Properties

Label 1584.4.a.bj.1.1
Level $1584$
Weight $4$
Character 1584.1
Self dual yes
Analytic conductor $93.459$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1584,4,Mod(1,1584)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1584, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1584.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1584.a (trivial)

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: yes
Analytic conductor: \(93.4590254491\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{97}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 24 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 33)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(5.42443\) of defining polynomial
Character \(\chi\) \(=\) 1584.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.84886 q^{5} -31.6977 q^{7} +O(q^{10})\) \(q-2.84886 q^{5} -31.6977 q^{7} -11.0000 q^{11} +5.15114 q^{13} -121.942 q^{17} -34.8489 q^{19} +116.244 q^{23} -116.884 q^{25} +69.4534 q^{29} -140.605 q^{31} +90.3023 q^{35} -420.070 q^{37} +322.058 q^{41} -321.035 q^{43} -231.408 q^{47} +661.745 q^{49} -4.91916 q^{53} +31.3374 q^{55} +406.443 q^{59} -556.431 q^{61} -14.6749 q^{65} -84.7452 q^{67} +49.0808 q^{71} +785.884 q^{73} +348.675 q^{77} +383.118 q^{79} -930.211 q^{83} +347.395 q^{85} +732.559 q^{89} -163.279 q^{91} +99.2794 q^{95} -1171.49 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 14 q^{5} - 24 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 14 q^{5} - 24 q^{7} - 22 q^{11} + 30 q^{13} - 106 q^{17} - 50 q^{19} + 134 q^{23} + 42 q^{25} + 198 q^{29} - 360 q^{31} + 220 q^{35} - 328 q^{37} + 782 q^{41} - 386 q^{43} + 266 q^{47} + 378 q^{49} + 522 q^{53} - 154 q^{55} - 172 q^{59} - 778 q^{61} + 404 q^{65} + 776 q^{67} + 630 q^{71} + 1296 q^{73} + 264 q^{77} - 652 q^{79} - 324 q^{83} + 616 q^{85} + 756 q^{89} + 28 q^{91} - 156 q^{95} - 452 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −2.84886 −0.254810 −0.127405 0.991851i \(-0.540665\pi\)
−0.127405 + 0.991851i \(0.540665\pi\)
\(6\) 0 0
\(7\) −31.6977 −1.71152 −0.855758 0.517377i \(-0.826909\pi\)
−0.855758 + 0.517377i \(0.826909\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −11.0000 −0.301511
\(12\) 0 0
\(13\) 5.15114 0.109898 0.0549488 0.998489i \(-0.482500\pi\)
0.0549488 + 0.998489i \(0.482500\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −121.942 −1.73972 −0.869861 0.493297i \(-0.835792\pi\)
−0.869861 + 0.493297i \(0.835792\pi\)
\(18\) 0 0
\(19\) −34.8489 −0.420783 −0.210391 0.977617i \(-0.567474\pi\)
−0.210391 + 0.977617i \(0.567474\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 116.244 1.05385 0.526926 0.849911i \(-0.323344\pi\)
0.526926 + 0.849911i \(0.323344\pi\)
\(24\) 0 0
\(25\) −116.884 −0.935072
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 69.4534 0.444730 0.222365 0.974963i \(-0.428622\pi\)
0.222365 + 0.974963i \(0.428622\pi\)
\(30\) 0 0
\(31\) −140.605 −0.814623 −0.407312 0.913289i \(-0.633534\pi\)
−0.407312 + 0.913289i \(0.633534\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 90.3023 0.436111
\(36\) 0 0
\(37\) −420.070 −1.86646 −0.933232 0.359276i \(-0.883024\pi\)
−0.933232 + 0.359276i \(0.883024\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 322.058 1.22676 0.613378 0.789789i \(-0.289810\pi\)
0.613378 + 0.789789i \(0.289810\pi\)
\(42\) 0 0
\(43\) −321.035 −1.13854 −0.569272 0.822149i \(-0.692775\pi\)
−0.569272 + 0.822149i \(0.692775\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −231.408 −0.718176 −0.359088 0.933304i \(-0.616912\pi\)
−0.359088 + 0.933304i \(0.616912\pi\)
\(48\) 0 0
\(49\) 661.745 1.92929
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −4.91916 −0.0127490 −0.00637452 0.999980i \(-0.502029\pi\)
−0.00637452 + 0.999980i \(0.502029\pi\)
\(54\) 0 0
\(55\) 31.3374 0.0768280
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 406.443 0.896854 0.448427 0.893820i \(-0.351984\pi\)
0.448427 + 0.893820i \(0.351984\pi\)
\(60\) 0 0
\(61\) −556.431 −1.16793 −0.583964 0.811779i \(-0.698499\pi\)
−0.583964 + 0.811779i \(0.698499\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −14.6749 −0.0280030
