Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2919,1,Mod(26,2919)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2919, base_ring=CyclotomicField(138))
chi = DirichletCharacter(H, H._module([69, 115, 65]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2919.26");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2919 = 3 \cdot 7 \cdot 139 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2919.cp (of order \(138\), degree \(44\), 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: | \(1.45677077188\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Coefficient field: | \(\Q(\zeta_{69})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{44} - x^{43} + x^{41} - x^{40} + x^{38} - x^{37} + x^{35} - x^{34} + x^{32} - x^{31} + x^{29} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{138}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{138} - \cdots)\) |
Embedding invariants
Embedding label | 509.1 | ||
Root | \(-0.247808 - 0.968809i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2919.509 |
Dual form | 2919.1.cp.a.1319.1 |
$q$-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 \(\left(\mathbb{Z}/2919\mathbb{Z}\right)^\times\).
\(n\) | \(974\) | \(1114\) | \(1669\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{29}{138}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 | 0.926043 | − | 0.377419i | \(-0.123188\pi\) | ||||
−0.926043 | + | 0.377419i | \(0.876812\pi\) | |||||||
\(3\) | −0.158683 | − | 0.987330i | −0.158683 | − | 0.987330i | ||||
\(4\) | 0.715110 | − | 0.699012i | 0.715110 | − | 0.699012i | ||||
\(5\) | 0 | 0 | −0.730836 | − | 0.682553i | \(-0.760870\pi\) | ||||
0.730836 | + | 0.682553i | \(0.239130\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.983462 | + | 0.181116i | −0.983462 | + | 0.181116i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.949640 | + | 0.313344i | −0.949640 | + | 0.313344i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.576680 | − | 0.816970i | \(-0.695652\pi\) | ||||
0.576680 | + | 0.816970i | \(0.304348\pi\) | |||||||
\(12\) | −0.803631 | − | 0.595128i | −0.803631 | − | 0.595128i | ||||
\(13\) | −1.66339 | + | 0.267339i | −1.66339 | + | 0.267339i | −0.917211 | − | 0.398401i | \(-0.869565\pi\) |
−0.746184 | + | 0.665740i | \(0.768116\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.0227632 | − | 0.999741i | 0.0227632 | − | 0.999741i | ||||
\(17\) | 0 | 0 | −0.538899 | − | 0.842371i | \(-0.681159\pi\) | ||||
0.538899 | + | 0.842371i | \(0.318841\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.96489 | + | 0.0895237i | −1.96489 | + | 0.0895237i | −0.990686 | − | 0.136167i | \(-0.956522\pi\) |
−0.974199 | + | 0.225690i | \(0.927536\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.334880 | + | 0.942261i | 0.334880 | + | 0.942261i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.480157 | − | 0.877183i | \(-0.659420\pi\) | ||||
0.480157 | + | 0.877183i | \(0.340580\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.0682424 | + | 0.997669i | 0.0682424 | + | 0.997669i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.460065 | + | 0.887885i | 0.460065 | + | 0.887885i | ||||
\(28\) | −0.576680 | + | 0.816970i | −0.576680 | + | 0.816970i | ||||
\(29\) | 0 | 0 | 0.715110 | − | 0.699012i | \(-0.246377\pi\) | ||||
−0.715110 | + | 0.699012i | \(0.753623\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.349651 | + | 1.05967i | −0.349651 | + | 1.05967i | 0.613267 | + | 0.789876i | \(0.289855\pi\) |
−0.962917 | + | 0.269797i | \(0.913043\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.460065 | + | 0.887885i | −0.460065 | + | 0.887885i | ||||
\(37\) | −0.116615 | − | 1.70486i | −0.116615 | − | 1.70486i | −0.576680 | − | 0.816970i | \(-0.695652\pi\) |
0.460065 | − | 0.887885i | \(-0.347826\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.527904 | + | 1.59990i | 0.527904 | + | 1.59990i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.761145 | − | 0.648582i | \(-0.775362\pi\) | ||||
0.761145 | + | 0.648582i | \(0.224638\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.41503 | − | 0.816970i | −1.41503 | − | 0.816970i | −0.419177 | − | 0.907905i | \(-0.637681\pi\) |
−0.995857 | + | 0.0909349i | \(0.971014\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.730836 | − | 0.682553i | \(-0.239130\pi\) | ||||
−0.730836 | + | 0.682553i | \(0.760870\pi\) | |||||||
\(48\) | −0.990686 | + | 0.136167i | −0.990686 | + | 0.136167i | ||||
\(49\) | 0.934394 | − | 0.356242i | 0.934394 | − | 0.356242i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.00264 | + | 1.35391i | −1.00264 | + | 1.35391i | ||||
\(53\) | 0 | 0 | −0.789876 | − | 0.613267i | \(-0.789855\pi\) | ||||
0.789876 | + | 0.613267i | \(0.210145\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.400182 | + | 1.92578i | 0.400182 | + | 1.92578i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.715110 | − | 0.699012i | \(-0.753623\pi\) | ||||
0.715110 | + | 0.699012i | \(0.246377\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.52576 | − | 0.280988i | 1.52576 | − | 0.280988i | 0.648582 | − | 0.761145i | \(-0.275362\pi\) |
0.877183 | + | 0.480157i | \(0.159420\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.877183 | − | 0.480157i | 0.877183 | − | 0.480157i | ||||
\(64\) | −0.682553 | − | 0.730836i | −0.682553 | − | 0.730836i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.12360 | − | 1.59178i | 1.12360 | − | 1.59178i | 0.377419 | − | 0.926043i | \(-0.376812\pi\) |
0.746184 | − | 0.665740i | \(-0.231884\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.291646 | − | 0.956526i | \(-0.594203\pi\) | ||||
0.291646 | + | 0.956526i | \(0.405797\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.25209 | − | 0.543860i | −1.25209 | − | 0.543860i | −0.334880 | − | 0.942261i | \(-0.608696\pi\) |
