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Properties

Label 1264.4.a.a.1.1
Level $1264$
Weight $4$
Character 1264.1
Self dual yes
Analytic conductor $74.578$
Analytic rank $1$
Dimension $1$
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] = [1264,4,Mod(1,1264)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1264, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("1264.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1264 = 2^{4} \cdot 79 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1264.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: \(74.5784142473\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 316)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1264.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-6.00000 q^{3} +6.00000 q^{5} +9.00000 q^{9} +O(q^{10})\) \(q-6.00000 q^{3} +6.00000 q^{5} +9.00000 q^{9} -4.00000 q^{11} +34.0000 q^{13} -36.0000 q^{15} +54.0000 q^{17} -144.000 q^{19} +8.00000 q^{23} -89.0000 q^{25} +108.000 q^{27} +180.000 q^{29} -128.000 q^{31} +24.0000 q^{33} -232.000 q^{37} -204.000 q^{39} +446.000 q^{41} +86.0000 q^{43} +54.0000 q^{45} +192.000 q^{47} -343.000 q^{49} -324.000 q^{51} -348.000 q^{53} -24.0000 q^{55} +864.000 q^{57} +838.000 q^{59} +780.000 q^{61} +204.000 q^{65} -904.000 q^{67} -48.0000 q^{69} -312.000 q^{71} -234.000 q^{73} +534.000 q^{75} -79.0000 q^{79} -891.000 q^{81} +316.000 q^{83} +324.000 q^{85} -1080.00 q^{87} +566.000 q^{89} +768.000 q^{93} -864.000 q^{95} -806.000 q^{97} -36.0000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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
\(3\) −6.00000 −1.15470 −0.577350 − 0.816497i \(-0.695913\pi\)
−0.577350 + 0.816497i \(0.695913\pi\)
\(4\) 0 0
\(5\) 6.00000 0.536656 0.268328 − 0.963328i \(-0.413529\pi\)
0.268328 + 0.963328i \(0.413529\pi\)
\(6\) 0 0
\(7\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 0 0
\(9\) 9.00000 0.333333
\(10\) 0 0
\(11\) −4.00000 −0.109640 −0.0548202 − 0.998496i \(-0.517459\pi\)
−0.0548202 + 0.998496i \(0.517459\pi\)
\(12\) 0 0
\(13\) 34.0000 0.725377 0.362689 − 0.931910i \(-0.381859\pi\)
0.362689 + 0.931910i \(0.381859\pi\)
\(14\) 0 0
\(15\) −36.0000 −0.619677
\(16\) 0 0
\(17\) 54.0000 0.770407 0.385204 − 0.922832i \(-0.374131\pi\)
0.385204 + 0.922832i \(0.374131\pi\)
\(18\) 0 0
\(19\) −144.000 −1.73873 −0.869365 − 0.494171i \(-0.835472\pi\)
−0.869365 + 0.494171i \(0.835472\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 8.00000 0.0725268 0.0362634 − 0.999342i \(-0.488454\pi\)
0.0362634 + 0.999342i \(0.488454\pi\)
\(24\) 0 0
\(25\) −89.0000 −0.712000
\(26\) 0 0
\(27\) 108.000 0.769800
\(28\) 0 0
\(29\) 180.000 1.15259 0.576296 − 0.817241i \(-0.304498\pi\)
0.576296 + 0.817241i \(0.304498\pi\)
\(30\) 0 0
\(31\) −128.000 −0.741596 −0.370798 − 0.928714i \(-0.620916\pi\)
−0.370798 + 0.928714i \(0.620916\pi\)
\(32\) 0 0
\(33\) 24.0000 0.126602
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −232.000 −1.03083 −0.515413 − 0.856942i \(-0.672361\pi\)
−0.515413 + 0.856942i \(0.672361\pi\)
\(38\) 0 0
\(39\) −204.000 −0.837593
\(40\) 0 0
\(41\) 446.000 1.69887 0.849433 − 0.527697i \(-0.176944\pi\)
0.849433 + 0.527697i \(0.176944\pi\)
\(42\) 0 0
\(43\) 86.0000 0.304997 0.152499 − 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) 0 0
\(45\) 54.0000 0.178885
\(46\) 0 0
\(47\) 192.000 0.595874 0.297937 − 0.954586i \(-0.403701\pi\)
0.297937 + 0.954586i \(0.403701\pi\)
\(48\) 0 0
\(49\) −343.000 −1.00000
\(50\) 0 0
\(51\) −324.000 −0.889590
\(52\) 0 0
\(53\) −348.000 −0.901915 −0.450957 − 0.892546i \(-0.648917\pi\)
−0.450957 + 0.892546i \(0.648917\pi\)
\(54\) 0 0
\(55\) −24.0000 −0.0588393
\(56\) 0 0
\(57\) 864.000 2.00771
\(58\) 0 0
\(59\) 838.000 1.84912 0.924562 − 0.381032i \(-0.124431\pi\)
0.924562 + 0.381032i \(0.124431\pi\)
\(60\) 0 0
\(61\) 780.000 1.63719 0.818596 − 0.574369i \(-0.194753\pi\)
0.818596 + 0.574369i \(0.194753\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 204.000 0.389278
\(66\) 0 0
\(67\) −904.000 −1.64838 −0.824188 − 0.566316i \(-0.808368\pi\)
−0.824188 + 0.566316i \(0.808368\pi\)
\(68\) 0 0
\(69\) −48.0000 −0.0837467