\(66\) 0 0
\(67\) −84.7452 −0.154526 −0.0772632 0.997011i \(-0.524618\pi\)
−0.0772632 + 0.997011i \(0.524618\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 49.0808 0.0820398 0.0410199 0.999158i \(-0.486939\pi\)
0.0410199 + 0.999158i \(0.486939\pi\)
\(72\) 0 0
\(73\) 785.884 1.26001 0.630005 0.776591i \(-0.283053\pi\)
0.630005 + 0.776591i \(0.283053\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 348.675 0.516041
\(78\) 0 0
\(79\) 383.118 0.545622 0.272811 0.962068i \(-0.412047\pi\)
0.272811 + 0.962068i \(0.412047\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −930.211 −1.23017 −0.615084 0.788462i \(-0.710878\pi\)
−0.615084 + 0.788462i \(0.710878\pi\)
\(84\) 0 0
\(85\) 347.395 0.443298
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 732.559 0.872484 0.436242 0.899829i \(-0.356309\pi\)
0.436242 + 0.899829i \(0.356309\pi\)
\(90\) 0 0
\(91\) −163.279 −0.188092
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 99.2794 0.107220
\(96\) 0 0
\(97\) −1171.49 −1.22626 −0.613128 0.789984i \(-0.710089\pi\)
−0.613128 + 0.789984i \(0.710089\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1221.27 1.20318 0.601589 0.798806i \(-0.294535\pi\)
0.601589 + 0.798806i \(0.294535\pi\)
\(102\) 0 0
\(103\) −516.745 −0.494334 −0.247167 0.968973i \(-0.579500\pi\)
−0.247167 + 0.968973i \(0.579500\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −152.025 −0.137353 −0.0686765 0.997639i \(-0.521878\pi\)
−0.0686765 + 0.997639i \(0.521878\pi\)
\(108\) 0 0
\(109\) 2170.32 1.90714 0.953572 0.301164i \(-0.0973752\pi\)
0.953572 + 0.301164i \(0.0973752\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 646.397 0.538123 0.269062 0.963123i \(-0.413286\pi\)
0.269062 + 0.963123i \(0.413286\pi\)
\(114\) 0 0
\(115\) −331.163 −0.268532
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 3865.28 2.97756
\(120\) 0 0
\(121\) 121.000 0.0909091
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 689.093 0.493075
\(126\) 0 0
\(127\) 993.304 0.694027 0.347014 0.937860i \(-0.387196\pi\)
0.347014 + 0.937860i \(0.387196\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 385.814 0.257318 0.128659 0.991689i \(-0.458933\pi\)
0.128659 + 0.991689i \(0.458933\pi\)
\(132\) 0 0
\(133\) 1104.63 0.720177
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −884.840 −0.551803 −0.275901 0.961186i \(-0.588976\pi\)
−0.275901 + 0.961186i \(0.588976\pi\)
\(138\) 0 0
\(139\) 1091.94 0.666312 0.333156 0.942872i \(-0.391886\pi\)
0.333156 + 0.942872i \(0.391886\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −56.6626 −0.0331354
\(144\) 0 0
\(145\) −197.863 −0.113322
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −297.014 −0.163304 −0.0816522 0.996661i \(-0.526020\pi\)
−0.0816522 + 0.996661i \(0.526020\pi\)
\(150\) 0 0
\(151\) 1887.86 1.01743 0.508716 0.860935i \(-0.330120\pi\)
0.508716 + 0.860935i \(0.330120\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 400.562 0.207574
\(156\) 0 0
\(157\) −56.5343 −0.0287384 −0.0143692 0.999897i \(-0.504574\pi\)
−0.0143692 + 0.999897i \(0.504574\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −3684.68 −1.80369
\(162\) 0 0
\(163\) 49.2338 0.0236582 0.0118291 0.999930i \(-0.496235\pi\)
0.0118291 + 0.999930i \(0.496235\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2068.75 0.958589 0.479294 0.877654i \(-0.340893\pi\)
0.479294 + 0.877654i \(0.340893\pi\)
\(168\) 0 0
\(169\) −2170.47 −0.987923
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 604.012 0.265446 0.132723 0.991153i \(-0.457628\pi\)
0.132723 + 0.991153i \(0.457628\pi\)
\(174\) 0 0
\(175\) 3704.96 1.60039
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −2132.02 −0.890251 −0.445126 0.895468i \(-0.646841\pi\)
−0.445126 + 0.895468i \(0.646841\pi\)
\(180\) 0 0
\(181\) −589.371 −0.242031 −0.121015 0.992651i \(-0.538615\pi\)
−0.121015 + 0.992651i \(0.538615\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1196.72 0.475593
\(186\) 0 0
\(187\) 1341.36 0.524546
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2160.90 −0.818624 −0.409312 0.912395i \(-0.634231\pi\)
−0.409312 + 0.912395i \(0.634231\pi\)
