Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(3025,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.3025");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.c (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: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3025.21 | ||
Character | \(\chi\) | \(=\) | 6048.3025 |
Dual form | 6048.2.c.f.3025.4 |
$q$-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 \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.04340i | 1.36105i | 0.732725 | + | 0.680525i | \(0.238248\pi\) | ||||
−0.732725 | + | 0.680525i | \(0.761752\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 0.128573i | − 0.0387662i | −0.999812 | − | 0.0193831i | \(-0.993830\pi\) | ||||
0.999812 | − | 0.0193831i | \(-0.00617022\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 6.30135i | − 1.74768i | −0.486214 | − | 0.873840i | \(-0.661622\pi\) | ||||
0.486214 | − | 0.873840i | \(-0.338378\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.32168 | 1.29070 | 0.645348 | − | 0.763889i | \(-0.276712\pi\) | ||||
0.645348 | + | 0.763889i | \(0.276712\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 6.68215i | − 1.53299i | −0.642250 | − | 0.766495i | \(-0.721999\pi\) | ||||
0.642250 | − | 0.766495i | \(-0.278001\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.18212 | −1.08055 | −0.540273 | − | 0.841490i | \(-0.681679\pi\) | ||||
−0.540273 | + | 0.841490i | \(0.681679\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.26229 | −0.852459 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.96821i | 1.85105i | 0.378686 | + | 0.925525i | \(0.376376\pi\) | ||||
−0.378686 | + | 0.925525i | \(0.623624\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.27122 | −0.587528 | −0.293764 | − | 0.955878i | \(-0.594908\pi\) | ||||
−0.293764 | + | 0.955878i | \(0.594908\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 3.04340i | − 0.514429i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.796970i | 0.131021i | 0.997852 | + | 0.0655106i | \(0.0208676\pi\) | ||||
−0.997852 | + | 0.0655106i | \(0.979132\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.96782 | −0.463496 | −0.231748 | − | 0.972776i | \(-0.574444\pi\) | ||||
−0.231748 | + | 0.972776i | \(0.574444\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.99100i | 1.06612i | 0.846078 | + | 0.533059i | \(0.178958\pi\) | ||||
−0.846078 | + | 0.533059i | \(0.821042\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.76595 | −0.695186 | −0.347593 | − | 0.937646i | \(-0.613001\pi\) | ||||
−0.347593 | + | 0.937646i | \(0.613001\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 1.14264i | − 0.156954i | −0.996916 | − | 0.0784772i | \(-0.974994\pi\) | ||||
0.996916 | − | 0.0784772i | \(-0.0250058\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.391299 | 0.0527627 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.0999i | 1.44508i | 0.691329 | + | 0.722540i | \(0.257025\pi\) | ||||
−0.691329 | + | 0.722540i | \(0.742975\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.6662i | 1.87782i | 0.344165 | + | 0.938909i | \(0.388162\pi\) | ||||
−0.344165 | + | 0.938909i | \(0.611838\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 19.1775 | 2.37868 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 1.05725i | − 0.129163i | −0.997912 | − | 0.0645816i | \(-0.979429\pi\) | ||||
0.997912 | − | 0.0645816i | \(-0.0205713\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.10582 | −0.131237 | −0.0656185 | − | 0.997845i | \(-0.520902\pi\) | ||||
−0.0656185 | + | 0.997845i | \(0.520902\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.1019 | −1.41642 | −0.708212 | − | 0.706000i | \(-0.750498\pi\) | ||||
−0.708212 | + | 0.706000i | \(0.750498\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.128573i | 0.0146522i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.62426 | −0.295253 | −0.147626 | − | 0.989043i | \(-0.547163\pi\) | ||||
−0.147626 | + | 0.989043i | \(0.547163\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 6.46403i | − 0.709520i | −0.934957 | − | 0.354760i | \(-0.884563\pi\) | ||||
0.934957 | − | 0.354760i | \(-0.115437\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.1960i | 1.75670i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.23283 | −0.236680 | −0.118340 | − | 0.992973i | \(-0.537757\pi\) | ||||
−0.118340 | + | 0.992973i | \(0.537757\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.30135i | 0.660561i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 20.3365 | 2.08648 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.88097 | −0.800192 | −0.400096 | − | 0.916473i | \(-0.631023\pi\) | ||||
−0.400096 | + | 0.916473i | \(0.631023\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.9693i | 1.68851i | 0.535945 | + | 0.844253i | \(0.319955\pi\) | ||||
−0.535945 | + | 0.844253i | \(0.680045\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.7049 | 1.05479 | 0.527393 | − | 0.849621i | \(-0.323170\pi\) | ||||
0.527393 | + | 0.849621i | \(0.323170\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1.31462i | − 0.127089i | −0.997979 | − | 0.0635445i | \(-0.979760\pi\) | ||||
