Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3072,2,Mod(1537,3072)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3072, 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("3072.1537");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3072 = 2^{10} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3072.d (of order \(2\), degree \(1\), not 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: | \(24.5300435009\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.18939904.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1537.6 | ||
Root | \(0.500000 - 0.0297061i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3072.1537 |
Dual form | 3072.2.d.i.1537.3 |
$q$-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 \(\left(\mathbb{Z}/3072\mathbb{Z}\right)^\times\).
\(n\) | \(1025\) | \(2047\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 0.473626i | − 0.211812i | −0.994376 | − | 0.105906i | \(-0.966226\pi\) | ||||
0.994376 | − | 0.105906i | \(-0.0337742\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.55765 | 1.72263 | 0.861314 | − | 0.508072i | \(-0.169642\pi\) | ||||
0.861314 | + | 0.508072i | \(0.169642\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 3.49824i | − 1.05476i | −0.849630 | − | 0.527379i | \(-0.823175\pi\) | ||||
0.849630 | − | 0.527379i | \(-0.176825\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.0840215i | 0.0233034i | 0.999932 | + | 0.0116517i | \(0.00370893\pi\) | ||||
−0.999932 | + | 0.0116517i | \(0.996291\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.473626 | 0.122290 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.61706 | −0.877266 | −0.438633 | − | 0.898666i | \(-0.644537\pi\) | ||||
−0.438633 | + | 0.898666i | \(0.644537\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.61706i | 0.829810i | 0.909865 | + | 0.414905i | \(0.136185\pi\) | ||||
−0.909865 | + | 0.414905i | \(0.863815\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.55765i | 0.994560i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.82843 | 0.589768 | 0.294884 | − | 0.955533i | \(-0.404719\pi\) | ||||
0.294884 | + | 0.955533i | \(0.404719\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.77568 | 0.955136 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 7.30205i | − 1.35596i | −0.735082 | − | 0.677979i | \(-0.762856\pi\) | ||||
0.735082 | − | 0.677979i | \(-0.237144\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.557647 | 0.100156 | 0.0500782 | − | 0.998745i | \(-0.484053\pi\) | ||||
0.0500782 | + | 0.998745i | \(0.484053\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.49824 | 0.608965 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 2.15862i | − 0.364873i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.20285i | 1.01974i | 0.860251 | + | 0.509871i | \(0.170307\pi\) | ||||
−0.860251 | + | 0.509871i | \(0.829693\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.0840215 | −0.0134542 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.27391 | 1.44834 | 0.724171 | − | 0.689620i | \(-0.242223\pi\) | ||||
0.724171 | + | 0.689620i | \(0.242223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 2.27744i | − 0.347307i | −0.984807 | − | 0.173653i | \(-0.944443\pi\) | ||||
0.984807 | − | 0.173653i | \(-0.0555573\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.473626i | 0.0706040i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.82843 | 0.412568 | 0.206284 | − | 0.978492i | \(-0.433863\pi\) | ||||
0.206284 | + | 0.978492i | \(0.433863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.7721 | 1.96745 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 3.61706i | − 0.506490i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.697947i | 0.0958704i | 0.998850 | + | 0.0479352i | \(0.0152641\pi\) | ||||
−0.998850 | + | 0.0479352i | \(0.984736\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.65685 | −0.223410 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.61706 | −0.479091 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 5.65685i | − 0.736460i | −0.929735 | − | 0.368230i | \(-0.879964\pi\) | ||||
0.929735 | − | 0.368230i | \(-0.120036\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.85970i | 0.494184i | 0.968992 | + | 0.247092i | \(0.0794750\pi\) | ||||
−0.968992 | + | 0.247092i | \(0.920525\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.55765 | −0.574210 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.0397948 | 0.00493593 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 5.33962i | − 0.652338i | −0.945311 | − | 0.326169i | \(-0.894242\pi\) | ||||
0.945311 | − | 0.326169i | \(-0.105758\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.82843i | 0.340503i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.11529 | −1.08179 | −0.540893 | − | 0.841091i | \(-0.681914\pi\) | ||||
−0.540893 | + | 0.841091i | \(0.681914\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.541560 | 0.0633848 | 0.0316924 | − | 0.999498i | \(-0.489910\pi\) | ||||
0.0316924 | + | 0.999498i | \(0.489910\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.77568i | 0.551448i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 15.9437i | − 1.81696i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.9937 | −1.23689 | −0.618445 | − | 0.785828i | \(-0.712237\pi\) | ||||
−0.618445 | + | 0.785828i | \(0.712237\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 15.0496i | − 1.65191i | −0.563738 | − | 0.825954i | \(-0.690637\pi\) | ||||
0.563738 | − | 0.825954i | \(-0.309363\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.71313i | 0.185815i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.30205 | 0.782862 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.6533 | 1.55325 | 0.776625 | − | 0.629964i | \(-0.216930\pi\) | ||||
0.776625 | + | 0.629964i | \(0.216930\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.382941i | 0.0401431i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.557647i | 0.0578253i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.71313 | 0.175764 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.31724 | 0.438349 | 0.219175 | − | 0.975686i | \(-0.429664\pi\) | ||||
0.219175 | + | 0.975686i | \(0.429664\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.49824i | 0.351586i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 0.641669i | − 0.0638484i | −0.999490 | − | 0.0319242i | \(-0.989836\pi\) | ||||
0.999490 | − | 0.0319242i | \(-0.0101635\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.33686 | −0.131724 | −0.0658622 | − | 0.997829i | \(-0.520980\pi\) | ||||
−0.0658622 | + | 0.997829i | \(0.520980\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.15862 | 0.210660 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.57373i | 0.828854i | 0.910083 | + | 0.414427i | \(0.136018\pi\) | ||||