−0.917211 | + | 0.398401i | \(0.869565\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.974199 | − | 0.225690i | 0.974199 | − | 0.225690i | ||||
\(76\) | −1.34253 | + | 1.43750i | −1.34253 | + | 1.43750i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.795508 | − | 0.933569i | −0.795508 | − | 0.933569i | 0.203456 | − | 0.979084i | \(-0.434783\pi\) |
−0.998964 | + | 0.0455146i | \(0.985507\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.803631 | − | 0.595128i | 0.803631 | − | 0.595128i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.907905 | − | 0.419177i | \(-0.862319\pi\) | ||||
0.907905 | + | 0.419177i | \(0.137681\pi\) | |||||||
\(84\) | 0.898128 | + | 0.439735i | 0.898128 | + | 0.439735i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.997669 | − | 0.0682424i | \(-0.978261\pi\) | ||||
0.997669 | + | 0.0682424i | \(0.0217391\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.58747 | − | 0.564185i | 1.58747 | − | 0.564185i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.10173 | + | 0.177069i | 1.10173 | + | 0.177069i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.715110 | − | 1.23861i | −0.715110 | − | 1.23861i | −0.962917 | − | 0.269797i | \(-0.913043\pi\) |
0.247808 | − | 0.968809i | \(-0.420290\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.746184 | + | 0.665740i | 0.746184 | + | 0.665740i | ||||
\(101\) | 0 | 0 | −0.419177 | − | 0.907905i | \(-0.637681\pi\) | ||||
0.419177 | + | 0.907905i | \(0.362319\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.122416 | − | 0.191353i | −0.122416 | − | 0.191353i | 0.775711 | − | 0.631088i | \(-0.217391\pi\) |
−0.898128 | + | 0.439735i | \(0.855072\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.775711 | − | 0.631088i | \(-0.782609\pi\) | ||||
0.775711 | + | 0.631088i | \(0.217391\pi\) | |||||||
\(108\) | 0.949640 | + | 0.313344i | 0.949640 | + | 0.313344i | ||||
\(109\) | 0.181303 | − | 0.203211i | 0.181303 | − | 0.203211i | −0.648582 | − | 0.761145i | \(-0.724638\pi\) |
0.829885 | + | 0.557934i | \(0.188406\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.66475 | + | 0.385668i | −1.66475 | + | 0.385668i | ||||
\(112\) | 0.158683 | + | 0.987330i | 0.158683 | + | 0.987330i | ||||
\(113\) | 0 | 0 | −0.877183 | − | 0.480157i | \(-0.840580\pi\) | ||||
0.877183 | + | 0.480157i | \(0.159420\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.49586 | − | 0.775091i | 1.49586 | − | 0.775091i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.334880 | + | 0.942261i | −0.334880 | + | 0.942261i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.490686 | + | 1.00219i | 0.490686 | + | 1.00219i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.226219 | + | 1.97882i | −0.226219 | + | 1.97882i | −0.0227632 | + | 0.999741i | \(0.507246\pi\) |
−0.203456 | + | 0.979084i | \(0.565217\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.582078 | + | 1.52674i | −0.582078 | + | 1.52674i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.595128 | − | 0.803631i | \(-0.702899\pi\) | ||||
0.595128 | + | 0.803631i | \(0.297101\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.91617 | − | 0.443916i | 1.91617 | − | 0.443916i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.990686 | − | 0.136167i | \(-0.956522\pi\) | ||||
0.990686 | + | 0.136167i | \(0.0434783\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.998964 | + | 0.0455146i | 0.998964 | + | 0.0455146i | ||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.291646 | + | 0.956526i | 0.291646 | + | 0.956526i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(148\) | −1.27511 | − | 1.13764i | −1.27511 | − | 1.13764i | ||||
\(149\) | 0 | 0 | 0.987330 | − | 0.158683i | \(-0.0507246\pi\) | ||||
−0.987330 | + | 0.158683i | \(0.949275\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.214975 | + | 0.494921i | 0.214975 | + | 0.494921i | 0.990686 | − | 0.136167i | \(-0.0434783\pi\) |
−0.775711 | + | 0.631088i | \(0.782609\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.49586 | + | 0.775091i | 1.49586 | + | 0.775091i | ||||
\(157\) | 1.07650 | + | 1.26333i | 1.07650 | + | 1.26333i | 0.962917 | + | 0.269797i | \(0.0869565\pi\) |
0.113580 | + | 0.993529i | \(0.463768\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.85442 | + | 0.519584i | −1.85442 | + | 0.519584i | −0.854419 | + | 0.519584i | \(0.826087\pi\) |
−1.00000 | \(1.00000\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.225690 | − | 0.974199i | \(-0.572464\pi\) | ||||
0.225690 | + | 0.974199i | \(0.427536\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.74577 | − | 0.576037i | 1.74577 | − | 0.576037i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.83788 | − | 0.700700i | 1.83788 | − | 0.700700i | ||||
\(172\) | −1.58298 | + | 0.404903i | −1.58298 | + | 0.404903i | ||||
\(173\) | 0 | 0 | 0.907905 | − | 0.419177i | \(-0.137681\pi\) | ||||
−0.907905 | + | 0.419177i | \(0.862319\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.247808 | − | 0.968809i | −0.247808 | − | 0.968809i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.993529 | − | 0.113580i | \(-0.963768\pi\) | ||||
0.993529 | + | 0.113580i | \(0.0362319\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.09308 | − | 0.631088i | 1.09308 | − | 0.631088i | 0.158683 | − | 0.987330i | \(-0.449275\pi\) |
0.934394 | + | 0.356242i | \(0.115942\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.519540 | − | 1.46184i | −0.519540 | − | 1.46184i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.613267 | − | 0.789876i | −0.613267 | − | 0.789876i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.113580 | − | 0.993529i | \(-0.463768\pi\) | ||||
−0.113580 | + | 0.993529i | \(0.536232\pi\) | |||||||
\(192\) | −0.613267 | + | 0.789876i | −0.613267 | + | 0.789876i | ||||
\(193\) | −0.663521 | − | 1.86697i | −0.663521 | − | 1.86697i | −0.460065 | − | 0.887885i | \(-0.652174\pi\) |
