Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [896,2,Mod(449,896)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(896, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("896.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 896 = 2^{7} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 896.b (of order \(2\), degree \(1\), 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: | \(7.15459602111\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.2048.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.2 | ||
Root | \(-1.84776i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 896.449 |
Dual form | 896.2.b.f.449.3 |
$q$-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 \(\left(\mathbb{Z}/896\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(645\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 1.08239i | − 0.624919i | −0.949931 | − | 0.312460i | \(-0.898847\pi\) | ||||
0.949931 | − | 0.312460i | \(-0.101153\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.08239i | 0.484061i | 0.970269 | + | 0.242030i | \(0.0778133\pi\) | ||||
−0.970269 | + | 0.242030i | \(0.922187\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.82843 | 0.609476 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.22625i | 1.57577i | 0.615820 | + | 0.787887i | \(0.288825\pi\) | ||||
−0.615820 | + | 0.787887i | \(0.711175\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 6.30864i | − 1.74970i | −0.484391 | − | 0.874852i | \(-0.660959\pi\) | ||||
0.484391 | − | 0.874852i | \(-0.339041\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.17157 | 0.302499 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.65685 | 0.886917 | 0.443459 | − | 0.896295i | \(-0.353751\pi\) | ||||
0.443459 | + | 0.896295i | \(0.353751\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.14386i | 0.950667i | 0.879806 | + | 0.475333i | \(0.157673\pi\) | ||||
−0.879806 | + | 0.475333i | \(0.842327\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.08239i | 0.236197i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.17157 | −0.244290 | −0.122145 | − | 0.992512i | \(-0.538977\pi\) | ||||
−0.122145 | + | 0.992512i | \(0.538977\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.82843 | 0.765685 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 5.22625i | − 1.00579i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.28772i | 1.53899i | 0.638652 | + | 0.769495i | \(0.279492\pi\) | ||||
−0.638652 | + | 0.769495i | \(0.720508\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.65685 | 1.01600 | 0.508001 | − | 0.861357i | \(-0.330385\pi\) | ||||
0.508001 | + | 0.861357i | \(0.330385\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.65685 | 0.984732 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 1.08239i | − 0.182958i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.16478i | 0.355888i | 0.984041 | + | 0.177944i | \(0.0569447\pi\) | ||||
−0.984041 | + | 0.177944i | \(0.943055\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.82843 | −1.09342 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.65685 | 1.19580 | 0.597900 | − | 0.801571i | \(-0.296002\pi\) | ||||
0.597900 | + | 0.801571i | \(0.296002\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 5.22625i | − 0.796996i | −0.917169 | − | 0.398498i | \(-0.869532\pi\) | ||||
0.917169 | − | 0.398498i | \(-0.130468\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.97908i | 0.295023i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.00000 | 1.16692 | 0.583460 | − | 0.812142i | \(-0.301699\pi\) | ||||
0.583460 | + | 0.812142i | \(0.301699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 3.95815i | − 0.554252i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 4.32957i | − 0.594712i | −0.954767 | − | 0.297356i | \(-0.903895\pi\) | ||||
0.954767 | − | 0.297356i | \(-0.0961048\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.65685 | −0.762770 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.48528 | 0.594090 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.30864i | 0.821315i | 0.911790 | + | 0.410658i | \(0.134701\pi\) | ||||
−0.911790 | + | 0.410658i | \(0.865299\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 7.20533i | − 0.922548i | −0.887258 | − | 0.461274i | \(-0.847393\pi\) | ||||
0.887258 | − | 0.461274i | \(-0.152607\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.82843 | −0.230360 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.82843 | 0.846962 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 7.39104i | − 0.902959i | −0.892282 | − | 0.451479i | \(-0.850896\pi\) | ||||
0.892282 | − | 0.451479i | \(-0.149104\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.26810i | 0.152661i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.6569 | −1.62077 | −0.810385 | − | 0.585897i | \(-0.800742\pi\) | ||||
−0.810385 | + | 0.585897i | \(0.800742\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.343146 | 0.0401622 | 0.0200811 | − | 0.999798i | \(-0.493608\pi\) | ||||
0.0200811 | + | 0.999798i | \(0.493608\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 4.14386i | − 0.478492i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 5.22625i | − 0.595587i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.6569 | 1.53652 | 0.768258 | − | 0.640140i | \(-0.221124\pi\) | ||||
0.768258 | + | 0.640140i | \(0.221124\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.171573 | −0.0190637 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.41196i | 0.594040i | 0.954871 | + | 0.297020i | \(0.0959928\pi\) | ||||
−0.954871 | + | 0.297020i | \(0.904007\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.95815i | 0.429322i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.97056 | 0.961745 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.00000 | −0.212000 | −0.106000 | − | 0.994366i | \(-0.533804\pi\) | ||||
−0.106000 | + | 0.994366i | \(0.533804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.30864i | 0.661326i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 6.12293i | − 0.634919i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.48528 | −0.460180 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.0000 | −1.01535 | −0.507673 | − | 0.861550i | \(-0.669494\pi\) | ||||
−0.507673 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.55582i | 0.960396i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.14386i | 0.412329i | 0.978517 | + | 0.206165i | \(0.0660983\pi\) | ||||
−0.978517 | + | 0.206165i | \(0.933902\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.34315 | −0.230877 | −0.115439 | − | 0.993315i | \(-0.536827\pi\) | ||||