−0.910083 | + | 0.414427i | \(0.863982\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 8.08402i | − 0.774309i | −0.922015 | − | 0.387154i | \(-0.873458\pi\) | ||||
0.922015 | − | 0.387154i | \(-0.126542\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.20285 | −0.588748 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.55136 | 0.898516 | 0.449258 | − | 0.893402i | \(-0.351688\pi\) | ||||
0.449258 | + | 0.893402i | \(0.351688\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 1.33962i | − 0.124920i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 0.0840215i | − 0.00776779i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −16.4853 | −1.51120 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.23765 | −0.112514 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.27391i | 0.836201i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 4.63001i | − 0.414121i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.09921 | −0.452481 | −0.226241 | − | 0.974071i | \(-0.572644\pi\) | ||||
−0.226241 | + | 0.974071i | \(0.572644\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.27744 | 0.200518 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 2.99647i | − 0.261803i | −0.991395 | − | 0.130901i | \(-0.958213\pi\) | ||||
0.991395 | − | 0.130901i | \(-0.0417871\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.4853i | 1.42946i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.473626 | −0.0407632 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.37941 | 0.288723 | 0.144361 | − | 0.989525i | \(-0.453887\pi\) | ||||
0.144361 | + | 0.989525i | \(0.453887\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.31724i | 0.705459i | 0.935725 | + | 0.352729i | \(0.114746\pi\) | ||||
−0.935725 | + | 0.352729i | \(0.885254\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.82843i | 0.238197i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.293927 | 0.0245794 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.45844 | −0.287208 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 13.7721i | 1.13591i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.1305i | 1.15761i | 0.815465 | + | 0.578807i | \(0.196482\pi\) | ||||
−0.815465 | + | 0.578807i | \(0.803518\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.97685 | 0.811905 | 0.405952 | − | 0.913894i | \(-0.366940\pi\) | ||||
0.405952 | + | 0.913894i | \(0.366940\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.61706 | 0.292422 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 0.264116i | − 0.0212143i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 22.8562i | − 1.82412i | −0.410056 | − | 0.912060i | \(-0.634491\pi\) | ||||
0.410056 | − | 0.912060i | \(-0.365509\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.697947 | −0.0553508 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.8910 | 1.01595 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.6135i | 0.831316i | 0.909521 | + | 0.415658i | \(0.136449\pi\) | ||||
−0.909521 | + | 0.415658i | \(0.863551\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 1.65685i | − 0.128986i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.83822 | 0.451775 | 0.225888 | − | 0.974153i | \(-0.427472\pi\) | ||||
0.225888 | + | 0.974153i | \(0.427472\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9929 | 0.999457 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 3.61706i | − 0.276603i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.12695i | 0.389795i | 0.980824 | + | 0.194897i | \(0.0624374\pi\) | ||||
−0.980824 | + | 0.194897i | \(0.937563\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 21.7659 | 1.64534 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.65685 | 0.425195 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.1286i | 0.981279i | 0.871363 | + | 0.490640i | \(0.163237\pi\) | ||||
−0.871363 | + | 0.490640i | \(0.836763\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.3181i | 1.13859i | 0.822134 | + | 0.569294i | \(0.192783\pi\) | ||||
−0.822134 | + | 0.569294i | \(0.807217\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.85970 | −0.285317 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.93783 | 0.215993 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.6533i | 0.925303i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 4.55765i | − 0.331520i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.63001 | 0.624446 | 0.312223 | − | 0.950009i | \(-0.398926\pi\) | ||||
0.312223 | + | 0.950009i | \(0.398926\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.4514 | 0.824288 | 0.412144 | − | 0.911119i | \(-0.364780\pi\) | ||||
0.412144 | + | 0.911119i | \(0.364780\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.0397948i | 0.00284976i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.5925i | 0.754681i | 0.926075 | + | 0.377340i | \(0.123161\pi\) | ||||
−0.926075 | + | 0.377340i | \(0.876839\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.68000 | 0.260868 | 0.130434 | − | 0.991457i | \(-0.458363\pi\) | ||||
0.130434 | + | 0.991457i | \(0.458363\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.33962 | 0.376627 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 33.2802i | − 2.33581i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 4.39236i | − 0.306776i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.82843 | −0.196589 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.6533 | 0.875249 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.3102i | 0.985153i | 0.870269 | + | 0.492577i | \(0.163945\pi\) | ||||
−0.870269 | + | 0.492577i | \(0.836055\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 9.11529i | − 0.624570i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.07866 | −0.0735637 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.54156 | 0.172532 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.541560i | 0.0365952i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 0.303911i | − 0.0204433i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.86156 | 0.325554 | 0.162777 | − | 0.986663i | \(-0.447955\pi\) | ||||
0.162777 | + | 0.986663i | \(0.447955\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.77568 | −0.318379 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 15.0496i | − 0.998877i | −0.866349 | − | 0.499438i | \(-0.833540\pi\) | ||||
0.866349 | − | 0.499438i | \(-0.166460\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 28.5264i | − 1.88507i | −0.334101 | − | 0.942537i | \(-0.608433\pi\) | ||||
0.334101 | − | 0.942537i | \(-0.391567\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 15.9437 | 1.04902 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.5702 | −0.889014 | −0.444507 | − | 0.895775i | \(-0.646621\pi\) | ||||
−0.444507 | + | 0.895775i | \(0.646621\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 1.33962i | − 0.0873869i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 10.9937i | − 0.714118i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 29.3629 | 1.89933 | 0.949665 | − | 0.313267i | \(-0.101424\pi\) | ||||