−0.203456 | − | 0.979084i | \(-0.565217\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.419177 | − | 0.907905i | 0.419177 | − | 0.907905i | ||||
\(197\) | 0 | 0 | 0.993529 | − | 0.113580i | \(-0.0362319\pi\) | ||||
−0.993529 | + | 0.113580i | \(0.963768\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.58068 | + | 0.291101i | −1.58068 | + | 0.291101i | −0.898128 | − | 0.439735i | \(-0.855072\pi\) |
−0.682553 | + | 0.730836i | \(0.739130\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.74991 | − | 0.856778i | −1.74991 | − | 0.856778i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.229406 | + | 1.66905i | 0.229406 | + | 1.66905i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.943465 | + | 0.435595i | −0.943465 | + | 0.435595i | −0.829885 | − | 0.557934i | \(-0.811594\pi\) |
−0.113580 | + | 0.993529i | \(0.536232\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.151944 | − | 1.10547i | 0.151944 | − | 1.10547i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.338284 | + | 1.32253i | −0.338284 | + | 1.32253i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.490999 | − | 0.0674863i | −0.490999 | − | 0.0674863i | −0.113580 | − | 0.993529i | \(-0.536232\pi\) |
−0.377419 | + | 0.926043i | \(0.623188\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.377419 | − | 0.926043i | −0.377419 | − | 0.926043i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.203456 | − | 0.979084i | \(-0.565217\pi\) | ||||
0.203456 | + | 0.979084i | \(0.434783\pi\) | |||||||
\(228\) | 1.63232 | + | 1.09741i | 1.63232 | + | 1.09741i | ||||
\(229\) | −0.0735515 | + | 0.114971i | −0.0735515 | + | 0.114971i | −0.877183 | − | 0.480157i | \(-0.840580\pi\) |
0.803631 | + | 0.595128i | \(0.202899\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.0909349 | − | 0.995857i | \(-0.528986\pi\) | ||||
0.0909349 | + | 0.995857i | \(0.471014\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.795508 | + | 0.933569i | −0.795508 | + | 0.933569i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.203456 | − | 0.979084i | \(-0.434783\pi\) | ||||
−0.203456 | + | 0.979084i | \(0.565217\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.285034 | + | 0.139556i | 0.285034 | + | 0.139556i | 0.576680 | − | 0.816970i | \(-0.304348\pi\) |
−0.291646 | + | 0.956526i | \(0.594203\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.715110 | − | 0.699012i | −0.715110 | − | 0.699012i | ||||
\(244\) | 0.894675 | − | 1.26747i | 0.894675 | − | 1.26747i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.24445 | − | 0.674204i | 3.24445 | − | 0.674204i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.887885 | − | 0.460065i | \(-0.152174\pi\) | ||||
−0.887885 | + | 0.460065i | \(0.847826\pi\) | |||||||
\(252\) | 0.291646 | − | 0.956526i | 0.291646 | − | 0.956526i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.998964 | − | 0.0455146i | −0.998964 | − | 0.0455146i | ||||
\(257\) | 0 | 0 | 0.789876 | − | 0.613267i | \(-0.210145\pi\) | ||||
−0.789876 | + | 0.613267i | \(0.789855\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.423464 | + | 1.65554i | 0.423464 | + | 1.65554i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.0682424 | − | 0.997669i | \(-0.478261\pi\) | ||||
−0.0682424 | + | 0.997669i | \(0.521739\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.309177 | − | 1.92371i | −0.309177 | − | 1.92371i | ||||
\(269\) | 0 | 0 | 0.203456 | − | 0.979084i | \(-0.434783\pi\) | ||||
−0.203456 | + | 0.979084i | \(0.565217\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.53476 | − | 0.933305i | −1.53476 | − | 0.933305i | −0.995857 | − | 0.0909349i | \(-0.971014\pi\) |
−0.538899 | − | 0.842371i | \(-0.681159\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.808940 | − | 1.47783i | −0.808940 | − | 1.47783i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.831656 | − | 0.480157i | 0.831656 | − | 0.480157i | −0.0227632 | − | 0.999741i | \(-0.507246\pi\) |
0.854419 | + | 0.519584i | \(0.173913\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 1.11587i | − | 1.11587i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.356242 | − | 0.934394i | \(-0.384058\pi\) | ||||
−0.356242 | + | 0.934394i | \(0.615942\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.45611 | − | 0.443970i | 1.45611 | − | 0.443970i | 0.538899 | − | 0.842371i | \(-0.318841\pi\) |
0.917211 | + | 0.398401i | \(0.130435\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.419177 | + | 0.907905i | −0.419177 | + | 0.907905i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.10944 | + | 0.902594i | −1.10944 | + | 0.902594i | ||||
\(292\) | −1.27555 | + | 0.486308i | −1.27555 | + | 0.486308i | ||||
\(293\) | 0 | 0 | −0.829885 | − | 0.557934i | \(-0.811594\pi\) | ||||
0.829885 | + | 0.557934i | \(0.188406\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.538899 | − | 0.842371i | 0.538899 | − | 0.842371i | ||||
\(301\) | 1.53960 | + | 0.547173i | 1.53960 | + | 0.547173i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.0447735 | + | 1.96641i | 0.0447735 | + | 1.96641i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.38898 | − | 1.42096i | −1.38898 | − | 1.42096i | −0.775711 | − | 0.631088i | \(-0.782609\pi\) |
−0.613267 | − | 0.789876i | \(-0.710145\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.169503 | + | 0.151230i | −0.169503 | + | 0.151230i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.247808 | − | 0.968809i | \(-0.579710\pi\) | ||||
0.247808 | + | 0.968809i | \(0.420290\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.315521 | + | 0.322787i | −0.315521 | + | 0.322787i | −0.854419 | − | 0.519584i | \(-0.826087\pi\) |
0.538899 | + | 0.842371i | \(0.318841\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.22145 | − | 0.111535i | −1.22145 | − | 0.111535i | ||||
\(317\) | 0 | 0 | 0.665740 | − | 0.746184i | \(-0.268116\pi\) | ||||