\(192\) 0 0
\(193\) −1490.91 −0.556052 −0.278026 0.960574i \(-0.589680\pi\)
−0.278026 + 0.960574i \(0.589680\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 230.529 0.0833732 0.0416866 0.999131i \(-0.486727\pi\)
0.0416866 + 0.999131i \(0.486727\pi\)
\(198\) 0 0
\(199\) −22.4007 −0.00797963 −0.00398982 0.999992i \(-0.501270\pi\)
−0.00398982 + 0.999992i \(0.501270\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −2201.51 −0.761163
\(204\) 0 0
\(205\) −917.497 −0.312589
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 383.337 0.126871
\(210\) 0 0
\(211\) 1051.64 0.343117 0.171558 0.985174i \(-0.445120\pi\)
0.171558 + 0.985174i \(0.445120\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 914.583 0.290112
\(216\) 0 0
\(217\) 4456.84 1.39424
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −628.141 −0.191191
\(222\) 0 0
\(223\) −3861.80 −1.15966 −0.579832 0.814736i \(-0.696882\pi\)
−0.579832 + 0.814736i \(0.696882\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −872.721 −0.255174 −0.127587 0.991827i \(-0.540723\pi\)
−0.127587 + 0.991827i \(0.540723\pi\)
\(228\) 0 0
\(229\) 1841.72 0.531459 0.265730 0.964048i \(-0.414387\pi\)
0.265730 + 0.964048i \(0.414387\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −3932.14 −1.10559 −0.552796 0.833317i \(-0.686439\pi\)
−0.552796 + 0.833317i \(0.686439\pi\)
\(234\) 0 0
\(235\) 659.248 0.182998
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 4772.10 1.29155 0.645777 0.763526i \(-0.276534\pi\)
0.645777 + 0.763526i \(0.276534\pi\)
\(240\) 0 0
\(241\) 3988.84 1.06616 0.533078 0.846066i \(-0.321035\pi\)
0.533078 + 0.846066i \(0.321035\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1885.22 −0.491601
\(246\) 0 0
\(247\) −179.511 −0.0462431
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −5474.22 −1.37661 −0.688306 0.725421i \(-0.741645\pi\)
−0.688306 + 0.725421i \(0.741645\pi\)
\(252\) 0 0
\(253\) −1278.69 −0.317749
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6434.01 1.56164 0.780822 0.624754i \(-0.214801\pi\)
0.780822 + 0.624754i \(0.214801\pi\)
\(258\) 0 0
\(259\) 13315.3 3.19448
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 7589.00 1.77931 0.889654 0.456636i \(-0.150946\pi\)
0.889654 + 0.456636i \(0.150946\pi\)
\(264\) 0 0
\(265\) 14.0140 0.00324858
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −478.178 −0.108383 −0.0541914 0.998531i \(-0.517258\pi\)
−0.0541914 + 0.998531i \(0.517258\pi\)
\(270\) 0 0
\(271\) 122.323 0.0274192 0.0137096 0.999906i \(-0.495636\pi\)
0.0137096 + 0.999906i \(0.495636\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1285.72 0.281935
\(276\) 0 0
\(277\) 8199.41 1.77854 0.889269 0.457385i \(-0.151214\pi\)
0.889269 + 0.457385i \(0.151214\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −6943.79 −1.47413 −0.737067 0.675820i \(-0.763790\pi\)
−0.737067 + 0.675820i \(0.763790\pi\)
\(282\) 0 0
\(283\) −1035.14 −0.217429 −0.108715 0.994073i \(-0.534673\pi\)
−0.108715 + 0.994073i \(0.534673\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −10208.5 −2.09961
\(288\) 0 0
\(289\) 9956.85 2.02663
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 6144.81 1.22520 0.612600 0.790393i \(-0.290124\pi\)
0.612600 + 0.790393i \(0.290124\pi\)
\(294\) 0 0
\(295\) −1157.90 −0.228527
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 598.791 0.115816
\(300\) 0 0
\(301\) 10176.1 1.94864
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1585.19 0.297599
\(306\) 0 0
\(307\) 2186.09 0.406406 0.203203 0.979137i \(-0.434865\pi\)
0.203203 + 0.979137i \(0.434865\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −7484.83 −1.36471 −0.682357 0.731019i \(-0.739045\pi\)
−0.682357 + 0.731019i \(0.739045\pi\)
\(312\) 0 0
\(313\) −6833.33 −1.23400 −0.617001 0.786962i \(-0.711653\pi\)
−0.617001 + 0.786962i \(0.711653\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −924.265 −0.163760 −0.0818800 0.996642i \(-0.526092\pi\)
−0.0818800 + 0.996642i \(0.526092\pi\)
\(318\) 0 0
\(319\) −763.988 −0.134091
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 4249.54 0.732046
\(324\) 0 0
