Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(2305,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.2305");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.q (of order \(3\), degree \(2\), 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: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2305.3 | ||
Character | \(\chi\) | \(=\) | 3024.2305 |
Dual form | 3024.2.q.l.2881.3 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.33425 | − | 2.31099i | −0.596696 | − | 1.03351i | −0.993305 | − | 0.115520i | \(-0.963146\pi\) |
0.396609 | − | 0.917988i | \(-0.370187\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.54743 | − | 0.714566i | −0.962838 | − | 0.270081i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.99189 | − | 3.45005i | 0.600577 | − | 1.04023i | −0.392157 | − | 0.919898i | \(-0.628271\pi\) |
0.992734 | − | 0.120332i | \(-0.0383958\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00103 | − | 1.73384i | 0.277636 | − | 0.480880i | −0.693161 | − | 0.720783i | \(-0.743782\pi\) |
0.970797 | + | 0.239903i | \(0.0771156\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.57175 | + | 6.18646i | 0.866278 | + | 1.50044i | 0.865773 | + | 0.500437i | \(0.166827\pi\) |
0.000504947 | 1.00000i | \(0.499839\pi\) | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.01956 | − | 6.96208i | 0.922150 | − | 1.59721i | 0.126068 | − | 0.992022i | \(-0.459764\pi\) |
0.796082 | − | 0.605189i | \(-0.206903\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.443909 | + | 0.768873i | 0.0925614 | + | 0.160321i | 0.908588 | − | 0.417693i | \(-0.137161\pi\) |
−0.816027 | + | 0.578014i | \(0.803828\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.06046 | + | 1.83677i | −0.212092 | + | 0.367355i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.35035 | + | 2.33887i | 0.250753 | + | 0.434317i | 0.963733 | − | 0.266867i | \(-0.0859885\pi\) |
−0.712980 | + | 0.701184i | \(0.752655\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.22989 | 0.220894 | 0.110447 | − | 0.993882i | \(-0.464772\pi\) | ||||
0.110447 | + | 0.993882i | \(0.464772\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.74756 | + | 6.84051i | 0.295391 | + | 1.15626i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.26528 | − | 9.11973i | 0.865607 | − | 1.49928i | −0.000836477 | − | 1.00000i | \(-0.500266\pi\) |
0.866443 | − | 0.499275i | \(-0.166400\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.43477 | − | 2.48509i | 0.224073 | − | 0.388105i | −0.731968 | − | 0.681339i | \(-0.761398\pi\) |
0.956041 | + | 0.293234i | \(0.0947313\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.40053 | − | 5.88989i | −0.518576 | − | 0.898200i | −0.999767 | − | 0.0215840i | \(-0.993129\pi\) |
0.481191 | − | 0.876616i | \(-0.340204\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.1369 | −1.77035 | −0.885175 | − | 0.465258i | \(-0.845961\pi\) | ||||
−0.885175 | + | 0.465258i | \(0.845961\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.97879 | + | 3.64061i | 0.854113 | + | 0.520088i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.38665 | + | 4.13380i | 0.327832 | + | 0.567821i | 0.982081 | − | 0.188457i | \(-0.0603487\pi\) |
−0.654250 | + | 0.756279i | \(0.727015\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.6307 | −1.43345 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.58058 | 1.24729 | 0.623643 | − | 0.781710i | \(-0.285652\pi\) | ||||
0.623643 | + | 0.781710i | \(0.285652\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.49962 | −1.21630 | −0.608151 | − | 0.793821i | \(-0.708089\pi\) | ||||
−0.608151 | + | 0.793821i | \(0.708089\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.34252 | −0.662658 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.9889 | −1.34251 | −0.671255 | − | 0.741227i | \(-0.734244\pi\) | ||||
−0.671255 | + | 0.741227i | \(0.734244\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.62888 | −0.549347 | −0.274673 | − | 0.961538i | \(-0.588570\pi\) | ||||
−0.274673 | + | 0.961538i | \(0.588570\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.01004 | + | 3.48149i | 0.235257 | + | 0.407478i | 0.959347 | − | 0.282228i | \(-0.0910733\pi\) |
−0.724090 | + | 0.689705i | \(0.757740\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.53949 | + | 7.36543i | −0.859204 | + | 0.839368i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.02997 | 0.115881 | 0.0579406 | − | 0.998320i | \(-0.481547\pi\) | ||||
0.0579406 | + | 0.998320i | \(0.481547\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.26656 | − | 9.12195i | −0.578080 | − | 1.00126i | −0.995699 | − | 0.0926419i | \(-0.970469\pi\) |
0.417620 | − | 0.908622i | \(-0.362865\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.53125 | − | 16.5086i | 1.03381 | − | 1.79061i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.72788 | + | 2.99278i | −0.183155 | + | 0.317234i | −0.942953 | − | 0.332925i | \(-0.891964\pi\) |
0.759798 | + | 0.650159i | \(0.225298\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.78900 | + | 3.70153i | −0.397195 | + | 0.388025i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −21.4524 | −2.20097 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.12061 | − | 1.94096i | −0.113781 | − | 0.197075i | 0.803511 | − | 0.595290i | \(-0.202963\pi\) |
−0.917292 | + | 0.398216i | \(0.869630\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.28415 | + | 3.95626i | −0.227281 | + | 0.393663i | −0.957001 | − | 0.290083i | \(-0.906317\pi\) |
0.729720 | + | 0.683746i | \(0.239650\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.37509 | − | 11.0420i | −0.628156 | − | 1.08800i | −0.987922 | − | 0.154955i | \(-0.950477\pi\) |
0.359766 | − | 0.933043i | \(-0.382857\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.659761 | + | 1.14274i | −0.0637815 | + | 0.110473i | −0.896153 | − | 0.443746i | \(-0.853649\pi\) |
0.832371 | + | 0.554218i | \(0.186983\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.31990 | − | 10.9464i | −0.605337 | − | 1.04847i | −0.991998 | − | 0.126252i | \(-0.959705\pi\) |