−0.115439 | + | 0.993315i | \(0.536827\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.17157 | −0.114334 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 11.7206i | − 1.13307i | −0.824036 | − | 0.566537i | \(-0.808283\pi\) | ||||
0.824036 | − | 0.566537i | \(-0.191717\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.9469i | 1.62321i | 0.584203 | + | 0.811607i | \(0.301407\pi\) | ||||
−0.584203 | + | 0.811607i | \(0.698593\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.34315 | 0.222402 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.17157 | 0.298356 | 0.149178 | − | 0.988810i | \(-0.452337\pi\) | ||||
0.149178 | + | 0.988810i | \(0.452337\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 1.26810i | − 0.118251i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 11.5349i | − 1.06640i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.65685 | −0.335223 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −16.3137 | −1.48306 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 8.28772i | − 0.747278i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.55582i | 0.854699i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.4853 | −1.10789 | −0.553945 | − | 0.832553i | \(-0.686878\pi\) | ||||
−0.553945 | + | 0.832553i | \(0.686878\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.65685 | −0.498058 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 7.57675i | − 0.661983i | −0.943634 | − | 0.330992i | \(-0.892617\pi\) | ||||
0.943634 | − | 0.330992i | \(-0.107383\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 4.14386i | − 0.359318i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.65685 | 0.486864 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.00000 | 0.170872 | 0.0854358 | − | 0.996344i | \(-0.472772\pi\) | ||||
0.0854358 | + | 0.996344i | \(0.472772\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.2668i | 0.870818i | 0.900233 | + | 0.435409i | \(0.143396\pi\) | ||||
−0.900233 | + | 0.435409i | \(0.856604\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 8.65914i | − 0.729231i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 32.9706 | 2.75714 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.97056 | −0.744965 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 1.08239i | − 0.0892742i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 19.1116i | − 1.56569i | −0.622219 | − | 0.782843i | \(-0.713769\pi\) | ||||
0.622219 | − | 0.782843i | \(-0.286231\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.1421 | −0.825355 | −0.412678 | − | 0.910877i | \(-0.635406\pi\) | ||||
−0.412678 | + | 0.910877i | \(0.635406\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.68629 | 0.540555 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.12293i | 0.491806i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.14386i | 0.330716i | 0.986234 | + | 0.165358i | \(0.0528780\pi\) | ||||
−0.986234 | + | 0.165358i | \(0.947122\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.68629 | −0.371647 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.17157 | 0.0923329 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.0083i | 1.56717i | 0.621283 | + | 0.783586i | \(0.286612\pi\) | ||||
−0.621283 | + | 0.783586i | \(0.713388\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.12293i | 0.476670i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.0000 | −1.23812 | −0.619059 | − | 0.785345i | \(-0.712486\pi\) | ||||
−0.619059 | + | 0.785345i | \(0.712486\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −26.7990 | −2.06146 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.57675i | 0.579408i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.8030i | 0.973394i | 0.873571 | + | 0.486697i | \(0.161798\pi\) | ||||
−0.873571 | + | 0.486697i | \(0.838202\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.82843 | −0.289402 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.82843 | 0.513256 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.18440i | 0.686474i | 0.939249 | + | 0.343237i | \(0.111523\pi\) | ||||
−0.939249 | + | 0.343237i | \(0.888477\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 1.08239i | − 0.0804536i | −0.999191 | − | 0.0402268i | \(-0.987192\pi\) | ||||
0.999191 | − | 0.0402268i | \(-0.0128080\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.79899 | −0.576518 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.34315 | −0.172272 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19.1116i | 1.39758i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.22625i | 0.380154i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.31371 | 0.239772 | 0.119886 | − | 0.992788i | \(-0.461747\pi\) | ||||
0.119886 | + | 0.992788i | \(0.461747\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −25.7990 | −1.85705 | −0.928526 | − | 0.371267i | \(-0.878923\pi\) | ||||
−0.928526 | + | 0.371267i | \(0.878923\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 7.39104i | − 0.529283i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.7821i | 1.05318i | 0.850120 | + | 0.526590i | \(0.176530\pi\) | ||||
−0.850120 | + | 0.526590i | \(0.823470\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.9706 | 1.77012 | 0.885058 | − | 0.465481i | \(-0.154118\pi\) | ||||
0.885058 | + | 0.465481i | \(0.154118\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.00000 | −0.564276 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 8.28772i | − 0.581684i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.28772i | 0.578839i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.14214 | −0.148889 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.6569 | −1.49804 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 22.1731i | − 1.52646i | −0.646127 | − | 0.763230i | \(-0.723612\pi\) | ||||
0.646127 | − | 0.763230i | \(-0.276388\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.7821i | 1.01285i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.65685 | 0.385794 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.65685 | −0.384012 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 0.371418i | − 0.0250981i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 23.0698i | − 1.55184i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.9706 | −1.67215 | −0.836076 | − | 0.548613i | \(-0.815156\pi\) | ||||
−0.836076 | + | 0.548613i | \(0.815156\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.00000 | 0.466667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 12.4316i | − 0.825113i | −0.910932 | − | 0.412556i | \(-0.864636\pi\) | ||||
0.910932 | − | 0.412556i | \(-0.135364\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 8.47343i | − 0.559940i | −0.960009 | − | 0.279970i | \(-0.909675\pi\) | ||||