\(325\) −602.086 −0.102762
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 7335.10 1.22917
\(330\) 0 0
\(331\) 9820.46 1.63076 0.815380 0.578927i \(-0.196528\pi\)
0.815380 + 0.578927i \(0.196528\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 241.427 0.0393748
\(336\) 0 0
\(337\) 600.808 0.0971161 0.0485580 0.998820i \(-0.484537\pi\)
0.0485580 + 0.998820i \(0.484537\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 1546.65 0.245618
\(342\) 0 0
\(343\) −10103.5 −1.59049
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −3143.41 −0.486303 −0.243152 0.969988i \(-0.578181\pi\)
−0.243152 + 0.969988i \(0.578181\pi\)
\(348\) 0 0
\(349\) 720.663 0.110533 0.0552667 0.998472i \(-0.482399\pi\)
0.0552667 + 0.998472i \(0.482399\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1207.12 −0.182007 −0.0910034 0.995851i \(-0.529007\pi\)
−0.0910034 + 0.995851i \(0.529007\pi\)
\(354\) 0 0
\(355\) −139.824 −0.0209045
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 8748.31 1.28612 0.643062 0.765814i \(-0.277664\pi\)
0.643062 + 0.765814i \(0.277664\pi\)
\(360\) 0 0
\(361\) −5644.56 −0.822942
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2238.87 −0.321063
\(366\) 0 0
\(367\) 6730.45 0.957293 0.478647 0.878008i \(-0.341128\pi\)
0.478647 + 0.878008i \(0.341128\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 155.926 0.0218202
\(372\) 0 0
\(373\) −227.394 −0.0315657 −0.0157828 0.999875i \(-0.505024\pi\)
−0.0157828 + 0.999875i \(0.505024\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 357.764 0.0488748
\(378\) 0 0
\(379\) −11356.2 −1.53913 −0.769565 0.638568i \(-0.779527\pi\)
−0.769565 + 0.638568i \(0.779527\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 10753.6 1.43468 0.717338 0.696725i \(-0.245360\pi\)
0.717338 + 0.696725i \(0.245360\pi\)
\(384\) 0 0
\(385\) −993.325 −0.131492
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 11727.1 1.52850 0.764252 0.644918i \(-0.223109\pi\)
0.764252 + 0.644918i \(0.223109\pi\)
\(390\) 0 0
\(391\) −14175.1 −1.83341
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1091.45 −0.139030
\(396\) 0 0
\(397\) −359.905 −0.0454990 −0.0227495 0.999741i \(-0.507242\pi\)
−0.0227495 + 0.999741i \(0.507242\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 4066.71 0.506438 0.253219 0.967409i \(-0.418511\pi\)
0.253219 + 0.967409i \(0.418511\pi\)
\(402\) 0 0
\(403\) −724.274 −0.0895252
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 4620.77 0.562760
\(408\) 0 0
\(409\) −13488.8 −1.63076 −0.815379 0.578927i \(-0.803472\pi\)
−0.815379 + 0.578927i \(0.803472\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −12883.3 −1.53498
\(414\) 0 0
\(415\) 2650.04 0.313459
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −7040.12 −0.820841 −0.410420 0.911896i \(-0.634618\pi\)
−0.410420 + 0.911896i \(0.634618\pi\)
\(420\) 0 0
\(421\) 9171.74 1.06177 0.530883 0.847445i \(-0.321860\pi\)
0.530883 + 0.847445i \(0.321860\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 14253.1 1.62677
\(426\) 0 0
\(427\) 17637.6 1.99893
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 992.995 0.110976 0.0554882 0.998459i \(-0.482328\pi\)
0.0554882 + 0.998459i \(0.482328\pi\)
\(432\) 0 0
\(433\) 3790.21 0.420660 0.210330 0.977630i \(-0.432546\pi\)
0.210330 + 0.977630i \(0.432546\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −4050.98 −0.443443
\(438\) 0 0
\(439\) 5136.97 0.558483 0.279242 0.960221i \(-0.409917\pi\)
0.279242 + 0.960221i \(0.409917\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 10676.8 1.14508 0.572541 0.819876i \(-0.305958\pi\)
0.572541 + 0.819876i \(0.305958\pi\)
\(444\) 0 0
\(445\) −2086.96 −0.222317
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −10529.9 −1.10676 −0.553379 0.832929i \(-0.686662\pi\)
−0.553379 + 0.832929i \(0.686662\pi\)
\(450\) 0 0
\(451\) −3542.64 −0.369881
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 465.160 0.0479275
\(456\) 0 0
\(457\) −14072.5 −1.44045 −0.720225 0.693741i \(-0.755961\pi\)
−0.720225 + 0.693741i \(0.755961\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 30.8173 0.00311346 0.00155673 0.999999i \(-0.499504\pi\)