\(70\) 0 0
\(71\) −312.000 −0.521515 −0.260758 − 0.965404i \(-0.583972\pi\)
−0.260758 + 0.965404i \(0.583972\pi\)
\(72\) 0 0
\(73\) −234.000 −0.375173 −0.187586 − 0.982248i \(-0.560066\pi\)
−0.187586 + 0.982248i \(0.560066\pi\)
\(74\) 0 0
\(75\) 534.000 0.822147
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −79.0000 −0.112509
\(80\) 0 0
\(81\) −891.000 −1.22222
\(82\) 0 0
\(83\) 316.000 0.417898 0.208949 − 0.977927i \(-0.432996\pi\)
0.208949 + 0.977927i \(0.432996\pi\)
\(84\) 0 0
\(85\) 324.000 0.413444
\(86\) 0 0
\(87\) −1080.00 −1.33090
\(88\) 0 0
\(89\) 566.000 0.674111 0.337056 − 0.941485i \(-0.390569\pi\)
0.337056 + 0.941485i \(0.390569\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 768.000 0.856321
\(94\) 0 0
\(95\) −864.000 −0.933100
\(96\) 0 0
\(97\) −806.000 −0.843679 −0.421840 − 0.906670i \(-0.638615\pi\)
−0.421840 + 0.906670i \(0.638615\pi\)
\(98\) 0 0
\(99\) −36.0000 −0.0365468
\(100\) 0 0
\(101\) −798.000 −0.786178 −0.393089 − 0.919500i \(-0.628594\pi\)
−0.393089 + 0.919500i \(0.628594\pi\)
\(102\) 0 0
\(103\) 392.000 0.374999 0.187500 − 0.982265i \(-0.439962\pi\)
0.187500 + 0.982265i \(0.439962\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 154.000 0.139138 0.0695689 − 0.997577i \(-0.477838\pi\)
0.0695689 + 0.997577i \(0.477838\pi\)
\(108\) 0 0
\(109\) −520.000 −0.456945 −0.228472 − 0.973550i \(-0.573373\pi\)
−0.228472 + 0.973550i \(0.573373\pi\)
\(110\) 0 0
\(111\) 1392.00 1.19030
\(112\) 0 0
\(113\) 258.000 0.214784 0.107392 − 0.994217i \(-0.465750\pi\)
0.107392 + 0.994217i \(0.465750\pi\)
\(114\) 0 0
\(115\) 48.0000 0.0389219
\(116\) 0 0
\(117\) 306.000 0.241792
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −1315.00 −0.987979
\(122\) 0 0
\(123\) −2676.00 −1.96168
\(124\) 0 0
\(125\) −1284.00 −0.918756
\(126\) 0 0
\(127\) 824.000 0.575734 0.287867 − 0.957670i \(-0.407054\pi\)
0.287867 + 0.957670i \(0.407054\pi\)
\(128\) 0 0
\(129\) −516.000 −0.352180
\(130\) 0 0
\(131\) 768.000 0.512217 0.256109 − 0.966648i \(-0.417560\pi\)
0.256109 + 0.966648i \(0.417560\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 648.000 0.413118
\(136\) 0 0
\(137\) −922.000 −0.574976 −0.287488 − 0.957784i \(-0.592820\pi\)
−0.287488 + 0.957784i \(0.592820\pi\)
\(138\) 0 0
\(139\) 910.000 0.555289 0.277645 − 0.960684i \(-0.410446\pi\)
0.277645 + 0.960684i \(0.410446\pi\)
\(140\) 0 0
\(141\) −1152.00 −0.688056
\(142\) 0 0
\(143\) −136.000 −0.0795307
\(144\) 0 0
\(145\) 1080.00 0.618546
\(146\) 0 0
\(147\) 2058.00 1.15470
\(148\) 0 0
\(149\) −1204.00 −0.661983 −0.330992 − 0.943634i \(-0.607383\pi\)
−0.330992 + 0.943634i \(0.607383\pi\)
\(150\) 0 0
\(151\) −1520.00 −0.819178 −0.409589 − 0.912270i \(-0.634328\pi\)
−0.409589 + 0.912270i \(0.634328\pi\)
\(152\) 0 0
\(153\) 486.000 0.256802
\(154\) 0 0
\(155\) −768.000 −0.397982
\(156\) 0 0
\(157\) −2432.00 −1.23627 −0.618136 − 0.786071i \(-0.712112\pi\)
−0.618136 + 0.786071i \(0.712112\pi\)
\(158\) 0 0
\(159\) 2088.00 1.04144
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 2396.00 1.15134 0.575672 − 0.817680i \(-0.304740\pi\)
0.575672 + 0.817680i \(0.304740\pi\)
\(164\) 0 0
\(165\) 144.000 0.0679417
\(166\) 0 0
\(167\) −2304.00 −1.06760 −0.533799 − 0.845611i \(-0.679236\pi\)
−0.533799 + 0.845611i \(0.679236\pi\)
\(168\) 0 0
\(169\) −1041.00 −0.473828
\(170\) 0 0
\(171\) −1296.00 −0.579577
\(172\) 0 0
\(173\) −3152.00 −1.38521 −0.692607 − 0.721315i \(-0.743538\pi\)
−0.692607 + 0.721315i \(0.743538\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −5028.00 −2.13518
\(178\) 0 0
\(179\) −404.000 −0.168695 −0.0843474 − 0.996436i \(-0.526881\pi\)
−0.0843474 + 0.996436i \(0.526881\pi\)
\(180\) 0 0
\(181\) −3498.00 −1.43649 −0.718244 − 0.695791i \(-0.755054\pi\)
−0.718244 + 0.695791i \(0.755054\pi\)
\(182\) 0 0
\(183\) −4680.00 −1.89047
\(184\) 0 0
\(185\) −1392.00 −0.553199
\(186\) 0 0
\(187\) −216.000 −0.0844678
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −4716.00 −1.78659 −0.893293 − 0.449476i \(-0.851611\pi\)
−0.893293 + 0.449476i \(0.851611\pi\)
\(192\) 0 0
\(193\) −3722.00 −1.38816 −0.694081 − 0.719897i \(-0.744189\pi\)
−0.694081 + 0.719897i \(0.744189\pi\)