−0.665740 | + | 0.746184i | \(0.731884\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.158683 | − | 0.987330i | 0.158683 | − | 0.987330i | ||||
\(325\) | −0.380230 | − | 1.64127i | −0.380230 | − | 1.64127i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.229406 | − | 0.146760i | −0.229406 | − | 0.146760i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.268883 | − | 1.95627i | 0.268883 | − | 1.95627i | −0.0227632 | − | 0.999741i | \(-0.507246\pi\) |
0.291646 | − | 0.956526i | \(-0.405797\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.644949 | + | 1.58246i | 0.644949 | + | 1.58246i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.949640 | − | 0.313344i | 0.949640 | − | 0.313344i | ||||
\(337\) | 0.489900 | + | 1.74847i | 0.489900 | + | 1.74847i | 0.648582 | + | 0.761145i | \(0.275362\pi\) |
−0.158683 | + | 0.987330i | \(0.550725\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.854419 | + | 0.519584i | −0.854419 | + | 0.519584i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.377419 | − | 0.926043i | \(-0.376812\pi\) | ||||
−0.377419 | + | 0.926043i | \(0.623188\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.346485 | + | 0.105644i | −0.346485 | + | 0.105644i | −0.460065 | − | 0.887885i | \(-0.652174\pi\) |
0.113580 | + | 0.993529i | \(0.463768\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00264 | − | 1.35391i | −1.00264 | − | 1.35391i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.291646 | − | 0.956526i | \(-0.405797\pi\) | ||||
−0.291646 | + | 0.956526i | \(0.594203\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.917211 | − | 0.398401i | \(-0.869565\pi\) | ||||
0.917211 | + | 0.398401i | \(0.130435\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.85690 | − | 0.260873i | 2.85690 | − | 0.260873i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.983462 | + | 0.181116i | 0.983462 | + | 0.181116i | ||||
\(364\) | 0.740839 | − | 1.51311i | 0.740839 | − | 1.51311i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.397519 | + | 0.591280i | −0.397519 | + | 0.591280i | −0.974199 | − | 0.225690i | \(-0.927536\pi\) |
0.576680 | + | 0.816970i | \(0.304348\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.911631 | − | 0.643499i | 0.911631 | − | 0.643499i | ||||
\(373\) | −0.321621 | + | 1.74640i | −0.321621 | + | 1.74640i | 0.291646 | + | 0.956526i | \(0.405797\pi\) |
−0.613267 | + | 0.789876i | \(0.710145\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.0165383 | + | 0.181116i | −0.0165383 | + | 0.181116i | 0.983462 | + | 0.181116i | \(0.0579710\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.98965 | − | 0.0906520i | 1.98965 | − | 0.0906520i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.419177 | − | 0.907905i | \(-0.637681\pi\) | ||||
0.419177 | + | 0.907905i | \(0.362319\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.59976 | + | 0.332435i | 1.59976 | + | 0.332435i | ||||
\(388\) | −1.37718 | − | 0.385868i | −1.37718 | − | 0.385868i | ||||
\(389\) | 0 | 0 | 0.730836 | − | 0.682553i | \(-0.239130\pi\) | ||||
−0.730836 | + | 0.682553i | \(0.760870\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.945425 | − | 0.517512i | −0.945425 | − | 0.517512i | −0.0682424 | − | 0.997669i | \(-0.521739\pi\) |
−0.877183 | + | 0.480157i | \(0.840580\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.742355 | − | 1.82145i | −0.742355 | − | 1.82145i | ||||
\(400\) | 0.998964 | − | 0.0455146i | 0.998964 | − | 0.0455146i | ||||
\(401\) | 0 | 0 | −0.999741 | − | 0.0227632i | \(-0.992754\pi\) | ||||
0.999741 | + | 0.0227632i | \(0.00724638\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.298315 | − | 1.85613i | 0.298315 | − | 1.85613i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.791646 | − | 0.0905009i | 0.791646 | − | 0.0905009i | 0.291646 | − | 0.956526i | \(-0.405797\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.221299 | − | 0.0512679i | −0.221299 | − | 0.0512679i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.113580 | − | 0.993529i | −0.113580 | − | 0.993529i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.613267 | − | 0.789876i | \(-0.289855\pi\) | ||||
−0.613267 | + | 0.789876i | \(0.710145\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.165972 | + | 0.648869i | 0.165972 | + | 0.648869i | 0.995857 | + | 0.0909349i | \(0.0289855\pi\) |
−0.829885 | + | 0.557934i | \(0.811594\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.44964 | + | 0.552681i | −1.44964 | + | 0.552681i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.987330 | − | 0.158683i | \(-0.949275\pi\) | ||||
0.987330 | + | 0.158683i | \(0.0507246\pi\) | |||||||
\(432\) | 0.898128 | − | 0.439735i | 0.898128 | − | 0.439735i | ||||
\(433\) | −0.918566 | − | 1.67810i | −0.918566 | − | 1.67810i | −0.715110 | − | 0.699012i | \(-0.753623\pi\) |
−0.203456 | − | 0.979084i | \(-0.565217\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.0123951 | − | 0.272051i | −0.0123951 | − | 0.272051i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.268352 | + | 0.517896i | 0.268352 | + | 0.517896i | 0.983462 | − | 0.181116i | \(-0.0579710\pi\) |
−0.715110 | + | 0.699012i | \(0.753623\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.775711 | + | 0.631088i | −0.775711 | + | 0.631088i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.519584 | − | 0.854419i | \(-0.673913\pi\) | ||||
0.519584 | + | 0.854419i | \(0.326087\pi\) | |||||||
\(444\) | −0.920891 | + | 1.43948i | −0.920891 | + | 1.43948i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.803631 | + | 0.595128i | 0.803631 | + | 0.595128i | ||||
\(449\) | 0 | 0 | −0.987330 | − | 0.158683i | \(-0.949275\pi\) | ||||
0.987330 | + | 0.158683i | \(0.0507246\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.454538 | − | 0.290786i | 0.454538 | − | 0.290786i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.474199 | − | 1.09172i | −0.474199 | − | 1.09172i | −0.974199 | − | 0.225690i | \(-0.927536\pi\) |
