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Properties

Label 1764.4.a.j.1.1
Level $1764$
Weight $4$
Character 1764.1
Self dual yes
Analytic conductor $104.079$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1764,4,Mod(1,1764)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1764, 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("1764.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1764.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: \(104.079369250\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 84)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1764.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+6.00000 q^{5} -36.0000 q^{11} -62.0000 q^{13} +114.000 q^{17} +76.0000 q^{19} +24.0000 q^{23} -89.0000 q^{25} -54.0000 q^{29} +112.000 q^{31} -178.000 q^{37} +378.000 q^{41} -172.000 q^{43} -192.000 q^{47} +402.000 q^{53} -216.000 q^{55} +396.000 q^{59} -254.000 q^{61} -372.000 q^{65} -1012.00 q^{67} -840.000 q^{71} -890.000 q^{73} +80.0000 q^{79} -108.000 q^{83} +684.000 q^{85} -1638.00 q^{89} +456.000 q^{95} -1010.00 q^{97} +O(q^{100})\)

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
\(5\) 6.00000 0.536656 0.268328 − 0.963328i \(-0.413529\pi\)
0.268328 + 0.963328i \(0.413529\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −36.0000 −0.986764 −0.493382 − 0.869813i \(-0.664240\pi\)
−0.493382 + 0.869813i \(0.664240\pi\)
\(12\) 0 0
\(13\) −62.0000 −1.32275 −0.661373 − 0.750057i \(-0.730026\pi\)
−0.661373 + 0.750057i \(0.730026\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 114.000 1.62642 0.813208 − 0.581974i \(-0.197719\pi\)
0.813208 + 0.581974i \(0.197719\pi\)
\(18\) 0 0
\(19\) 76.0000 0.917663 0.458831 − 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 24.0000 0.217580 0.108790 − 0.994065i \(-0.465302\pi\)
0.108790 + 0.994065i \(0.465302\pi\)
\(24\) 0 0
\(25\) −89.0000 −0.712000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −54.0000 −0.345778 −0.172889 − 0.984941i \(-0.555310\pi\)
−0.172889 + 0.984941i \(0.555310\pi\)
\(30\) 0 0
\(31\) 112.000 0.648897 0.324448 − 0.945903i \(-0.394821\pi\)
0.324448 + 0.945903i \(0.394821\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −178.000 −0.790892 −0.395446 − 0.918489i \(-0.629410\pi\)
−0.395446 + 0.918489i \(0.629410\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 378.000 1.43985 0.719923 − 0.694054i \(-0.244177\pi\)
0.719923 + 0.694054i \(0.244177\pi\)
\(42\) 0 0
\(43\) −172.000 −0.609994 −0.304997 − 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −192.000 −0.595874 −0.297937 − 0.954586i \(-0.596299\pi\)
−0.297937 + 0.954586i \(0.596299\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 402.000 1.04187 0.520933 − 0.853597i \(-0.325584\pi\)
0.520933 + 0.853597i \(0.325584\pi\)
\(54\) 0 0
\(55\) −216.000 −0.529553
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 396.000 0.873810 0.436905 − 0.899508i \(-0.356075\pi\)
0.436905 + 0.899508i \(0.356075\pi\)
\(60\) 0 0
\(61\) −254.000 −0.533137 −0.266569 − 0.963816i \(-0.585890\pi\)
−0.266569 + 0.963816i \(0.585890\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −372.000 −0.709860
\(66\) 0 0
\(67\) −1012.00 −1.84531 −0.922653 − 0.385632i \(-0.873984\pi\)
−0.922653 + 0.385632i \(0.873984\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −840.000 −1.40408 −0.702040 − 0.712138i \(-0.747727\pi\)
−0.702040 + 0.712138i \(0.747727\pi\)
\(72\) 0 0
\(73\) −890.000 −1.42694 −0.713470 − 0.700686i \(-0.752878\pi\)
−0.713470 + 0.700686i \(0.752878\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 80.0000 0.113933 0.0569665 − 0.998376i \(-0.481857\pi\)
0.0569665 + 0.998376i \(0.481857\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −108.000 −0.142826 −0.0714129 − 0.997447i \(-0.522751\pi\)