\(194\) 0 0
\(195\) −1224.00 −0.449500
\(196\) 0 0
\(197\) −48.0000 −0.0173597 −0.00867984 − 0.999962i \(-0.502763\pi\)
−0.00867984 + 0.999962i \(0.502763\pi\)
\(198\) 0 0
\(199\) 516.000 0.183810 0.0919052 − 0.995768i \(-0.470704\pi\)
0.0919052 + 0.995768i \(0.470704\pi\)
\(200\) 0 0
\(201\) 5424.00 1.90338
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 2676.00 0.911707
\(206\) 0 0
\(207\) 72.0000 0.0241756
\(208\) 0 0
\(209\) 576.000 0.190635
\(210\) 0 0
\(211\) 374.000 0.122025 0.0610124 − 0.998137i \(-0.480567\pi\)
0.0610124 + 0.998137i \(0.480567\pi\)
\(212\) 0 0
\(213\) 1872.00 0.602194
\(214\) 0 0
\(215\) 516.000 0.163679
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 1404.00 0.433212
\(220\) 0 0
\(221\) 1836.00 0.558836
\(222\) 0 0
\(223\) −5912.00 −1.77532 −0.887661 − 0.460498i \(-0.847671\pi\)
−0.887661 + 0.460498i \(0.847671\pi\)
\(224\) 0 0
\(225\) −801.000 −0.237333
\(226\) 0 0
\(227\) −3402.00 −0.994708 −0.497354 − 0.867548i \(-0.665695\pi\)
−0.497354 + 0.867548i \(0.665695\pi\)
\(228\) 0 0
\(229\) −16.0000 −0.00461707 −0.00230854 − 0.999997i \(-0.500735\pi\)
−0.00230854 + 0.999997i \(0.500735\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1874.00 0.526909 0.263455 − 0.964672i \(-0.415138\pi\)
0.263455 + 0.964672i \(0.415138\pi\)
\(234\) 0 0
\(235\) 1152.00 0.319780
\(236\) 0 0
\(237\) 474.000 0.129914
\(238\) 0 0
\(239\) −3024.00 −0.818436 −0.409218 − 0.912437i \(-0.634199\pi\)
−0.409218 + 0.912437i \(0.634199\pi\)
\(240\) 0 0
\(241\) 826.000 0.220777 0.110389 − 0.993888i \(-0.464790\pi\)
0.110389 + 0.993888i \(0.464790\pi\)
\(242\) 0 0
\(243\) 2430.00 0.641500
\(244\) 0 0
\(245\) −2058.00 −0.536656
\(246\) 0 0
\(247\) −4896.00 −1.26123
\(248\) 0 0
\(249\) −1896.00 −0.482547
\(250\) 0 0
\(251\) −1826.00 −0.459188 −0.229594 − 0.973287i \(-0.573740\pi\)
−0.229594 + 0.973287i \(0.573740\pi\)
\(252\) 0 0
\(253\) −32.0000 −0.00795187
\(254\) 0 0
\(255\) −1944.00 −0.477404
\(256\) 0 0
\(257\) −4034.00 −0.979121 −0.489560 − 0.871969i \(-0.662843\pi\)
−0.489560 + 0.871969i \(0.662843\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 1620.00 0.384197
\(262\) 0 0
\(263\) −8040.00 −1.88505 −0.942524 − 0.334138i \(-0.891555\pi\)
−0.942524 + 0.334138i \(0.891555\pi\)
\(264\) 0 0
\(265\) −2088.00 −0.484018
\(266\) 0 0
\(267\) −3396.00 −0.778396
\(268\) 0 0
\(269\) 3614.00 0.819143 0.409572 − 0.912278i \(-0.365678\pi\)
0.409572 + 0.912278i \(0.365678\pi\)
\(270\) 0 0
\(271\) −356.000 −0.0797987 −0.0398994 − 0.999204i \(-0.512704\pi\)
−0.0398994 + 0.999204i \(0.512704\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 356.000 0.0780640
\(276\) 0 0
\(277\) −1750.00 −0.379593 −0.189797 − 0.981823i \(-0.560783\pi\)
−0.189797 + 0.981823i \(0.560783\pi\)
\(278\) 0 0
\(279\) −1152.00 −0.247199
\(280\) 0 0
\(281\) −3330.00 −0.706944 −0.353472 − 0.935445i \(-0.614999\pi\)
−0.353472 + 0.935445i \(0.614999\pi\)
\(282\) 0 0
\(283\) 2868.00 0.602420 0.301210 − 0.953558i \(-0.402609\pi\)
0.301210 + 0.953558i \(0.402609\pi\)
\(284\) 0 0
\(285\) 5184.00 1.07745
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −1997.00 −0.406473
\(290\) 0 0
\(291\) 4836.00 0.974197
\(292\) 0 0
\(293\) 5972.00 1.19074 0.595372 − 0.803450i \(-0.297005\pi\)
0.595372 + 0.803450i \(0.297005\pi\)
\(294\) 0 0
\(295\) 5028.00 0.992344
\(296\) 0 0
\(297\) −432.000 −0.0844013
\(298\) 0 0
\(299\) 272.000 0.0526093
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 4788.00 0.907800
\(304\) 0 0
\(305\) 4680.00 0.878610
\(306\) 0 0
\(307\) 4434.00 0.824305 0.412153 − 0.911115i \(-0.364777\pi\)
0.412153 + 0.911115i \(0.364777\pi\)
\(308\) 0 0
\(309\) −2352.00 −0.433012
\(310\) 0 0
\(311\) 5116.00 0.932803 0.466402 − 0.884573i \(-0.345550\pi\)
0.466402 + 0.884573i \(0.345550\pi\)
\(312\) 0 0
\(313\) −538.000 −0.0971551 −0.0485776 − 0.998819i \(-0.515469\pi\)
−0.0485776 + 0.998819i \(0.515469\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 8346.00 1.47873 0.739366 − 0.673304i \(-0.235125\pi\)
0.739366 + 0.673304i \(0.235125\pi\)
\(318\) 0 0
\(319\) −720.000 −0.126371
\(320\) 0 0
\(321\) −924.000 −0.160662
\(322\) 0 0
\(323\) −7776.00 −1.33953