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.942261 | − | 0.334880i | \(-0.108696\pi\) | ||||
−0.942261 | + | 0.334880i | \(0.891304\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.07769 | − | 0.410875i | 1.07769 | − | 0.410875i | 0.247808 | − | 0.968809i | \(-0.420290\pi\) |
0.829885 | + | 0.557934i | \(0.188406\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.0682424 | − | 0.997669i | \(-0.478261\pi\) | ||||
−0.0682424 | + | 0.997669i | \(0.521739\pi\) | |||||||
\(468\) | 0.527904 | − | 1.59990i | 0.527904 | − | 1.59990i | ||||
\(469\) | −0.816723 | + | 1.76896i | −0.816723 | + | 1.76896i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.07650 | − | 1.26333i | 1.07650 | − | 1.26333i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.223404 | − | 1.95420i | −0.223404 | − | 1.95420i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.829885 | − | 0.557934i | \(-0.188406\pi\) | ||||
−0.829885 | + | 0.557934i | \(0.811594\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.649752 | + | 2.80467i | 0.649752 | + | 2.80467i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.419177 | + | 0.907905i | 0.419177 | + | 0.907905i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.84777 | + | 0.753079i | 1.84777 | + | 0.753079i | 0.949640 | + | 0.313344i | \(0.101449\pi\) |
0.898128 | + | 0.439735i | \(0.144928\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.807265 | + | 1.74847i | 0.807265 | + | 1.74847i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.997669 | − | 0.0682424i | \(-0.978261\pi\) | ||||
0.997669 | + | 0.0682424i | \(0.0217391\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.05144 | + | 0.373681i | 1.05144 | + | 0.373681i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.0285235 | + | 0.0864449i | −0.0285235 | + | 0.0864449i | −0.962917 | − | 0.269797i | \(-0.913043\pi\) |
0.934394 | + | 0.356242i | \(0.115942\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.926043 | − | 0.377419i | \(-0.123188\pi\) | ||||
−0.926043 | + | 0.377419i | \(0.876812\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.845762 | − | 1.63225i | −0.845762 | − | 1.63225i | ||||
\(508\) | 1.22145 | + | 1.57321i | 1.22145 | + | 1.57321i | ||||
\(509\) | 0 | 0 | −0.682553 | − | 0.730836i | \(-0.739130\pi\) | ||||
0.682553 | + | 0.730836i | \(0.260870\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.32989 | + | 0.308091i | 1.32989 | + | 0.308091i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.983462 | − | 1.70341i | −0.983462 | − | 1.70341i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.650963 | + | 1.49867i | 0.650963 | + | 1.49867i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.962917 | − | 0.269797i | \(-0.0869565\pi\) | ||||
−0.962917 | + | 0.269797i | \(0.913043\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.39477 | − | 1.42688i | −1.39477 | − | 1.42688i | −0.746184 | − | 0.665740i | \(-0.768116\pi\) |
−0.648582 | − | 0.761145i | \(-0.724638\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.917211 | + | 0.398401i | −0.917211 | + | 0.398401i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.538899 | + | 0.842371i | −0.538899 | + | 0.842371i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.05997 | − | 1.65688i | 1.05997 | − | 1.65688i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.523871 | + | 0.256494i | −0.523871 | + | 0.256494i | −0.682553 | − | 0.730836i | \(-0.739130\pi\) |
0.158683 | + | 0.987330i | \(0.449275\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.796544 | − | 0.979084i | −0.796544 | − | 0.979084i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.27360 | − | 1.42749i | 1.27360 | − | 1.42749i | 0.419177 | − | 0.907905i | \(-0.362319\pi\) |
0.854419 | − | 0.519584i | \(-0.173913\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.36088 | + | 0.744926i | −1.36088 | + | 0.744926i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.951436 | + | 0.774051i | 0.951436 | + | 0.774051i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.746184 | − | 0.665740i | 0.746184 | − | 0.665740i | ||||
\(557\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.57217 | + | 0.980650i | 2.57217 | + | 0.980650i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.480157 | − | 0.877183i | \(-0.659420\pi\) | ||||
0.480157 | + | 0.877183i | \(0.340580\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.682553 | + | 0.730836i | −0.682553 | + | 0.730836i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.934394 | − | 0.356242i | \(-0.884058\pi\) | ||||
0.934394 | + | 0.356242i | \(0.115942\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.877419 | + | 0.0600171i | 0.877419 | + | 0.0600171i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
0.377419 | + | 0.926043i | \(0.376812\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.877183 | + | 0.480157i | 0.877183 | + | 0.480157i | ||||
\(577\) | −1.73802 | + | 0.238886i | −1.73802 | + | 0.238886i | −0.934394 | − | 0.356242i | \(-0.884058\pi\) |
−0.803631 | + | 0.595128i | \(0.797101\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.73802 | + | 0.951369i | −1.73802 | + | 0.951369i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.665740 | − | 0.746184i | \(-0.731884\pi\) | ||||
0.665740 | + | 0.746184i | \(0.268116\pi\) | |||||||
\(588\) | −0.962917 | − | 0.269797i | −0.962917 | − | 0.269797i | ||||
\(589\) | 0.592157 | − | 2.11344i | 0.592157 | − | 2.11344i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.70707 | + | 0.0777771i | −1.70707 | + | 0.0777771i | ||||
\(593\) | 0 | 0 | 0.997669 | − | 0.0682424i | \(-0.0217391\pi\) | ||||