0.997979 | − | 0.0635445i | \(-0.0202405\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.2677i | 0.983465i | 0.870746 | + | 0.491732i | \(0.163636\pi\) | ||||
−0.870746 | + | 0.491732i | \(0.836364\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.1796 | −1.23983 | −0.619916 | − | 0.784668i | \(-0.712834\pi\) | ||||
−0.619916 | + | 0.784668i | \(0.712834\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 15.7713i | − 1.47068i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.32168 | −0.487837 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9835 | 0.998497 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.24514i | 0.200811i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.840201 | 0.0745558 | 0.0372779 | − | 0.999305i | \(-0.488131\pi\) | ||||
0.0372779 | + | 0.999305i | \(0.488131\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 7.39979i | − 0.646523i | −0.946310 | − | 0.323261i | \(-0.895221\pi\) | ||||
0.946310 | − | 0.323261i | \(-0.104779\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.68215i | 0.579416i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.61682 | 0.479877 | 0.239939 | − | 0.970788i | \(-0.422873\pi\) | ||||
0.239939 | + | 0.970788i | \(0.422873\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 5.19553i | − 0.440679i | −0.975423 | − | 0.220339i | \(-0.929284\pi\) | ||||
0.975423 | − | 0.220339i | \(-0.0707165\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.810183 | −0.0677509 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −30.3373 | −2.51937 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.6207i | 0.952009i | 0.879443 | + | 0.476004i | \(0.157915\pi\) | ||||
−0.879443 | + | 0.476004i | \(0.842085\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.5154 | −1.75090 | −0.875448 | − | 0.483313i | \(-0.839433\pi\) | ||||
−0.875448 | + | 0.483313i | \(0.839433\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 9.95563i | − 0.799655i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 18.3001i | − 1.46050i | −0.683178 | − | 0.730252i | \(-0.739403\pi\) | ||||
0.683178 | − | 0.730252i | \(-0.260597\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.18212 | 0.408408 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.8550i | 1.47684i | 0.674344 | + | 0.738418i | \(0.264427\pi\) | ||||
−0.674344 | + | 0.738418i | \(0.735573\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.8283 | −1.61174 | −0.805872 | − | 0.592089i | \(-0.798303\pi\) | ||||
−0.805872 | + | 0.592089i | \(0.798303\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −26.7070 | −2.05438 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.49174i | 0.417529i | 0.977966 | + | 0.208765i | \(0.0669443\pi\) | ||||
−0.977966 | + | 0.208765i | \(0.933056\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.26229 | 0.322199 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 7.62941i | − 0.570249i | −0.958491 | − | 0.285124i | \(-0.907965\pi\) | ||||
0.958491 | − | 0.285124i | \(-0.0920349\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 10.0176i | − 0.744600i | −0.928113 | − | 0.372300i | \(-0.878569\pi\) | ||||
0.928113 | − | 0.372300i | \(-0.121431\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.42550 | −0.178326 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 0.684223i | − 0.0500354i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.25601 | 0.452669 | 0.226335 | − | 0.974050i | \(-0.427326\pi\) | ||||
0.226335 | + | 0.974050i | \(0.427326\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.46446 | 0.177396 | 0.0886980 | − | 0.996059i | \(-0.471729\pi\) | ||||
0.0886980 | + | 0.996059i | \(0.471729\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 23.8105i | − 1.69643i | −0.529654 | − | 0.848214i | \(-0.677678\pi\) | ||||
0.529654 | − | 0.848214i | \(-0.322322\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.1296 | −1.71050 | −0.855252 | − | 0.518212i | \(-0.826598\pi\) | ||||
−0.855252 | + | 0.518212i | \(0.826598\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 9.96821i | − 0.699631i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 9.03227i | − 0.630841i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.859144 | −0.0594282 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.9668i | 1.03036i | 0.857083 | + | 0.515179i | \(0.172274\pi\) | ||||
−0.857083 | + | 0.515179i | \(0.827726\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −21.2764 | −1.45104 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.27122 | 0.222065 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 33.5337i | − 2.25572i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.6108 | −0.777518 | −0.388759 | − | 0.921340i | \(-0.627096\pi\) | ||||
−0.388759 | + | 0.921340i | \(0.627096\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 0.939445i | − 0.0623531i | −0.999514 | − | 0.0311766i | \(-0.990075\pi\) | ||||
0.999514 | − | 0.0311766i | \(-0.00992542\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 0.0137124i | 0 0.000906143i | −1.00000 | 0.000453071i | \(-0.999856\pi\) | |||||
