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: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + x^{18} + 4x^{16} + 8x^{12} + 4x^{10} + 32x^{8} + 256x^{4} + 256x^{2} + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{18}\cdot 3^{8} \) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3025.11 | ||
Root | \(-1.37874 + 0.314750i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.3025 |
Dual form | 6048.2.c.e.3025.10 |
$q$-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 | ||||||||
\(5\) | 0.114591i | 0.0512468i | 0.999672 | + | 0.0256234i | \(0.00815707\pi\) | ||||
−0.999672 | + | 0.0256234i | \(0.991843\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 0.412956i | − 0.124511i | −0.998060 | − | 0.0622555i | \(-0.980171\pi\) | ||||
0.998060 | − | 0.0622555i | \(-0.0198294\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.73584i | − 0.481435i | −0.970595 | − | 0.240717i | \(-0.922617\pi\) | ||||
0.970595 | − | 0.240717i | \(-0.0773827\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.50762 | 0.608188 | 0.304094 | − | 0.952642i | \(-0.401646\pi\) | ||||
0.304094 | + | 0.952642i | \(0.401646\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 6.85261i | − 1.57210i | −0.618166 | − | 0.786048i | \(-0.712124\pi\) | ||||
0.618166 | − | 0.786048i | \(-0.287876\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.42226 | −0.922106 | −0.461053 | − | 0.887373i | \(-0.652528\pi\) | ||||
−0.461053 | + | 0.887373i | \(0.652528\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.98687 | 0.997374 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.85559i | 0.344575i | 0.985047 | + | 0.172287i | \(0.0551158\pi\) | ||||
−0.985047 | + | 0.172287i | \(0.944884\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.60373 | −1.00646 | −0.503230 | − | 0.864153i | \(-0.667855\pi\) | ||||
−0.503230 | + | 0.864153i | \(0.667855\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.114591i | 0.0193695i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.39099i | 0.721875i | 0.932590 | + | 0.360938i | \(0.117543\pi\) | ||||
−0.932590 | + | 0.360938i | \(0.882457\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.39907 | −0.374672 | −0.187336 | − | 0.982296i | \(-0.559985\pi\) | ||||
−0.187336 | + | 0.982296i | \(0.559985\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 4.35614i | − 0.664306i | −0.943226 | − | 0.332153i | \(-0.892225\pi\) | ||||
0.943226 | − | 0.332153i | \(-0.107775\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.23070 | 1.05471 | 0.527353 | − | 0.849646i | \(-0.323185\pi\) | ||||
0.527353 | + | 0.849646i | \(0.323185\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 11.2241i | − 1.54175i | −0.636983 | − | 0.770877i | \(-0.719818\pi\) | ||||
0.636983 | − | 0.770877i | \(-0.280182\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.0473212 | 0.00638079 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.25900i | 0.554475i | 0.960801 | + | 0.277237i | \(0.0894188\pi\) | ||||
−0.960801 | + | 0.277237i | \(0.910581\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 7.35936i | − 0.942269i | −0.882061 | − | 0.471135i | \(-0.843845\pi\) | ||||
0.882061 | − | 0.471135i | \(-0.156155\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.198912 | 0.0246720 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 6.25549i | − 0.764230i | −0.924115 | − | 0.382115i | \(-0.875196\pi\) | ||||
0.924115 | − | 0.382115i | \(-0.124804\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.608276 | 0.0721891 | 0.0360946 | − | 0.999348i | \(-0.488508\pi\) | ||||
0.0360946 | + | 0.999348i | \(0.488508\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.1550 | −1.65671 | −0.828357 | − | 0.560201i | \(-0.810724\pi\) | ||||
−0.828357 | + | 0.560201i | \(0.810724\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 0.412956i | − 0.0470607i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.19950 | −0.922516 | −0.461258 | − | 0.887266i | \(-0.652602\pi\) | ||||
−0.461258 | + | 0.887266i | \(0.652602\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.88023i | 0.535675i | 0.963464 | + | 0.267838i | \(0.0863091\pi\) | ||||
−0.963464 | + | 0.267838i | \(0.913691\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.287352i | 0.0311677i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.4217 | −1.10469 | −0.552347 | − | 0.833614i | \(-0.686268\pi\) | ||||
−0.552347 | + | 0.833614i | \(0.686268\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 1.73584i | − 0.181965i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.785249 | 0.0805649 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.42009 | −0.347258 | −0.173629 | − | 0.984811i | \(-0.555549\pi\) | ||||
−0.173629 | + | 0.984811i | \(0.555549\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 0.203905i | − 0.0202893i | −0.999949 | − | 0.0101446i | \(-0.996771\pi\) | ||||
0.999949 | − | 0.0101446i | \(-0.00322920\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.16809 | −0.706293 | −0.353147 | − | 0.935568i | \(-0.614888\pi\) | ||||