−0.997669 | + | 0.0682424i | \(0.978261\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.538239 | + | 1.51446i | 0.538239 | + | 1.51446i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.58298 | − | 1.11739i | 1.58298 | − | 1.11739i | 0.648582 | − | 0.761145i | \(-0.275362\pi\) |
0.934394 | − | 0.356242i | \(-0.115942\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.568242 | + | 1.86369i | −0.568242 | + | 1.86369i | ||||
\(604\) | 0.499687 | + | 0.203653i | 0.499687 | + | 0.203653i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.792401 | − | 0.888149i | −0.792401 | − | 0.888149i | 0.203456 | − | 0.979084i | \(-0.434783\pi\) |
−0.995857 | + | 0.0909349i | \(0.971014\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.30908 | − | 1.16795i | 1.30908 | − | 1.16795i | 0.334880 | − | 0.942261i | \(-0.391304\pi\) |
0.974199 | − | 0.225690i | \(-0.0724638\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.761145 | − | 0.648582i | \(-0.224638\pi\) | ||||
−0.761145 | + | 0.648582i | \(0.775362\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.356535 | − | 1.53899i | 0.356535 | − | 1.53899i | −0.419177 | − | 0.907905i | \(-0.637681\pi\) |
0.775711 | − | 0.631088i | \(-0.217391\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.61150 | − | 0.491348i | 1.61150 | − | 0.491348i | ||||
\(625\) | −0.990686 | + | 0.136167i | −0.990686 | + | 0.136167i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.65289 | + | 0.150931i | 1.65289 | + | 0.150931i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.15454 | − | 1.07826i | 1.15454 | − | 1.07826i | 0.158683 | − | 0.987330i | \(-0.449275\pi\) |
0.995857 | − | 0.0909349i | \(-0.0289855\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.579787 | + | 0.862390i | 0.579787 | + | 0.862390i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.45903 | + | 0.842371i | −1.45903 | + | 0.842371i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.942261 | − | 0.334880i | \(-0.108696\pi\) | ||||
−0.942261 | + | 0.334880i | \(0.891304\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.0417573 | − | 0.0181378i | 0.0417573 | − | 0.0181378i | −0.377419 | − | 0.926043i | \(-0.623188\pi\) |
0.419177 | + | 0.907905i | \(0.362319\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.789876 | − | 0.613267i | \(-0.210145\pi\) | ||||
−0.789876 | + | 0.613267i | \(0.789855\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.11558 | + | 0.0254007i | −1.11558 | + | 0.0254007i | ||||
\(652\) | −0.962917 | + | 1.66782i | −0.962917 | + | 1.66782i | ||||
\(653\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.35945 | + | 0.124136i | 1.35945 | + | 0.124136i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.887885 | − | 0.460065i | \(-0.847826\pi\) | ||||
0.887885 | + | 0.460065i | \(0.152174\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.82682 | + | 0.166813i | 1.82682 | + | 0.166813i | 0.949640 | − | 0.313344i | \(-0.101449\pi\) |
0.877183 | + | 0.480157i | \(0.159420\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.0112818 | + | 0.495487i | 0.0112818 | + | 0.495487i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.699040 | + | 1.09269i | −0.699040 | + | 1.09269i | 0.291646 | + | 0.956526i | \(0.405797\pi\) |
−0.990686 | + | 0.136167i | \(0.956522\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.854419 | + | 0.519584i | −0.854419 | + | 0.519584i | ||||
\(676\) | 0.845762 | − | 1.63225i | 0.845762 | − | 1.63225i | ||||
\(677\) | 0 | 0 | −0.942261 | − | 0.334880i | \(-0.891304\pi\) | ||||
0.942261 | + | 0.334880i | \(0.108696\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.927614 | + | 1.08860i | 0.927614 | + | 1.08860i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.917211 | − | 0.398401i | \(-0.130435\pi\) | ||||
−0.917211 | + | 0.398401i | \(0.869565\pi\) | |||||||
\(684\) | 0.824488 | − | 1.78578i | 0.824488 | − | 1.78578i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.125185 | + | 0.0543757i | 0.125185 | + | 0.0543757i | ||||
\(688\) | −0.848969 | + | 1.39607i | −0.848969 | + | 1.39607i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.82885 | − | 0.512419i | −1.82885 | − | 0.512419i | −0.829885 | − | 0.557934i | \(-0.811594\pi\) |
−0.998964 | + | 0.0455146i | \(0.985507\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.854419 | − | 0.519584i | −0.854419 | − | 0.519584i | ||||
\(701\) | 0 | 0 | 0.854419 | − | 0.519584i | \(-0.173913\pi\) | ||||
−0.854419 | + | 0.519584i | \(0.826087\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.381761 | + | 3.33940i | 0.381761 | + | 3.33940i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.712299 | + | 1.86830i | 0.712299 | + | 1.86830i | 0.377419 | + | 0.926043i | \(0.376812\pi\) |
0.334880 | + | 0.942261i | \(0.391304\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.04797 | + | 0.637287i | 1.04797 | + | 0.637287i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.269797 | − | 0.962917i | \(-0.586957\pi\) | ||||
0.269797 | + | 0.962917i | \(0.413043\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.155049 | + | 0.166017i | 0.155049 | + | 0.166017i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.0925582 | − | 0.303568i | 0.0925582 | − | 0.303568i | ||||
\(724\) | 0.340531 | − | 1.21537i | 0.340531 | − | 1.21537i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.183018 | + | 1.13875i | −0.183018 | + | 1.13875i | 0.715110 | + | 0.699012i | \(0.246377\pi\) |
−0.898128 | + | 0.439735i | \(0.855072\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.576680 | + | 0.816970i | −0.576680 | + | 0.816970i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −1.39338 | − | 0.682214i | −1.39338 | − | 0.682214i | ||||
\(733\) | 1.61324 | + | 1.13875i | 1.61324 | + | 1.13875i | 0.898128 | + | 0.439735i | \(0.144928\pi\) |
0.715110 | + | 0.699012i | \(0.246377\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.489575 | + | 0.574541i | −0.489575 | + | 0.574541i | −0.949640 | − | 0.313344i | \(-0.898551\pi\) |