\(324\) 0 0
\(325\) −3026.00 −0.516469
\(326\) 0 0
\(327\) 3120.00 0.527634
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −7026.00 −1.16672 −0.583359 − 0.812214i \(-0.698262\pi\)
−0.583359 + 0.812214i \(0.698262\pi\)
\(332\) 0 0
\(333\) −2088.00 −0.343609
\(334\) 0 0
\(335\) −5424.00 −0.884611
\(336\) 0 0
\(337\) −5354.00 −0.865433 −0.432717 − 0.901530i \(-0.642445\pi\)
−0.432717 + 0.901530i \(0.642445\pi\)
\(338\) 0 0
\(339\) −1548.00 −0.248011
\(340\) 0 0
\(341\) 512.000 0.0813090
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −288.000 −0.0449432
\(346\) 0 0
\(347\) 2788.00 0.431319 0.215659 − 0.976469i \(-0.430810\pi\)
0.215659 + 0.976469i \(0.430810\pi\)
\(348\) 0 0
\(349\) −6352.00 −0.974254 −0.487127 − 0.873331i \(-0.661955\pi\)
−0.487127 + 0.873331i \(0.661955\pi\)
\(350\) 0 0
\(351\) 3672.00 0.558396
\(352\) 0 0
\(353\) −2358.00 −0.355534 −0.177767 − 0.984073i \(-0.556887\pi\)
−0.177767 + 0.984073i \(0.556887\pi\)
\(354\) 0 0
\(355\) −1872.00 −0.279874
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 2728.00 0.401054 0.200527 − 0.979688i \(-0.435735\pi\)
0.200527 + 0.979688i \(0.435735\pi\)
\(360\) 0 0
\(361\) 13877.0 2.02318
\(362\) 0 0
\(363\) 7890.00 1.14082
\(364\) 0 0
\(365\) −1404.00 −0.201339
\(366\) 0 0
\(367\) −64.0000 −0.00910292 −0.00455146 − 0.999990i \(-0.501449\pi\)
−0.00455146 + 0.999990i \(0.501449\pi\)
\(368\) 0 0
\(369\) 4014.00 0.566289
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 7388.00 1.02557 0.512783 − 0.858518i \(-0.328615\pi\)
0.512783 + 0.858518i \(0.328615\pi\)
\(374\) 0 0
\(375\) 7704.00 1.06089
\(376\) 0 0
\(377\) 6120.00 0.836064
\(378\) 0 0
\(379\) 8610.00 1.16693 0.583464 − 0.812139i \(-0.301697\pi\)
0.583464 + 0.812139i \(0.301697\pi\)
\(380\) 0 0
\(381\) −4944.00 −0.664800
\(382\) 0 0
\(383\) −5784.00 −0.771667 −0.385834 − 0.922568i \(-0.626086\pi\)
−0.385834 + 0.922568i \(0.626086\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 774.000 0.101666
\(388\) 0 0
\(389\) 10074.0 1.31304 0.656519 − 0.754309i \(-0.272028\pi\)
0.656519 + 0.754309i \(0.272028\pi\)
\(390\) 0 0
\(391\) 432.000 0.0558751
\(392\) 0 0
\(393\) −4608.00 −0.591458
\(394\) 0 0
\(395\) −474.000 −0.0603786
\(396\) 0 0
\(397\) 13186.0 1.66697 0.833484 − 0.552543i \(-0.186343\pi\)
0.833484 + 0.552543i \(0.186343\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 15294.0 1.90460 0.952302 − 0.305158i \(-0.0987094\pi\)
0.952302 + 0.305158i \(0.0987094\pi\)
\(402\) 0 0
\(403\) −4352.00 −0.537937
\(404\) 0 0
\(405\) −5346.00 −0.655913
\(406\) 0 0
\(407\) 928.000 0.113020
\(408\) 0 0
\(409\) −8554.00 −1.03415 −0.517076 − 0.855940i \(-0.672980\pi\)
−0.517076 + 0.855940i \(0.672980\pi\)
\(410\) 0 0
\(411\) 5532.00 0.663926
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 1896.00 0.224267
\(416\) 0 0
\(417\) −5460.00 −0.641193
\(418\) 0 0
\(419\) 5214.00 0.607925 0.303962 − 0.952684i \(-0.401690\pi\)
0.303962 + 0.952684i \(0.401690\pi\)
\(420\) 0 0
\(421\) −4510.00 −0.522100 −0.261050 − 0.965325i \(-0.584069\pi\)
−0.261050 + 0.965325i \(0.584069\pi\)
\(422\) 0 0
\(423\) 1728.00 0.198625
\(424\) 0 0
\(425\) −4806.00 −0.548530
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 816.000 0.0918342
\(430\) 0 0
\(431\) −2568.00 −0.286998 −0.143499 − 0.989650i \(-0.545835\pi\)
−0.143499 + 0.989650i \(0.545835\pi\)
\(432\) 0 0
\(433\) 4590.00 0.509426 0.254713 − 0.967017i \(-0.418019\pi\)
0.254713 + 0.967017i \(0.418019\pi\)
\(434\) 0 0
\(435\) −6480.00 −0.714235
\(436\) 0 0
\(437\) −1152.00 −0.126104
\(438\) 0 0
\(439\) 3376.00 0.367033 0.183517 − 0.983017i \(-0.441252\pi\)
0.183517 + 0.983017i \(0.441252\pi\)
\(440\) 0 0
\(441\) −3087.00 −0.333333
\(442\) 0 0
\(443\) 8718.00 0.934999 0.467500 − 0.883993i \(-0.345155\pi\)
0.467500 + 0.883993i \(0.345155\pi\)
\(444\) 0 0
\(445\) 3396.00 0.361766
\(446\) 0 0
\(447\) 7224.00 0.764393
\(448\) 0 0
\(449\) 670.000 0.0704215 0.0352108 − 0.999380i \(-0.488790\pi\)
0.0352108 + 0.999380i \(0.488790\pi\)
\(450\) 0 0
\(451\) −1784.00 −0.186264
\(452\) 0 0
\(453\) 9120.00 0.945905
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −13594.0 −1.39147 −0.695734 − 0.718300i \(-0.744921\pi\)