0.386661 | − | 0.922222i | \(-0.373628\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.503200 | − | 0.871568i | 0.0473371 | − | 0.0819903i | −0.841386 | − | 0.540435i | \(-0.818260\pi\) |
0.888723 | + | 0.458444i | \(0.151593\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.18457 | − | 2.05174i | 0.110462 | − | 0.191326i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.67815 | − | 18.3118i | −0.428846 | − | 1.67864i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.43524 | − | 4.21796i | −0.221386 | − | 0.383451i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.68283 | −0.687173 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.38400 | −0.122810 | −0.0614051 | − | 0.998113i | \(-0.519558\pi\) | ||||
−0.0614051 | + | 0.998113i | \(0.519558\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.164862 | + | 0.285550i | 0.0144041 | + | 0.0249486i | 0.873138 | − | 0.487474i | \(-0.162082\pi\) |
−0.858734 | + | 0.512422i | \(0.828748\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −15.2144 | + | 14.8632i | −1.31926 | + | 1.28880i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.47095 | − | 7.74391i | 0.381979 | − | 0.661607i | −0.609366 | − | 0.792889i | \(-0.708576\pi\) |
0.991345 | + | 0.131282i | \(0.0419094\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.92869 | + | 6.80470i | −0.333227 | + | 0.577167i | −0.983143 | − | 0.182840i | \(-0.941471\pi\) |
0.649915 | + | 0.760007i | \(0.274804\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.98789 | − | 6.90723i | −0.333484 | − | 0.577611i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.60341 | − | 6.24128i | 0.299247 | − | 0.518310i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.16075 | + | 14.1348i | 0.668554 | + | 1.15797i | 0.978308 | + | 0.207153i | \(0.0664199\pi\) |
−0.309754 | + | 0.950817i | \(0.600247\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.31677 | + | 4.01276i | −0.188536 | + | 0.326554i | −0.944762 | − | 0.327756i | \(-0.893708\pi\) |
0.756226 | + | 0.654310i | \(0.227041\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.64098 | − | 2.84226i | −0.131807 | − | 0.228296i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.51852 | −0.679852 | −0.339926 | − | 0.940452i | \(-0.610402\pi\) | ||||
−0.339926 | + | 0.940452i | \(0.610402\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.581416 | − | 2.27585i | −0.0458220 | − | 0.179362i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.22354 | + | 2.11923i | −0.0958350 | + | 0.165991i | −0.909957 | − | 0.414703i | \(-0.863885\pi\) |
0.814122 | + | 0.580694i | \(0.197219\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.0713948 | + | 0.123659i | −0.00552470 | + | 0.00956906i | −0.868775 | − | 0.495208i | \(-0.835092\pi\) |
0.863250 | + | 0.504777i | \(0.168425\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.49587 | + | 7.78708i | 0.345836 | + | 0.599006i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.9967 | −1.36826 | −0.684131 | − | 0.729359i | \(-0.739818\pi\) | ||||
−0.684131 | + | 0.729359i | \(0.739818\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.01395 | − | 3.92128i | 0.303426 | − | 0.296421i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.02413 | − | 1.77384i | −0.0765468 | − | 0.132583i | 0.825211 | − | 0.564824i | \(-0.191056\pi\) |
−0.901758 | + | 0.432242i | \(0.857723\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.81165 | 0.134659 | 0.0673294 | − | 0.997731i | \(-0.478552\pi\) | ||||
0.0673294 | + | 0.997731i | \(0.478552\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −28.1009 | −2.06602 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 28.4582 | 2.08107 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.8091 | 1.36098 | 0.680491 | − | 0.732757i | \(-0.261767\pi\) | ||||
0.680491 | + | 0.732757i | \(0.261767\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.48714 | 0.466954 | 0.233477 | − | 0.972362i | \(-0.424990\pi\) | ||||
0.233477 | + | 0.972362i | \(0.424990\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.8356 | 0.772007 | 0.386003 | − | 0.922497i | \(-0.373855\pi\) | ||||
0.386003 | + | 0.922497i | \(0.373855\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.43873 | + | 16.3484i | 0.669094 | + | 1.15890i | 0.978158 | + | 0.207863i | \(0.0666508\pi\) |
−0.309064 | + | 0.951041i | \(0.600016\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.76863 | − | 6.92301i | −0.124134 | − | 0.485900i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.65736 | −0.534813 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.0130 | − | 27.7354i | −1.10764 | − | 1.91850i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.9133 | − | 20.6344i | 0.820145 | − | 1.42053i | −0.0854297 | − | 0.996344i | \(-0.527226\pi\) |
0.905574 | − | 0.424188i | \(-0.139440\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.07433 | + | 15.7172i | −0.618864 | + | 1.07190i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.13305 | − | 0.878836i | −0.212685 | − | 0.0596593i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.3018 | 0.962041 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.53734 | − | 11.3230i | −0.437773 | − | 0.758245i | 0.559745 | − | 0.828665i | \(-0.310899\pi\) |
−0.997517 | + | 0.0704203i | \(0.977566\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.5845 | + | 20.0649i | −0.768890 | + | 1.33176i | 0.169275 | + | 0.985569i | \(0.445858\pi\) |
−0.938165 | + | 0.346188i | \(0.887476\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.7794 | + | 18.6705i | 0.712323 | + | 1.23378i | 0.963983 | + | 0.265964i | \(0.0856904\pi\) |
−0.251660 | + | 0.967816i | \(0.580976\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.05558 | − | 13.9527i | 0.527739 | − | 0.914070i | −0.471738 | − | 0.881739i | \(-0.656373\pi\) |