0.960009 | − | 0.279970i | \(-0.0903245\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.65685 | −0.372194 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.0000 | −0.655122 | −0.327561 | − | 0.944830i | \(-0.606227\pi\) | ||||
−0.327561 | + | 0.944830i | \(0.606227\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.65914i | 0.564860i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 14.7821i | − 0.960199i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.1421 | −0.656040 | −0.328020 | − | 0.944671i | \(-0.606381\pi\) | ||||
−0.328020 | + | 0.944671i | \(0.606381\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.3137 | −1.37294 | −0.686468 | − | 0.727160i | \(-0.740840\pi\) | ||||
−0.686468 | + | 0.727160i | \(0.740840\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 15.4930i | − 0.993879i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.08239i | 0.0691515i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.1421 | 1.66338 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.85786 | 0.371227 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 24.1522i | − 1.52447i | −0.647299 | − | 0.762236i | \(-0.724101\pi\) | ||||
0.647299 | − | 0.762236i | \(-0.275899\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 6.12293i | − 0.384946i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.28427 | 0.268291 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.3137 | 0.830486 | 0.415243 | − | 0.909710i | \(-0.363696\pi\) | ||||
0.415243 | + | 0.909710i | \(0.363696\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 2.16478i | − 0.134513i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.1535i | 0.937978i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.6569 | −0.842118 | −0.421059 | − | 0.907033i | \(-0.638341\pi\) | ||||
−0.421059 | + | 0.907033i | \(0.638341\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.68629 | 0.287877 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.16478i | 0.132483i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 27.2137i | − 1.65925i | −0.558324 | − | 0.829623i | \(-0.688555\pi\) | ||||
0.558324 | − | 0.829623i | \(-0.311445\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.6569 | 0.829595 | 0.414797 | − | 0.909914i | \(-0.363852\pi\) | ||||
0.414797 | + | 0.909914i | \(0.363852\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.82843 | 0.413275 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 20.0083i | 1.20655i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 6.12293i | − 0.367892i | −0.982936 | − | 0.183946i | \(-0.941113\pi\) | ||||
0.982936 | − | 0.183946i | \(-0.0588871\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.3431 | 0.619228 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.00000 | −0.119310 | −0.0596550 | − | 0.998219i | \(-0.519000\pi\) | ||||
−0.0596550 | + | 0.998219i | \(0.519000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 28.1103i | − 1.67099i | −0.549501 | − | 0.835493i | \(-0.685182\pi\) | ||||
0.549501 | − | 0.835493i | \(-0.314818\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.85483i | 0.287576i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.65685 | −0.451970 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.62742 | −0.213377 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.8239i | 0.634510i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 10.6382i | − 0.621491i | −0.950493 | − | 0.310746i | \(-0.899421\pi\) | ||||
0.950493 | − | 0.310746i | \(-0.100579\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.82843 | −0.397566 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 27.3137 | 1.58490 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.39104i | 0.427435i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.22625i | 0.301236i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.48528 | 0.257673 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.79899 | 0.446569 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.8645i | 0.905433i | 0.891655 | + | 0.452716i | \(0.149545\pi\) | ||||
−0.891655 | + | 0.452716i | \(0.850455\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.53620i | 0.144280i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.6274 | 1.73672 | 0.868361 | − | 0.495933i | \(-0.165174\pi\) | ||||
0.868361 | + | 0.495933i | \(0.165174\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.6569 | −1.11107 | −0.555536 | − | 0.831493i | \(-0.687487\pi\) | ||||
−0.555536 | + | 0.831493i | \(0.687487\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 1.97908i | − 0.111508i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.9050i | 1.17414i | 0.809535 | + | 0.587071i | \(0.199719\pi\) | ||||
−0.809535 | + | 0.587071i | \(0.800281\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −43.3137 | −2.42510 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.6863 | −0.708080 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.1535i | 0.843163i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 24.1522i | − 1.33972i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.3431 | 1.01438 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.00000 | −0.441054 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 13.8854i | − 0.763210i | −0.924325 | − | 0.381605i | \(-0.875371\pi\) | ||||
0.924325 | − | 0.381605i | \(-0.124629\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.95815i | 0.216905i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.00000 | 0.437087 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.8284 | 0.916703 | 0.458351 | − | 0.888771i | \(-0.348440\pi\) | ||||
0.458351 | + | 0.888771i | \(0.348440\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 3.43289i | − 0.186449i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 29.5641i | 1.60099i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.37258 | −0.0738974 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.896683i | 0.0481365i | 0.999710 | + | 0.0240682i | \(0.00766190\pi\) | ||||
−0.999710 | + | 0.0240682i | \(0.992338\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.87576i | 0.153936i | 0.997034 | + | 0.0769679i | \(0.0245239\pi\) | ||||
−0.997034 | + | 0.0769679i | \(0.975476\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −32.9706 | −1.75984 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.34315 | 0.231162 | 0.115581 | − | 0.993298i | \(-0.463127\pi\) | ||||
0.115581 | + | 0.993298i | \(0.463127\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 14.7821i | − 0.784551i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.95815i | 0.209488i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.17157 | −0.0618333 | −0.0309166 | − | 0.999522i | \(-0.509843\pi\) | ||||