−0.353147 | + | 0.935568i | \(0.614888\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.46742i | 0.721902i | 0.932585 | + | 0.360951i | \(0.117548\pi\) | ||||
−0.932585 | + | 0.360951i | \(0.882452\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 2.11355i | − 0.202442i | −0.994864 | − | 0.101221i | \(-0.967725\pi\) | ||||
0.994864 | − | 0.101221i | \(-0.0322749\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.72972 | 0.444935 | 0.222467 | − | 0.974940i | \(-0.428589\pi\) | ||||
0.222467 | + | 0.974940i | \(0.428589\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 0.506753i | − 0.0472550i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.50762 | 0.229873 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.8295 | 0.984497 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.14441i | 0.102359i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.55123 | 0.847535 | 0.423767 | − | 0.905771i | \(-0.360707\pi\) | ||||
0.423767 | + | 0.905771i | \(0.360707\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.5084i | 1.61709i | 0.588435 | + | 0.808544i | \(0.299744\pi\) | ||||
−0.588435 | + | 0.808544i | \(0.700256\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 6.85261i | − 0.594196i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.42852 | −0.720097 | −0.360048 | − | 0.932934i | \(-0.617240\pi\) | ||||
−0.360048 | + | 0.932934i | \(0.617240\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 13.8639i | − 1.17592i | −0.808890 | − | 0.587961i | \(-0.799931\pi\) | ||||
0.808890 | − | 0.587961i | \(-0.200069\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.716825 | −0.0599439 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.212635 | −0.0176583 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 22.0358i | − 1.80525i | −0.430432 | − | 0.902623i | \(-0.641639\pi\) | ||||
0.430432 | − | 0.902623i | \(-0.358361\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.40696 | −0.440012 | −0.220006 | − | 0.975498i | \(-0.570608\pi\) | ||||
−0.220006 | + | 0.975498i | \(0.570608\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 0.642139i | − 0.0515778i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 13.1081i | − 1.04614i | −0.852290 | − | 0.523070i | \(-0.824787\pi\) | ||||
0.852290 | − | 0.523070i | \(-0.175213\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.42226 | −0.348523 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 23.1785i | − 1.81548i | −0.419533 | − | 0.907740i | \(-0.637806\pi\) | ||||
0.419533 | − | 0.907740i | \(-0.362194\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.12880 | 0.551643 | 0.275821 | − | 0.961209i | \(-0.411050\pi\) | ||||
0.275821 | + | 0.961209i | \(0.411050\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.98687 | 0.768221 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 20.8217i | − 1.58305i | −0.611138 | − | 0.791524i | \(-0.709288\pi\) | ||||
0.611138 | − | 0.791524i | \(-0.290712\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.98687 | 0.376972 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.51282i | 0.561535i | 0.959776 | + | 0.280767i | \(0.0905890\pi\) | ||||
−0.959776 | + | 0.280767i | \(0.909411\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 4.48480i | − 0.333353i | −0.986012 | − | 0.166676i | \(-0.946697\pi\) | ||||
0.986012 | − | 0.166676i | \(-0.0533035\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.503170 | −0.0369938 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 1.03554i | − 0.0757260i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.6726 | 1.78525 | 0.892624 | − | 0.450802i | \(-0.148862\pi\) | ||||
0.892624 | + | 0.450802i | \(0.148862\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.335818 | −0.0241727 | −0.0120863 | − | 0.999927i | \(-0.503847\pi\) | ||||
−0.0120863 | + | 0.999927i | \(0.503847\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.3089i | 0.948221i | 0.880465 | + | 0.474111i | \(0.157230\pi\) | ||||
−0.880465 | + | 0.474111i | \(0.842770\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.24682 | 0.655490 | 0.327745 | − | 0.944766i | \(-0.393711\pi\) | ||||
0.327745 | + | 0.944766i | \(0.393711\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.85559i | 0.130237i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 0.274913i | − 0.0192008i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.82983 | −0.195743 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.73424i | 0.325918i | 0.986633 | + | 0.162959i | \(0.0521039\pi\) | ||||
−0.986633 | + | 0.162959i | \(0.947896\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.499176 | 0.0340435 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.60373 | −0.380406 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 4.35282i | − 0.292803i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.68005 | −0.648224 | −0.324112 | − | 0.946019i | \(-0.605065\pi\) | ||||
−0.324112 | + | 0.946019i | \(0.605065\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 22.8566i | − 1.51705i | −0.651646 | − | 0.758523i | \(-0.725921\pi\) | ||||
0.651646 | − | 0.758523i | \(-0.274079\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 16.7944i | − 1.10980i | −0.831916 | − | 0.554901i | \(-0.812756\pi\) | ||||