0.999477 | − | 0.0323318i | \(-0.0102933\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.1937 | + | 28.0483i | 1.05636 | + | 1.82967i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.216059 | − | 0.374225i | 0.0139757 | − | 0.0242066i | −0.858953 | − | 0.512054i | \(-0.828885\pi\) |
0.872929 | + | 0.487848i | \(0.162218\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.52837 | + | 2.64721i | −0.0984509 | + | 0.170522i | −0.911044 | − | 0.412310i | \(-0.864722\pi\) |
0.812593 | + | 0.582832i | \(0.198055\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.436221 | − | 18.6744i | 0.0278691 | − | 1.19307i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.04741 | − | 13.9385i | −0.512045 | − | 0.886887i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.9066 | 0.751541 | 0.375770 | − | 0.926713i | \(-0.377378\pi\) | ||||
0.375770 | + | 0.926713i | \(0.377378\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.53687 | 0.222361 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.9726 | − | 27.6654i | −0.996346 | − | 1.72572i | −0.572142 | − | 0.820155i | \(-0.693887\pi\) |
−0.424204 | − | 0.905567i | \(-0.639446\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.9296 | + | 19.4695i | −1.23836 | + | 1.20977i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.35495 | + | 5.81094i | −0.206875 | + | 0.358318i | −0.950728 | − | 0.310025i | \(-0.899663\pi\) |
0.743854 | + | 0.668343i | \(0.232996\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.36879 | − | 11.0311i | 0.391232 | − | 0.677634i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.66510 | − | 9.81225i | −0.345408 | − | 0.598263i | 0.640020 | − | 0.768358i | \(-0.278926\pi\) |
−0.985428 | + | 0.170095i | \(0.945593\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.06846 | − | 8.77884i | 0.307887 | − | 0.533276i | −0.670013 | − | 0.742350i | \(-0.733711\pi\) |
0.977900 | + | 0.209073i | \(0.0670447\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.22465 | + | 7.31730i | 0.254756 | + | 0.441250i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.6433 | − | 18.4347i | 0.639492 | − | 1.10763i | −0.346052 | − | 0.938215i | \(-0.612478\pi\) |
0.985544 | − | 0.169418i | \(-0.0541886\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.26945 | + | 10.8590i | 0.374004 | + | 0.647794i | 0.990177 | − | 0.139817i | \(-0.0446513\pi\) |
−0.616174 | + | 0.787610i | \(0.711318\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.9497 | −1.48311 | −0.741554 | − | 0.670893i | \(-0.765911\pi\) | ||||
−0.741554 | + | 0.670893i | \(0.765911\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.43072 | + | 5.30535i | −0.320565 | + | 0.313165i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.0149 | + | 29.4706i | −1.00087 | + | 1.73357i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.42625 | + | 12.8626i | −0.433846 | + | 0.751443i | −0.997201 | − | 0.0747718i | \(-0.976177\pi\) |
0.563355 | + | 0.826215i | \(0.309510\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.7829 | − | 22.1407i | −0.744250 | − | 1.28908i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.77747 | 0.102794 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.45389 | + | 17.4340i | 0.256718 | + | 1.00488i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.6749 | + | 21.9536i | 0.725763 | + | 1.25706i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.9045 | 1.25016 | 0.625079 | − | 0.780561i | \(-0.285067\pi\) | ||||
0.625079 | + | 0.780561i | \(0.285067\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.5672 | −0.996143 | −0.498072 | − | 0.867136i | \(-0.665958\pi\) | ||||
−0.498072 | + | 0.867136i | \(0.665958\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.9764 | −0.676946 | −0.338473 | − | 0.940976i | \(-0.609910\pi\) | ||||
−0.338473 | + | 0.940976i | \(0.609910\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.73327 | 0.0973499 | 0.0486750 | − | 0.998815i | \(-0.484500\pi\) | ||||
0.0486750 | + | 0.998815i | \(0.484500\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.7590 | 0.602386 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 57.4275 | 3.19535 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.12311 | + | 3.67734i | 0.117769 | + | 0.203982i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 30.9179 | + | 8.67263i | 1.70456 | + | 0.478137i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.726254 | 0.0399185 | 0.0199593 | − | 0.999801i | \(-0.493646\pi\) | ||||
0.0199593 | + | 0.999801i | \(0.493646\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.6620 | + | 25.3953i | 0.801070 | + | 1.38749i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.84810 | + | 11.8613i | −0.373040 | + | 0.646124i | −0.990032 | − | 0.140846i | \(-0.955018\pi\) |
0.616992 | + | 0.786970i | \(0.288351\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.44980 | − | 4.24317i | 0.132664 | − | 0.229781i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.6291 | − | 13.5465i | −0.681906 | − | 0.731440i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.21417 | −0.226229 | −0.113114 | − | 0.993582i | \(-0.536083\pi\) | ||||
−0.113114 | + | 0.993582i | \(0.536083\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.8070 | − | 18.7183i | −0.578486 | − | 1.00197i | −0.995653 | − | 0.0931372i | \(-0.970310\pi\) |
0.417167 | − | 0.908830i | \(-0.363023\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.42558 | − | 4.20122i | 0.129100 | − | 0.223609i | −0.794228 | − | 0.607620i | \(-0.792124\pi\) |
0.923328 | + | 0.384012i | \(0.125458\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.17609 | + | 10.6973i | 0.327793 | + | 0.567754i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.90433 | − | 5.03045i | 0.153285 | − | 0.265497i | −0.779148 | − | 0.626839i | \(-0.784348\pi\) |
0.932433 | + | 0.361343i | \(0.117682\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −22.8137 | − | 39.5145i | −1.20072 | − | 2.07971i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.36381 | − | 9.29038i | 0.280754 | − | 0.486281i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.8445 | − | 18.7832i | 0.566078 | − | 0.980476i | −0.430871 | − | 0.902414i | \(-0.641793\pi\) |