0.949665 | + | 0.313267i | \(0.101424\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.0063 | −1.54638 | −0.773190 | − | 0.634175i | \(-0.781340\pi\) | ||||
−0.773190 | + | 0.634175i | \(0.781340\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 6.52284i | − 0.416729i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.303911 | −0.0193374 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.0496 | 0.953729 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 22.2837i | − 1.40654i | −0.710925 | − | 0.703268i | \(-0.751724\pi\) | ||||
0.710925 | − | 0.703268i | \(-0.248276\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 9.89450i | − 0.622062i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.71313 | −0.107281 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.66038 | 0.540220 | 0.270110 | − | 0.962829i | \(-0.412940\pi\) | ||||
0.270110 | + | 0.962829i | \(0.412940\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 28.2704i | 1.75664i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.30205i | 0.451986i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.3208 | −0.821394 | −0.410697 | − | 0.911772i | \(-0.634715\pi\) | ||||
−0.410697 | + | 0.911772i | \(0.634715\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.330566 | 0.0203065 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.6533i | 0.896769i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.5058i | 1.00638i | 0.864177 | + | 0.503188i | \(0.167840\pi\) | ||||
−0.864177 | + | 0.503188i | \(0.832160\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.9769 | −1.33500 | −0.667499 | − | 0.744610i | \(-0.732635\pi\) | ||||
−0.667499 | + | 0.744610i | \(0.732635\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.382941 | −0.0231766 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 16.7064i | − 1.00744i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.4862i | 0.930475i | 0.885186 | + | 0.465237i | \(0.154031\pi\) | ||||
−0.885186 | + | 0.465237i | \(0.845969\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.557647 | −0.0333855 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.8910 | −1.36556 | −0.682780 | − | 0.730624i | \(-0.739229\pi\) | ||||
−0.682780 | + | 0.730624i | \(0.739229\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 6.34315i | − 0.377061i | −0.982067 | − | 0.188530i | \(-0.939628\pi\) | ||||
0.982067 | − | 0.188530i | \(-0.0603724\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.71313i | 0.101477i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 42.2672 | 2.49496 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.91688 | −0.230405 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.31724i | 0.253081i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 30.5783i | 1.78641i | 0.449654 | + | 0.893203i | \(0.351547\pi\) | ||||
−0.449654 | + | 0.893203i | \(0.648453\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.67923 | −0.155991 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.49824 | −0.202988 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.237649i | 0.0137436i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 10.3798i | − 0.598281i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.641669 | 0.0368629 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.82805 | 0.104674 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 17.1286i | − 0.977582i | −0.872401 | − | 0.488791i | \(-0.837438\pi\) | ||||
0.872401 | − | 0.488791i | \(-0.162562\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 1.33686i | − 0.0760511i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.8651 | −1.52338 | −0.761689 | − | 0.647943i | \(-0.775630\pi\) | ||||
−0.761689 | + | 0.647943i | \(0.775630\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.6890 | 1.11289 | 0.556445 | − | 0.830885i | \(-0.312165\pi\) | ||||
0.556445 | + | 0.830885i | \(0.312165\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.15862i | 0.121624i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 30.1860i | 1.69541i | 0.530466 | + | 0.847706i | \(0.322017\pi\) | ||||
−0.530466 | + | 0.847706i | \(0.677983\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −25.5443 | −1.43021 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.57373 | −0.478539 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 13.0831i | − 0.727964i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.401260i | 0.0222579i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.08402 | 0.447047 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.8910 | 0.710702 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.7784i | 1.14209i | 0.820920 | + | 0.571043i | \(0.193461\pi\) | ||||
−0.820920 | + | 0.571043i | \(0.806539\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 6.20285i | − 0.339914i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.52898 | −0.138173 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.0098 | 1.25342 | 0.626712 | − | 0.779251i | \(-0.284400\pi\) | ||||
0.626712 | + | 0.779251i | \(0.284400\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.55136i | 0.518759i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 1.95078i | − 0.105641i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 30.8651 | 1.66656 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.33962 | 0.0721225 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.4186i | 0.827716i | 0.910341 | + | 0.413858i | \(0.135819\pi\) | ||||
−0.910341 | + | 0.413858i | \(0.864181\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.3638i | 1.51828i | 0.650927 | + | 0.759140i | \(0.274380\pi\) | ||||
−0.650927 | + | 0.759140i | \(0.725620\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.0840215 | 0.00448474 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.2117 | −0.649965 | −0.324983 | − | 0.945720i | \(-0.605358\pi\) | ||||
−0.324983 | + | 0.945720i | \(0.605358\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.31724i | 0.229135i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 16.4853i | − 0.872494i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −33.4780 | −1.76690 | −0.883452 | − | 0.468522i | \(-0.844786\pi\) | ||||
−0.883452 | + | 0.468522i | \(0.844786\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.91688 | 0.311415 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 1.23765i | − 0.0649597i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 0.256497i | − 0.0134256i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.702379 | −0.0366639 | −0.0183319 | − | 0.999832i | \(-0.505836\pi\) | ||||
−0.0183319 | + | 0.999832i | \(0.505836\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.27391 | −0.482781 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.18100i | 0.165149i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 26.8132i | − 1.38834i | −0.719813 | − | 0.694168i | \(-0.755773\pi\) | ||||