0.00155673 + 0.999999i \(0.499504\pi\)
\(462\) 0 0
\(463\) −17591.3 −1.76573 −0.882867 0.469622i \(-0.844390\pi\)
−0.882867 + 0.469622i \(0.844390\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 13273.1 1.31522 0.657609 0.753360i \(-0.271568\pi\)
0.657609 + 0.753360i \(0.271568\pi\)
\(468\) 0 0
\(469\) 2686.23 0.264474
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 3531.39 0.343284
\(474\) 0 0
\(475\) 4073.27 0.393462
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 2496.68 0.238155 0.119077 0.992885i \(-0.462006\pi\)
0.119077 + 0.992885i \(0.462006\pi\)
\(480\) 0 0
\(481\) −2163.84 −0.205120
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 3337.41 0.312462
\(486\) 0 0
\(487\) 3464.42 0.322357 0.161178 0.986925i \(-0.448471\pi\)
0.161178 + 0.986925i \(0.448471\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −16224.6 −1.49125 −0.745625 0.666366i \(-0.767849\pi\)
−0.745625 + 0.666366i \(0.767849\pi\)
\(492\) 0 0
\(493\) −8469.29 −0.773707
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1555.75 −0.140412
\(498\) 0 0
\(499\) −9993.81 −0.896562 −0.448281 0.893893i \(-0.647964\pi\)
−0.448281 + 0.893893i \(0.647964\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −15334.8 −1.35933 −0.679667 0.733520i \(-0.737876\pi\)
−0.679667 + 0.733520i \(0.737876\pi\)
\(504\) 0 0
\(505\) −3479.23 −0.306581
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 7291.23 0.634927 0.317464 0.948270i \(-0.397169\pi\)
0.317464 + 0.948270i \(0.397169\pi\)
\(510\) 0 0
\(511\) −24910.7 −2.15653
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1472.13 0.125961
\(516\) 0 0
\(517\) 2545.49 0.216538
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −16794.3 −1.41223 −0.706114 0.708098i \(-0.749553\pi\)
−0.706114 + 0.708098i \(0.749553\pi\)
\(522\) 0 0
\(523\) 21009.4 1.75655 0.878275 0.478157i \(-0.158695\pi\)
0.878275 + 0.478157i \(0.158695\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 17145.6 1.41722
\(528\) 0 0
\(529\) 1345.73 0.110605
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1658.97 0.134818
\(534\) 0 0
\(535\) 433.097 0.0349989
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −7279.20 −0.581702
\(540\) 0 0
\(541\) −16802.8 −1.33532 −0.667662 0.744464i \(-0.732705\pi\)
−0.667662 + 0.744464i \(0.732705\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −6182.93 −0.485959
\(546\) 0 0
\(547\) −16784.5 −1.31198 −0.655990 0.754770i \(-0.727749\pi\)
−0.655990 + 0.754770i \(0.727749\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −2420.37 −0.187135
\(552\) 0 0
\(553\) −12144.0 −0.933840
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −18127.0 −1.37893 −0.689467 0.724317i \(-0.742155\pi\)
−0.689467 + 0.724317i \(0.742155\pi\)
\(558\) 0 0
\(559\) −1653.70 −0.125123
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 2090.88 0.156518 0.0782592 0.996933i \(-0.475064\pi\)
0.0782592 + 0.996933i \(0.475064\pi\)
\(564\) 0 0
\(565\) −1841.49 −0.137119
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −6249.23 −0.460424 −0.230212 0.973140i \(-0.573942\pi\)
−0.230212 + 0.973140i \(0.573942\pi\)
\(570\) 0 0
\(571\) −6048.79 −0.443317 −0.221659 0.975124i \(-0.571147\pi\)
−0.221659 + 0.975124i \(0.571147\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −13587.1 −0.985428
\(576\) 0 0
\(577\) −15729.1 −1.13486 −0.567429 0.823423i \(-0.692062\pi\)
−0.567429 + 0.823423i \(0.692062\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 29485.6 2.10545
\(582\) 0 0
\(583\) 54.1108 0.00384398
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 15620.5 1.09835 0.549173 0.835709i \(-0.314943\pi\)
0.549173 + 0.835709i \(0.314943\pi\)
\(588\) 0 0
\(589\) 4899.91 0.342780
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 493.541 0.0341776 0.0170888 0.999854i \(-0.494560\pi\)
0.0170888 + 0.999854i \(0.494560\pi\)
\(594\) 0 0
\(595\) −11011.6 −0.758711
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −12455.1 −0.849585 −0.424793 0.905291i \(-0.639653\pi\)
−0.424793 + 0.905291i \(0.639653\pi\)
\(600\) 0 0
\(601\) 12454.8 0.845329 0.422664 0.906286i \(-0.361095\pi\)