1.00000 | 0.000453071i | \(-0.000144217\pi\) | ||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.2195 | −1.19360 | −0.596800 | − | 0.802390i | \(-0.703561\pi\) | ||||
−0.596800 | + | 0.802390i | \(0.703561\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 14.5047i | − 0.946183i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.37153 | −0.0887169 | −0.0443585 | − | 0.999016i | \(-0.514124\pi\) | ||||
−0.0443585 | + | 0.999016i | \(0.514124\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.5054 | −0.676711 | −0.338355 | − | 0.941018i | \(-0.609871\pi\) | ||||
−0.338355 | + | 0.941018i | \(0.609871\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.04340i | 0.194436i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −42.1066 | −2.67918 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 20.0556i | − 1.26590i | −0.774192 | − | 0.632950i | \(-0.781844\pi\) | ||||
0.774192 | − | 0.632950i | \(-0.218156\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.666280i | 0.0418887i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.6631 | 1.53844 | 0.769220 | − | 0.638984i | \(-0.220645\pi\) | ||||
0.769220 | + | 0.638984i | \(0.220645\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 0.796970i | − 0.0495213i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.0542 | −0.866616 | −0.433308 | − | 0.901246i | \(-0.642654\pi\) | ||||
−0.433308 | + | 0.901246i | \(0.642654\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.47753 | 0.213623 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.1276i | 0.800404i | 0.916427 | + | 0.400202i | \(0.131060\pi\) | ||||
−0.916427 | + | 0.400202i | \(0.868940\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.4626 | 0.939285 | 0.469642 | − | 0.882857i | \(-0.344383\pi\) | ||||
0.469642 | + | 0.882857i | \(0.344383\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.548015i | 0.0330466i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 11.1880i | − 0.672223i | −0.941822 | − | 0.336112i | \(-0.890888\pi\) | ||||
0.941822 | − | 0.336112i | \(-0.109112\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.179766 | −0.0107240 | −0.00536198 | − | 0.999986i | \(-0.501707\pi\) | ||||
−0.00536198 | + | 0.999986i | \(0.501707\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 29.0480i | 1.72673i | 0.504583 | + | 0.863363i | \(0.331646\pi\) | ||||
−0.504583 | + | 0.863363i | \(0.668354\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.96782 | 0.175185 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.3202 | 0.665897 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.42498i | 0.258510i | 0.991611 | + | 0.129255i | \(0.0412586\pi\) | ||||
−0.991611 | + | 0.129255i | \(0.958741\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −33.7813 | −1.96683 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 32.6543i | 1.88845i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 6.99100i | − 0.402955i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −44.6352 | −2.55581 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 8.36831i | − 0.477605i | −0.971068 | − | 0.238802i | \(-0.923245\pi\) | ||||
0.971068 | − | 0.238802i | \(-0.0767548\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.1701 | 1.59738 | 0.798690 | − | 0.601743i | \(-0.205527\pi\) | ||||
0.798690 | + | 0.601743i | \(0.205527\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.0081 | 0.791784 | 0.395892 | − | 0.918297i | \(-0.370435\pi\) | ||||
0.395892 | + | 0.918297i | \(0.370435\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.4390i | 0.810974i | 0.914101 | + | 0.405487i | \(0.132898\pi\) | ||||
−0.914101 | + | 0.405487i | \(0.867102\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.28164 | 0.0717582 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 35.5603i | − 1.97863i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 26.8582i | 1.48982i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.76595 | 0.262756 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.5738i | 1.79042i | 0.445648 | + | 0.895208i | \(0.352973\pi\) | ||||
−0.445648 | + | 0.895208i | \(0.647027\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.21762 | 0.175798 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.17181 | −0.118306 | −0.0591529 | − | 0.998249i | \(-0.518840\pi\) | ||||
−0.0591529 | + | 0.998249i | \(0.518840\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.420590i | 0.0227762i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.79477i | 0.150031i | 0.997182 | + | 0.0750157i | \(0.0239007\pi\) | ||||
−0.997182 | + | 0.0750157i | \(0.976099\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 3.19085i | − 0.170802i | −0.996347 | − | 0.0854011i | \(-0.972783\pi\) | ||||
0.996347 | − | 0.0854011i | \(-0.0272172\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.10245 | 0.431250 | 0.215625 | − | 0.976476i | \(-0.430821\pi\) | ||||
0.215625 | + | 0.976476i | \(0.430821\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 3.36546i | − 0.178620i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.2635 | 0.911134 | 0.455567 | − | 0.890202i | \(-0.349437\pi\) | ||||