0.719813 | − | 0.694168i | \(-0.244227\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.63001 | 0.239093 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.613530 | 0.0315984 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.51509i | 0.129192i | 0.997912 | + | 0.0645958i | \(0.0205758\pi\) | ||||
−0.997912 | + | 0.0645958i | \(0.979424\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 5.09921i | − 0.261240i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.4880 | −1.30238 | −0.651188 | − | 0.758916i | \(-0.725729\pi\) | ||||
−0.651188 | + | 0.758916i | \(0.725729\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.55136 | −0.384853 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.27744i | 0.115769i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 16.5532i | − 0.839281i | −0.907690 | − | 0.419641i | \(-0.862156\pi\) | ||||
0.907690 | − | 0.419641i | \(-0.137844\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.2306 | −0.517383 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.99647 | 0.151152 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.20690i | 0.261988i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.7936i | 0.642094i | 0.947063 | + | 0.321047i | \(0.104035\pi\) | ||||
−0.947063 | + | 0.321047i | \(0.895965\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −16.4853 | −0.825296 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.0853 | 0.903137 | 0.451568 | − | 0.892237i | \(-0.350865\pi\) | ||||
0.451568 | + | 0.892237i | \(0.350865\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.0468544i | 0.00233398i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 0.473626i | − 0.0235347i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.6990 | 1.07558 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.2271 | −1.24740 | −0.623699 | − | 0.781665i | \(-0.714371\pi\) | ||||
−0.623699 | + | 0.781665i | \(0.714371\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.37941i | 0.166694i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 25.7819i | − 1.26865i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.12787 | −0.349894 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.31724 | −0.407297 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 10.2571i | − 0.501090i | −0.968105 | − | 0.250545i | \(-0.919390\pi\) | ||||
0.968105 | − | 0.250545i | \(-0.0806098\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.38775i | 0.165109i | 0.996587 | + | 0.0825543i | \(0.0263078\pi\) | ||||
−0.996587 | + | 0.0825543i | \(0.973692\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.82843 | −0.137523 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −17.2739 | −0.837908 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.5912i | 0.851296i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.293927i | 0.0141909i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.42454 | −0.213123 | −0.106561 | − | 0.994306i | \(-0.533984\pi\) | ||||
−0.106561 | + | 0.994306i | \(0.533984\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.31371 | −0.351474 | −0.175737 | − | 0.984437i | \(-0.556231\pi\) | ||||
−0.175737 | + | 0.984437i | \(0.556231\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 3.45844i | − 0.165820i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.2306i | 0.489395i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −29.6533 | −1.41527 | −0.707637 | − | 0.706576i | \(-0.750239\pi\) | ||||
−0.707637 | + | 0.706576i | \(0.750239\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.7721 | −0.655817 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 14.5743i | − 0.692446i | −0.938152 | − | 0.346223i | \(-0.887464\pi\) | ||||
0.938152 | − | 0.346223i | \(-0.112536\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 6.94019i | − 0.328997i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.1305 | −0.668349 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.48844 | −0.306208 | −0.153104 | − | 0.988210i | \(-0.548927\pi\) | ||||
−0.153104 | + | 0.988210i | \(0.548927\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 32.4423i | − 1.52765i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.97685i | 0.468753i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.181370 | 0.00850278 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.00353 | 0.421167 | 0.210584 | − | 0.977576i | \(-0.432464\pi\) | ||||
0.210584 | + | 0.977576i | \(0.432464\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.61706i | 0.168830i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 20.6783i | − 0.963085i | −0.876423 | − | 0.481542i | \(-0.840077\pi\) | ||||
0.876423 | − | 0.481542i | \(-0.159923\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.6435 | −0.866437 | −0.433219 | − | 0.901289i | \(-0.642622\pi\) | ||||
−0.433219 | + | 0.901289i | \(0.642622\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.264116 | 0.0122481 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 33.2535i | − 1.53879i | −0.638773 | − | 0.769395i | \(-0.720558\pi\) | ||||
0.638773 | − | 0.769395i | \(-0.279442\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 24.3361i | − 1.12374i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.8562 | 1.05316 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.96703 | −0.366325 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 17.2739i | 0.792582i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 0.697947i | − 0.0319568i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.08864 | 0.0497412 | 0.0248706 | − | 0.999691i | \(-0.492083\pi\) | ||||
0.0248706 | + | 0.999691i | \(0.492083\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.521173 | −0.0237634 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.8910i | 0.586560i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 2.04476i | − 0.0928476i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 35.3298 | 1.60095 | 0.800473 | − | 0.599369i | \(-0.204582\pi\) | ||||
0.800473 | + | 0.599369i | \(0.204582\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.6135 | −0.479960 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 18.2306i | − 0.822735i | −0.911470 | − | 0.411367i | \(-0.865051\pi\) | ||||
0.911470 | − | 0.411367i | \(-0.134949\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.4120i | 1.18953i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.65685 | 0.0744701 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −41.5443 | −1.86352 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.3361i | 0.910368i | 0.890397 | + | 0.455184i | \(0.150427\pi\) | ||||
−0.890397 | + | 0.455184i | \(0.849573\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.83822i | 0.260833i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.2969 | −1.35087 | −0.675435 | − | 0.737420i | \(-0.736044\pi\) | ||||