−0.0309166 | + | 0.999522i | \(0.509843\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.82843 | 0.0962330 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 17.6578i | 0.926796i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.371418i | 0.0194409i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.97056 | 0.468260 | 0.234130 | − | 0.972205i | \(-0.424776\pi\) | ||||
0.234130 | + | 0.972205i | \(0.424776\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 14.0000 | 0.728811 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.32957i | 0.224780i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.6984i | 1.17528i | 0.809124 | + | 0.587639i | \(0.199942\pi\) | ||||
−0.809124 | + | 0.587639i | \(0.800058\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.3431 | 0.534118 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 52.2843 | 2.69278 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 3.43289i | − 0.176335i | −0.996106 | − | 0.0881677i | \(-0.971899\pi\) | ||||
0.996106 | − | 0.0881677i | \(-0.0281012\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.5140i | 0.692342i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.31371 | −0.169323 | −0.0846613 | − | 0.996410i | \(-0.526981\pi\) | ||||
−0.0846613 | + | 0.996410i | \(0.526981\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.65685 | 0.288300 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 9.55582i | − 0.485750i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 3.95815i | − 0.200686i | −0.994953 | − | 0.100343i | \(-0.968006\pi\) | ||||
0.994953 | − | 0.100343i | \(-0.0319940\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.28427 | −0.216665 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.20101 | −0.413686 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14.7821i | 0.743767i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 7.57675i | − 0.380266i | −0.981758 | − | 0.190133i | \(-0.939108\pi\) | ||||
0.981758 | − | 0.190133i | \(-0.0608919\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.48528 | −0.224545 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.4853 | 1.32261 | 0.661306 | − | 0.750116i | \(-0.270003\pi\) | ||||
0.661306 | + | 0.750116i | \(0.270003\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 35.6871i | − 1.77770i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 0.185709i | − 0.00922796i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.3137 | −0.560800 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.3137 | −0.856108 | −0.428054 | − | 0.903753i | \(-0.640801\pi\) | ||||
−0.428054 | + | 0.903753i | \(0.640801\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 2.16478i | − 0.106781i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 6.30864i | − 0.310428i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.85786 | −0.287551 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.1127 | 0.544191 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 5.41196i | − 0.264392i | −0.991224 | − | 0.132196i | \(-0.957797\pi\) | ||||
0.991224 | − | 0.132196i | \(-0.0422028\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 35.6871i | − 1.73928i | −0.493685 | − | 0.869641i | \(-0.664350\pi\) | ||||
0.493685 | − | 0.869641i | \(-0.335650\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 14.6274 | 0.711209 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.0000 | 0.679100 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.20533i | 0.348690i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 35.6871i | − 1.72299i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.17157 | −0.0564327 | −0.0282163 | − | 0.999602i | \(-0.508983\pi\) | ||||
−0.0282163 | + | 0.999602i | \(0.508983\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.6569 | −1.13688 | −0.568438 | − | 0.822726i | \(-0.692452\pi\) | ||||
−0.568438 | + | 0.822726i | \(0.692452\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.70967i | 0.465543i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 4.85483i | − 0.232238i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.9706 | 1.57360 | 0.786800 | − | 0.617209i | \(-0.211737\pi\) | ||||
0.786800 | + | 0.617209i | \(0.211737\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.82843 | 0.0870680 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.1731i | 1.05348i | 0.850028 | + | 0.526738i | \(0.176585\pi\) | ||||
−0.850028 | + | 0.526738i | \(0.823415\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 2.16478i | − 0.102621i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −20.6863 | −0.978428 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.6274 | 0.973468 | 0.486734 | − | 0.873550i | \(-0.338188\pi\) | ||||
0.486734 | + | 0.873550i | \(0.338188\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 40.0166i | 1.88431i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.9778i | 0.515781i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.82843 | −0.320122 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.48528 | 0.303369 | 0.151684 | − | 0.988429i | \(-0.451530\pi\) | ||||
0.151684 | + | 0.988429i | \(0.451530\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 19.1116i | − 0.892055i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.4399i | 1.51088i | 0.655220 | + | 0.755438i | \(0.272576\pi\) | ||||
−0.655220 | + | 0.755438i | \(0.727424\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.00000 | 0.371792 | 0.185896 | − | 0.982569i | \(-0.440481\pi\) | ||||
0.185896 | + | 0.982569i | \(0.440481\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.62742 | 0.307339 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.9259i | 0.875788i | 0.899027 | + | 0.437894i | \(0.144275\pi\) | ||||
−0.899027 | + | 0.437894i | \(0.855725\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.39104i | 0.341286i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.48528 | 0.206671 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 27.3137 | 1.25589 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.8645i | 0.727912i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 7.91630i | − 0.362463i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.65685 | 0.258468 | 0.129234 | − | 0.991614i | \(-0.458748\pi\) | ||||
0.129234 | + | 0.991614i | \(0.458748\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.6569 | 0.622699 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 1.26810i | − 0.0577006i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 10.8239i | − 0.491489i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.79899 | −0.353406 | −0.176703 | − | 0.984264i | \(-0.556543\pi\) | ||||