0.831916 | − | 0.554901i | \(-0.187244\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.6756 | −1.28899 | −0.644494 | − | 0.764609i | \(-0.722932\pi\) | ||||
−0.644494 | + | 0.764609i | \(0.722932\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.828576i | 0.0540503i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.8874 | −1.54515 | −0.772573 | − | 0.634926i | \(-0.781030\pi\) | ||||
−0.772573 | + | 0.634926i | \(0.781030\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.03141 | −0.259686 | −0.129843 | − | 0.991535i | \(-0.541447\pi\) | ||||
−0.129843 | + | 0.991535i | \(0.541447\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.114591i | 0.00732097i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.8950 | −0.756861 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.40404i | 0.530459i | 0.964185 | + | 0.265229i | \(0.0854476\pi\) | ||||
−0.964185 | + | 0.265229i | \(0.914552\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.82620i | 0.114812i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.32955 | 0.207692 | 0.103846 | − | 0.994593i | \(-0.466885\pi\) | ||||
0.103846 | + | 0.994593i | \(0.466885\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.39099i | 0.272843i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.2375 | 1.00124 | 0.500622 | − | 0.865666i | \(-0.333105\pi\) | ||||
0.500622 | + | 0.865666i | \(0.333105\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.28619 | 0.0790100 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.74732i | 0.350420i | 0.984531 | + | 0.175210i | \(0.0560605\pi\) | ||||
−0.984531 | + | 0.175210i | \(0.943940\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.6089 | 0.705189 | 0.352595 | − | 0.935776i | \(-0.385300\pi\) | ||||
0.352595 | + | 0.935776i | \(0.385300\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 2.05936i | − 0.124184i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 19.1097i | − 1.14819i | −0.818788 | − | 0.574096i | \(-0.805354\pi\) | ||||
0.818788 | − | 0.574096i | \(-0.194646\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.9611 | 1.19078 | 0.595389 | − | 0.803438i | \(-0.296998\pi\) | ||||
0.595389 | + | 0.803438i | \(0.296998\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.1413i | 0.959503i | 0.877404 | + | 0.479752i | \(0.159273\pi\) | ||||
−0.877404 | + | 0.479752i | \(0.840727\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.39907 | −0.141613 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.7118 | −0.630108 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 7.16969i | − 0.418858i | −0.977824 | − | 0.209429i | \(-0.932840\pi\) | ||||
0.977824 | − | 0.209429i | \(-0.0671604\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.488044 | −0.0284150 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.67633i | 0.443934i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 4.35614i | − 0.251084i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.843319 | 0.0482883 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 15.4062i | − 0.879278i | −0.898175 | − | 0.439639i | \(-0.855106\pi\) | ||||
0.898175 | − | 0.439639i | \(-0.144894\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.3442 | −1.15361 | −0.576806 | − | 0.816881i | \(-0.695701\pi\) | ||||
−0.576806 | + | 0.816881i | \(0.695701\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.5540 | −1.50092 | −0.750460 | − | 0.660916i | \(-0.770168\pi\) | ||||
−0.750460 | + | 0.660916i | \(0.770168\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.8006i | 0.999782i | 0.866088 | + | 0.499891i | \(0.166627\pi\) | ||||
−0.866088 | + | 0.499891i | \(0.833373\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.766278 | 0.0429033 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 17.1837i | − 0.956129i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 8.65639i | − 0.480170i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.23070 | 0.398641 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 27.1007i | − 1.48959i | −0.667295 | − | 0.744793i | \(-0.732548\pi\) | ||||
0.667295 | − | 0.744793i | \(-0.267452\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.716825 | 0.0391643 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.19674 | −0.500978 | −0.250489 | − | 0.968119i | \(-0.580591\pi\) | ||||
−0.250489 | + | 0.968119i | \(0.580591\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.31409i | 0.125315i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 33.4386i | 1.79508i | 0.440935 | + | 0.897539i | \(0.354647\pi\) | ||||
−0.440935 | + | 0.897539i | \(0.645353\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 17.5598i | − 0.939954i | −0.882679 | − | 0.469977i | \(-0.844262\pi\) | ||||
0.882679 | − | 0.469977i | \(-0.155738\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.4376 | 0.981335 | 0.490668 | − | 0.871347i | \(-0.336753\pi\) | ||||
0.490668 | + | 0.871347i | \(0.336753\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.0697032i | 0.00369946i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.80894 | −0.412140 | −0.206070 | − | 0.978537i | \(-0.566067\pi\) | ||||