0.422664 + 0.906286i \(0.361095\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −344.712 −0.0231645
\(606\) 0 0
\(607\) 4243.19 0.283733 0.141867 0.989886i \(-0.454690\pi\)
0.141867 + 0.989886i \(0.454690\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1192.01 −0.0789259
\(612\) 0 0
\(613\) 5733.14 0.377748 0.188874 0.982001i \(-0.439516\pi\)
0.188874 + 0.982001i \(0.439516\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −15642.1 −1.02063 −0.510314 0.859988i \(-0.670471\pi\)
−0.510314 + 0.859988i \(0.670471\pi\)
\(618\) 0 0
\(619\) 7467.40 0.484879 0.242440 0.970167i \(-0.422052\pi\)
0.242440 + 0.970167i \(0.422052\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −23220.4 −1.49327
\(624\) 0 0
\(625\) 12647.4 0.809432
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 51224.2 3.24713
\(630\) 0 0
\(631\) 1486.38 0.0937745 0.0468872 0.998900i \(-0.485070\pi\)
0.0468872 + 0.998900i \(0.485070\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −2829.78 −0.176845
\(636\) 0 0
\(637\) 3408.74 0.212024
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −12386.0 −0.763211 −0.381606 0.924325i \(-0.624629\pi\)
−0.381606 + 0.924325i \(0.624629\pi\)
\(642\) 0 0
\(643\) 14458.1 0.886737 0.443369 0.896339i \(-0.353783\pi\)
0.443369 + 0.896339i \(0.353783\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 15792.8 0.959625 0.479813 0.877371i \(-0.340705\pi\)
0.479813 + 0.877371i \(0.340705\pi\)
\(648\) 0 0
\(649\) −4470.87 −0.270412
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 3179.93 0.190567 0.0952837 0.995450i \(-0.469624\pi\)
0.0952837 + 0.995450i \(0.469624\pi\)
\(654\) 0 0
\(655\) −1099.13 −0.0655672
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 11593.5 0.685308 0.342654 0.939462i \(-0.388674\pi\)
0.342654 + 0.939462i \(0.388674\pi\)
\(660\) 0 0
\(661\) 3233.88 0.190293 0.0951464 0.995463i \(-0.469668\pi\)
0.0951464 + 0.995463i \(0.469668\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −3146.93 −0.183508
\(666\) 0 0
\(667\) 8073.56 0.468680
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 6120.74 0.352144
\(672\) 0 0
\(673\) −5495.72 −0.314776 −0.157388 0.987537i \(-0.550307\pi\)
−0.157388 + 0.987537i \(0.550307\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −33836.7 −1.92090 −0.960451 0.278448i \(-0.910180\pi\)
−0.960451 + 0.278448i \(0.910180\pi\)
\(678\) 0 0
\(679\) 37133.6 2.09876
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −21080.3 −1.18099 −0.590493 0.807043i \(-0.701067\pi\)
−0.590493 + 0.807043i \(0.701067\pi\)
\(684\) 0 0
\(685\) 2520.78 0.140605
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −25.3393 −0.00140109
\(690\) 0 0
\(691\) −11811.3 −0.650253 −0.325127 0.945671i \(-0.605407\pi\)
−0.325127 + 0.945671i \(0.605407\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −3110.79 −0.169783
\(696\) 0 0
\(697\) −39272.4 −2.13422
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −4244.99 −0.228718 −0.114359 0.993440i \(-0.536481\pi\)
−0.114359 + 0.993440i \(0.536481\pi\)
\(702\) 0 0
\(703\) 14639.0 0.785376
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −38711.5 −2.05926
\(708\) 0 0
\(709\) −898.822 −0.0476107 −0.0238053 0.999717i \(-0.507578\pi\)
−0.0238053 + 0.999717i \(0.507578\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −16344.5 −0.858493
\(714\) 0 0
\(715\) 161.424 0.00844322
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 10741.8 0.557165 0.278582 0.960412i \(-0.410135\pi\)
0.278582 + 0.960412i \(0.410135\pi\)
\(720\) 0 0
\(721\) 16379.6 0.846061
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −8117.99 −0.415855
\(726\) 0 0
\(727\) −16794.2 −0.856758 −0.428379 0.903599i \(-0.640915\pi\)
−0.428379 + 0.903599i \(0.640915\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 39147.7 1.98075
\(732\) 0 0
\(733\) 8659.40 0.436347 0.218173 0.975910i \(-0.429990\pi\)
0.218173 + 0.975910i \(0.429990\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 932.197 0.0465915
\(738\) 0 0
\(739\) −16705.7 −0.831567 −0.415783 0.909464i \(-0.636493\pi\)
−0.415783 + 0.909464i \(0.636493\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1292.12 0.0637996 0.0318998 0.999491i \(-0.489844\pi\)