0.460065 | + | 0.887885i | \(0.347826\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.18050 | − | 3.09635i | −1.18050 | − | 3.09635i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.136167 | − | 0.990686i | \(-0.543478\pi\) | ||||
0.136167 | + | 0.990686i | \(0.456522\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.58298 | + | 1.11739i | −1.58298 | + | 1.11739i | −0.648582 | + | 0.761145i | \(0.724638\pi\) |
−0.934394 | + | 0.356242i | \(0.884058\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.990686 | − | 0.136167i | −0.990686 | − | 0.136167i | ||||
\(757\) | −1.95360 | + | 0.133630i | −1.95360 | + | 0.133630i | −0.990686 | − | 0.136167i | \(-0.956522\pi\) |
−0.962917 | + | 0.269797i | \(0.913043\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.993529 | − | 0.113580i | \(-0.0362319\pi\) | ||||
−0.993529 | + | 0.113580i | \(0.963768\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.141500 | + | 0.232687i | −0.141500 | + | 0.232687i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.113580 | + | 0.993529i | 0.113580 | + | 0.993529i | ||||
\(769\) | 0.0627919 | − | 0.917985i | 0.0627919 | − | 0.917985i | −0.854419 | − | 0.519584i | \(-0.826087\pi\) |
0.917211 | − | 0.398401i | \(-0.130435\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.77952 | − | 0.871278i | −1.77952 | − | 0.871278i | ||||
\(773\) | 0 | 0 | −0.942261 | − | 0.334880i | \(-0.891304\pi\) | ||||
0.942261 | + | 0.334880i | \(0.108696\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.08106 | − | 0.276521i | −1.08106 | − | 0.276521i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.56737 | − | 0.680803i | 1.56737 | − | 0.680803i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.334880 | − | 0.942261i | −0.334880 | − | 0.942261i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.26370 | + | 0.292757i | −1.26370 | + | 0.292757i | −0.803631 | − | 0.595128i | \(-0.797101\pi\) |
−0.460065 | + | 0.887885i | \(0.652174\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.46283 | + | 0.875290i | −2.46283 | + | 0.875290i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.926877 | + | 1.31308i | −0.926877 | + | 1.31308i | ||||
\(797\) | 0 | 0 | 0.829885 | − | 0.557934i | \(-0.188406\pi\) | ||||
−0.829885 | + | 0.557934i | \(0.811594\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −1.85028 | + | 0.610519i | −1.85028 | + | 0.610519i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.997669 | − | 0.0682424i | \(-0.0217391\pi\) | ||||
−0.997669 | + | 0.0682424i | \(0.978261\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.0944966 | − | 0.155393i | 0.0944966 | − | 0.155393i | −0.803631 | − | 0.595128i | \(-0.797101\pi\) |
0.898128 | + | 0.439735i | \(0.144928\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.677941 | + | 1.66341i | −0.677941 | + | 1.66341i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.85352 | + | 1.47857i | 2.85352 | + | 1.47857i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.33074 | + | 1.03320i | −1.33074 | + | 1.03320i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.356242 | − | 0.934394i | \(-0.384058\pi\) | ||||
−0.356242 | + | 0.934394i | \(0.615942\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.368764 | − | 0.260302i | 0.368764 | − | 0.260302i | −0.377419 | − | 0.926043i | \(-0.623188\pi\) |
0.746184 | + | 0.665740i | \(0.231884\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.999741 | − | 0.0227632i | \(-0.992754\pi\) | ||||
0.999741 | + | 0.0227632i | \(0.00724638\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.195333 | − | 0.640642i | −0.195333 | − | 0.640642i | −0.998964 | − | 0.0455146i | \(-0.985507\pi\) |
0.803631 | − | 0.595128i | \(-0.202899\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.606043 | − | 0.744926i | −0.606043 | − | 0.744926i | ||||
\(832\) | 1.33074 | + | 1.03320i | 1.33074 | + | 1.03320i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.10173 | + | 0.177069i | −1.10173 | + | 0.177069i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.225690 | − | 0.974199i | \(-0.427536\pi\) | ||||
−0.225690 | + | 0.974199i | \(0.572464\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.0227632 | − | 0.999741i | 0.0227632 | − | 0.999741i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.370195 | + | 0.970992i | −0.370195 | + | 0.970992i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.158683 | − | 0.987330i | 0.158683 | − | 0.987330i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.669404 | − | 1.36721i | −0.669404 | − | 1.36721i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.219284 | − | 0.342771i | −0.219284 | − | 0.342771i | 0.715110 | − | 0.699012i | \(-0.246377\pi\) |
−0.934394 | + | 0.356242i | \(0.884058\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.0227632 | − | 0.999741i | \(-0.492754\pi\) | ||||
−0.0227632 | + | 0.999741i | \(0.507246\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.535792 | + | 0.796950i | 0.535792 | + | 0.796950i | 0.995857 | − | 0.0909349i | \(-0.0289855\pi\) |
−0.460065 | + | 0.887885i | \(0.652174\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.247808 | − | 0.968809i | \(-0.579710\pi\) | ||||
0.247808 | + | 0.968809i | \(0.420290\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.962917 | + | 0.269797i | 0.962917 | + | 0.269797i | ||||
\(868\) | −0.664084 | − | 0.896746i | −0.664084 | − | 0.896746i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.44345 | + | 2.94815i | −1.44345 | + | 2.94815i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.06721 | + | 0.952154i | 1.06721 | + | 0.952154i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.682553 | + | 1.18222i | 0.682553 | + | 1.18222i | ||||
\(877\) | 0.617029 | − | 0.356242i | 0.617029 | − | 0.356242i | −0.158683 | − | 0.987330i | \(-0.550725\pi\) |