−0.206070 | + | 0.978537i | \(0.566067\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −27.9582 | −1.47148 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 1.62204i | − 0.0849012i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.2964 | 0.955066 | 0.477533 | − | 0.878614i | \(-0.341531\pi\) | ||||
0.477533 | + | 0.878614i | \(0.341531\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 11.2241i | − 0.582729i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 29.4005i | − 1.52230i | −0.648575 | − | 0.761150i | \(-0.724635\pi\) | ||||
0.648575 | − | 0.761150i | \(-0.275365\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.22100 | 0.165890 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.46161i | 0.126444i | 0.997999 | + | 0.0632222i | \(0.0201377\pi\) | ||||
−0.997999 | + | 0.0632222i | \(0.979862\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.59739 | 0.439306 | 0.219653 | − | 0.975578i | \(-0.429507\pi\) | ||||
0.219653 | + | 0.975578i | \(0.429507\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0473212 | 0.00241171 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 3.93550i | − 0.199538i | −0.995011 | − | 0.0997688i | \(-0.968190\pi\) | ||||
0.995011 | − | 0.0997688i | \(-0.0318103\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.0894 | −0.560813 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 0.939592i | − 0.0472760i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 27.3549i | − 1.37290i | −0.727175 | − | 0.686452i | \(-0.759167\pi\) | ||||
0.727175 | − | 0.686452i | \(-0.240833\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.49913 | −0.324551 | −0.162276 | − | 0.986745i | \(-0.551883\pi\) | ||||
−0.162276 | + | 0.986745i | \(0.551883\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.72716i | 0.484545i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.81329 | 0.0898814 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.9897 | 0.889531 | 0.444765 | − | 0.895647i | \(-0.353287\pi\) | ||||
0.444765 | + | 0.895647i | \(0.353287\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.25900i | 0.209572i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.559232 | −0.0274516 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 40.4247i | − 1.97487i | −0.158014 | − | 0.987437i | \(-0.550509\pi\) | ||||
0.158014 | − | 0.987437i | \(-0.449491\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.3043i | 0.550938i | 0.961310 | + | 0.275469i | \(0.0888332\pi\) | ||||
−0.961310 | + | 0.275469i | \(0.911167\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.5052 | 0.606590 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 7.35936i | − 0.356144i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.2412 | −1.02315 | −0.511575 | − | 0.859238i | \(-0.670938\pi\) | ||||
−0.511575 | + | 0.859238i | \(0.670938\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.34136 | −0.256690 | −0.128345 | − | 0.991730i | \(-0.540966\pi\) | ||||
−0.128345 | + | 0.991730i | \(0.540966\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 30.3040i | 1.44964i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.0290 | 0.955933 | 0.477966 | − | 0.878378i | \(-0.341374\pi\) | ||||
0.477966 | + | 0.878378i | \(0.341374\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.3027i | 1.01212i | 0.862497 | + | 0.506062i | \(0.168899\pi\) | ||||
−0.862497 | + | 0.506062i | \(0.831101\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 1.19423i | − 0.0566121i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.8880 | −0.844185 | −0.422093 | − | 0.906553i | \(-0.638704\pi\) | ||||
−0.422093 | + | 0.906553i | \(0.638704\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.990712i | 0.0466508i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.198912 | 0.00932513 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.3625 | 0.905740 | 0.452870 | − | 0.891577i | \(-0.350400\pi\) | ||||
0.452870 | + | 0.891577i | \(0.350400\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.8751i | 1.01882i | 0.860523 | + | 0.509412i | \(0.170137\pi\) | ||||
−0.860523 | + | 0.509412i | \(0.829863\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.0449 | −1.21041 | −0.605204 | − | 0.796070i | \(-0.706909\pi\) | ||||
−0.605204 | + | 0.796070i | \(0.706909\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 11.8214i | − 0.547028i | −0.961868 | − | 0.273514i | \(-0.911814\pi\) | ||||
0.961868 | − | 0.273514i | \(-0.0881860\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 6.25549i | − 0.288852i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.79890 | −0.0827133 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 34.1730i | − 1.56797i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 29.0868 | 1.32901 | 0.664504 | − | 0.747284i | \(-0.268643\pi\) | ||||
0.664504 | + | 0.747284i | \(0.268643\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.62205 | 0.347536 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 0.391913i | − 0.0177959i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.3338 | 0.966728 | 0.483364 | − | 0.875419i | \(-0.339415\pi\) | ||||