0.0318998 + 0.999491i \(0.489844\pi\)
\(744\) 0 0
\(745\) 846.151 0.0416115
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 4818.83 0.235082
\(750\) 0 0
\(751\) 14980.4 0.727886 0.363943 0.931421i \(-0.381430\pi\)
0.363943 + 0.931421i \(0.381430\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −5378.25 −0.259251
\(756\) 0 0
\(757\) 3003.41 0.144202 0.0721010 0.997397i \(-0.477030\pi\)
0.0721010 + 0.997397i \(0.477030\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 20375.0 0.970555 0.485277 0.874360i \(-0.338719\pi\)
0.485277 + 0.874360i \(0.338719\pi\)
\(762\) 0 0
\(763\) −68794.1 −3.26411
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2093.65 0.0985621
\(768\) 0 0
\(769\) −12372.4 −0.580184 −0.290092 0.956999i \(-0.593686\pi\)
−0.290092 + 0.956999i \(0.593686\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −21023.6 −0.978225 −0.489113 0.872221i \(-0.662679\pi\)
−0.489113 + 0.872221i \(0.662679\pi\)
\(774\) 0 0
\(775\) 16434.4 0.761732
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −11223.4 −0.516198
\(780\) 0 0
\(781\) −539.889 −0.0247359
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 161.058 0.00732281
\(786\) 0 0
\(787\) −30286.2 −1.37177 −0.685886 0.727709i \(-0.740585\pi\)
−0.685886 + 0.727709i \(0.740585\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −20489.3 −0.921007
\(792\) 0 0
\(793\) −2866.25 −0.128353
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −32337.8 −1.43722 −0.718610 0.695413i \(-0.755221\pi\)
−0.718610 + 0.695413i \(0.755221\pi\)
\(798\) 0 0
\(799\) 28218.3 1.24943
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −8644.72 −0.379907
\(804\) 0 0
\(805\) 10497.1 0.459596
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 891.707 0.0387525 0.0193762 0.999812i \(-0.493832\pi\)
0.0193762 + 0.999812i \(0.493832\pi\)
\(810\) 0 0
\(811\) 10114.9 0.437957 0.218978 0.975730i \(-0.429728\pi\)
0.218978 + 0.975730i \(0.429728\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −140.260 −0.00602833
\(816\) 0 0
\(817\) 11187.7 0.479080
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −10833.5 −0.460525 −0.230262 0.973129i \(-0.573958\pi\)
−0.230262 + 0.973129i \(0.573958\pi\)
\(822\) 0 0
\(823\) −31958.5 −1.35359 −0.676794 0.736173i \(-0.736631\pi\)
−0.676794 + 0.736173i \(0.736631\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 34847.3 1.46525 0.732624 0.680634i \(-0.238296\pi\)
0.732624 + 0.680634i \(0.238296\pi\)
\(828\) 0 0
\(829\) 6537.91 0.273910 0.136955 0.990577i \(-0.456268\pi\)
0.136955 + 0.990577i \(0.456268\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −80694.5 −3.35642
\(834\) 0 0
\(835\) −5893.56 −0.244258
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 2710.34 0.111527 0.0557635 0.998444i \(-0.482241\pi\)
0.0557635 + 0.998444i \(0.482241\pi\)
\(840\) 0 0
\(841\) −19565.2 −0.802215
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 6183.35 0.251732
\(846\) 0 0
\(847\) −3835.42 −0.155592
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −48830.8 −1.96698
\(852\) 0 0
\(853\) 9759.32 0.391738 0.195869 0.980630i \(-0.437247\pi\)
0.195869 + 0.980630i \(0.437247\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 13649.8 0.544072 0.272036 0.962287i \(-0.412303\pi\)
0.272036 + 0.962287i \(0.412303\pi\)
\(858\) 0 0
\(859\) −7796.42 −0.309674 −0.154837 0.987940i \(-0.549485\pi\)
−0.154837 + 0.987940i \(0.549485\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 7183.57 0.283350 0.141675 0.989913i \(-0.454751\pi\)
0.141675 + 0.989913i \(0.454751\pi\)
\(864\) 0 0
\(865\) −1720.75 −0.0676383
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −4214.30 −0.164511
\(870\) 0 0
\(871\) −436.534 −0.0169821
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −21842.7 −0.843905
\(876\) 0 0
\(877\) 17063.1 0.656991 0.328495 0.944506i \(-0.393458\pi\)
0.328495 + 0.944506i \(0.393458\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 32174.9 1.23042 0.615210 0.788363i \(-0.289071\pi\)
0.615210 + 0.788363i \(0.289071\pi\)
\(882\) 0 0