−0.675435 | + | 0.737420i | \(0.736044\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.303911 | −0.0135239 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.9929i | 0.577037i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.9660i | 0.663355i | 0.943393 | + | 0.331677i | \(0.107615\pi\) | ||||
−0.943393 | + | 0.331677i | \(0.892385\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.46824 | 0.109188 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.61706 | 0.159697 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.633169i | 0.0279008i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 9.89450i | − 0.435160i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.12695 | −0.225048 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.9049 | −1.09110 | −0.545551 | − | 0.838078i | \(-0.683680\pi\) | ||||
−0.545551 | + | 0.838078i | \(0.683680\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 18.2445i | − 0.797775i | −0.917000 | − | 0.398888i | \(-0.869396\pi\) | ||||
0.917000 | − | 0.398888i | \(-0.130604\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 21.7659i | 0.949940i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.01704 | −0.0878638 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0000 | −0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.65685i | 0.245487i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.779208i | 0.0337513i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.06074 | 0.175561 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.1286 | −0.566542 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 48.1782i | − 2.07518i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.8471i | 1.11125i | 0.831432 | + | 0.555627i | \(0.187522\pi\) | ||||
−0.831432 | + | 0.555627i | \(0.812478\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.3181 | −0.657364 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.82880 | −0.164008 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 19.4249i | − 0.830549i | −0.909696 | − | 0.415275i | \(-0.863685\pi\) | ||||
0.909696 | − | 0.415275i | \(-0.136315\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 3.85970i | − 0.164728i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 26.4120 | 1.12519 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −50.1055 | −2.13070 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.93783i | 0.124704i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 38.9652i | 1.65101i | 0.564397 | + | 0.825504i | \(0.309109\pi\) | ||||
−0.564397 | + | 0.825504i | \(0.690891\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.191354 | 0.00809342 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.6533 | −0.534224 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 28.1327i | − 1.18565i | −0.805330 | − | 0.592826i | \(-0.798012\pi\) | ||||
0.805330 | − | 0.592826i | \(-0.201988\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 4.52377i | − 0.190316i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.55765 | 0.191403 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.4849 | 0.565317 | 0.282658 | − | 0.959221i | \(-0.408784\pi\) | ||||
0.282658 | + | 0.959221i | \(0.408784\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.9706i | 0.877591i | 0.898587 | + | 0.438795i | \(0.144595\pi\) | ||||
−0.898587 | + | 0.438795i | \(0.855405\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.63001i | 0.360524i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.5077 | 0.563308 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.6176 | −0.483648 | −0.241824 | − | 0.970320i | \(-0.577746\pi\) | ||||
−0.241824 | + | 0.970320i | \(0.577746\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.4514i | 0.475903i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 68.5907i | − 2.84562i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.44158 | 0.101120 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.0397948 | −0.00164531 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 24.0796i | − 0.993871i | −0.867787 | − | 0.496936i | \(-0.834459\pi\) | ||||
0.867787 | − | 0.496936i | \(-0.165541\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.01704i | 0.0831108i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.5925 | −0.435715 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −41.5372 | −1.70573 | −0.852865 | − | 0.522132i | \(-0.825137\pi\) | ||||
−0.852865 | + | 0.522132i | \(0.825137\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.80785i | 0.320091i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.68000i | 0.150612i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.43160 | −0.262788 | −0.131394 | − | 0.991330i | \(-0.541945\pi\) | ||||
−0.131394 | + | 0.991330i | \(0.541945\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.45844 | 0.141073 | 0.0705364 | − | 0.997509i | \(-0.477529\pi\) | ||||
0.0705364 | + | 0.997509i | \(0.477529\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.33962i | 0.217446i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.586182i | 0.0238317i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.1019 | 1.22180 | 0.610900 | − | 0.791708i | \(-0.290808\pi\) | ||||
0.610900 | + | 0.791708i | \(0.290808\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 33.2802 | 1.34858 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.237649i | 0.00961424i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.54246i | 0.143079i | 0.997438 | + | 0.0715393i | \(0.0227911\pi\) | ||||
−0.997438 | + | 0.0715393i | \(0.977209\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.39236 | 0.177117 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.9098 | 0.922315 | 0.461157 | − | 0.887318i | \(-0.347434\pi\) | ||||
0.461157 | + | 0.887318i | \(0.347434\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 40.4612i | − 1.62627i | −0.582074 | − | 0.813136i | \(-0.697758\pi\) | ||||
0.582074 | − | 0.813136i | \(-0.302242\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 2.82843i | − 0.113501i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 66.7847 | 2.67567 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.6855 | 0.867420 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.6533i | 0.505325i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 22.4361i | − 0.894584i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.1851 | −0.445270 | −0.222635 | − | 0.974902i | \(-0.571466\pi\) | ||||
−0.222635 | + | 0.974902i | \(0.571466\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.3102 | −0.568779 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.41512i | 0.0958409i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.15716i | 0.0458482i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.11529 | 0.360595 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.69312 | −0.264362 | −0.132181 | − | 0.991226i | \(-0.542198\pi\) | ||||