0.483364 | + | 0.875419i | \(0.339415\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 20.2052i | − 0.911846i | −0.890019 | − | 0.455923i | \(-0.849309\pi\) | ||||
0.890019 | − | 0.455923i | \(-0.150691\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.65312i | 0.209566i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.608276 | 0.0272849 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 25.2662i | − 1.13107i | −0.824724 | − | 0.565535i | \(-0.808670\pi\) | ||||
0.824724 | − | 0.565535i | \(-0.191330\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.2176 | −1.34734 | −0.673669 | − | 0.739033i | \(-0.735283\pi\) | ||||
−0.673669 | + | 0.739033i | \(0.735283\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.0233657 | 0.00103976 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.78140i | 0.0789592i | 0.999220 | + | 0.0394796i | \(0.0125700\pi\) | ||||
−0.999220 | + | 0.0394796i | \(0.987430\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.1550 | −0.626179 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 0.821401i | − 0.0361953i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 2.98596i | − 0.131322i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.72198 | 0.250685 | 0.125342 | − | 0.992114i | \(-0.459997\pi\) | ||||
0.125342 | + | 0.992114i | \(0.459997\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 0.348058i | − 0.0152195i | −0.999971 | − | 0.00760976i | \(-0.997578\pi\) | ||||
0.999971 | − | 0.00760976i | \(-0.00242229\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14.0520 | −0.612116 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.44359 | −0.149721 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.16440i | 0.180380i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.855701 | −0.0369952 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 0.412956i | − 0.0177873i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.49464i | 0.365213i | 0.983186 | + | 0.182606i | \(0.0584534\pi\) | ||||
−0.983186 | + | 0.182606i | \(0.941547\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.242195 | 0.0103745 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.5175i | 1.34759i | 0.738918 | + | 0.673796i | \(0.235337\pi\) | ||||
−0.738918 | + | 0.673796i | \(0.764663\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.7156 | 0.541704 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.19950 | −0.348678 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 25.5635i | − 1.08316i | −0.840649 | − | 0.541581i | \(-0.817826\pi\) | ||||
0.840649 | − | 0.541581i | \(-0.182174\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.56156 | −0.319820 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 18.6212i | − 0.784791i | −0.919796 | − | 0.392396i | \(-0.871646\pi\) | ||||
0.919796 | − | 0.392396i | \(-0.128354\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.541985i | 0.0228015i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 40.8350 | 1.71189 | 0.855946 | − | 0.517065i | \(-0.172975\pi\) | ||||
0.855946 | + | 0.517065i | \(0.172975\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.7134i | 0.866831i | 0.901194 | + | 0.433415i | \(0.142692\pi\) | ||||
−0.901194 | + | 0.433415i | \(0.857308\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −22.0532 | −0.919684 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.58023 | 0.357200 | 0.178600 | − | 0.983922i | \(-0.442843\pi\) | ||||
0.178600 | + | 0.983922i | \(0.442843\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.88023i | 0.202466i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.63508 | −0.191965 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 28.7023i | − 1.18467i | −0.805692 | − | 0.592334i | \(-0.798206\pi\) | ||||
0.805692 | − | 0.592334i | \(-0.201794\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 38.4001i | 1.58225i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −42.2499 | −1.73500 | −0.867498 | − | 0.497440i | \(-0.834273\pi\) | ||||
−0.867498 | + | 0.497440i | \(0.834273\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.287352i | 0.0117803i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.3138 | 1.27945 | 0.639723 | − | 0.768605i | \(-0.279049\pi\) | ||||
0.639723 | + | 0.768605i | \(0.279049\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.40650 | 0.383699 | 0.191850 | − | 0.981424i | \(-0.438551\pi\) | ||||
0.191850 | + | 0.981424i | \(0.438551\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.24096i | 0.0504523i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.95314 | −0.201042 | −0.100521 | − | 0.994935i | \(-0.532051\pi\) | ||||
−0.100521 | + | 0.994935i | \(0.532051\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 12.5513i | − 0.507772i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.61633i | 0.267231i | 0.991033 | + | 0.133616i | \(0.0426587\pi\) | ||||
−0.991033 | + | 0.133616i | \(0.957341\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.3584 | 0.859855 | 0.429928 | − | 0.902863i | \(-0.358539\pi\) | ||||