0.455567 | + | 0.890202i | \(0.349437\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −25.6511 | −1.35006 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 36.8310i | − 1.92782i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.5508 | 0.707348 | 0.353674 | − | 0.935369i | \(-0.384932\pi\) | ||||
0.353674 | + | 0.935369i | \(0.384932\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.14264i | 0.0593232i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 16.3399i | − 0.846048i | −0.906118 | − | 0.423024i | \(-0.860969\pi\) | ||||
0.906118 | − | 0.423024i | \(-0.139031\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 62.8132 | 3.23504 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 2.37754i | − 0.122126i | −0.998134 | − | 0.0610630i | \(-0.980551\pi\) | ||||
0.998134 | − | 0.0610630i | \(-0.0194491\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.6210 | 0.900389 | 0.450194 | − | 0.892931i | \(-0.351355\pi\) | ||||
0.450194 | + | 0.892931i | \(0.351355\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.391299 | −0.0199424 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 12.6831i | − 0.643058i | −0.946900 | − | 0.321529i | \(-0.895803\pi\) | ||||
0.946900 | − | 0.321529i | \(-0.104197\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −27.5776 | −1.39466 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 7.98668i | − 0.401854i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 34.3856i | 1.72576i | 0.505405 | + | 0.862882i | \(0.331343\pi\) | ||||
−0.505405 | + | 0.862882i | \(0.668657\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.75947 | −0.187739 | −0.0938696 | − | 0.995585i | \(-0.529924\pi\) | ||||
−0.0938696 | + | 0.995585i | \(0.529924\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.6131i | 1.02681i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.102469 | 0.00507919 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.0996 | 0.647731 | 0.323866 | − | 0.946103i | \(-0.395017\pi\) | ||||
0.323866 | + | 0.946103i | \(0.395017\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 11.0999i | − 0.546189i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19.6726 | 0.965692 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 24.4344i | − 1.19370i | −0.802353 | − | 0.596849i | \(-0.796419\pi\) | ||||
0.802353 | − | 0.596849i | \(-0.203581\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 26.3907i | − 1.28620i | −0.765781 | − | 0.643101i | \(-0.777647\pi\) | ||||
0.765781 | − | 0.643101i | \(-0.222353\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −22.6825 | −1.10027 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 14.6662i | − 0.709749i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −32.7161 | −1.57588 | −0.787940 | − | 0.615751i | \(-0.788853\pi\) | ||||
−0.787940 | + | 0.615751i | \(0.788853\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.3235 | 0.592228 | 0.296114 | − | 0.955153i | \(-0.404309\pi\) | ||||
0.296114 | + | 0.955153i | \(0.404309\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 34.6277i | 1.65647i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.67878 | −0.223306 | −0.111653 | − | 0.993747i | \(-0.535615\pi\) | ||||
−0.111653 | + | 0.993747i | \(0.535615\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 35.6471i | 1.69364i | 0.531877 | + | 0.846821i | \(0.321487\pi\) | ||||
−0.531877 | + | 0.846821i | \(0.678513\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 6.79540i | − 0.322133i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.02786 | 0.284472 | 0.142236 | − | 0.989833i | \(-0.454571\pi\) | ||||
0.142236 | + | 0.989833i | \(0.454571\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.381581i | 0.0179680i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −19.1775 | −0.899057 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.88761 | 0.228633 | 0.114316 | − | 0.993444i | \(-0.463532\pi\) | ||||
0.114316 | + | 0.993444i | \(0.463532\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.16306i | 0.426766i | 0.976969 | + | 0.213383i | \(0.0684483\pi\) | ||||
−0.976969 | + | 0.213383i | \(0.931552\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −32.8412 | −1.52626 | −0.763130 | − | 0.646245i | \(-0.776338\pi\) | ||||
−0.763130 | + | 0.646245i | \(0.776338\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.40559i | 0.296415i | 0.988956 | + | 0.148208i | \(0.0473504\pi\) | ||||
−0.988956 | + | 0.148208i | \(0.952650\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.05725i | 0.0488191i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.898854 | 0.0413293 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 28.4813i | 1.30681i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −27.3218 | −1.24837 | −0.624184 | − | 0.781278i | \(-0.714568\pi\) | ||||
−0.624184 | + | 0.781278i | \(0.714568\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.02199 | 0.228983 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 23.9850i | − 1.08910i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.05264 | −0.410214 | −0.205107 | − | 0.978740i | \(-0.565754\pi\) | ||||