0.775711 | + | 0.631088i | \(0.217391\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.956526 | − | 0.291646i | \(-0.905797\pi\) | ||||
0.956526 | + | 0.291646i | \(0.0942029\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.79439 | − | 0.0817558i | −1.79439 | − | 0.0817558i | −0.877183 | − | 0.480157i | \(-0.840580\pi\) |
−0.917211 | + | 0.398401i | \(0.869565\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.990686 | − | 0.136167i | \(-0.956522\pi\) | ||||
0.990686 | + | 0.136167i | \(0.0434783\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.135919 | − | 1.98707i | −0.135919 | − | 1.98707i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.398292 | + | 0.294955i | −0.398292 | + | 0.294955i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.917211 | − | 0.398401i | −0.917211 | − | 0.398401i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.295933 | − | 1.60692i | 0.295933 | − | 1.60692i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.530463 | + | 1.22125i | −0.530463 | + | 1.22125i | 0.419177 | + | 0.907905i | \(0.362319\pi\) |
−0.949640 | + | 0.313344i | \(0.898551\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.0682424 | − | 0.997669i | \(-0.521739\pi\) | ||||
0.0682424 | + | 0.997669i | \(0.478261\pi\) | |||||||
\(912\) | 1.93439 | − | 0.356242i | 1.93439 | − | 0.356242i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.0277687 | + | 0.133630i | 0.0277687 | + | 0.133630i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.43439 | − | 1.22227i | −1.43439 | − | 1.22227i | −0.934394 | − | 0.356242i | \(-0.884058\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.18255 | + | 1.59686i | −1.18255 | + | 1.59686i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.69292 | − | 0.232687i | 1.69292 | − | 0.232687i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.176211 | + | 0.143358i | 0.176211 | + | 0.143358i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.983462 | − | 0.181116i | \(-0.942029\pi\) | ||||
0.983462 | + | 0.181116i | \(0.0579710\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.80408 | + | 0.783624i | −1.80408 | + | 0.783624i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.423320 | − | 0.816970i | 0.423320 | − | 0.816970i | −0.576680 | − | 0.816970i | \(-0.695652\pi\) |
1.00000 | \(0\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.368764 | + | 0.260302i | 0.368764 | + | 0.260302i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.356242 | − | 0.934394i | \(-0.615942\pi\) | ||||
0.356242 | + | 0.934394i | \(0.384058\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.854419 | − | 0.519584i | \(-0.173913\pi\) | ||||
−0.854419 | + | 0.519584i | \(0.826087\pi\) | |||||||
\(948\) | 0.0837016 | + | 1.22367i | 0.0837016 | + | 1.22367i | ||||
\(949\) | 2.22812 | + | 0.569921i | 2.22812 | + | 0.569921i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.999741 | − | 0.0227632i | \(-0.00724638\pi\) | ||||
−0.999741 | + | 0.0227632i | \(0.992754\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.197019 | − | 0.145902i | −0.197019 | − | 0.145902i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.301382 | − | 0.0994444i | 0.301382 | − | 0.0994444i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.370195 | − | 0.608760i | −0.370195 | − | 0.608760i | 0.613267 | − | 0.789876i | \(-0.289855\pi\) |
−0.983462 | + | 0.181116i | \(0.942029\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.926043 | − | 0.377419i | \(-0.123188\pi\) | ||||
−0.926043 | + | 0.377419i | \(0.876812\pi\) | |||||||
\(972\) | −1.00000 | −1.00000 | ||||||||
\(973\) | −0.990686 | + | 0.136167i | −0.990686 | + | 0.136167i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.56014 | + | 0.635854i | −1.56014 | + | 0.635854i | ||||
\(976\) | −0.246184 | − | 1.53177i | −0.246184 | − | 1.53177i | ||||
\(977\) | 0 | 0 | 0.715110 | − | 0.699012i | \(-0.246377\pi\) | ||||
−0.715110 | + | 0.699012i | \(0.753623\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.108498 | + | 0.249787i | −0.108498 | + | 0.249787i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.934394 | − | 0.356242i | \(-0.884058\pi\) | ||||
0.934394 | + | 0.356242i | \(0.115942\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.84886 | − | 2.75004i | 1.84886 | − | 2.75004i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.01345 | + | 0.863574i | −1.01345 | + | 0.863574i | −0.990686 | − | 0.136167i | \(-0.956522\pi\) |
−0.0227632 | + | 0.999741i | \(0.507246\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.97415 | + | 0.0449496i | −1.97415 | + | 0.0449496i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.41608 | + | 0.362214i | 1.41608 | + | 0.362214i | 0.877183 | − | 0.480157i | \(-0.159420\pi\) |
0.538899 | + | 0.842371i | \(0.318841\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.46007 | − | 0.887885i | 1.46007 | − | 0.887885i |
(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 | 2919.1.cp.a.509.1 | yes | 44 | |
3.2 | odd | 2 | CM | 2919.1.cp.a.509.1 | yes | 44 | |
7.3 | odd | 6 | 2919.1.cc.a.1760.1 | yes | 44 | ||
21.17 | even | 6 | 2919.1.cc.a.1760.1 | yes | 44 | ||
139.68 | odd | 138 | 2919.1.cc.a.68.1 | ✓ | 44 | ||
417.68 | even | 138 | 2919.1.cc.a.68.1 | ✓ | 44 | ||
973.346 | even | 138 | inner | 2919.1.cp.a.1319.1 | yes | 44 | |
2919.1319 | odd | 138 | inner | 2919.1.cp.a.1319.1 | yes | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2919.1.cc.a.68.1 | ✓ | 44 | 139.68 | odd | 138 | ||
2919.1.cc.a.68.1 | ✓ | 44 | 417.68 | even | 138 | ||
2919.1.cc.a.1760.1 | yes | 44 | 7.3 | odd | 6 | ||
2919.1.cc.a.1760.1 | yes | 44 | 21.17 | even | 6 | ||
2919.1.cp.a.509.1 | yes | 44 | 1.1 | even | 1 | trivial | |
2919.1.cp.a.509.1 | yes | 44 | 3.2 | odd | 2 | CM | |
2919.1.cp.a.1319.1 | yes | 44 | 973.346 | even | 138 | inner | |
2919.1.cp.a.1319.1 | yes | 44 | 2919.1319 | odd | 138 | inner |