−0.176703 | + | 0.984264i | \(0.556543\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 21.6569 | 0.979357 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 4.85483i | − 0.219096i | −0.993982 | − | 0.109548i | \(-0.965060\pi\) | ||||
0.993982 | − | 0.109548i | \(-0.0349403\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 30.3070i | 1.36496i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.3431 | −0.464890 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.6569 | 0.612594 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 13.5140i | − 0.604968i | −0.953154 | − | 0.302484i | \(-0.902184\pi\) | ||||
0.953154 | − | 0.302484i | \(-0.0978160\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.3183i | 0.773723i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.65685 | 0.252227 | 0.126113 | − | 0.992016i | \(-0.459750\pi\) | ||||
0.126113 | + | 0.992016i | \(0.459750\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.48528 | −0.199592 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 29.0070i | 1.28825i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 13.6997i | − 0.607228i | −0.952795 | − | 0.303614i | \(-0.901807\pi\) | ||||
0.952795 | − | 0.303614i | \(-0.0981933\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.343146 | −0.0151799 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 21.6569 | 0.956173 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 2.53620i | − 0.111758i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 41.8100i | 1.83880i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.8579 | 0.608293 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.3137 | 1.63474 | 0.817372 | − | 0.576111i | \(-0.195430\pi\) | ||||
0.817372 | + | 0.576111i | \(0.195430\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 33.7080i | − 1.47395i | −0.675921 | − | 0.736974i | \(-0.736254\pi\) | ||||
0.675921 | − | 0.736974i | \(-0.263746\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.14386i | 0.180853i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.6863 | 0.901109 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.6274 | −0.940322 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.5349i | 0.500572i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 48.3044i | − 2.09229i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.6863 | 0.548476 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.94113 | 0.428991 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.22625i | 0.225111i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 12.9887i | − 0.558428i | −0.960229 | − | 0.279214i | \(-0.909926\pi\) | ||||
0.960229 | − | 0.279214i | \(-0.0900739\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.17157 | −0.0502770 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.3431 | −0.785734 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.0920i | 0.517018i | 0.966009 | + | 0.258509i | \(0.0832311\pi\) | ||||
−0.966009 | + | 0.258509i | \(0.916769\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 13.1744i | − 0.562270i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −34.3431 | −1.46307 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.6569 | −0.580749 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.53620i | 0.107656i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 6.12293i | − 0.259437i | −0.991551 | − | 0.129719i | \(-0.958593\pi\) | ||||
0.991551 | − | 0.129719i | \(-0.0414074\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −32.9706 | −1.39451 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.6863 | 0.873376 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 35.5014i | − 1.49620i | −0.663584 | − | 0.748102i | \(-0.730965\pi\) | ||||
0.663584 | − | 0.748102i | \(-0.269035\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.43289i | 0.144423i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.171573 | 0.00720538 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −34.4853 | −1.44570 | −0.722849 | − | 0.691006i | \(-0.757168\pi\) | ||||
−0.722849 | + | 0.691006i | \(0.757168\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.8854i | 0.581085i | 0.956862 | + | 0.290543i | \(0.0938358\pi\) | ||||
−0.956862 | + | 0.290543i | \(0.906164\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 3.58673i | − 0.149838i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.48528 | −0.187049 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.9706 | 0.456711 | 0.228355 | − | 0.973578i | \(-0.426665\pi\) | ||||
0.228355 | + | 0.973578i | \(0.426665\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 27.9246i | 1.16051i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 5.41196i | − 0.224526i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.6274 | 0.937132 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.4853 | 0.516203 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 29.0070i | − 1.19725i | −0.801030 | − | 0.598624i | \(-0.795714\pi\) | ||||
0.801030 | − | 0.598624i | \(-0.204286\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.4412i | 0.965878i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.0000 | 0.658152 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.68629 | −0.110313 | −0.0551564 | − | 0.998478i | \(-0.517566\pi\) | ||||
−0.0551564 | + | 0.998478i | \(0.517566\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 3.95815i | − 0.162268i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 27.0279i | − 1.10618i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.00000 | −0.326871 | −0.163436 | − | 0.986554i | \(-0.552258\pi\) | ||||
−0.163436 | + | 0.986554i | \(0.552258\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.6863 | 0.762230 | 0.381115 | − | 0.924528i | \(-0.375540\pi\) | ||||
0.381115 | + | 0.924528i | \(0.375540\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 13.5140i | − 0.550331i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 17.6578i | − 0.717893i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.68629 | −0.190211 | −0.0951054 | − | 0.995467i | \(-0.530319\pi\) | ||||
−0.0951054 | + | 0.995467i | \(0.530319\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.97056 | −0.363506 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 50.4692i | − 2.04176i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 10.8239i | − 0.437174i | −0.975817 | − | 0.218587i | \(-0.929855\pi\) | ||||
0.975817 | − | 0.218587i | \(-0.0701448\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.97056 | 0.361728 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.20101 | −0.0886093 | −0.0443047 | − | 0.999018i | \(-0.514107\pi\) | ||||