0.996949 | − | 0.0780619i | \(-0.0248732\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.12595 | − | 12.2360i | −0.162291 | − | 0.635261i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.3552 | − | 21.3999i | −0.639729 | − | 1.10804i | −0.985492 | − | 0.169721i | \(-0.945713\pi\) |
0.345764 | − | 0.938322i | \(-0.387620\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.40696 | 0.278473 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.9950 | 1.43801 | 0.719005 | − | 0.695005i | \(-0.244598\pi\) | ||||
0.719005 | + | 0.695005i | \(0.244598\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.3113 | + | 17.8598i | 0.526884 | + | 0.912591i | 0.999509 | + | 0.0313269i | \(0.00997329\pi\) |
−0.472625 | + | 0.881264i | \(0.656693\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 27.0810 | + | 7.59637i | 1.38018 | + | 0.387147i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.70035 | − | 15.0694i | 0.441125 | − | 0.764051i | −0.556648 | − | 0.830748i | \(-0.687913\pi\) |
0.997773 | + | 0.0666973i | \(0.0212462\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.17107 | + | 5.49245i | −0.160368 | + | 0.277765i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.37425 | − | 2.38026i | −0.0691458 | − | 0.119764i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.74152 | − | 16.8728i | 0.488913 | − | 0.846822i | −0.511006 | − | 0.859577i | \(-0.670727\pi\) |
0.999919 | + | 0.0127553i | \(0.00406024\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.85264 | + | 6.67297i | 0.192392 | + | 0.333232i | 0.946042 | − | 0.324043i | \(-0.105042\pi\) |
−0.753651 | + | 0.657275i | \(0.771709\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.23116 | − | 2.13242i | 0.0613282 | − | 0.106224i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.9757 | − | 36.3310i | −1.03973 | − | 1.80086i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.7351 | −0.778050 | −0.389025 | − | 0.921227i | \(-0.627188\pi\) | ||||
−0.389025 | + | 0.921227i | \(0.627188\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −24.4058 | − | 6.84596i | −1.20093 | − | 0.336868i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.0538 | + | 24.3420i | −0.689876 | + | 1.19490i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.3452 | + | 30.0428i | −0.847369 | + | 1.46769i | 0.0361784 | + | 0.999345i | \(0.488482\pi\) |
−0.883548 | + | 0.468341i | \(0.844852\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.607053 | − | 1.05145i | −0.0295860 | − | 0.0512444i | 0.850853 | − | 0.525403i | \(-0.176086\pi\) |
−0.880439 | + | 0.474159i | \(0.842752\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −15.1508 | −0.734924 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.1996 | + | 6.78811i | 1.17110 | + | 0.328500i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.68495 | + | 2.91841i | 0.0811610 | + | 0.140575i | 0.903749 | − | 0.428063i | \(-0.140804\pi\) |
−0.822588 | + | 0.568638i | \(0.807471\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.8651 | −1.48328 | −0.741640 | − | 0.670798i | \(-0.765952\pi\) | ||||
−0.741640 | + | 0.670798i | \(0.765952\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.13727 | 0.341422 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 33.0789 | 1.57877 | 0.789385 | − | 0.613898i | \(-0.210400\pi\) | ||||
0.789385 | + | 0.613898i | \(0.210400\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.73364 | 0.129879 | 0.0649397 | − | 0.997889i | \(-0.479315\pi\) | ||||
0.0649397 | + | 0.997889i | \(0.479315\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.22172 | 0.437152 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.7472 | −1.07351 | −0.536753 | − | 0.843740i | \(-0.680349\pi\) | ||||
−0.536753 | + | 0.843740i | \(0.680349\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.71579 | − | 9.90003i | −0.269146 | − | 0.466174i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.6097 | + | 3.81759i | 0.638032 | + | 0.178971i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.36324 | 0.157326 | 0.0786628 | − | 0.996901i | \(-0.474935\pi\) | ||||
0.0786628 | + | 0.996901i | \(0.474935\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.0040 | + | 17.3275i | 0.465934 | + | 0.807021i | 0.999243 | − | 0.0388994i | \(-0.0123852\pi\) |
−0.533309 | + | 0.845920i | \(0.679052\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.29434 | + | 12.6342i | −0.338997 | + | 0.587160i | −0.984244 | − | 0.176814i | \(-0.943421\pi\) |
0.645247 | + | 0.763974i | \(0.276754\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.26334 | − | 12.5805i | 0.336107 | − | 0.582155i | −0.647590 | − | 0.761989i | \(-0.724223\pi\) |
0.983697 | + | 0.179834i | \(0.0575562\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 27.9935 | + | 7.85231i | 1.29262 | + | 0.362586i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −27.0939 | −1.24578 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.52518 | + | 14.7660i | 0.391162 | + | 0.677513i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.66216 | − | 9.80714i | 0.258710 | − | 0.448100i | −0.707186 | − | 0.707027i | \(-0.750036\pi\) |
0.965897 | + | 0.258928i | \(0.0833691\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.5414 | − | 18.2583i | −0.480648 | − | 0.832506i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.99036 | + | 5.17946i | −0.135785 | + | 0.235187i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.93684 | − | 10.2829i | −0.269024 | − | 0.465963i | 0.699586 | − | 0.714548i | \(-0.253368\pi\) |
−0.968610 | + | 0.248585i | \(0.920034\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.9598 | − | 20.7150i | 0.539738 | − | 0.934853i | −0.459180 | − | 0.888343i | \(-0.651857\pi\) |
