \(0.153846\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(676\) | 0.935016 | − | 0.354605i | 0.935016 | − | 0.354605i | ||||
\(677\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.648531 | − | 1.81974i | 0.648531 | − | 1.81974i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.999797 | − | 0.0201371i | \(-0.00641026\pi\) | ||||
−0.999797 | + | 0.0201371i | \(0.993590\pi\) | |||||||
\(684\) | 0.0260942 | + | 1.29557i | 0.0260942 | + | 1.29557i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.839981 | − | 0.714491i | −0.839981 | − | 0.714491i | ||||
\(688\) | −0.456763 | − | 1.36817i | −0.456763 | − | 1.36817i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.564016 | + | 1.02399i | −0.564016 | + | 1.02399i | 0.428693 | + | 0.903450i | \(0.358974\pi\) |
−0.992709 | + | 0.120537i | \(0.961538\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.948536 | + | 0.316668i | 0.948536 | + | 0.316668i | ||||
\(701\) | 0 | 0 | 0.992709 | − | 0.120537i | \(-0.0384615\pi\) | ||||
−0.992709 | + | 0.120537i | \(0.961538\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.01564 | + | 2.38379i | 1.01564 | + | 2.38379i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.0835998 | − | 0.268281i | −0.0835998 | − | 0.268281i | 0.903450 | − | 0.428693i | \(-0.141026\pi\) |
−0.987050 | + | 0.160411i | \(0.948718\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.926432 | + | 0.0747894i | −0.926432 | + | 0.0747894i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.120537 | − | 0.992709i | \(-0.538462\pi\) | ||||
0.120537 | + | 0.992709i | \(0.461538\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.41998 | + | 1.25799i | −1.41998 | + | 1.25799i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.183332 | − | 1.81456i | 0.183332 | − | 1.81456i | ||||
\(724\) | 1.23850 | − | 1.01121i | 1.23850 | − | 1.01121i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.464723 | + | 0.114544i | −0.464723 | + | 0.114544i | −0.464723 | − | 0.885456i | \(-0.653846\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.970942 | + | 0.239316i | 0.970942 | + | 0.239316i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −1.05509 | − | 1.66849i | −1.05509 | − | 1.66849i | ||||
\(733\) | −1.25801 | + | 1.16054i | −1.25801 | + | 1.16054i | −0.278217 | + | 0.960518i | \(0.589744\pi\) |
−0.979791 | + | 0.200026i | \(0.935897\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.16691 | + | 0.0705851i | 1.16691 | + | 0.0705851i | 0.632445 | − | 0.774605i | \(-0.282051\pi\) |
0.534466 | + | 0.845190i | \(0.320513\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.952443 | − | 0.878652i | 0.952443 | − | 0.878652i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.994935 | − | 0.100522i | \(-0.967949\pi\) | ||||
0.994935 | + | 0.100522i | \(0.0320513\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.77038 | + | 0.840058i | 1.77038 | + | 0.840058i | 0.970942 | + | 0.239316i | \(0.0769231\pi\) |
0.799443 | + | 0.600742i | \(0.205128\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.885456 | + | 0.464723i | −0.885456 | + | 0.464723i | ||||
\(757\) | −0.472433 | − | 0.0767779i | −0.472433 | − | 0.0767779i | −0.0804666 | − | 0.996757i | \(-0.525641\pi\) |
−0.391967 | + | 0.919979i | \(0.628205\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.983620 | − | 0.180255i | \(-0.942308\pi\) | ||||
0.983620 | + | 0.180255i | \(0.0576923\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.35379 | + | 0.975282i | −1.35379 | + | 0.975282i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.160411 | + | 0.987050i | −0.160411 | + | 0.987050i | ||||
\(769\) | 0.436476 | + | 0.605874i | 0.436476 | + | 0.605874i | 0.970942 | − | 0.239316i | \(-0.0769231\pi\) |
−0.534466 | + | 0.845190i | \(0.679487\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.13504 | + | 1.33440i | −1.13504 | + | 1.33440i | ||||
\(773\) | 0 | 0 | 0.551377 | − | 0.834256i | \(-0.314103\pi\) | ||||
−0.551377 | + | 0.834256i | \(0.685897\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.212445 | + | 0.792857i | 0.212445 | + | 0.792857i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.29557 | + | 1.52312i | −1.29557 | + | 1.52312i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.354605 | − | 0.935016i | 0.354605 | − | 0.935016i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.725045 | − | 0.522327i | 0.725045 | − | 0.522327i | −0.160411 | − | 0.987050i | \(-0.551282\pi\) |
0.885456 | + | 0.464723i | \(0.153846\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.549229 | + | 1.89616i | −0.549229 | + | 1.89616i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.160803 | − | 0.00648012i | 0.160803 | − | 0.00648012i | ||||