−0.0443047 | + | 0.999018i | \(0.514107\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 14.0711i | − 0.565565i | −0.959184 | − | 0.282783i | \(-0.908743\pi\) | ||||
0.959184 | − | 0.282783i | \(-0.0912575\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.12293i | 0.245705i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.00000 | 0.0801283 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.79899 | 0.351960 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 23.4412i | 0.936152i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.91630i | 0.315644i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.6274 | 0.582308 | 0.291154 | − | 0.956676i | \(-0.405961\pi\) | ||||
0.291154 | + | 0.956676i | \(0.405961\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −24.0000 | −0.953914 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 13.5140i | − 0.536286i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 6.30864i | − 0.249958i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −24.9706 | −0.987820 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.4558 | −0.926450 | −0.463225 | − | 0.886241i | \(-0.653308\pi\) | ||||
−0.463225 | + | 0.886241i | \(0.653308\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 29.3784i | − 1.15857i | −0.815124 | − | 0.579286i | \(-0.803331\pi\) | ||||
0.815124 | − | 0.579286i | \(-0.196669\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 6.12293i | − 0.241090i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.3431 | −0.721143 | −0.360572 | − | 0.932731i | \(-0.617418\pi\) | ||||
−0.360572 | + | 0.932731i | \(0.617418\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −32.9706 | −1.29421 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.12293i | 0.239977i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.6452i | 1.55144i | 0.631079 | + | 0.775719i | \(0.282613\pi\) | ||||
−0.631079 | + | 0.775719i | \(0.717387\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.20101 | 0.320440 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.627417 | 0.0244779 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 34.7904i | − 1.35524i | −0.735412 | − | 0.677621i | \(-0.763011\pi\) | ||||
0.735412 | − | 0.677621i | \(-0.236989\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 6.30864i | − 0.245378i | −0.992445 | − | 0.122689i | \(-0.960848\pi\) | ||||
0.992445 | − | 0.122689i | \(-0.0391517\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −24.9706 | −0.969776 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.48528 | 0.173932 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 9.70967i | − 0.375960i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 27.0279i | 1.04496i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 37.6569 | 1.45373 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.6274 | −0.640940 | −0.320470 | − | 0.947259i | \(-0.603841\pi\) | ||||
−0.320470 | + | 0.947259i | \(0.603841\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 20.0083i | − 0.770121i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 15.8645i | − 0.609721i | −0.952397 | − | 0.304860i | \(-0.901390\pi\) | ||||
0.952397 | − | 0.304860i | \(-0.0986098\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.0000 | 0.383765 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13.4558 | −0.515629 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.2960i | 1.08272i | 0.840792 | + | 0.541359i | \(0.182090\pi\) | ||||
−0.840792 | + | 0.541359i | \(0.817910\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.16478i | 0.0827122i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.17157 | −0.349917 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −27.3137 | −1.04057 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.3057i | 1.49526i | 0.664116 | + | 0.747629i | \(0.268808\pi\) | ||||
−0.664116 | + | 0.747629i | \(0.731192\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 9.55582i | − 0.362996i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.1127 | −0.421529 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 28.0000 | 1.06058 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.8239i | 0.409398i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 4.70099i | − 0.177554i | −0.996052 | − | 0.0887769i | \(-0.971704\pi\) | ||||
0.996052 | − | 0.0887769i | \(-0.0282958\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.97056 | −0.338331 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.37258 | 0.352992 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 4.14386i | − 0.155846i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.7289i | 1.19160i | 0.803131 | + | 0.595802i | \(0.203166\pi\) | ||||
−0.803131 | + | 0.595802i | \(0.796834\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 24.9706 | 0.936469 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.62742 | −0.248199 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 35.6871i | 1.33462i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.9778i | 0.409972i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.3137 | 0.720280 | 0.360140 | − | 0.932898i | \(-0.382729\pi\) | ||||
0.360140 | + | 0.932898i | \(0.382729\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.34315 | 0.0872633 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 23.0698i | 0.857975i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 31.7289i | 1.17838i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −43.3137 | −1.60642 | −0.803208 | − | 0.595698i | \(-0.796875\pi\) | ||||
−0.803208 | + | 0.595698i | \(0.796875\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −17.2843 | −0.640158 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 19.1116i | − 0.706870i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.4930i | 0.572249i | 0.958192 | + | 0.286124i | \(0.0923670\pi\) | ||||
−0.958192 | + | 0.286124i | \(0.907633\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.17157 | 0.0432141 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 38.6274 | 1.42286 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.6675i | 1.05455i | 0.849695 | + | 0.527275i | \(0.176786\pi\) | ||||
−0.849695 | + | 0.527275i | \(0.823214\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 28.2960i | − 1.03948i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −44.4853 | −1.63201 | −0.816003 | − | 0.578047i | \(-0.803815\pi\) | ||||
−0.816003 | + | 0.578047i | \(0.803815\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.6863 | 0.757887 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.89538i | 0.362053i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.7206i | 0.428262i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.45584 | 0.199087 | 0.0995433 | − | 0.995033i | \(-0.468262\pi\) | ||||