−0.132181 | + | 0.991226i | \(0.542198\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.3724i | 1.00059i | 0.865856 | + | 0.500294i | \(0.166775\pi\) | ||||
−0.865856 | + | 0.500294i | \(0.833225\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 1.07866i | − 0.0424720i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.72999 | 0.264583 | 0.132292 | − | 0.991211i | \(-0.457766\pi\) | ||||
0.132292 | + | 0.991211i | \(0.457766\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.7890 | −0.776786 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.54156i | 0.0996116i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 37.0144i | − 1.44849i | −0.689545 | − | 0.724243i | \(-0.742190\pi\) | ||||
0.689545 | − | 0.724243i | \(-0.257810\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.41921 | −0.0554529 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.541560 | −0.0211283 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.7624i | 0.769832i | 0.922952 | + | 0.384916i | \(0.125770\pi\) | ||||
−0.922952 | + | 0.384916i | \(0.874230\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 16.8632i | − 0.655904i | −0.944694 | − | 0.327952i | \(-0.893642\pi\) | ||||
0.944694 | − | 0.327952i | \(-0.106358\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.303911 | 0.0118029 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.80785 | 0.302776 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 20.6533i | − 0.799700i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.86156i | 0.187959i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.5021 | 0.521244 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.3066 | −1.43807 | −0.719033 | − | 0.694976i | \(-0.755415\pi\) | ||||
−0.719033 | + | 0.694976i | \(0.755415\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 4.77568i | − 0.183816i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.632805i | 0.0243207i | 0.999926 | + | 0.0121603i | \(0.00387085\pi\) | ||||
−0.999926 | + | 0.0121603i | \(0.996129\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.6764 | 0.755113 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.0496 | 0.576702 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 6.04606i | − 0.231346i | −0.993287 | − | 0.115673i | \(-0.963098\pi\) | ||||
0.993287 | − | 0.115673i | \(-0.0369025\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 1.60058i | − 0.0611549i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 28.5264 | 1.08835 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.0586426 | −0.00223410 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.3955i | 1.08021i | 0.841596 | + | 0.540107i | \(0.181616\pi\) | ||||
−0.841596 | + | 0.540107i | \(0.818384\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 15.9437i | 0.605652i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.93926 | 0.149425 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −33.5443 | −1.27058 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 13.5702i | − 0.513272i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 14.7738i | − 0.558000i | −0.960291 | − | 0.279000i | \(-0.909997\pi\) | ||||
0.960291 | − | 0.279000i | \(-0.0900029\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22.4361 | −0.846192 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.33962 | 0.0504529 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 2.92450i | − 0.109987i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.7569i | 0.854655i | 0.904097 | + | 0.427327i | \(0.140545\pi\) | ||||
−0.904097 | + | 0.427327i | \(0.859455\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.9937 | 0.412296 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.57726 | 0.0590690 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 0.139211i | − 0.00520621i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 29.3629i | 1.09658i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.9957 | −1.15594 | −0.577972 | − | 0.816057i | \(-0.696156\pi\) | ||||
−0.577972 | + | 0.816057i | \(0.696156\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.09292 | −0.226912 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 24.0063i | − 0.892803i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 34.8723i | − 1.29512i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.1117 | 1.52475 | 0.762375 | − | 0.647135i | \(-0.224033\pi\) | ||||
0.762375 | + | 0.647135i | \(0.224033\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.23765i | 0.304680i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.206562i | 0.00762954i | 0.999993 | + | 0.00381477i | \(0.00121428\pi\) | ||||
−0.999993 | + | 0.00381477i | \(0.998786\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.52284 | 0.240599 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.6792 | −0.688058 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.13215i | 0.0784325i | 0.999231 | + | 0.0392162i | \(0.0124861\pi\) | ||||
−0.999231 | + | 0.0392162i | \(0.987514\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 0.303911i | − 0.0111644i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −40.5175 | −1.48644 | −0.743221 | − | 0.669046i | \(-0.766703\pi\) | ||||
−0.743221 | + | 0.669046i | \(0.766703\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.69256 | 0.245196 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 15.0496i | 0.550636i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 39.0761i | 1.42781i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.5843 | −0.459208 | −0.229604 | − | 0.973284i | \(-0.573743\pi\) | ||||
−0.229604 | + | 0.973284i | \(0.573743\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 22.2837 | 0.812064 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 4.72529i | − 0.171971i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.6052i | 0.385452i | 0.981253 | + | 0.192726i | \(0.0617329\pi\) | ||||
−0.981253 | + | 0.192726i | \(0.938267\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.89450 | 0.359148 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −42.8182 | −1.55216 | −0.776079 | − | 0.630635i | \(-0.782794\pi\) | ||||
−0.776079 | + | 0.630635i | \(0.782794\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 36.8441i | − 1.33385i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 1.71313i | − 0.0619384i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.475298 | 0.0171620 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.7455 | 0.459614 | 0.229807 | − | 0.973236i | \(-0.426190\pi\) | ||||
0.229807 | + | 0.973236i | \(0.426190\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.66038i | 0.311896i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 32.3522i | − 1.16363i | −0.813322 | − | 0.581814i | \(-0.802343\pi\) | ||||