−0.205107 | + | 0.978740i | \(0.565754\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.1183i | 0.456632i | 0.973587 | + | 0.228316i | \(0.0733219\pi\) | ||||
−0.973587 | + | 0.228316i | \(0.926678\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 53.0476i | 2.38914i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.10582 | 0.0496029 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.9396i | 0.892621i | 0.894878 | + | 0.446310i | \(0.147262\pi\) | ||||
−0.894878 | + | 0.446310i | \(0.852738\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −24.3936 | −1.08766 | −0.543828 | − | 0.839197i | \(-0.683026\pi\) | ||||
−0.543828 | + | 0.839197i | \(0.683026\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −51.6443 | −2.29814 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 7.20394i | − 0.319309i | −0.987173 | − | 0.159655i | \(-0.948962\pi\) | ||||
0.987173 | − | 0.159655i | \(-0.0510381\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.1019 | 0.535358 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 32.5793i | 1.43562i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.612773i | 0.0269497i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.8648 | 0.651240 | 0.325620 | − | 0.945501i | \(-0.394427\pi\) | ||||
0.325620 | + | 0.945501i | \(0.394427\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 32.1286i | − 1.40489i | −0.711740 | − | 0.702443i | \(-0.752093\pi\) | ||||
0.711740 | − | 0.702443i | \(-0.247907\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17.4084 | −0.758320 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.85438 | 0.167582 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.7013i | 0.810042i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.00091 | 0.172975 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 0.128573i | − 0.00553803i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 30.6123i | − 1.31612i | −0.752964 | − | 0.658062i | \(-0.771376\pi\) | ||||
0.752964 | − | 0.658062i | \(-0.228624\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −31.2487 | −1.33855 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 7.64518i | − 0.326884i | −0.986553 | − | 0.163442i | \(-0.947740\pi\) | ||||
0.986553 | − | 0.163442i | \(-0.0522597\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 66.6091 | 2.83764 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.62426 | 0.111595 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 24.9682i | − 1.05794i | −0.848641 | − | 0.528969i | \(-0.822579\pi\) | ||||
0.848641 | − | 0.528969i | \(-0.177421\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 44.0527 | 1.86323 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 33.1836i | 1.39852i | 0.714865 | + | 0.699262i | \(0.246488\pi\) | ||||
−0.714865 | + | 0.699262i | \(0.753512\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 40.1108i | − 1.68748i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.0679 | −0.715523 | −0.357761 | − | 0.933813i | \(-0.616460\pi\) | ||||
−0.357761 | + | 0.933813i | \(0.616460\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 5.13058i | − 0.214708i | −0.994221 | − | 0.107354i | \(-0.965762\pi\) | ||||
0.994221 | − | 0.107354i | \(-0.0342378\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 22.0877 | 0.921121 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −47.5819 | −1.98086 | −0.990429 | − | 0.138021i | \(-0.955926\pi\) | ||||
−0.990429 | + | 0.138021i | \(0.955926\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.46403i | 0.268173i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.146913 | −0.00608452 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.6803i | 0.977390i | 0.872455 | + | 0.488695i | \(0.162527\pi\) | ||||
−0.872455 | + | 0.488695i | \(0.837473\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.8588i | 0.900675i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.8919 | −0.734734 | −0.367367 | − | 0.930076i | \(-0.619741\pi\) | ||||
−0.367367 | + | 0.930076i | \(0.619741\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 16.1960i | − 0.663971i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.0167 | 1.30817 | 0.654083 | − | 0.756423i | \(-0.273055\pi\) | ||||
0.654083 | + | 0.756423i | \(0.273055\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.7187 | 0.967507 | 0.483754 | − | 0.875204i | \(-0.339273\pi\) | ||||
0.483754 | + | 0.875204i | \(0.339273\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 33.4271i | 1.35901i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.4444 | 0.586281 | 0.293141 | − | 0.956069i | \(-0.405300\pi\) | ||||
0.293141 | + | 0.956069i | \(0.405300\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30.0319i | 1.21496i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.2817i | 0.657610i | 0.944398 | + | 0.328805i | \(0.106646\pi\) | ||||
−0.944398 | + | 0.328805i | \(0.893354\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.7753 | −1.15845 | −0.579225 | − | 0.815167i | \(-0.696645\pi\) | ||||