0.0995433 | + | 0.995033i | \(0.468262\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −26.1421 | −0.952672 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 10.9778i | − 0.399522i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.6452i | 1.44093i | 0.693491 | + | 0.720465i | \(0.256072\pi\) | ||||
−0.693491 | + | 0.720465i | \(0.743928\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.62742 | −0.240560 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.9706 | −0.542682 | −0.271341 | − | 0.962483i | \(-0.587467\pi\) | ||||
−0.271341 | + | 0.962483i | \(0.587467\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 16.9469i | − 0.613517i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.23719i | 0.261661i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 39.7990 | 1.43706 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −55.2548 | −1.99254 | −0.996270 | − | 0.0862891i | \(-0.972499\pi\) | ||||
−0.996270 | + | 0.0862891i | \(0.972499\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 14.4107i | − 0.518987i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.8645i | 0.570605i | 0.958438 | + | 0.285303i | \(0.0920941\pi\) | ||||
−0.958438 | + | 0.285303i | \(0.907906\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.6569 | 0.777937 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.34315 | −0.0840599 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 31.7289i | 1.13681i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 71.3742i | − 2.55397i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 43.3137 | 1.54791 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.48528 | −0.160087 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.7080i | 1.20156i | 0.799414 | + | 0.600780i | \(0.205143\pi\) | ||||
−0.799414 | + | 0.600780i | \(0.794857\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14.7821i | 0.526256i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.17157 | −0.112768 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −45.4558 | −1.61418 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 5.07241i | − 0.179900i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 29.7499i | − 1.05379i | −0.849929 | − | 0.526897i | \(-0.823355\pi\) | ||||
0.849929 | − | 0.526897i | \(-0.176645\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 29.2548 | 1.03496 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.65685 | −0.129209 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.79337i | 0.0632865i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.26810i | 0.0446947i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −29.4558 | −1.03689 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36.8284 | −1.29482 | −0.647409 | − | 0.762143i | \(-0.724148\pi\) | ||||
−0.647409 | + | 0.762143i | \(0.724148\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 45.4286i | − 1.59521i | −0.603177 | − | 0.797607i | \(-0.706099\pi\) | ||||
0.603177 | − | 0.797607i | \(-0.293901\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 14.7821i | − 0.518430i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −21.6569 | −0.758607 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.6569 | 0.757677 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 11.5349i | 0.403062i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.9050i | 0.729590i | 0.931088 | + | 0.364795i | \(0.118861\pi\) | ||||
−0.931088 | + | 0.364795i | \(0.881139\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.02944 | −0.245031 | −0.122515 | − | 0.992467i | \(-0.539096\pi\) | ||||
−0.122515 | + | 0.992467i | \(0.539096\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 21.6569 | 0.753995 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 47.4077i | − 1.64853i | −0.566207 | − | 0.824263i | \(-0.691590\pi\) | ||||
0.566207 | − | 0.824263i | \(-0.308410\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 51.5515i | − 1.79046i | −0.445605 | − | 0.895230i | \(-0.647011\pi\) | ||||
0.445605 | − | 0.895230i | \(-0.352989\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.62742 | −0.229903 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.65685 | 0.126702 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 17.3183i | − 0.599324i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 29.5641i | − 1.02189i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.2843 | 0.700291 | 0.350145 | − | 0.936695i | \(-0.386132\pi\) | ||||
0.350145 | + | 0.936695i | \(0.386132\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −39.6863 | −1.36849 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.16478i | 0.0745591i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 29.0070i | − 0.997872i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.3137 | 0.560546 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −30.4264 | −1.04423 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 2.53620i | − 0.0869399i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 47.7472i | − 1.63483i | −0.576046 | − | 0.817417i | \(-0.695405\pi\) | ||||
0.576046 | − | 0.817417i | \(-0.304595\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.20101 | −0.280469 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −44.6274 | −1.52444 | −0.762222 | − | 0.647316i | \(-0.775891\pi\) | ||||
−0.762222 | + | 0.647316i | \(0.775891\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 13.6997i | − 0.467427i | −0.972306 | − | 0.233714i | \(-0.924912\pi\) | ||||
0.972306 | − | 0.233714i | \(-0.0750878\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.28772i | 0.282445i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.6863 | 0.976493 | 0.488246 | − | 0.872706i | \(-0.337637\pi\) | ||||
0.488246 | + | 0.872706i | \(0.337637\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.8579 | −0.471182 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.92629i | 0.133344i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 71.3742i | 2.42120i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −46.6274 | −1.57991 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −18.2843 | −0.618829 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 9.55582i | − 0.323046i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 25.6060i | − 0.864653i | −0.901717 | − | 0.432326i | \(-0.857693\pi\) | ||||
0.901717 | − | 0.432326i | \(-0.142307\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −11.5147 | −0.388382 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.9706 | −0.773898 | −0.386949 | − | 0.922101i | \(-0.626471\pi\) | ||||