0.429928 | + | 0.902863i | \(0.358539\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.0210409i | 0 0.000845707i | 1.00000 | 0.000422854i | \(0.000134598\pi\) | |||||
−1.00000 | 0.000422854i | \(0.999865\pi\) | ||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.4217 | −0.417535 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.8032 | 0.992128 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.0110i | 0.439036i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.6037 | −0.780411 | −0.390206 | − | 0.920728i | \(-0.627596\pi\) | ||||
−0.390206 | + | 0.920728i | \(0.627596\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.09449i | 0.0434335i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 1.73584i | − 0.0687764i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.84692 | 0.191442 | 0.0957210 | − | 0.995408i | \(-0.469484\pi\) | ||||
0.0957210 | + | 0.995408i | \(0.469484\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 3.72899i | − 0.147057i | −0.997293 | − | 0.0735285i | \(-0.976574\pi\) | ||||
0.997293 | − | 0.0735285i | \(-0.0234260\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −45.6179 | −1.79342 | −0.896712 | − | 0.442615i | \(-0.854051\pi\) | ||||
−0.896712 | + | 0.442615i | \(0.854051\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.75878 | 0.0690382 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.34542i | 0.248315i | 0.992263 | + | 0.124158i | \(0.0396229\pi\) | ||||
−0.992263 | + | 0.124158i | \(0.960377\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.12090 | −0.0828706 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 12.6820i | − 0.494022i | −0.969013 | − | 0.247011i | \(-0.920552\pi\) | ||||
0.969013 | − | 0.247011i | \(-0.0794484\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 7.30385i | − 0.284087i | −0.989860 | − | 0.142043i | \(-0.954633\pi\) | ||||
0.989860 | − | 0.142043i | \(-0.0453672\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.785249 | 0.0304507 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 8.20591i | − 0.317734i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.03909 | −0.117323 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.21222 | −0.162369 | −0.0811846 | − | 0.996699i | \(-0.525870\pi\) | ||||
−0.0811846 | + | 0.996699i | \(0.525870\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 18.0658i | − 0.694326i | −0.937805 | − | 0.347163i | \(-0.887145\pi\) | ||||
0.937805 | − | 0.347163i | \(-0.112855\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.42009 | −0.131251 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 41.3196i | 1.58105i | 0.612429 | + | 0.790526i | \(0.290192\pi\) | ||||
−0.612429 | + | 0.790526i | \(0.709808\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 0.965835i | − 0.0369027i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19.4833 | −0.742254 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 44.2400i | − 1.68297i | −0.540281 | − | 0.841485i | \(-0.681682\pi\) | ||||
0.540281 | − | 0.841485i | \(-0.318318\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.58868 | 0.0602622 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.01597 | −0.227871 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.0921i | 1.24987i | 0.780676 | + | 0.624936i | \(0.214875\pi\) | ||||
−0.780676 | + | 0.624936i | \(0.785125\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.0898 | 1.13486 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 0.203905i | − 0.00766863i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.0152i | 1.05213i | 0.850444 | + | 0.526066i | \(0.176333\pi\) | ||||
−0.850444 | + | 0.526066i | \(0.823667\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.7812 | 0.928062 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 0.0821419i | − 0.00307193i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.44311 | 0.202994 | 0.101497 | − | 0.994836i | \(-0.467637\pi\) | ||||
0.101497 | + | 0.994836i | \(0.467637\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.16809 | −0.266954 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.25359i | 0.343670i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.7480 | −0.546972 | −0.273486 | − | 0.961876i | \(-0.588177\pi\) | ||||
−0.273486 | + | 0.961876i | \(0.588177\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 10.9236i | − 0.404022i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 45.4197i | − 1.67762i | −0.544428 | − | 0.838808i | \(-0.683253\pi\) | ||||
0.544428 | − | 0.838808i | \(-0.316747\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.58324 | −0.0951550 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 3.03287i | − 0.111566i | −0.998443 | − | 0.0557830i | \(-0.982234\pi\) | ||||
0.998443 | − | 0.0557830i | \(-0.0177655\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 41.3290 | 1.51621 | 0.758106 | − | 0.652131i | \(-0.226125\pi\) | ||||
0.758106 | + | 0.652131i | \(0.226125\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.52512 | 0.0925131 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.46742i | 0.272853i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.6220 | −0.679527 | −0.339763 | − | 0.940511i | \(-0.610347\pi\) | ||||