0.813322 | − | 0.581814i | \(-0.197657\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.66314 | 0.0956630 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −28.2704 | −1.01419 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 33.5443i | 1.20185i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 31.8874i | 1.14102i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.30205 | −0.260954 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.8253 | −0.386370 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.36056i | 0.262376i | 0.991358 | + | 0.131188i | \(0.0418791\pi\) | ||||
−0.991358 | + | 0.131188i | \(0.958121\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 13.3208i | − 0.474232i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 43.5317 | 1.54781 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.324298 | −0.0115162 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.330566i | 0.0117240i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.0627i | 0.852344i | 0.904642 | + | 0.426172i | \(0.140138\pi\) | ||||
−0.904642 | + | 0.426172i | \(0.859862\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.2306 | −0.361932 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.6533 | −0.517750 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 1.89450i | − 0.0668556i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 6.10550i | − 0.215190i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.5058 | −0.581032 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.83586 | 0.275494 | 0.137747 | − | 0.990467i | \(-0.456014\pi\) | ||||
0.137747 | + | 0.990467i | \(0.456014\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.7351i | 1.60598i | 0.595995 | + | 0.802988i | \(0.296758\pi\) | ||||
−0.595995 | + | 0.802988i | \(0.703242\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 21.9769i | − 0.770762i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.02684 | 0.176083 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.23765 | 0.288199 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 0.382941i | − 0.0133810i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 27.3709i | − 0.955250i | −0.878564 | − | 0.477625i | \(-0.841498\pi\) | ||||
0.878564 | − | 0.477625i | \(-0.158502\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.8560 | −1.00586 | −0.502929 | − | 0.864328i | \(-0.667744\pi\) | ||||
−0.502929 | + | 0.864328i | \(0.667744\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 16.7064 | 0.581644 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.4227i | 0.501528i | 0.968048 | + | 0.250764i | \(0.0806818\pi\) | ||||
−0.968048 | + | 0.250764i | \(0.919318\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.7497i | 0.755400i | 0.925928 | + | 0.377700i | \(0.123285\pi\) | ||||
−0.925928 | + | 0.377700i | \(0.876715\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.4862 | −0.537210 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −49.8147 | −1.72598 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 2.76513i | − 0.0956914i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 0.557647i | − 0.0192751i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −44.4557 | −1.53478 | −0.767390 | − | 0.641181i | \(-0.778445\pi\) | ||||
−0.767390 | + | 0.641181i | \(0.778445\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.3200 | −0.838620 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 22.8910i | − 0.788407i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 6.15379i | − 0.211697i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.64077 | −0.193819 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.34315 | 0.217696 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.5443i | 0.601411i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.5648i | 0.567169i | 0.958947 | + | 0.283585i | \(0.0915237\pi\) | ||||
−0.958947 | + | 0.283585i | \(0.908476\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.71313 | −0.0585879 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.0888 | 0.652062 | 0.326031 | − | 0.945359i | \(-0.394289\pi\) | ||||
0.326031 | + | 0.945359i | \(0.394289\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 53.9272i | 1.83997i | 0.391949 | + | 0.919987i | \(0.371801\pi\) | ||||
−0.391949 | + | 0.919987i | \(0.628199\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 42.2672i | 1.44046i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.64533 | −0.124089 | −0.0620443 | − | 0.998073i | \(-0.519762\pi\) | ||||
−0.0620443 | + | 0.998073i | \(0.519762\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.42826 | 0.0825632 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 3.91688i | − 0.133024i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 38.4586i | 1.30462i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.448643 | 0.0152017 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.31724 | −0.146116 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 21.1020i | − 0.713377i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 56.6481i | − 1.91287i | −0.291945 | − | 0.956435i | \(-0.594302\pi\) | ||||
0.291945 | − | 0.956435i | \(-0.405698\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −30.5783 | −1.03138 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.0118 | 0.674214 | 0.337107 | − | 0.941466i | \(-0.390552\pi\) | ||||
0.337107 | + | 0.941466i | \(0.390552\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 15.0292i | − 0.505773i | −0.967496 | − | 0.252887i | \(-0.918620\pi\) | ||||
0.967496 | − | 0.252887i | \(-0.0813799\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 2.67923i | − 0.0900614i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26.1180 | −0.876958 | −0.438479 | − | 0.898742i | \(-0.644483\pi\) | ||||
−0.438479 | + | 0.898742i | \(0.644483\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23.2404 | −0.779458 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 3.49824i | − 0.117195i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.2306i | 0.342354i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.21805 | 0.207847 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.237649 | −0.00793486 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 4.07197i | − 0.135808i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 2.52452i | − 0.0841038i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.3798 | 0.345418 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.25507 | 0.241167 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 51.2480i | 1.70166i | 0.525439 | + | 0.850831i | \(0.323901\pi\) | ||||
−0.525439 | + | 0.850831i | \(0.676099\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.641669i | 0.0212828i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.0535 | −0.697533 | −0.348767 | − | 0.937210i | \(-0.613399\pi\) | ||||