−0.386949 | + | 0.922101i | \(0.626471\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.4303i | 0.721186i | 0.932723 | + | 0.360593i | \(0.117426\pi\) | ||||
−0.932723 | + | 0.360593i | \(0.882574\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.39104i | 0.248447i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.6274 | −0.759754 | −0.379877 | − | 0.925037i | \(-0.624034\pi\) | ||||
−0.379877 | + | 0.925037i | \(0.624034\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.4853 | 0.418743 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 0.896683i | − 0.0300400i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 33.1509i | 1.10935i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.94113 | −0.332295 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.00000 | 0.267112 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 46.8824i | 1.56362i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 15.8326i | − 0.527460i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.65685 | 0.188248 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.17157 | 0.0389444 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 17.8435i | − 0.592485i | −0.955113 | − | 0.296243i | \(-0.904266\pi\) | ||||
0.955113 | − | 0.296243i | \(-0.0957337\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.57675i | 0.251305i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.1716 | 1.09902 | 0.549512 | − | 0.835486i | \(-0.314814\pi\) | ||||
0.549512 | + | 0.835486i | \(0.314814\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.2843 | −0.936073 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 8.44157i | − 0.279070i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.57675i | 0.250206i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.6569 | −0.450498 | −0.225249 | − | 0.974301i | \(-0.572320\pi\) | ||||
−0.225249 | + | 0.974301i | \(0.572320\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17.1716 | 0.565823 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 86.1562i | 2.83587i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.28772i | 0.272499i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.28427 | −0.140714 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −46.2843 | −1.51854 | −0.759269 | − | 0.650777i | \(-0.774443\pi\) | ||||
−0.759269 | + | 0.650777i | \(0.774443\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.14386i | 0.135810i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 33.1509i | − 1.08531i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −20.6863 | −0.676514 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.2843 | 0.597321 | 0.298661 | − | 0.954359i | \(-0.403460\pi\) | ||||
0.298661 | + | 0.954359i | \(0.403460\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 21.2764i | 0.694330i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 39.4595i | 1.28634i | 0.765722 | + | 0.643172i | \(0.222382\pi\) | ||||
−0.765722 | + | 0.643172i | \(0.777618\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.97056 | −0.292122 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.65685 | −0.184017 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1.63952i | − 0.0532772i | −0.999645 | − | 0.0266386i | \(-0.991520\pi\) | ||||
0.999645 | − | 0.0266386i | \(-0.00848034\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 2.16478i | − 0.0702719i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.6274 | 0.733744 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.6863 | 0.475736 | 0.237868 | − | 0.971298i | \(-0.423551\pi\) | ||||
0.237868 | + | 0.971298i | \(0.423551\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.58673i | 0.116064i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 46.8824i | 1.51549i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.00000 | −0.0645834 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 21.4303i | − 0.690581i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 27.9246i | − 0.898925i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 58.1421 | 1.86973 | 0.934863 | − | 0.355010i | \(-0.115523\pi\) | ||||
0.934863 | + | 0.355010i | \(0.115523\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.4020 | 0.526909 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 45.5825i | 1.46281i | 0.681943 | + | 0.731405i | \(0.261135\pi\) | ||||
−0.681943 | + | 0.731405i | \(0.738865\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 10.2668i | − 0.329138i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −26.1421 | −0.837218 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.0000 | 0.959785 | 0.479893 | − | 0.877327i | \(-0.340676\pi\) | ||||
0.479893 | + | 0.877327i | \(0.340676\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 10.4525i | − 0.334063i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 30.9861i | 0.989310i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −56.9706 | −1.81708 | −0.908539 | − | 0.417799i | \(-0.862802\pi\) | ||||
−0.908539 | + | 0.417799i | \(0.862802\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.0000 | −0.509802 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.65914i | 0.275623i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.12293i | 0.194698i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.3431 | 0.582689 | 0.291345 | − | 0.956618i | \(-0.405897\pi\) | ||||
0.291345 | + | 0.956618i | \(0.405897\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −15.0294 | −0.476945 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 27.0279i | 0.856843i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36.7695i | 1.16450i | 0.813009 | + | 0.582250i | \(0.197828\pi\) | ||||
−0.813009 | + | 0.582250i | \(0.802172\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11.3137 | 0.357950 |
(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 | 896.2.b.f.449.2 | ✓ | 4 | |
4.3 | odd | 2 | 896.2.b.h.449.3 | yes | 4 | ||
8.3 | odd | 2 | 896.2.b.h.449.2 | yes | 4 | ||
8.5 | even | 2 | inner | 896.2.b.f.449.3 | yes | 4 | |
16.3 | odd | 4 | 1792.2.a.u.1.2 | 4 | |||
16.5 | even | 4 | 1792.2.a.w.1.2 | 4 | |||
16.11 | odd | 4 | 1792.2.a.u.1.3 | 4 | |||
16.13 | even | 4 | 1792.2.a.w.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
896.2.b.f.449.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
896.2.b.f.449.3 | yes | 4 | 8.5 | even | 2 | inner | |
896.2.b.h.449.2 | yes | 4 | 8.3 | odd | 2 | ||
896.2.b.h.449.3 | yes | 4 | 4.3 | odd | 2 | ||
1792.2.a.u.1.2 | 4 | 16.3 | odd | 4 | |||
1792.2.a.u.1.3 | 4 | 16.11 | odd | 4 | |||
1792.2.a.w.1.2 | 4 | 16.5 | even | 4 | |||
1792.2.a.w.1.3 | 4 | 16.13 | even | 4 |