−0.339763 | + | 0.940511i | \(0.610347\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 0.619591i | − 0.0225492i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 48.7279i | 1.77104i | 0.464597 | + | 0.885522i | \(0.346199\pi\) | ||||
−0.464597 | + | 0.885522i | \(0.653801\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.1095 | −0.946468 | −0.473234 | − | 0.880937i | \(-0.656913\pi\) | ||||
−0.473234 | + | 0.880937i | \(0.656913\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 2.11355i | − 0.0765157i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.39293 | 0.266943 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.6590 | 0.889225 | 0.444612 | − | 0.895723i | \(-0.353341\pi\) | ||||
0.444612 | + | 0.895723i | \(0.353341\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.7370i | 0.566019i | 0.959117 | + | 0.283010i | \(0.0913329\pi\) | ||||
−0.959117 | + | 0.283010i | \(0.908667\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −27.9451 | −1.00382 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16.4399i | 0.589021i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 0.251191i | − 0.00898834i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.50207 | 0.0536113 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 48.6354i | 1.73367i | 0.498599 | + | 0.866833i | \(0.333848\pi\) | ||||
−0.498599 | + | 0.866833i | \(0.666152\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.72972 | 0.168170 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.7746 | −0.453641 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 53.4156i | 1.89208i | 0.324054 | + | 0.946038i | \(0.394954\pi\) | ||||
−0.324054 | + | 0.946038i | \(0.605046\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.1319 | 0.641459 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.84538i | 0.206279i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 0.506753i | − 0.0178607i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −46.1176 | −1.62141 | −0.810704 | − | 0.585456i | \(-0.800915\pi\) | ||||
−0.810704 | + | 0.585456i | \(0.800915\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 13.2874i | − 0.466585i | −0.972407 | − | 0.233293i | \(-0.925050\pi\) | ||||
0.972407 | − | 0.233293i | \(-0.0749500\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.65606 | 0.0930376 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −29.8509 | −1.04435 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 30.5087i | − 1.06476i | −0.846505 | − | 0.532380i | \(-0.821298\pi\) | ||||
0.846505 | − | 0.532380i | \(-0.178702\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.6955 | 0.686542 | 0.343271 | − | 0.939236i | \(-0.388465\pi\) | ||||
0.343271 | + | 0.939236i | \(0.388465\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.77145i | 0.200693i | 0.994953 | + | 0.100347i | \(0.0319951\pi\) | ||||
−0.994953 | + | 0.100347i | \(0.968005\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 50.3002i | 1.74700i | 0.486826 | + | 0.873499i | \(0.338155\pi\) | ||||
−0.486826 | + | 0.873499i | \(0.661845\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.50762 | 0.0868840 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.816898i | 0.0282699i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 26.5035 | 0.915004 | 0.457502 | − | 0.889209i | \(-0.348744\pi\) | ||||
0.457502 | + | 0.889209i | \(0.348744\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.5568 | 0.881268 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.14441i | 0.0393688i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.8295 | 0.372105 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 19.4181i | − 0.665645i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.22041i | 0.315701i | 0.987463 | + | 0.157850i | \(0.0504564\pi\) | ||||
−0.987463 | + | 0.157850i | \(0.949544\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41.1124 | 1.40437 | 0.702187 | − | 0.711993i | \(-0.252207\pi\) | ||||
0.702187 | + | 0.711993i | \(0.252207\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 7.51805i | − 0.256513i | −0.991741 | − | 0.128256i | \(-0.959062\pi\) | ||||
0.991741 | − | 0.128256i | \(-0.0409380\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.5122 | 0.698245 | 0.349122 | − | 0.937077i | \(-0.386480\pi\) | ||||
0.349122 | + | 0.937077i | \(0.386480\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.38599 | 0.0811261 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.38604i | 0.114863i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.8585 | −0.367927 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.14441i | 0.0386881i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 53.2820i | 1.79921i | 0.436710 | + | 0.899603i | \(0.356144\pi\) | ||||
−0.436710 | + | 0.899603i | \(0.643856\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.1591 | 1.25192 | 0.625960 | − | 0.779855i | \(-0.284707\pi\) | ||||
0.625960 | + | 0.779855i | \(0.284707\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.5599i | 1.02842i | 0.857664 | + | 0.514211i | \(0.171915\pi\) | ||||