0.998918 | − | 0.0465101i | \(-0.0148100\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.64621 | + | 16.7077i | −0.434443 | + | 0.752478i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.7917 | + | 3.30764i | 0.528932 | + | 0.148368i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.225984 | − | 0.391416i | −0.0101164 | − | 0.0175222i | 0.860923 | − | 0.508736i | \(-0.169887\pi\) |
−0.871039 | + | 0.491213i | \(0.836554\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.6077 | −0.651326 | −0.325663 | − | 0.945486i | \(-0.605587\pi\) | ||||
−0.325663 | + | 0.945486i | \(0.605587\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.1905 | 0.542471 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.246585 | − | 0.427099i | −0.0109297 | − | 0.0189308i | 0.860509 | − | 0.509436i | \(-0.170146\pi\) |
−0.871439 | + | 0.490505i | \(0.836812\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.63268 | − | 10.3052i | −0.116463 | − | 0.455874i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.0120 | + | 29.4656i | −0.749636 | + | 1.29841i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −24.1754 | + | 41.8730i | −1.06323 | + | 1.84157i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.06874 | + | 10.5114i | 0.265876 | + | 0.460511i | 0.967793 | − | 0.251748i | \(-0.0810054\pi\) |
−0.701917 | + | 0.712259i | \(0.747672\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.34058 | + | 2.32195i | −0.0586193 | + | 0.101532i | −0.893846 | − | 0.448374i | \(-0.852003\pi\) |
0.835227 | + | 0.549906i | \(0.185336\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.39285 | + | 7.60865i | 0.191356 | + | 0.331438i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.1059 | − | 19.2360i | 0.482865 | − | 0.836346i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.87249 | − | 4.97530i | −0.124421 | − | 0.215504i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.52115 | 0.152233 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 24.4694 | − | 13.3754i | 1.05397 | − | 0.576121i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.5072 | + | 23.3951i | −0.580719 | + | 1.00583i | 0.414676 | + | 0.909969i | \(0.363895\pi\) |
−0.995394 | + | 0.0958650i | \(0.969438\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.8647 | + | 29.2105i | −0.722404 | + | 1.25124i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.2496 | + | 26.4132i | 0.652028 | + | 1.12935i | 0.982630 | + | 0.185575i | \(0.0594149\pi\) |
−0.330602 | + | 0.943770i | \(0.607252\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.7112 | 0.924927 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.62379 | − | 0.735985i | −0.111575 | − | 0.0312973i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.39250 | + | 12.8042i | 0.313230 | + | 0.542531i | 0.979060 | − | 0.203573i | \(-0.0652555\pi\) |
−0.665829 | + | 0.746104i | \(0.731922\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.6162 | −0.575902 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.62822 | 0.110766 | 0.0553831 | − | 0.998465i | \(-0.482362\pi\) | ||||
0.0553831 | + | 0.998465i | \(0.482362\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.68559 | −0.112983 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 32.1162 | 1.34638 | 0.673191 | − | 0.739469i | \(-0.264923\pi\) | ||||
0.673191 | + | 0.739469i | \(0.264923\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −41.1815 | −1.72339 | −0.861696 | − | 0.507425i | \(-0.830597\pi\) | ||||
−0.861696 | + | 0.507425i | \(0.830597\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.88300 | −0.0785263 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.0735 | + | 20.9119i | 0.502625 | + | 0.870573i | 0.999995 | + | 0.00303429i | \(0.000965847\pi\) |
−0.497370 | + | 0.867539i | \(0.665701\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.89795 | + | 27.0008i | 0.286175 | + | 1.12018i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.0158 | 0.787553 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.98618 | − | 6.90426i | −0.164527 | − | 0.284969i | 0.771960 | − | 0.635671i | \(-0.219277\pi\) |
−0.936487 | + | 0.350702i | \(0.885943\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.94360 | − | 8.56257i | 0.203698 | − | 0.352815i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.10338 | − | 3.64316i | 0.0863753 | − | 0.149606i | −0.819601 | − | 0.572935i | \(-0.805805\pi\) |
0.905976 | + | 0.423328i | \(0.139138\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −36.0767 | + | 35.2438i | −1.47900 | + | 1.44485i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.3771 | −1.52719 | −0.763594 | − | 0.645696i | \(-0.776567\pi\) | ||||
−0.763594 | + | 0.645696i | \(0.776567\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.81596 | + | 11.8056i | 0.278029 | + | 0.481560i | 0.970895 | − | 0.239506i | \(-0.0769856\pi\) |
−0.692866 | + | 0.721066i | \(0.743652\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.49846 | + | 11.2557i | −0.264200 | + | 0.457607i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.37114 | + | 2.37489i | 0.0556529 | + | 0.0963937i | 0.892510 | − | 0.451028i | \(-0.148943\pi\) |
−0.836857 | + | 0.547422i | \(0.815609\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.1494 | + | 21.0434i | −0.491513 | + | 0.851326i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.798502 | + | 1.38305i | 0.0322512 | + | 0.0558607i | 0.881700 | − | 0.471810i | \(-0.156399\pi\) |
−0.849449 | + | 0.527670i | \(0.823066\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.6551 | + | 21.9192i | −0.509473 | + | 0.882433i | 0.490467 | + | 0.871460i | \(0.336826\pi\) |
−0.999940 | + | 0.0109734i | \(0.996507\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.5808 | + | 23.5226i | −0.545859 | + | 0.945455i | 0.452694 | + | 0.891666i | \(0.350463\pi\) |
−0.998552 | + | 0.0537888i | \(0.982870\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.54019 | − | 6.38920i | 0.262027 | − | 0.255978i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.5532 | + | 26.9388i | 0.622126 | + | 1.07755i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 75.2252 | 2.99942 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.6597 | 1.18073 | 0.590366 | − | 0.807136i | \(-0.298983\pi\) | ||||