−0.0714129 + 0.997447i \(0.522751\pi\)
\(84\) 0 0
\(85\) 684.000 0.872826
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1638.00 −1.95087 −0.975436 − 0.220282i \(-0.929302\pi\)
−0.975436 + 0.220282i \(0.929302\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 456.000 0.492470
\(96\) 0 0
\(97\) −1010.00 −1.05722 −0.528608 − 0.848866i \(-0.677286\pi\)
−0.528608 + 0.848866i \(0.677286\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 6.00000 0.00591111 0.00295556 − 0.999996i \(-0.499059\pi\)
0.00295556 + 0.999996i \(0.499059\pi\)
\(102\) 0 0
\(103\) 472.000 0.451530 0.225765 − 0.974182i \(-0.427512\pi\)
0.225765 + 0.974182i \(0.427512\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 972.000 0.878194 0.439097 − 0.898440i \(-0.355298\pi\)
0.439097 + 0.898440i \(0.355298\pi\)
\(108\) 0 0
\(109\) −1786.00 −1.56943 −0.784715 − 0.619857i \(-0.787190\pi\)
−0.784715 + 0.619857i \(0.787190\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 2286.00 1.90309 0.951543 − 0.307515i \(-0.0994973\pi\)
0.951543 + 0.307515i \(0.0994973\pi\)
\(114\) 0 0
\(115\) 144.000 0.116766
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −35.0000 −0.0262960
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1284.00 −0.918756
\(126\) 0 0
\(127\) 1328.00 0.927881 0.463941 − 0.885866i \(-0.346435\pi\)
0.463941 + 0.885866i \(0.346435\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1212.00 −0.808343 −0.404171 − 0.914683i \(-0.632440\pi\)
−0.404171 + 0.914683i \(0.632440\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1254.00 0.782018 0.391009 − 0.920387i \(-0.372126\pi\)
0.391009 + 0.920387i \(0.372126\pi\)
\(138\) 0 0
\(139\) 340.000 0.207471 0.103735 − 0.994605i \(-0.466921\pi\)
0.103735 + 0.994605i \(0.466921\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 2232.00 1.30524
\(144\) 0 0
\(145\) −324.000 −0.185564
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1038.00 −0.570713 −0.285357 − 0.958421i \(-0.592112\pi\)
−0.285357 + 0.958421i \(0.592112\pi\)
\(150\) 0 0
\(151\) 2936.00 1.58231 0.791153 − 0.611618i \(-0.209481\pi\)
0.791153 + 0.611618i \(0.209481\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 672.000 0.348234
\(156\) 0 0
\(157\) 1330.00 0.676086 0.338043 − 0.941131i \(-0.390235\pi\)
0.338043 + 0.941131i \(0.390235\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −3364.00 −1.61650 −0.808248 − 0.588842i \(-0.799584\pi\)
−0.808248 + 0.588842i \(0.799584\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3048.00 1.41234 0.706172 − 0.708041i \(-0.250421\pi\)
0.706172 + 0.708041i \(0.250421\pi\)
\(168\) 0 0
\(169\) 1647.00 0.749659
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −2706.00 −1.18921 −0.594605 − 0.804018i \(-0.702692\pi\)
−0.594605 + 0.804018i \(0.702692\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −4716.00 −1.96922 −0.984610 − 0.174766i \(-0.944083\pi\)
−0.984610 + 0.174766i \(0.944083\pi\)
\(180\) 0 0
\(181\) −1910.00 −0.784360 −0.392180 − 0.919888i \(-0.628279\pi\)
−0.392180 + 0.919888i \(0.628279\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1068.00 −0.424437
\(186\) 0 0
\(187\) −4104.00 −1.60489
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −4080.00 −1.54565 −0.772823 − 0.634621i \(-0.781156\pi\)
−0.772823 + 0.634621i \(0.781156\pi\)
\(192\) 0 0
\(193\) −2686.00 −1.00177 −0.500887 − 0.865512i \(-0.666993\pi\)
−0.500887 + 0.865512i \(0.666993\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −510.000 −0.184447 −0.0922233 − 0.995738i \(-0.529397\pi\)
−0.0922233 + 0.995738i \(0.529397\pi\)
\(198\) 0 0
\(199\) −1352.00 −0.481612 −0.240806 − 0.970573i \(-0.577412\pi\)
−0.240806 + 0.970573i \(0.577412\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 2268.00 0.772702