−0.857664 | + | 0.514211i | \(0.828085\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −47.5640 | −1.59704 | −0.798521 | − | 0.601967i | \(-0.794384\pi\) | ||||
−0.798521 | + | 0.601967i | \(0.794384\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.55123 | 0.320338 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 49.5491i | − 1.65810i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.860905 | −0.0287769 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 10.3982i | − 0.346800i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 28.1459i | − 0.937676i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.513919 | 0.0170833 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 45.9789i | 1.52670i | 0.645982 | + | 0.763352i | \(0.276448\pi\) | ||||
−0.645982 | + | 0.763352i | \(0.723552\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.42797 | −0.312363 | −0.156181 | − | 0.987728i | \(-0.549918\pi\) | ||||
−0.156181 | + | 0.987728i | \(0.549918\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.01532 | 0.0666974 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18.5084i | 0.611202i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.64588 | 0.0542924 | 0.0271462 | − | 0.999631i | \(-0.491358\pi\) | ||||
0.0271462 | + | 0.999631i | \(0.491358\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 1.05587i | − 0.0347543i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.8973i | 0.719979i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 52.1072 | 1.70958 | 0.854791 | − | 0.518973i | \(-0.173685\pi\) | ||||
0.854791 | + | 0.518973i | \(0.173685\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 6.85261i | − 0.224585i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.118664 | 0.00388072 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.2023 | 0.333294 | 0.166647 | − | 0.986017i | \(-0.446706\pi\) | ||||
0.166647 | + | 0.986017i | \(0.446706\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.500685i | 0.0163219i | 0.999967 | + | 0.00816093i | \(0.00259773\pi\) | ||||
−0.999967 | + | 0.00816093i | \(0.997402\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.6093 | 0.345487 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 49.4247i | − 1.60609i | −0.595921 | − | 0.803043i | \(-0.703213\pi\) | ||||
0.595921 | − | 0.803043i | \(-0.296787\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.5707i | 0.797599i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −32.0038 | −1.03670 | −0.518352 | − | 0.855167i | \(-0.673454\pi\) | ||||
−0.518352 | + | 0.855167i | \(0.673454\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.82727i | 0.0914882i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.42852 | −0.272171 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.401788 | 0.0129609 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 0.0384818i | − 0.00123877i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.6934 | 1.46940 | 0.734700 | − | 0.678392i | \(-0.237323\pi\) | ||||
0.734700 | + | 0.678392i | \(0.237323\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.06582i | 0.290936i | 0.989363 | + | 0.145468i | \(0.0464688\pi\) | ||||
−0.989363 | + | 0.145468i | \(0.953531\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 13.8639i | − 0.444456i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.6361 | −0.660207 | −0.330103 | − | 0.943945i | \(-0.607084\pi\) | ||||
−0.330103 | + | 0.943945i | \(0.607084\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.30369i | 0.137547i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.4308 | 0.492167 | 0.246083 | − | 0.969249i | \(-0.420856\pi\) | ||||
0.246083 | + | 0.969249i | \(0.420856\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.52509 | −0.0485933 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.2640i | 0.612560i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.7039 | 0.816510 | 0.408255 | − | 0.912868i | \(-0.366137\pi\) | ||||
0.408255 | + | 0.912868i | \(0.366137\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.05961i | 0.0335918i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.0217i | 0.570753i | 0.958416 | + | 0.285376i | \(0.0921186\pi\) | ||||
−0.958416 | + | 0.285376i | \(0.907881\pi\) | |||||||
\(998\) | 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.e.3025.11 | 20 | ||
3.2 | odd | 2 | inner | 6048.2.c.e.3025.9 | 20 | ||
4.3 | odd | 2 | 1512.2.c.e.757.20 | yes | 20 | ||
8.3 | odd | 2 | 1512.2.c.e.757.19 | yes | 20 | ||
8.5 | even | 2 | inner | 6048.2.c.e.3025.10 | 20 | ||
12.11 | even | 2 | 1512.2.c.e.757.1 | ✓ | 20 | ||
24.5 | odd | 2 | inner | 6048.2.c.e.3025.12 | 20 | ||
24.11 | even | 2 | 1512.2.c.e.757.2 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.e.757.1 | ✓ | 20 | 12.11 | even | 2 | ||
1512.2.c.e.757.2 | yes | 20 | 24.11 | even | 2 | ||
1512.2.c.e.757.19 | yes | 20 | 8.3 | odd | 2 | ||
1512.2.c.e.757.20 | yes | 20 | 4.3 | odd | 2 | ||
6048.2.c.e.3025.9 | 20 | 3.2 | odd | 2 | inner | ||
6048.2.c.e.3025.10 | 20 | 8.5 | even | 2 | inner | ||
6048.2.c.e.3025.11 | 20 | 1.1 | even | 1 | trivial | ||
6048.2.c.e.3025.12 | 20 | 24.5 | odd | 2 | inner |