0.590366 | + | 0.807136i | \(0.298983\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.84661 | + | 3.19842i | 0.0732804 | + | 0.126925i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.2972 | − | 6.72188i | 0.487233 | − | 0.266331i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.0987 | − | 36.5441i | 0.833350 | − | 1.44340i | −0.0620175 | − | 0.998075i | \(-0.519753\pi\) |
0.895367 | − | 0.445329i | \(-0.146913\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.1099 | + | 17.5109i | −0.398696 | + | 0.690562i | −0.993565 | − | 0.113260i | \(-0.963871\pi\) |
0.594869 | + | 0.803823i | \(0.297204\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.08988 | − | 1.88772i | −0.0428475 | − | 0.0742141i | 0.843806 | − | 0.536648i | \(-0.180310\pi\) |
−0.886654 | + | 0.462434i | \(0.846976\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.0834 | − | 33.0535i | 0.749091 | − | 1.29746i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.0535 | − | 29.5375i | −0.667354 | − | 1.15589i | −0.978641 | − | 0.205575i | \(-0.934094\pi\) |
0.311288 | − | 0.950316i | \(-0.399240\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.439936 | − | 0.761991i | 0.0171897 | − | 0.0297734i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.994211 | − | 1.72202i | −0.0387290 | − | 0.0670805i | 0.846011 | − | 0.533165i | \(-0.178998\pi\) |
−0.884740 | + | 0.466085i | \(0.845664\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.48409 | −0.329993 | −0.164997 | − | 0.986294i | \(-0.552761\pi\) | ||||
−0.164997 | + | 0.986294i | \(0.552761\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 54.6486 | + | 15.3292i | 2.11918 | + | 0.594440i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.19886 | + | 2.07649i | −0.0464201 | + | 0.0804020i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.9222 | + | 32.7742i | −0.730483 | + | 1.26523i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.4056 | + | 38.8077i | 0.863674 | + | 1.49593i | 0.868358 | + | 0.495938i | \(0.165176\pi\) |
−0.00468438 | + | 0.999989i | \(0.501491\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.05367 | −0.309528 | −0.154764 | − | 0.987951i | \(-0.549462\pi\) | ||||
−0.154764 | + | 0.987951i | \(0.549462\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.46774 | + | 5.74521i | 0.0563267 | + | 0.220481i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.8446 | + | 36.1039i | 0.797597 | + | 1.38148i | 0.921177 | + | 0.389144i | \(0.127229\pi\) |
−0.123580 | + | 0.992335i | \(0.539438\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −23.8615 | −0.911701 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.55646 | 0.364072 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.3269 | −0.430895 | −0.215448 | − | 0.976515i | \(-0.569121\pi\) | ||||
−0.215448 | + | 0.976515i | \(0.569121\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 20.9675 | 0.795342 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.4985 | 0.776437 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.6560 | 0.855705 | 0.427853 | − | 0.903849i | \(-0.359270\pi\) | ||||
0.427853 | + | 0.903849i | \(0.359270\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −42.3282 | − | 73.3146i | −1.59644 | − | 2.76511i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.64572 | − | 8.44612i | 0.325156 | − | 0.317649i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 45.2147 | 1.69807 | 0.849037 | − | 0.528333i | \(-0.177183\pi\) | ||||
0.849037 | + | 0.528333i | \(0.177183\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.545958 | + | 0.945626i | 0.0204463 | + | 0.0354140i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.6417 | + | 18.4320i | −0.397977 | + | 0.689317i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.3171 | − | 19.6018i | 0.422057 | − | 0.731024i | −0.574084 | − | 0.818797i | \(-0.694642\pi\) |
0.996141 | + | 0.0877727i | \(0.0279749\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.34986 | + | 32.6841i | 0.310965 | + | 1.21722i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.72797 | −0.212731 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.04956 | − | 1.81789i | −0.0389259 | − | 0.0674217i | 0.845906 | − | 0.533332i | \(-0.179060\pi\) |
−0.884832 | + | 0.465910i | \(0.845727\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.2917 | − | 42.0745i | 0.898461 | − | 1.55618i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.6453 | + | 27.0985i | 0.577872 | + | 1.00090i | 0.995723 | + | 0.0923886i | \(0.0294502\pi\) |
−0.417851 | + | 0.908516i | \(0.637216\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −21.8887 | + | 37.9123i | −0.806280 | + | 1.39652i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.1229 | − | 36.5859i | −0.777017 | − | 1.34583i | −0.933654 | − | 0.358177i | \(-0.883399\pi\) |
0.156637 | − | 0.987656i | \(-0.449935\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.48482 | − | 11.2320i | 0.237905 | − | 0.412064i | −0.722208 | − | 0.691676i | \(-0.756873\pi\) |
0.960113 | + | 0.279612i | \(0.0902060\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21.7770 | − | 37.7189i | 0.797848 | − | 1.38191i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.49726 | − | 2.43960i | 0.0912478 | − | 0.0891412i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.3649 | + | 28.3448i | 0.597164 | + | 1.03432i | 0.993238 | + | 0.116099i | \(0.0370391\pi\) |
−0.396074 | + | 0.918219i | \(0.629628\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.3646 | 0.449995 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.6305 | 1.14963 | 0.574815 | − | 0.818283i | \(-0.305074\pi\) | ||||
0.574815 | + | 0.818283i | \(0.305074\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.1468 | − | 33.1632i | −0.694070 | − | 1.20217i | −0.970493 | − | 0.241129i | \(-0.922482\pi\) |