−0.695734 + 0.718300i \(0.744921\pi\)
\(458\) 0 0
\(459\) 5832.00 0.593060
\(460\) 0 0
\(461\) −6224.00 −0.628808 −0.314404 − 0.949289i \(-0.601805\pi\)
−0.314404 + 0.949289i \(0.601805\pi\)
\(462\) 0 0
\(463\) −2188.00 −0.219622 −0.109811 − 0.993952i \(-0.535025\pi\)
−0.109811 + 0.993952i \(0.535025\pi\)
\(464\) 0 0
\(465\) 4608.00 0.459550
\(466\) 0 0
\(467\) 17092.0 1.69363 0.846813 − 0.531891i \(-0.178518\pi\)
0.846813 + 0.531891i \(0.178518\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 14592.0 1.42752
\(472\) 0 0
\(473\) −344.000 −0.0334400
\(474\) 0 0
\(475\) 12816.0 1.23798
\(476\) 0 0
\(477\) −3132.00 −0.300638
\(478\) 0 0
\(479\) −9552.00 −0.911152 −0.455576 − 0.890197i \(-0.650567\pi\)
−0.455576 + 0.890197i \(0.650567\pi\)
\(480\) 0 0
\(481\) −7888.00 −0.747738
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −4836.00 −0.452766
\(486\) 0 0
\(487\) 4216.00 0.392290 0.196145 − 0.980575i \(-0.437158\pi\)
0.196145 + 0.980575i \(0.437158\pi\)
\(488\) 0 0
\(489\) −14376.0 −1.32946
\(490\) 0 0
\(491\) −14210.0 −1.30609 −0.653043 − 0.757321i \(-0.726508\pi\)
−0.653043 + 0.757321i \(0.726508\pi\)
\(492\) 0 0
\(493\) 9720.00 0.887965
\(494\) 0 0
\(495\) −216.000 −0.0196131
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 6680.00 0.599274 0.299637 − 0.954053i \(-0.403134\pi\)
0.299637 + 0.954053i \(0.403134\pi\)
\(500\) 0 0
\(501\) 13824.0 1.23276
\(502\) 0 0
\(503\) −5340.00 −0.473358 −0.236679 − 0.971588i \(-0.576059\pi\)
−0.236679 + 0.971588i \(0.576059\pi\)
\(504\) 0 0
\(505\) −4788.00 −0.421907
\(506\) 0 0
\(507\) 6246.00 0.547129
\(508\) 0 0
\(509\) 18116.0 1.57756 0.788780 − 0.614676i \(-0.210713\pi\)
0.788780 + 0.614676i \(0.210713\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −15552.0 −1.33847
\(514\) 0 0
\(515\) 2352.00 0.201246
\(516\) 0 0
\(517\) −768.000 −0.0653319
\(518\) 0 0
\(519\) 18912.0 1.59951
\(520\) 0 0
\(521\) −20578.0 −1.73040 −0.865200 − 0.501427i \(-0.832809\pi\)
−0.865200 + 0.501427i \(0.832809\pi\)
\(522\) 0 0
\(523\) −19432.0 −1.62467 −0.812335 − 0.583192i \(-0.801804\pi\)
−0.812335 + 0.583192i \(0.801804\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −6912.00 −0.571331
\(528\) 0 0
\(529\) −12103.0 −0.994740
\(530\) 0 0
\(531\) 7542.00 0.616375
\(532\) 0 0
\(533\) 15164.0 1.23232
\(534\) 0 0
\(535\) 924.000 0.0746692
\(536\) 0 0
\(537\) 2424.00 0.194792
\(538\) 0 0
\(539\) 1372.00 0.109640
\(540\) 0 0
\(541\) −24150.0 −1.91920 −0.959602 − 0.281360i \(-0.909214\pi\)
−0.959602 + 0.281360i \(0.909214\pi\)
\(542\) 0 0
\(543\) 20988.0 1.65871
\(544\) 0 0
\(545\) −3120.00 −0.245222
\(546\) 0 0
\(547\) −1376.00 −0.107557 −0.0537783 − 0.998553i \(-0.517126\pi\)
−0.0537783 + 0.998553i \(0.517126\pi\)
\(548\) 0 0
\(549\) 7020.00 0.545731
\(550\) 0 0
\(551\) −25920.0 −2.00405
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 8352.00 0.638780
\(556\) 0 0
\(557\) 12678.0 0.964424 0.482212 − 0.876055i \(-0.339834\pi\)
0.482212 + 0.876055i \(0.339834\pi\)
\(558\) 0 0
\(559\) 2924.00 0.221238
\(560\) 0 0
\(561\) 1296.00 0.0975350
\(562\) 0 0
\(563\) −20056.0 −1.50135 −0.750675 − 0.660672i \(-0.770271\pi\)
−0.750675 + 0.660672i \(0.770271\pi\)
\(564\) 0 0
\(565\) 1548.00 0.115265
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 9766.00 0.719529 0.359765 − 0.933043i \(-0.382857\pi\)
0.359765 + 0.933043i \(0.382857\pi\)
\(570\) 0 0
\(571\) −15712.0 −1.15154 −0.575768 − 0.817613i \(-0.695297\pi\)
−0.575768 + 0.817613i \(0.695297\pi\)
\(572\) 0 0
\(573\) 28296.0 2.06297
\(574\) 0 0
\(575\) −712.000 −0.0516390
\(576\) 0 0
\(577\) −17382.0 −1.25411 −0.627056 − 0.778975i \(-0.715740\pi\)
−0.627056 + 0.778975i \(0.715740\pi\)
\(578\) 0 0
\(579\) 22332.0 1.60291
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 1392.00 0.0988864
\(584\) 0 0
\(585\) 1836.00 0.129759
\(586\) 0 0
\(587\) 4554.00 0.320211 0.160105 − 0.987100i \(-0.448817\pi\)
0.160105 + 0.987100i \(0.448817\pi\)
\(588\) 0 0
\(589\) 18432.0 1.28944
\(590\) 0 0
\(591\) 288.000 0.0200452
\(592\) 0 0
\(593\) −7898.00 −0.546934 −0.273467 − 0.961881i \(-0.588170\pi\)