\(883\) −2843.68 −0.108378 −0.0541889 0.998531i \(-0.517257\pi\)
−0.0541889 + 0.998531i \(0.517257\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −31417.8 −1.18930 −0.594649 0.803985i \(-0.702709\pi\)
−0.594649 + 0.803985i \(0.702709\pi\)
\(888\) 0 0
\(889\) −31485.5 −1.18784
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 8064.30 0.302196
\(894\) 0 0
\(895\) 6073.83 0.226845
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −9765.47 −0.362288
\(900\) 0 0
\(901\) 599.852 0.0221798
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 1679.03 0.0616718
\(906\) 0 0
\(907\) −12253.1 −0.448573 −0.224287 0.974523i \(-0.572005\pi\)
−0.224287 + 0.974523i \(0.572005\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −48422.4 −1.76104 −0.880518 0.474012i \(-0.842805\pi\)
−0.880518 + 0.474012i \(0.842805\pi\)
\(912\) 0 0
\(913\) 10232.3 0.370909
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −12229.4 −0.440404
\(918\) 0 0
\(919\) −5546.18 −0.199077 −0.0995385 0.995034i \(-0.531737\pi\)
−0.0995385 + 0.995034i \(0.531737\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 252.822 0.00901598
\(924\) 0 0
\(925\) 49099.5 1.74528
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 35684.5 1.26025 0.630125 0.776494i \(-0.283004\pi\)
0.630125 + 0.776494i \(0.283004\pi\)
\(930\) 0 0
\(931\) −23061.1 −0.811811
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −3821.35 −0.133659
\(936\) 0 0
\(937\) −48903.6 −1.70503 −0.852514 0.522705i \(-0.824923\pi\)
−0.852514 + 0.522705i \(0.824923\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 23741.9 0.822490 0.411245 0.911525i \(-0.365094\pi\)
0.411245 + 0.911525i \(0.365094\pi\)
\(942\) 0 0
\(943\) 37437.4 1.29282
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 37612.4 1.29064 0.645321 0.763911i \(-0.276724\pi\)
0.645321 + 0.763911i \(0.276724\pi\)
\(948\) 0 0
\(949\) 4048.20 0.138472
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 48294.3 1.64156 0.820779 0.571246i \(-0.193540\pi\)
0.820779 + 0.571246i \(0.193540\pi\)
\(954\) 0 0
\(955\) 6156.09 0.208593
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 28047.4 0.944419
\(960\) 0 0
\(961\) −10021.4 −0.336389
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 4247.39 0.141687
\(966\) 0 0
\(967\) −1840.92 −0.0612204 −0.0306102 0.999531i \(-0.509745\pi\)
−0.0306102 + 0.999531i \(0.509745\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 31461.8 1.03981 0.519906 0.854223i \(-0.325967\pi\)
0.519906 + 0.854223i \(0.325967\pi\)
\(972\) 0 0
\(973\) −34612.1 −1.14040
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 7040.11 0.230535 0.115268 0.993334i \(-0.463227\pi\)
0.115268 + 0.993334i \(0.463227\pi\)
\(978\) 0 0
\(979\) −8058.15 −0.263064
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −24610.9 −0.798541 −0.399270 0.916833i \(-0.630737\pi\)
−0.399270 + 0.916833i \(0.630737\pi\)
\(984\) 0 0
\(985\) −656.744 −0.0212443
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −37318.5 −1.19986
\(990\) 0 0
\(991\) 40003.3 1.28229 0.641144 0.767421i \(-0.278460\pi\)
0.641144 + 0.767421i \(0.278460\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 63.8165 0.00203329
\(996\) 0 0
\(997\) −7342.61 −0.233242 −0.116621 0.993176i \(-0.537206\pi\)
−0.116621 + 0.993176i \(0.537206\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 1584.4.a.bj.1.1 2
3.2 odd 2 528.4.a.p.1.2 2
4.3 odd 2 99.4.a.f.1.2 2
12.11 even 2 33.4.a.c.1.1 2
20.19 odd 2 2475.4.a.p.1.1 2
24.5 odd 2 2112.4.a.bg.1.1 2
24.11 even 2 2112.4.a.bn.1.1 2
44.43 even 2 1089.4.a.u.1.1 2
60.23 odd 4 825.4.c.h.199.3 4
60.47 odd 4 825.4.c.h.199.2 4
60.59 even 2 825.4.a.l.1.2 2
84.83 odd 2 1617.4.a.k.1.1 2
132.131 odd 2 363.4.a.i.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.4.a.c.1.1 2 12.11 even 2
99.4.a.f.1.2 2 4.3 odd 2
363.4.a.i.1.2 2 132.131 odd 2
528.4.a.p.1.2 2 3.2 odd 2
825.4.a.l.1.2 2 60.59 even 2
825.4.c.h.199.2 4 60.47 odd 4
825.4.c.h.199.3 4 60.23 odd 4
1089.4.a.u.1.1 2 44.43 even 2
1584.4.a.bj.1.1 2 1.1 even 1 trivial
1617.4.a.k.1.1 2 84.83 odd 2
2112.4.a.bg.1.1 2 24.5 odd 2
2112.4.a.bn.1.1 2 24.11 even 2
2475.4.a.p.1.1 2 20.19 odd 2