−0.579225 | + | 0.815167i | \(0.696645\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 36.0871i | − 1.45046i | −0.688506 | − | 0.725231i | \(-0.741733\pi\) | ||||
0.688506 | − | 0.725231i | \(-0.258267\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.23283 | 0.0894564 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.1443 | −1.12577 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.24122i | 0.169108i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.0509 | −0.718595 | −0.359297 | − | 0.933223i | \(-0.616984\pi\) | ||||
−0.359297 | + | 0.933223i | \(0.616984\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.55707i | 0.101474i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 6.30135i | − 0.249668i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.0253 | −0.474971 | −0.237486 | − | 0.971391i | \(-0.576323\pi\) | ||||
−0.237486 | + | 0.971391i | \(0.576323\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.54316i | 0.376345i | 0.982136 | + | 0.188173i | \(0.0602565\pi\) | ||||
−0.982136 | + | 0.188173i | \(0.939744\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32.2201 | 1.26670 | 0.633351 | − | 0.773865i | \(-0.281679\pi\) | ||||
0.633351 | + | 0.773865i | \(0.281679\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.42714 | 0.0560202 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.5245i | 0.568388i | 0.958767 | + | 0.284194i | \(0.0917259\pi\) | ||||
−0.958767 | + | 0.284194i | \(0.908274\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.5205 | 0.879950 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.5726i | 0.411849i | 0.978568 | + | 0.205924i | \(0.0660201\pi\) | ||||
−0.978568 | + | 0.205924i | \(0.933980\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.0965i | 1.05393i | 0.849887 | + | 0.526965i | \(0.176670\pi\) | ||||
−0.849887 | + | 0.526965i | \(0.823330\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −20.3365 | −0.788614 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 51.6565i | − 2.00015i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.88568 | 0.0727959 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 38.2417 | 1.47411 | 0.737055 | − | 0.675833i | \(-0.236216\pi\) | ||||
0.737055 | + | 0.675833i | \(0.236216\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 14.2289i | − 0.546860i | −0.961892 | − | 0.273430i | \(-0.911842\pi\) | ||||
0.961892 | − | 0.273430i | \(-0.0881582\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.88097 | 0.302444 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 39.0552i | 1.49441i | 0.664596 | + | 0.747203i | \(0.268603\pi\) | ||||
−0.664596 | + | 0.747203i | \(0.731397\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.0942i | 0.653137i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.20020 | −0.274306 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.1602i | 0.766929i | 0.923556 | + | 0.383464i | \(0.125269\pi\) | ||||
−0.923556 | + | 0.383464i | \(0.874731\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.8121 | 0.599786 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.7938 | −0.598232 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.4760i | 0.848908i | 0.905449 | + | 0.424454i | \(0.139534\pi\) | ||||
−0.905449 | + | 0.424454i | \(0.860466\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.32548 | 0.200854 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 16.9693i | − 0.638195i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.2609i | 0.760915i | 0.924798 | + | 0.380458i | \(0.124233\pi\) | ||||
−0.924798 | + | 0.380458i | \(0.875767\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.9518 | 0.634852 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 2.46571i | − 0.0922124i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.2440 | 0.792269 | 0.396134 | − | 0.918193i | \(-0.370351\pi\) | ||||
0.396134 | + | 0.918193i | \(0.370351\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.7049 | −0.398672 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 42.4874i | − 1.57794i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.9048 | 1.22037 | 0.610185 | − | 0.792259i | \(-0.291095\pi\) | ||||
0.610185 | + | 0.792259i | \(0.291095\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 37.2039i | 1.37603i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 32.0598i | − 1.18415i | −0.805881 | − | 0.592077i | \(-0.798308\pi\) | ||||
0.805881 | − | 0.592077i | \(-0.201692\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.135933 | −0.00500716 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 46.3826i | 1.70621i | 0.521738 | + | 0.853106i | \(0.325284\pi\) | ||||
−0.521738 | + | 0.853106i | \(0.674716\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.1782 | −0.446777 | −0.223388 | − | 0.974730i | \(-0.571712\pi\) | ||||
−0.223388 | + | 0.974730i | \(0.571712\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −35.3666 | −1.29573 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.31462i | 0.0480351i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.4371 | −0.891723 | −0.445862 | − | 0.895102i | \(-0.647103\pi\) | ||||