−0.273467 + 0.961881i \(0.588170\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −3096.00 −0.212246
\(598\) 0 0
\(599\) −10256.0 −0.699581 −0.349790 − 0.936828i \(-0.613747\pi\)
−0.349790 + 0.936828i \(0.613747\pi\)
\(600\) 0 0
\(601\) 8322.00 0.564828 0.282414 − 0.959293i \(-0.408865\pi\)
0.282414 + 0.959293i \(0.408865\pi\)
\(602\) 0 0
\(603\) −8136.00 −0.549459
\(604\) 0 0
\(605\) −7890.00 −0.530205
\(606\) 0 0
\(607\) −9628.00 −0.643803 −0.321902 − 0.946773i \(-0.604322\pi\)
−0.321902 + 0.946773i \(0.604322\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 6528.00 0.432233
\(612\) 0 0
\(613\) 22252.0 1.46615 0.733075 − 0.680148i \(-0.238084\pi\)
0.733075 + 0.680148i \(0.238084\pi\)
\(614\) 0 0
\(615\) −16056.0 −1.05275
\(616\) 0 0
\(617\) 15302.0 0.998437 0.499218 − 0.866476i \(-0.333621\pi\)
0.499218 + 0.866476i \(0.333621\pi\)
\(618\) 0 0
\(619\) −27406.0 −1.77955 −0.889774 − 0.456401i \(-0.849138\pi\)
−0.889774 + 0.456401i \(0.849138\pi\)
\(620\) 0 0
\(621\) 864.000 0.0558311
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 3421.00 0.218944
\(626\) 0 0
\(627\) −3456.00 −0.220127
\(628\) 0 0
\(629\) −12528.0 −0.794156
\(630\) 0 0
\(631\) −12088.0 −0.762624 −0.381312 − 0.924446i \(-0.624528\pi\)
−0.381312 + 0.924446i \(0.624528\pi\)
\(632\) 0 0
\(633\) −2244.00 −0.140902
\(634\) 0 0
\(635\) 4944.00 0.308971
\(636\) 0 0
\(637\) −11662.0 −0.725377
\(638\) 0 0
\(639\) −2808.00 −0.173838
\(640\) 0 0
\(641\) 10514.0 0.647860 0.323930 − 0.946081i \(-0.394996\pi\)
0.323930 + 0.946081i \(0.394996\pi\)
\(642\) 0 0
\(643\) 18268.0 1.12040 0.560202 − 0.828356i \(-0.310724\pi\)
0.560202 + 0.828356i \(0.310724\pi\)
\(644\) 0 0
\(645\) −3096.00 −0.189000
\(646\) 0 0
\(647\) 27416.0 1.66590 0.832948 − 0.553352i \(-0.186652\pi\)
0.832948 + 0.553352i \(0.186652\pi\)
\(648\) 0 0
\(649\) −3352.00 −0.202739
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 7254.00 0.434718 0.217359 − 0.976092i \(-0.430256\pi\)
0.217359 + 0.976092i \(0.430256\pi\)
\(654\) 0 0
\(655\) 4608.00 0.274885
\(656\) 0 0
\(657\) −2106.00 −0.125058
\(658\) 0 0
\(659\) −8238.00 −0.486960 −0.243480 − 0.969906i \(-0.578289\pi\)
−0.243480 + 0.969906i \(0.578289\pi\)
\(660\) 0 0
\(661\) 15548.0 0.914897 0.457449 − 0.889236i \(-0.348763\pi\)
0.457449 + 0.889236i \(0.348763\pi\)
\(662\) 0 0
\(663\) −11016.0 −0.645288
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 1440.00 0.0835937
\(668\) 0 0
\(669\) 35472.0 2.04997
\(670\) 0 0
\(671\) −3120.00 −0.179503
\(672\) 0 0
\(673\) 1622.00 0.0929027 0.0464513 − 0.998921i \(-0.485209\pi\)
0.0464513 + 0.998921i \(0.485209\pi\)
\(674\) 0 0
\(675\) −9612.00 −0.548098
\(676\) 0 0
\(677\) −20794.0 −1.18047 −0.590235 − 0.807231i \(-0.700965\pi\)
−0.590235 + 0.807231i \(0.700965\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 20412.0 1.14859
\(682\) 0 0
\(683\) −33840.0 −1.89583 −0.947915 − 0.318524i \(-0.896813\pi\)
−0.947915 + 0.318524i \(0.896813\pi\)
\(684\) 0 0
\(685\) −5532.00 −0.308565
\(686\) 0 0
\(687\) 96.0000 0.00533134
\(688\) 0 0
\(689\) −11832.0 −0.654228
\(690\) 0 0
\(691\) −16678.0 −0.918178 −0.459089 − 0.888390i \(-0.651824\pi\)
−0.459089 + 0.888390i \(0.651824\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 5460.00 0.297999
\(696\) 0 0
\(697\) 24084.0 1.30882
\(698\) 0 0
\(699\) −11244.0 −0.608422
\(700\) 0 0
\(701\) 6380.00 0.343751 0.171875 − 0.985119i \(-0.445017\pi\)
0.171875 + 0.985119i \(0.445017\pi\)
\(702\) 0 0
\(703\) 33408.0 1.79233
\(704\) 0 0
\(705\) −6912.00 −0.369250
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −24452.0 −1.29522 −0.647612 − 0.761970i \(-0.724232\pi\)
−0.647612 + 0.761970i \(0.724232\pi\)
\(710\) 0 0
\(711\) −711.000 −0.0375029
\(712\) 0 0
\(713\) −1024.00 −0.0537856
\(714\) 0 0
\(715\) −816.000 −0.0426807
\(716\) 0 0
\(717\) 18144.0 0.945049
\(718\) 0 0
\(719\) −11352.0 −0.588815 −0.294408 − 0.955680i \(-0.595122\pi\)
−0.294408 + 0.955680i \(0.595122\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −4956.00 −0.254932
\(724\) 0 0
\(725\) −16020.0 −0.820645
\(726\) 0 0
\(727\) 28776.0 1.46801 0.734005 − 0.679144i \(-0.237649\pi\)
0.734005 + 0.679144i \(0.237649\pi\)
\(728\) 0 0