\(797\) | 0 | 0 | 0.987050 | − | 0.160411i | \(-0.0512821\pi\) | ||||
−0.987050 | + | 0.160411i | \(0.948718\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −1.06752 | − | 1.15717i | −1.06752 | − | 1.15717i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.970942 | − | 0.239316i | \(-0.923077\pi\) | ||||
0.970942 | + | 0.239316i | \(0.0769231\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.52065 | + | 0.0919821i | 1.52065 | + | 0.0919821i | 0.799443 | − | 0.600742i | \(-0.205128\pi\) |
0.721202 | + | 0.692724i | \(0.243590\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.199050 | + | 0.0282472i | 0.199050 | + | 0.0282472i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.262615 | + | 1.85057i | −0.262615 | + | 1.85057i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.935016 | + | 0.354605i | 0.935016 | + | 0.354605i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.999797 | − | 0.0201371i | \(-0.993590\pi\) | ||||
0.999797 | + | 0.0201371i | \(0.00641026\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.42545 | − | 0.822984i | −1.42545 | − | 0.822984i | −0.428693 | − | 0.903450i | \(-0.641026\pi\) |
−0.996757 | + | 0.0804666i | \(0.974359\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.410413 | − | 0.911900i | \(-0.365385\pi\) | ||||
−0.410413 | + | 0.911900i | \(0.634615\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.46677 | + | 1.29944i | −1.46677 | + | 1.29944i | −0.600742 | + | 0.799443i | \(0.705128\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.213814 | − | 1.04733i | −0.213814 | − | 1.04733i | ||||
\(832\) | 0.845190 | − | 0.534466i | 0.845190 | − | 0.534466i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.718976 | − | 0.396015i | −0.718976 | − | 0.396015i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.373361 | − | 0.927686i | \(-0.378205\pi\) | ||||
−0.373361 | + | 0.927686i | \(0.621795\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.632445 | + | 0.774605i | −0.632445 | + | 0.774605i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.04052 | − | 0.600742i | 1.04052 | − | 0.600742i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.391967 | − | 0.919979i | −0.391967 | − | 0.919979i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.592179 | + | 0.224584i | −0.592179 | + | 0.224584i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.70844 | − | 1.03279i | 1.70844 | − | 1.03279i | 0.822984 | − | 0.568065i | \(-0.192308\pi\) |
0.885456 | − | 0.464723i | \(-0.153846\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.200026 | − | 0.979791i | \(-0.435897\pi\) | ||||
−0.200026 | + | 0.979791i | \(0.564103\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.0789044 | − | 0.0161084i | 0.0789044 | − | 0.0161084i | −0.160411 | − | 0.987050i | \(-0.551282\pi\) |
0.239316 | + | 0.970942i | \(0.423077\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.811378 | − | 0.584522i | \(-0.198718\pi\) | ||||
−0.811378 | + | 0.584522i | \(0.801282\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(868\) | 0.800768 | − | 0.180348i | 0.800768 | − | 0.180348i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.158259 | + | 1.56639i | −0.158259 | + | 1.56639i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.91269 | + | 0.271430i | 1.91269 | + | 0.271430i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.10348 | − | 1.40848i | −1.10348 | − | 1.40848i | ||||
\(877\) | −1.34731 | − | 1.05555i | −1.34731 | − | 1.05555i | −0.992709 | − | 0.120537i | \(-0.961538\pi\) |
−0.354605 | − | 0.935016i | \(-0.615385\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.692724 | − | 0.721202i | \(-0.256410\pi\) | ||||
−0.692724 | + | 0.721202i | \(0.743590\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.14020 | + | 0.787025i | 1.14020 | + | 0.787025i | 0.979791 | − | 0.200026i | \(-0.0641026\pi\) |
0.160411 | + | 0.987050i | \(0.448718\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.160411 | − | 0.987050i | \(-0.551282\pi\) | ||||
0.160411 | + | 0.987050i | \(0.448718\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.397135 | + | 0.0482209i | 0.397135 | + | 0.0482209i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.826639 | + | 1.14746i | −0.826639 | + | 1.14746i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.120537 | + | 0.992709i | −0.120537 | + | 0.992709i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.36817 | + | 0.456763i | −1.36817 | + | 0.456763i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.22012 | + | 1.37723i | −1.22012 | + | 1.37723i | −0.316668 | + | 0.948536i | \(0.602564\pi\) |
−0.903450 | + | 0.428693i | \(0.858974\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.885456 | − | 0.464723i | \(-0.153846\pi\) | ||||