−0.348767 | + | 0.937210i | \(0.613399\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −52.6470 | −1.74236 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.82805i | 0.0604336i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 13.6569i | − 0.450989i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.8839 | 0.589937 | 0.294968 | − | 0.955507i | \(-0.404691\pi\) | ||||
0.294968 | + | 0.955507i | \(0.404691\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17.1286 | 0.564407 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 0.765881i | − 0.0252093i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 29.6228i | 0.973992i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.33686 | 0.0439081 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.2774 | 0.337192 | 0.168596 | − | 0.985685i | \(-0.446077\pi\) | ||||
0.168596 | + | 0.985685i | \(0.446077\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 49.8147i | 1.63261i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 26.8651i | − 0.879523i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.99294 | 0.195990 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.5780 | 0.443574 | 0.221787 | − | 0.975095i | \(-0.428811\pi\) | ||||
0.221787 | + | 0.975095i | \(0.428811\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.6890i | 0.642527i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.59890i | 0.182519i | 0.995827 | + | 0.0912595i | \(0.0290893\pi\) | ||||
−0.995827 | + | 0.0912595i | \(0.970911\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26.2306 | 0.854186 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.15862 | −0.0702199 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 46.9106i | − 1.52439i | −0.647348 | − | 0.762194i | \(-0.724122\pi\) | ||||
0.647348 | − | 0.762194i | \(-0.275878\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.0455027i | 0.00147708i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −30.1860 | −0.978847 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.59115 | −0.181115 | −0.0905576 | − | 0.995891i | \(-0.528865\pi\) | ||||
−0.0905576 | + | 0.995891i | \(0.528865\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 4.08740i | − 0.132265i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 25.5443i | − 0.825730i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.4022 | 0.497362 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6890 | −0.989969 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 8.57373i | − 0.276285i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 5.42367i | − 0.174594i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.7561 | −0.989048 | −0.494524 | − | 0.869164i | \(-0.664658\pi\) | ||||
−0.494524 | + | 0.869164i | \(0.664658\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13.0831 | 0.420290 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.3668i | 0.364779i | 0.983226 | + | 0.182389i | \(0.0583832\pi\) | ||||
−0.983226 | + | 0.182389i | \(0.941617\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 37.9070i | 1.21524i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.401260 | −0.0128506 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.8323 | −0.730471 | −0.365235 | − | 0.930915i | \(-0.619012\pi\) | ||||
−0.365235 | + | 0.930915i | \(0.619012\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 51.2608i | − 1.63830i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.08402i | 0.258103i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −46.3557 | −1.47852 | −0.739258 | − | 0.673422i | \(-0.764824\pi\) | ||||
−0.739258 | + | 0.673422i | \(0.764824\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.01686 | 0.159850 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12.8910i | 0.410324i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 6.44158i | − 0.204830i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.43683 | −0.109175 | −0.0545873 | − | 0.998509i | \(-0.517384\pi\) | ||||
−0.0545873 | + | 0.998509i | \(0.517384\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20.7784 | −0.659383 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 1.74294i | − 0.0552550i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 31.0320i | − 0.982794i | −0.870936 | − | 0.491397i | \(-0.836486\pi\) | ||||
0.870936 | − | 0.491397i | \(-0.163514\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.20285 | 0.196249 |
(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 | 3072.2.d.i.1537.6 | 8 | ||
4.3 | odd | 2 | 3072.2.d.f.1537.2 | 8 | |||
8.3 | odd | 2 | 3072.2.d.f.1537.7 | 8 | |||
8.5 | even | 2 | inner | 3072.2.d.i.1537.3 | 8 | ||
16.3 | odd | 4 | 3072.2.a.t.1.2 | 4 | |||
16.5 | even | 4 | 3072.2.a.o.1.3 | 4 | |||
16.11 | odd | 4 | 3072.2.a.i.1.3 | 4 | |||
16.13 | even | 4 | 3072.2.a.n.1.2 | 4 | |||
32.3 | odd | 8 | 384.2.j.b.97.4 | 8 | |||
32.5 | even | 8 | 384.2.j.a.289.2 | 8 | |||
32.11 | odd | 8 | 48.2.j.a.13.4 | ✓ | 8 | ||
32.13 | even | 8 | 192.2.j.a.49.3 | 8 | |||
32.19 | odd | 8 | 48.2.j.a.37.4 | yes | 8 | ||
32.21 | even | 8 | 192.2.j.a.145.3 | 8 | |||
32.27 | odd | 8 | 384.2.j.b.289.4 | 8 | |||
32.29 | even | 8 | 384.2.j.a.97.2 | 8 | |||
48.5 | odd | 4 | 9216.2.a.bn.1.2 | 4 | |||
48.11 | even | 4 | 9216.2.a.bo.1.2 | 4 | |||
48.29 | odd | 4 | 9216.2.a.x.1.3 | 4 | |||
48.35 | even | 4 | 9216.2.a.y.1.3 | 4 | |||
96.5 | odd | 8 | 1152.2.k.f.289.2 | 8 | |||
96.11 | even | 8 | 144.2.k.b.109.1 | 8 | |||
96.29 | odd | 8 | 1152.2.k.f.865.2 | 8 | |||
96.35 | even | 8 | 1152.2.k.c.865.2 | 8 | |||
96.53 | odd | 8 | 576.2.k.b.145.3 | 8 | |||
96.59 | even | 8 | 1152.2.k.c.289.2 | 8 | |||
96.77 | odd | 8 | 576.2.k.b.433.3 | 8 | |||
96.83 | even | 8 | 144.2.k.b.37.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.2.j.a.13.4 | ✓ | 8 | 32.11 | odd | 8 | ||
48.2.j.a.37.4 | yes | 8 | 32.19 | odd | 8 | ||
144.2.k.b.37.1 | 8 | 96.83 | even | 8 | |||
144.2.k.b.109.1 | 8 | 96.11 | even | 8 | |||
192.2.j.a.49.3 | 8 | 32.13 | even | 8 | |||
192.2.j.a.145.3 | 8 | 32.21 | even | 8 | |||
384.2.j.a.97.2 | 8 | 32.29 | even | 8 | |||
384.2.j.a.289.2 | 8 | 32.5 | even | 8 | |||
384.2.j.b.97.4 | 8 | 32.3 | odd | 8 | |||
384.2.j.b.289.4 | 8 | 32.27 | odd | 8 | |||
576.2.k.b.145.3 | 8 | 96.53 | odd | 8 | |||
576.2.k.b.433.3 | 8 | 96.77 | odd | 8 | |||
1152.2.k.c.289.2 | 8 | 96.59 | even | 8 | |||
1152.2.k.c.865.2 | 8 | 96.35 | even | 8 | |||
1152.2.k.f.289.2 | 8 | 96.5 | odd | 8 | |||
1152.2.k.f.865.2 | 8 | 96.29 | odd | 8 | |||
3072.2.a.i.1.3 | 4 | 16.11 | odd | 4 | |||
3072.2.a.n.1.2 | 4 | 16.13 | even | 4 | |||
3072.2.a.o.1.3 | 4 | 16.5 | even | 4 | |||
3072.2.a.t.1.2 | 4 | 16.3 | odd | 4 | |||
3072.2.d.f.1537.2 | 8 | 4.3 | odd | 2 | |||
3072.2.d.f.1537.7 | 8 | 8.3 | odd | 2 | |||
3072.2.d.i.1537.3 | 8 | 8.5 | even | 2 | inner | ||
3072.2.d.i.1537.6 | 8 | 1.1 | even | 1 | trivial | ||
9216.2.a.x.1.3 | 4 | 48.29 | odd | 4 | |||
9216.2.a.y.1.3 | 4 | 48.35 | even | 4 | |||
9216.2.a.bn.1.2 | 4 | 48.5 | odd | 4 | |||
9216.2.a.bo.1.2 | 4 | 48.11 | even | 4 |