0.276423 | − | 0.961036i | \(-0.410851\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.27758 | + | 32.4011i | 0.299668 | + | 1.17300i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.59047 | − | 16.6112i | 0.346292 | − | 0.599795i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.0674 | − | 19.1693i | 0.399100 | − | 0.691262i | −0.594515 | − | 0.804085i | \(-0.702656\pi\) |
0.993615 | + | 0.112823i | \(0.0359892\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.8165 | − | 44.7155i | −0.928555 | − | 1.60830i | −0.785742 | − | 0.618555i | \(-0.787719\pi\) |
−0.142813 | − | 0.989750i | \(-0.545615\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.30425 | + | 2.25902i | −0.0468500 | + | 0.0811466i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.5342 | − | 19.9779i | −0.413257 | − | 0.715783i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.22021 | + | 15.9699i | −0.329925 | + | 0.571447i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.3659 | + | 19.6862i | 0.405665 | + | 0.702632i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.3046 | 1.15153 | 0.575767 | − | 0.817614i | \(-0.304704\pi\) | ||||
0.575767 | + | 0.817614i | \(0.304704\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.90466 | + | 1.86069i | −0.0677219 | + | 0.0661585i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.50943 | + | 16.4708i | −0.337690 | + | 0.584896i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.6877 | − | 20.2438i | 0.414001 | − | 0.717071i | −0.581322 | − | 0.813674i | \(-0.697464\pi\) |
0.995323 | + | 0.0966026i | \(0.0307976\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −43.3501 | − | 75.0845i | −1.53361 | − | 2.65630i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.0151 | 0.565161 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.48372 | + | 4.38021i | −0.158030 | + | 0.154382i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.2503 | − | 26.4143i | −0.536171 | − | 0.928676i | −0.999106 | − | 0.0422832i | \(-0.986537\pi\) |
0.462935 | − | 0.886392i | \(-0.346797\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 51.6454 | 1.81352 | 0.906758 | − | 0.421652i | \(-0.138550\pi\) | ||||
0.906758 | + | 0.421652i | \(0.138550\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.53004 | 0.228737 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −54.6745 | −1.91282 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.7575 | 0.933843 | 0.466921 | − | 0.884299i | \(-0.345363\pi\) | ||||
0.466921 | + | 0.884299i | \(0.345363\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.4898 | 1.41139 | 0.705693 | − | 0.708517i | \(-0.250636\pi\) | ||||
0.705693 | + | 0.708517i | \(0.250636\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.9452 | −0.971749 | −0.485875 | − | 0.874029i | \(-0.661499\pi\) | ||||
−0.485875 | + | 0.874029i | \(0.661499\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.0226 | − | 34.6802i | −0.695415 | − | 1.20449i | −0.970040 | − | 0.242943i | \(-0.921887\pi\) |
0.274625 | − | 0.961551i | \(-0.411446\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.16775 | + | 49.9909i | −0.0404601 | + | 1.73208i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.381035 | 0.0131863 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.6312 | − | 28.8061i | −0.574174 | − | 0.994499i | −0.996131 | − | 0.0878827i | \(-0.971990\pi\) |
0.421957 | − | 0.906616i | \(-0.361343\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.8531 | − | 18.7982i | 0.374246 | − | 0.648213i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.9973 | − | 20.7799i | 0.412718 | − | 0.714849i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.18959 | + | 12.4851i | 0.109596 | + | 0.428993i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.34922 | 0.320487 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.38730 | − | 7.59902i | −0.150218 | − | 0.260186i | 0.781089 | − | 0.624419i | \(-0.214664\pi\) |
−0.931308 | + | 0.364234i | \(0.881331\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.677198 | + | 1.17294i | −0.0231327 | + | 0.0400669i | −0.877360 | − | 0.479833i | \(-0.840697\pi\) |
0.854227 | + | 0.519900i | \(0.174031\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.01934 | − | 15.6220i | −0.307736 | − | 0.533014i | 0.670131 | − | 0.742243i | \(-0.266238\pi\) |
−0.977867 | + | 0.209229i | \(0.932905\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.37624 | + | 11.0440i | −0.217050 | + | 0.375941i | −0.953905 | − | 0.300110i | \(-0.902977\pi\) |
0.736855 | + | 0.676051i | \(0.236310\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.0121 | + | 41.5902i | 0.816437 | + | 1.41411i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.05159 | − | 3.55347i | 0.0695956 | − | 0.120543i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.0003 | + | 19.0530i | −0.372729 | + | 0.645586i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 19.5715 | + | 5.48989i | 0.661636 | + | 0.185592i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.79034 | + | 15.2253i | 0.296829 | + | 0.514122i | 0.975409 | − | 0.220404i | \(-0.0707376\pi\) |
−0.678580 | + | 0.734527i | \(0.737404\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.8682 | 0.871523 | 0.435762 | − | 0.900062i | \(-0.356479\pi\) | ||||
0.435762 | + | 0.900062i | \(0.356479\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.5923 | −1.36604 | −0.683020 | − | 0.730400i | \(-0.739334\pi\) | ||||
−0.683020 | + | 0.730400i | \(0.739334\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.46786 | + | 2.54240i | 0.0492858 | + | 0.0853655i | 0.889616 | − | 0.456710i | \(-0.150972\pi\) |