−0.445862 | + | 0.895102i | \(0.647103\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 65.4799i | − 2.38306i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 7.15224i | − 0.259953i | −0.991517 | − | 0.129976i | \(-0.958510\pi\) | ||||
0.991517 | − | 0.129976i | \(-0.0414902\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.7809 | 0.535806 | 0.267903 | − | 0.963446i | \(-0.413669\pi\) | ||||
0.267903 | + | 0.963446i | \(0.413669\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 10.2677i | − 0.371715i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 69.9441 | 2.52554 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.90576 | −0.0687235 | −0.0343618 | − | 0.999409i | \(-0.510940\pi\) | ||||
−0.0343618 | + | 0.999409i | \(0.510940\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 6.63435i | − 0.238621i | −0.992857 | − | 0.119310i | \(-0.961932\pi\) | ||||
0.992857 | − | 0.119310i | \(-0.0380684\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.9429 | 0.500843 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19.8314i | 0.710534i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.142179i | 0.00508756i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 55.6944 | 1.98782 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 2.91096i | − 0.103765i | −0.998653 | − | 0.0518823i | \(-0.983478\pi\) | ||||
0.998653 | − | 0.0518823i | \(-0.0165221\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.1796 | 0.468613 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 92.4170 | 3.28182 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 6.96910i | − 0.246858i | −0.992353 | − | 0.123429i | \(-0.960611\pi\) | ||||
0.992353 | − | 0.123429i | \(-0.0393891\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25.3629 | −0.897274 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.55598i | 0.0549094i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.7713i | 0.555864i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21.3012 | −0.748909 | −0.374454 | − | 0.927245i | \(-0.622170\pi\) | ||||
−0.374454 | + | 0.927245i | \(0.622170\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.1357i | 0.636832i | 0.947951 | + | 0.318416i | \(0.103151\pi\) | ||||
−0.947951 | + | 0.318416i | \(0.896849\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −57.3832 | −2.01005 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 46.7149 | 1.63435 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 24.3030i | − 0.848180i | −0.905620 | − | 0.424090i | \(-0.860594\pi\) | ||||
0.905620 | − | 0.424090i | \(-0.139406\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.29306 | −0.0450734 | −0.0225367 | − | 0.999746i | \(-0.507174\pi\) | ||||
−0.0225367 | + | 0.999746i | \(0.507174\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.6268i | 0.821585i | 0.911729 | + | 0.410792i | \(0.134748\pi\) | ||||
−0.911729 | + | 0.410792i | \(0.865252\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 5.66492i | − 0.196751i | −0.995149 | − | 0.0983754i | \(-0.968635\pi\) | ||||
0.995149 | − | 0.0983754i | \(-0.0313646\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.32168 | 0.184385 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 63.3890i | − 2.19367i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.1554 | 0.730366 | 0.365183 | − | 0.930936i | \(-0.381006\pi\) | ||||
0.365183 | + | 0.930936i | \(0.381006\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −70.3652 | −2.42639 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 81.2801i | − 2.79612i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.9835 | −0.377396 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 4.13000i | − 0.141574i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 4.41255i | − 0.151083i | −0.997143 | − | 0.0755413i | \(-0.975932\pi\) | ||||
0.997143 | − | 0.0755413i | \(-0.0240685\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.9783 | 0.716606 | 0.358303 | − | 0.933605i | \(-0.383356\pi\) | ||||
0.358303 | + | 0.933605i | \(0.383356\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 15.6318i | − 0.533351i | −0.963786 | − | 0.266676i | \(-0.914075\pi\) | ||||
0.963786 | − | 0.266676i | \(-0.0859253\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16.1880 | −0.551047 | −0.275523 | − | 0.961294i | \(-0.588851\pi\) | ||||
−0.275523 | + | 0.961294i | \(0.588851\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.7136 | −0.568278 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.337409i | 0.0114458i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.66208 | −0.225736 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 2.24514i | − 0.0758995i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 38.1001i | − 1.28655i | −0.765636 | − | 0.643274i | \(-0.777576\pi\) | ||||
0.765636 | − | 0.643274i | \(-0.222424\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −46.4289 | −1.56423 | −0.782114 | − | 0.623135i | \(-0.785859\pi\) | ||||
−0.782114 | + | 0.623135i | \(0.785859\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 17.8873i | − 0.601956i | −0.953631 | − | 0.300978i | \(-0.902687\pi\) | ||||