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2736.00 −0.905517
\(210\) 0 0
\(211\) −3364.00 −1.09757 −0.548785 − 0.835963i \(-0.684909\pi\)
−0.548785 + 0.835963i \(0.684909\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1032.00 −0.327357
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −7068.00 −2.15134
\(222\) 0 0
\(223\) 4768.00 1.43179 0.715894 − 0.698209i \(-0.246019\pi\)
0.715894 + 0.698209i \(0.246019\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 420.000 0.122803 0.0614017 − 0.998113i \(-0.480443\pi\)
0.0614017 + 0.998113i \(0.480443\pi\)
\(228\) 0 0
\(229\) 1882.00 0.543083 0.271542 − 0.962427i \(-0.412467\pi\)
0.271542 + 0.962427i \(0.412467\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −5082.00 −1.42890 −0.714448 − 0.699688i \(-0.753322\pi\)
−0.714448 + 0.699688i \(0.753322\pi\)
\(234\) 0 0
\(235\) −1152.00 −0.319780
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 5424.00 1.46799 0.733995 − 0.679155i \(-0.237654\pi\)
0.733995 + 0.679155i \(0.237654\pi\)
\(240\) 0 0
\(241\) 2590.00 0.692268 0.346134 − 0.938185i \(-0.387494\pi\)
0.346134 + 0.938185i \(0.387494\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −4712.00 −1.21384
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −4932.00 −1.24026 −0.620130 − 0.784499i \(-0.712920\pi\)
−0.620130 + 0.784499i \(0.712920\pi\)
\(252\) 0 0
\(253\) −864.000 −0.214700
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −3438.00 −0.834461 −0.417231 − 0.908801i \(-0.636999\pi\)
−0.417231 + 0.908801i \(0.636999\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −6120.00 −1.43489 −0.717444 − 0.696617i \(-0.754688\pi\)
−0.717444 + 0.696617i \(0.754688\pi\)
\(264\) 0 0
\(265\) 2412.00 0.559124
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −18.0000 −0.00407985 −0.00203992 − 0.999998i \(-0.500649\pi\)
−0.00203992 + 0.999998i \(0.500649\pi\)
\(270\) 0 0
\(271\) −6896.00 −1.54576 −0.772882 − 0.634549i \(-0.781186\pi\)
−0.772882 + 0.634549i \(0.781186\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 3204.00 0.702576
\(276\) 0 0
\(277\) 6254.00 1.35656 0.678279 − 0.734805i \(-0.262726\pi\)
0.678279 + 0.734805i \(0.262726\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1194.00 −0.253481 −0.126740 − 0.991936i \(-0.540451\pi\)
−0.126740 + 0.991936i \(0.540451\pi\)
\(282\) 0 0
\(283\) 7156.00 1.50311 0.751555 − 0.659671i \(-0.229304\pi\)
0.751555 + 0.659671i \(0.229304\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 8083.00 1.64523
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −3738.00 −0.745312 −0.372656 − 0.927970i \(-0.621553\pi\)
−0.372656 + 0.927970i \(0.621553\pi\)
\(294\) 0 0
\(295\) 2376.00 0.468936
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1488.00 −0.287804
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1524.00 −0.286111
\(306\) 0 0
\(307\) 844.000 0.156904 0.0784522 − 0.996918i \(-0.475002\pi\)
0.0784522 + 0.996918i \(0.475002\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 6312.00 1.15087 0.575435 − 0.817847i \(-0.304833\pi\)
0.575435 + 0.817847i \(0.304833\pi\)
\(312\) 0 0
\(313\) −8282.00 −1.49561 −0.747806 − 0.663918i \(-0.768892\pi\)
−0.747806 + 0.663918i \(0.768892\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −9318.00 −1.65095 −0.825475 − 0.564439i \(-0.809093\pi\)
−0.825475 + 0.564439i \(0.809093\pi\)
\(318\) 0 0
\(319\) 1944.00 0.341201
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 8664.00 1.49250
\(324\) 0 0
\(325\) 5518.00 0.941796
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 1652.00 0.274327 0.137163 − 0.990548i \(-0.456201\pi\)
0.137163 + 0.990548i \(0.456201\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −6072.00 −0.990295
\(336\) 0 0
\(337\) −1294.00 −0.209165 −0.104583 − 0.994516i \(-0.533351\pi\)