−0.840330 | + | 0.542075i | \(0.817639\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.52564 | + | 0.988961i | 0.118246 | + | 0.0331687i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −48.7850 | + | 84.4981i | −1.63253 | + | 2.82762i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.73289 | + | 4.73350i | −0.0913504 | + | 0.158223i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.66077 | + | 2.87654i | 0.0553899 | + | 0.0959381i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.0491 | + | 29.5299i | −0.567987 | + | 0.983782i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.41720 | − | 4.18671i | −0.0803503 | − | 0.139171i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.1395 | + | 29.6865i | −0.569108 | + | 0.985723i | 0.427547 | + | 0.903993i | \(0.359378\pi\) |
−0.996655 | + | 0.0817300i | \(0.973955\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.98338 | − | 8.63146i | −0.165107 | − | 0.285973i | 0.771586 | − | 0.636124i | \(-0.219464\pi\) |
−0.936693 | + | 0.350151i | \(0.886130\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −41.9616 | −1.38873 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.215930 | − | 0.845222i | −0.00713065 | − | 0.0279117i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.9444 | + | 24.1524i | −0.459983 | + | 0.796714i | −0.998959 | − | 0.0456069i | \(-0.985478\pi\) |
0.538976 | + | 0.842321i | \(0.318811\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.63365 | + | 8.02573i | −0.152519 | + | 0.264170i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.1673 | + | 19.3423i | 0.367177 | + | 0.635970i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.3059 | 0.600597 | 0.300298 | − | 0.953845i | \(-0.402914\pi\) | ||||
0.300298 | + | 0.953845i | \(0.402914\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 49.3783 | − | 26.9911i | 1.61831 | − | 0.884599i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −37.9704 | − | 65.7666i | −1.24176 | − | 2.15080i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.2063 | 1.50950 | 0.754748 | − | 0.656015i | \(-0.227759\pi\) | ||||
0.754748 | + | 0.656015i | \(0.227759\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −36.4501 | −1.18824 | −0.594120 | − | 0.804376i | \(-0.702500\pi\) | ||||
−0.594120 | + | 0.804376i | \(0.702500\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.54762 | 0.0829620 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 47.4404 | 1.54161 | 0.770803 | − | 0.637074i | \(-0.219855\pi\) | ||||
0.770803 | + | 0.637074i | \(0.219855\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.04846 | 0.261264 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.68090 | 0.216415 | 0.108208 | − | 0.994128i | \(-0.465489\pi\) | ||||
0.108208 | + | 0.994128i | \(0.465489\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.0961 | − | 43.4678i | −0.812092 | − | 1.40659i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16.9230 | + | 16.5323i | −0.546471 | + | 0.533855i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.4874 | −0.951206 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.65548 | − | 14.9917i | −0.278630 | − | 0.482601i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.60180 | + | 13.1667i | −0.244457 | + | 0.423413i | −0.961979 | − | 0.273124i | \(-0.911943\pi\) |
0.717522 | + | 0.696536i | \(0.245276\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.363057 | − | 0.628834i | 0.0116511 | − | 0.0201802i | −0.860141 | − | 0.510056i | \(-0.829625\pi\) |
0.871792 | + | 0.489876i | \(0.162958\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.8705 | − | 14.5272i | 0.476726 | − | 0.465720i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 43.0405 | 1.37699 | 0.688494 | − | 0.725242i | \(-0.258272\pi\) | ||||
0.688494 | + | 0.725242i | \(0.258272\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.88350 | + | 11.9226i | 0.219997 | + | 0.381047i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.5191 | + | 37.2722i | −0.686353 | + | 1.18880i | 0.286657 | + | 0.958033i | \(0.407456\pi\) |
−0.973010 | + | 0.230765i | \(0.925877\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.4575 | − | 25.0411i | −0.460653 | − | 0.797875i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.01905 | − | 5.22915i | 0.0960002 | − | 0.166277i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.2758 | + | 19.5302i | 0.358187 | + | 0.620398i | 0.987658 | − | 0.156626i | \(-0.0500618\pi\) |
−0.629471 | + | 0.777024i | \(0.716728\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 25.1873 | − | 43.6257i | 0.798491 | − | 1.38303i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.1670 | − | 24.5380i | 0.448675 | − | 0.777128i | −0.549625 | − | 0.835411i | \(-0.685229\pi\) |
0.998300 | + | 0.0582836i | \(0.0185628\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3024.2.q.l.2305.3 | 22 | ||
3.2 | odd | 2 | 1008.2.q.l.625.3 | 22 | |||
4.3 | odd | 2 | 1512.2.q.d.793.3 | 22 | |||
7.4 | even | 3 | 3024.2.t.k.1873.9 | 22 | |||
9.2 | odd | 6 | 1008.2.t.l.961.4 | 22 | |||
9.7 | even | 3 | 3024.2.t.k.289.9 | 22 | |||
12.11 | even | 2 | 504.2.q.c.121.9 | yes | 22 | ||
21.11 | odd | 6 | 1008.2.t.l.193.4 | 22 | |||
28.11 | odd | 6 | 1512.2.t.c.361.9 | 22 | |||
36.7 | odd | 6 | 1512.2.t.c.289.9 | 22 | |||
36.11 | even | 6 | 504.2.t.c.457.8 | yes | 22 | ||
63.11 | odd | 6 | 1008.2.q.l.529.3 | 22 | |||
63.25 | even | 3 | inner | 3024.2.q.l.2881.3 | 22 | ||
84.11 | even | 6 | 504.2.t.c.193.8 | yes | 22 | ||
252.11 | even | 6 | 504.2.q.c.25.9 | ✓ | 22 | ||
252.151 | odd | 6 | 1512.2.q.d.1369.3 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.c.25.9 | ✓ | 22 | 252.11 | even | 6 | ||
504.2.q.c.121.9 | yes | 22 | 12.11 | even | 2 | ||
504.2.t.c.193.8 | yes | 22 | 84.11 | even | 6 | ||
504.2.t.c.457.8 | yes | 22 | 36.11 | even | 6 | ||
1008.2.q.l.529.3 | 22 | 63.11 | odd | 6 | |||
1008.2.q.l.625.3 | 22 | 3.2 | odd | 2 | |||
1008.2.t.l.193.4 | 22 | 21.11 | odd | 6 | |||
1008.2.t.l.961.4 | 22 | 9.2 | odd | 6 | |||
1512.2.q.d.793.3 | 22 | 4.3 | odd | 2 | |||
1512.2.q.d.1369.3 | 22 | 252.151 | odd | 6 | |||
1512.2.t.c.289.9 | 22 | 36.7 | odd | 6 | |||
1512.2.t.c.361.9 | 22 | 28.11 | odd | 6 | |||
3024.2.q.l.2305.3 | 22 | 1.1 | even | 1 | trivial | ||
3024.2.q.l.2881.3 | 22 | 63.25 | even | 3 | inner | ||
3024.2.t.k.289.9 | 22 | 9.7 | even | 3 | |||
3024.2.t.k.1873.9 | 22 | 7.4 | even | 3 |