−0.885456 | + | 0.464723i | \(0.846154\pi\) | |||||||
\(912\) | 0.757442 | − | 1.05141i | 0.757442 | − | 1.05141i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.242292 | + | 1.07581i | 0.242292 | + | 1.07581i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.586782 | − | 0.519844i | −0.586782 | − | 0.519844i | 0.316668 | − | 0.948536i | \(-0.397436\pi\) |
−0.903450 | + | 0.428693i | \(0.858974\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.424644 | − | 0.943521i | 0.424644 | − | 0.943521i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.517533 | + | 1.93146i | 0.517533 | + | 1.93146i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.51660 | − | 1.13965i | −1.51660 | − | 1.13965i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.180255 | − | 0.983620i | \(-0.442308\pi\) | ||||
−0.180255 | + | 0.983620i | \(0.557692\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.952443 | + | 0.878652i | −0.952443 | + | 0.878652i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.801669 | + | 0.304033i | −0.801669 | + | 0.304033i | −0.721202 | − | 0.692724i | \(-0.756410\pi\) |
−0.0804666 | + | 0.996757i | \(0.525641\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.68490 | + | 0.136019i | −1.68490 | + | 0.136019i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.941967 | − | 0.335705i | \(-0.108974\pi\) | ||||
−0.941967 | + | 0.335705i | \(0.891026\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.811378 | − | 0.584522i | \(-0.801282\pi\) | ||||
0.811378 | + | 0.584522i | \(0.198718\pi\) | |||||||
\(948\) | 0.785559 | + | 0.496757i | 0.785559 | + | 0.496757i | ||||
\(949\) | −0.322525 | + | 1.75996i | −0.322525 | + | 1.75996i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.721202 | − | 0.692724i | \(-0.243590\pi\) | ||||
−0.721202 | + | 0.692724i | \(0.756410\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.235289 | − | 0.225998i | −0.235289 | − | 0.225998i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.23665 | + | 1.34050i | −1.23665 | + | 1.34050i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.666000 | − | 1.47979i | −0.666000 | − | 1.47979i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
0.200026 | − | 0.979791i | \(-0.435897\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.992709 | − | 0.120537i | \(-0.0384615\pi\) | ||||
−0.992709 | + | 0.120537i | \(0.961538\pi\) | |||||||
\(972\) | −0.632445 | − | 0.774605i | −0.632445 | − | 0.774605i | ||||
\(973\) | 1.79373 | − | 0.851134i | 1.79373 | − | 0.851134i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.822984 | − | 0.568065i | 0.822984 | − | 0.568065i | ||||
\(976\) | −0.158849 | + | 1.96770i | −0.158849 | + | 1.96770i | ||||
\(977\) | 0 | 0 | −0.616719 | − | 0.787183i | \(-0.711538\pi\) | ||||
0.616719 | + | 0.787183i | \(0.288462\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.22637 | − | 1.13135i | −1.22637 | − | 1.13135i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.373361 | − | 0.927686i | \(-0.378205\pi\) | ||||
−0.373361 | + | 0.927686i | \(0.621795\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.28927 | + | 0.130260i | −1.28927 | + | 0.130260i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.99351 | 1.99351 | 0.996757 | − | 0.0804666i | \(-0.0256410\pi\) | ||||
0.996757 | + | 0.0804666i | \(0.0256410\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.58779 | + | 0.959854i | 1.58779 | + | 0.959854i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.565375 | − | 0.543050i | −0.565375 | − | 0.543050i | 0.354605 | − | 0.935016i | \(-0.384615\pi\) |
−0.919979 | + | 0.391967i | \(0.871795\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.75148 | − | 0.964723i | −1.75148 | − | 0.964723i |
(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 | 3549.1.ea.a.2294.1 | yes | 48 | |
3.2 | odd | 2 | CM | 3549.1.ea.a.2294.1 | yes | 48 | |
7.3 | odd | 6 | 3549.1.ep.a.773.1 | yes | 48 | ||
21.17 | even | 6 | 3549.1.ep.a.773.1 | yes | 48 | ||
169.115 | odd | 156 | 3549.1.ep.a.2819.1 | yes | 48 | ||
507.284 | even | 156 | 3549.1.ep.a.2819.1 | yes | 48 | ||
1183.115 | even | 156 | inner | 3549.1.ea.a.1298.1 | ✓ | 48 | |
3549.1298 | odd | 156 | inner | 3549.1.ea.a.1298.1 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3549.1.ea.a.1298.1 | ✓ | 48 | 1183.115 | even | 156 | inner | |
3549.1.ea.a.1298.1 | ✓ | 48 | 3549.1298 | odd | 156 | inner | |
3549.1.ea.a.2294.1 | yes | 48 | 1.1 | even | 1 | trivial | |
3549.1.ea.a.2294.1 | yes | 48 | 3.2 | odd | 2 | CM | |
3549.1.ep.a.773.1 | yes | 48 | 7.3 | odd | 6 | ||
3549.1.ep.a.773.1 | yes | 48 | 21.17 | even | 6 | ||
3549.1.ep.a.2819.1 | yes | 48 | 169.115 | odd | 156 | ||
3549.1.ep.a.2819.1 | yes | 48 | 507.284 | even | 156 |