\(729\) 9477.00 0.481481
\(730\) 0 0
\(731\) 4644.00 0.234972
\(732\) 0 0
\(733\) 30302.0 1.52692 0.763458 − 0.645857i \(-0.223500\pi\)
0.763458 + 0.645857i \(0.223500\pi\)
\(734\) 0 0
\(735\) 12348.0 0.619677
\(736\) 0 0
\(737\) 3616.00 0.180729
\(738\) 0 0
\(739\) −18130.0 −0.902467 −0.451233 − 0.892406i \(-0.649016\pi\)
−0.451233 + 0.892406i \(0.649016\pi\)
\(740\) 0 0
\(741\) 29376.0 1.45635
\(742\) 0 0
\(743\) 12944.0 0.639124 0.319562 − 0.947565i \(-0.396464\pi\)
0.319562 + 0.947565i \(0.396464\pi\)
\(744\) 0 0
\(745\) −7224.00 −0.355258
\(746\) 0 0
\(747\) 2844.00 0.139299
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 12120.0 0.588902 0.294451 − 0.955667i \(-0.404863\pi\)
0.294451 + 0.955667i \(0.404863\pi\)
\(752\) 0 0
\(753\) 10956.0 0.530224
\(754\) 0 0
\(755\) −9120.00 −0.439617
\(756\) 0 0
\(757\) −12926.0 −0.620612 −0.310306 − 0.950637i \(-0.600432\pi\)
−0.310306 + 0.950637i \(0.600432\pi\)
\(758\) 0 0
\(759\) 192.000 0.00918203
\(760\) 0 0
\(761\) −14198.0 −0.676317 −0.338158 − 0.941089i \(-0.609804\pi\)
−0.338158 + 0.941089i \(0.609804\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 2916.00 0.137815
\(766\) 0 0
\(767\) 28492.0 1.34131
\(768\) 0 0
\(769\) −37634.0 −1.76478 −0.882391 − 0.470518i \(-0.844067\pi\)
−0.882391 + 0.470518i \(0.844067\pi\)
\(770\) 0 0
\(771\) 24204.0 1.13059
\(772\) 0 0
\(773\) −18734.0 −0.871688 −0.435844 − 0.900022i \(-0.643550\pi\)
−0.435844 + 0.900022i \(0.643550\pi\)
\(774\) 0 0
\(775\) 11392.0 0.528016
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −64224.0 −2.95387
\(780\) 0 0
\(781\) 1248.00 0.0571792
\(782\) 0 0
\(783\) 19440.0 0.887266
\(784\) 0 0
\(785\) −14592.0 −0.663453
\(786\) 0 0
\(787\) 24648.0 1.11640 0.558200 − 0.829707i \(-0.311492\pi\)
0.558200 + 0.829707i \(0.311492\pi\)
\(788\) 0 0
\(789\) 48240.0 2.17667
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 26520.0 1.18758
\(794\) 0 0
\(795\) 12528.0 0.558896
\(796\) 0 0
\(797\) 3796.00 0.168709 0.0843546 − 0.996436i \(-0.473117\pi\)
0.0843546 + 0.996436i \(0.473117\pi\)
\(798\) 0 0
\(799\) 10368.0 0.459066
\(800\) 0 0
\(801\) 5094.00 0.224704
\(802\) 0 0
\(803\) 936.000 0.0411342
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −21684.0 −0.945865
\(808\) 0 0
\(809\) 15162.0 0.658922 0.329461 − 0.944169i \(-0.393133\pi\)
0.329461 + 0.944169i \(0.393133\pi\)
\(810\) 0 0
\(811\) 34424.0 1.49049 0.745247 − 0.666789i \(-0.232332\pi\)
0.745247 + 0.666789i \(0.232332\pi\)
\(812\) 0 0
\(813\) 2136.00 0.0921437
\(814\) 0 0
\(815\) 14376.0 0.617876
\(816\) 0 0
\(817\) −12384.0 −0.530308
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −7470.00 −0.317545 −0.158773 − 0.987315i \(-0.550754\pi\)
−0.158773 + 0.987315i \(0.550754\pi\)
\(822\) 0 0
\(823\) 38540.0 1.63235 0.816173 − 0.577808i \(-0.196092\pi\)
0.816173 + 0.577808i \(0.196092\pi\)
\(824\) 0 0
\(825\) −2136.00 −0.0901406
\(826\) 0 0
\(827\) −5998.00 −0.252202 −0.126101 − 0.992017i \(-0.540246\pi\)
−0.126101 + 0.992017i \(0.540246\pi\)
\(828\) 0 0
\(829\) 5440.00 0.227912 0.113956 − 0.993486i \(-0.463648\pi\)
0.113956 + 0.993486i \(0.463648\pi\)
\(830\) 0 0
\(831\) 10500.0 0.438316
\(832\) 0 0
\(833\) −18522.0 −0.770407
\(834\) 0 0
\(835\) −13824.0 −0.572933
\(836\) 0 0
\(837\) −13824.0 −0.570881
\(838\) 0 0
\(839\) 37720.0 1.55213 0.776066 − 0.630651i \(-0.217212\pi\)
0.776066 + 0.630651i \(0.217212\pi\)
\(840\) 0 0
\(841\) 8011.00 0.328468
\(842\) 0 0
\(843\) 19980.0 0.816308
\(844\) 0 0
\(845\) −6246.00 −0.254283
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −17208.0 −0.695615
\(850\) 0 0
\(851\) −1856.00 −0.0747625
\(852\) 0 0
\(853\) −11572.0 −0.464499 −0.232250 − 0.972656i \(-0.574609\pi\)
−0.232250 + 0.972656i \(0.574609\pi\)
\(854\) 0 0
\(855\) −7776.00 −0.311033
\(856\) 0 0
\(857\) 9602.00 0.382728 0.191364 − 0.981519i \(-0.438709\pi\)
0.191364 + 0.981519i \(0.438709\pi\)
\(858\) 0 0
\(859\) −15274.0 −0.606685 −0.303342 − 0.952882i \(-0.598103\pi\)
−0.303342 + 0.952882i \(0.598103\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −42120.0 −1.66139 −0.830696 − 0.556726i \(-0.812057\pi\)
−0.830696 + 0.556726i \(0.812057\pi\)
\(864\) 0 0