0.953631 | − | 0.300978i | \(-0.0973131\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −35.5228 | −1.19274 | −0.596369 | − | 0.802711i | \(-0.703390\pi\) | ||||
−0.596369 | + | 0.802711i | \(0.703390\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.840201 | −0.0281795 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 31.8468i | 1.06571i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23.2194 | 0.776137 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 32.6082i | − 1.08754i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 6.08079i | − 0.202580i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 30.4875 | 1.01344 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 41.8996i | − 1.39125i | −0.718404 | − | 0.695627i | \(-0.755127\pi\) | ||||
0.718404 | − | 0.695627i | \(-0.244873\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.35427 | −0.177395 | −0.0886974 | − | 0.996059i | \(-0.528270\pi\) | ||||
−0.0886974 | + | 0.996059i | \(0.528270\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.831099 | −0.0275054 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.39979i | 0.244363i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 54.8843 | 1.81047 | 0.905234 | − | 0.424914i | \(-0.139696\pi\) | ||||
0.905234 | + | 0.424914i | \(0.139696\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.96817i | 0.229360i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 3.39692i | − 0.111690i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.4091 | −0.341512 | −0.170756 | − | 0.985313i | \(-0.554621\pi\) | ||||
−0.170756 | + | 0.985313i | \(0.554621\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 6.68215i | − 0.218999i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.08237 | 0.0681007 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 49.8177 | 1.62747 | 0.813737 | − | 0.581233i | \(-0.197430\pi\) | ||||
0.813737 | + | 0.581233i | \(0.197430\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 5.61503i | − 0.183045i | −0.995803 | − | 0.0915224i | \(-0.970827\pi\) | ||||
0.995803 | − | 0.0915224i | \(-0.0291733\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.3796 | 0.500829 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 22.3495i | − 0.726262i | −0.931738 | − | 0.363131i | \(-0.881708\pi\) | ||||
0.931738 | − | 0.363131i | \(-0.118292\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 76.2585i | 2.47545i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.9449 | −0.646080 | −0.323040 | − | 0.946385i | \(-0.604705\pi\) | ||||
−0.323040 | + | 0.946385i | \(0.604705\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.0396i | 0.616106i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.61682 | −0.181376 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.2991 | −0.654811 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.50035i | 0.241445i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.6951 | −1.05140 | −0.525702 | − | 0.850669i | \(-0.676197\pi\) | ||||
−0.525702 | + | 0.850669i | \(0.676197\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.7391i | 1.08274i | 0.840785 | + | 0.541369i | \(0.182094\pi\) | ||||
−0.840785 | + | 0.541369i | \(0.817906\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.19553i | 0.166561i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −45.8374 | −1.46647 | −0.733235 | − | 0.679976i | \(-0.761990\pi\) | ||||
−0.733235 | + | 0.679976i | \(0.761990\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.287081i | 0.00917516i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14.0557 | −0.448307 | −0.224154 | − | 0.974554i | \(-0.571962\pi\) | ||||
−0.224154 | + | 0.974554i | \(0.571962\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 72.4649 | 2.30892 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 36.2282i | − 1.15199i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.3875 | −0.584099 | −0.292050 | − | 0.956403i | \(-0.594337\pi\) | ||||
−0.292050 | + | 0.956403i | \(0.594337\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 73.4362i | − 2.32808i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 20.8011i | − 0.658776i | −0.944195 | − | 0.329388i | \(-0.893158\pi\) | ||||
0.944195 | − | 0.329388i | \(-0.106842\pi\) | |||||||
\(998\) | 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 | 6048.2.c.f.3025.21 | 24 | ||
3.2 | odd | 2 | inner | 6048.2.c.f.3025.3 | 24 | ||
4.3 | odd | 2 | 1512.2.c.g.757.12 | yes | 24 | ||
8.3 | odd | 2 | 1512.2.c.g.757.11 | ✓ | 24 | ||
8.5 | even | 2 | inner | 6048.2.c.f.3025.4 | 24 | ||
12.11 | even | 2 | 1512.2.c.g.757.13 | yes | 24 | ||
24.5 | odd | 2 | inner | 6048.2.c.f.3025.22 | 24 | ||
24.11 | even | 2 | 1512.2.c.g.757.14 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.g.757.11 | ✓ | 24 | 8.3 | odd | 2 | ||
1512.2.c.g.757.12 | yes | 24 | 4.3 | odd | 2 | ||
1512.2.c.g.757.13 | yes | 24 | 12.11 | even | 2 | ||
1512.2.c.g.757.14 | yes | 24 | 24.11 | even | 2 | ||
6048.2.c.f.3025.3 | 24 | 3.2 | odd | 2 | inner | ||
6048.2.c.f.3025.4 | 24 | 8.5 | even | 2 | inner | ||
6048.2.c.f.3025.21 | 24 | 1.1 | even | 1 | trivial | ||
6048.2.c.f.3025.22 | 24 | 24.5 | odd | 2 | inner |