\(865\) −18912.0 −0.743384
\(866\) 0 0
\(867\) 11982.0 0.469354
\(868\) 0 0
\(869\) 316.000 0.0123355
\(870\) 0 0
\(871\) −30736.0 −1.19569
\(872\) 0 0
\(873\) −7254.00 −0.281226
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 33650.0 1.29564 0.647822 − 0.761792i \(-0.275680\pi\)
0.647822 + 0.761792i \(0.275680\pi\)
\(878\) 0 0
\(879\) −35832.0 −1.37495
\(880\) 0 0
\(881\) −13654.0 −0.522151 −0.261075 − 0.965318i \(-0.584077\pi\)
−0.261075 + 0.965318i \(0.584077\pi\)
\(882\) 0 0
\(883\) 13262.0 0.505438 0.252719 − 0.967540i \(-0.418675\pi\)
0.252719 + 0.967540i \(0.418675\pi\)
\(884\) 0 0
\(885\) −30168.0 −1.14586
\(886\) 0 0
\(887\) 16432.0 0.622021 0.311010 − 0.950406i \(-0.399333\pi\)
0.311010 + 0.950406i \(0.399333\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 3564.00 0.134005
\(892\) 0 0
\(893\) −27648.0 −1.03606
\(894\) 0 0
\(895\) −2424.00 −0.0905312
\(896\) 0 0
\(897\) −1632.00 −0.0607479
\(898\) 0 0
\(899\) −23040.0 −0.854758
\(900\) 0 0
\(901\) −18792.0 −0.694842
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −20988.0 −0.770900
\(906\) 0 0
\(907\) 6096.00 0.223169 0.111585 − 0.993755i \(-0.464407\pi\)
0.111585 + 0.993755i \(0.464407\pi\)
\(908\) 0 0
\(909\) −7182.00 −0.262059
\(910\) 0 0
\(911\) −49216.0 −1.78990 −0.894950 − 0.446167i \(-0.852789\pi\)
−0.894950 + 0.446167i \(0.852789\pi\)
\(912\) 0 0
\(913\) −1264.00 −0.0458185
\(914\) 0 0
\(915\) −28080.0 −1.01453
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −9520.00 −0.341715 −0.170857 − 0.985296i \(-0.554654\pi\)
−0.170857 + 0.985296i \(0.554654\pi\)
\(920\) 0 0
\(921\) −26604.0 −0.951826
\(922\) 0 0
\(923\) −10608.0 −0.378295
\(924\) 0 0
\(925\) 20648.0 0.733948
\(926\) 0 0
\(927\) 3528.00 0.125000
\(928\) 0 0
\(929\) 38742.0 1.36823 0.684114 − 0.729375i \(-0.260189\pi\)
0.684114 + 0.729375i \(0.260189\pi\)
\(930\) 0 0
\(931\) 49392.0 1.73873
\(932\) 0 0
\(933\) −30696.0 −1.07711
\(934\) 0 0
\(935\) −1296.00 −0.0453302
\(936\) 0 0
\(937\) 21714.0 0.757060 0.378530 − 0.925589i \(-0.376430\pi\)
0.378530 + 0.925589i \(0.376430\pi\)
\(938\) 0 0
\(939\) 3228.00 0.112185
\(940\) 0 0
\(941\) −21062.0 −0.729651 −0.364825 − 0.931076i \(-0.618871\pi\)
−0.364825 + 0.931076i \(0.618871\pi\)
\(942\) 0 0
\(943\) 3568.00 0.123213
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 46446.0 1.59376 0.796881 − 0.604137i \(-0.206482\pi\)
0.796881 + 0.604137i \(0.206482\pi\)
\(948\) 0 0
\(949\) −7956.00 −0.272142
\(950\) 0 0
\(951\) −50076.0 −1.70749
\(952\) 0 0
\(953\) −40670.0 −1.38240 −0.691202 − 0.722662i \(-0.742918\pi\)
−0.691202 + 0.722662i \(0.742918\pi\)
\(954\) 0 0
\(955\) −28296.0 −0.958782
\(956\) 0 0
\(957\) 4320.00 0.145920
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −13407.0 −0.450035
\(962\) 0 0
\(963\) 1386.00 0.0463793
\(964\) 0 0
\(965\) −22332.0 −0.744966
\(966\) 0 0
\(967\) 38512.0 1.28073 0.640363 − 0.768072i \(-0.278784\pi\)
0.640363 + 0.768072i \(0.278784\pi\)
\(968\) 0 0
\(969\) 46656.0 1.54676
\(970\) 0 0
\(971\) −9840.00 −0.325212 −0.162606 − 0.986691i \(-0.551990\pi\)
−0.162606 + 0.986691i \(0.551990\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 18156.0 0.596367
\(976\) 0 0
\(977\) −25922.0 −0.848842 −0.424421 − 0.905465i \(-0.639522\pi\)
−0.424421 + 0.905465i \(0.639522\pi\)
\(978\) 0 0
\(979\) −2264.00 −0.0739099
\(980\) 0 0
\(981\) −4680.00 −0.152315
\(982\) 0 0
\(983\) 34360.0 1.11487 0.557433 − 0.830222i \(-0.311786\pi\)
0.557433 + 0.830222i \(0.311786\pi\)
\(984\) 0 0
\(985\) −288.000 −0.00931619
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 688.000 0.0221205
\(990\) 0 0
\(991\) −25624.0 −0.821365 −0.410683 − 0.911778i \(-0.634710\pi\)
−0.410683 + 0.911778i \(0.634710\pi\)
\(992\) 0 0
\(993\) 42156.0 1.34721
\(994\) 0 0
\(995\) 3096.00 0.0986430
\(996\) 0 0
\(997\) 11530.0 0.366258 0.183129 − 0.983089i \(-0.441377\pi\)
0.183129 + 0.983089i \(0.441377\pi\)
\(998\) 0 0
\(999\) −25056.0 −0.793530
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 1264.4.a.a.1.1 1
4.3 odd 2 316.4.a.a.1.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
316.4.a.a.1.1 ✓ 1 4.3 odd 2
1264.4.a.a.1.1 1 1.1 even 1 trivial