−0.104583 + 0.994516i \(0.533351\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −4032.00 −0.640308
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −3636.00 −0.562509 −0.281255 − 0.959633i \(-0.590751\pi\)
−0.281255 + 0.959633i \(0.590751\pi\)
\(348\) 0 0
\(349\) −10478.0 −1.60709 −0.803545 − 0.595244i \(-0.797055\pi\)
−0.803545 + 0.595244i \(0.797055\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −7566.00 −1.14079 −0.570393 − 0.821372i \(-0.693209\pi\)
−0.570393 + 0.821372i \(0.693209\pi\)
\(354\) 0 0
\(355\) −5040.00 −0.753508
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 8040.00 1.18199 0.590996 − 0.806675i \(-0.298735\pi\)
0.590996 + 0.806675i \(0.298735\pi\)
\(360\) 0 0
\(361\) −1083.00 −0.157895
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −5340.00 −0.765776
\(366\) 0 0
\(367\) −7568.00 −1.07642 −0.538210 − 0.842811i \(-0.680899\pi\)
−0.538210 + 0.842811i \(0.680899\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −13522.0 −1.87706 −0.938529 − 0.345200i \(-0.887811\pi\)
−0.938529 + 0.345200i \(0.887811\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 3348.00 0.457376
\(378\) 0 0
\(379\) 2468.00 0.334492 0.167246 − 0.985915i \(-0.446513\pi\)
0.167246 + 0.985915i \(0.446513\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −12336.0 −1.64580 −0.822898 − 0.568189i \(-0.807644\pi\)
−0.822898 + 0.568189i \(0.807644\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 3762.00 0.490337 0.245168 − 0.969481i \(-0.421157\pi\)
0.245168 + 0.969481i \(0.421157\pi\)
\(390\) 0 0
\(391\) 2736.00 0.353876
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 480.000 0.0611428
\(396\) 0 0
\(397\) 8770.00 1.10870 0.554350 − 0.832284i \(-0.312967\pi\)
0.554350 + 0.832284i \(0.312967\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −6642.00 −0.827146 −0.413573 − 0.910471i \(-0.635719\pi\)
−0.413573 + 0.910471i \(0.635719\pi\)
\(402\) 0 0
\(403\) −6944.00 −0.858326
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 6408.00 0.780424
\(408\) 0 0
\(409\) 1510.00 0.182554 0.0912771 − 0.995826i \(-0.470905\pi\)
0.0912771 + 0.995826i \(0.470905\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −648.000 −0.0766484
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −1260.00 −0.146909 −0.0734547 − 0.997299i \(-0.523402\pi\)
−0.0734547 + 0.997299i \(0.523402\pi\)
\(420\) 0 0
\(421\) 3998.00 0.462828 0.231414 − 0.972855i \(-0.425665\pi\)
0.231414 + 0.972855i \(0.425665\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −10146.0 −1.15801
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2736.00 0.305774 0.152887 − 0.988244i \(-0.451143\pi\)
0.152887 + 0.988244i \(0.451143\pi\)
\(432\) 0 0
\(433\) −2690.00 −0.298552 −0.149276 − 0.988796i \(-0.547694\pi\)
−0.149276 + 0.988796i \(0.547694\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1824.00 0.199665
\(438\) 0 0
\(439\) 1240.00 0.134811 0.0674054 − 0.997726i \(-0.478528\pi\)
0.0674054 + 0.997726i \(0.478528\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 3900.00 0.418272 0.209136 − 0.977887i \(-0.432935\pi\)
0.209136 + 0.977887i \(0.432935\pi\)
\(444\) 0 0
\(445\) −9828.00 −1.04695
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 10878.0 1.14335 0.571675 − 0.820480i \(-0.306294\pi\)
0.571675 + 0.820480i \(0.306294\pi\)
\(450\) 0 0
\(451\) −13608.0 −1.42079
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 2330.00 0.238496 0.119248 − 0.992864i \(-0.461952\pi\)
0.119248 + 0.992864i \(0.461952\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 15150.0 1.53060 0.765299 − 0.643675i \(-0.222591\pi\)
0.765299 + 0.643675i \(0.222591\pi\)
\(462\) 0 0
\(463\) −2992.00 −0.300324 −0.150162 − 0.988661i \(-0.547980\pi\)
−0.150162 + 0.988661i \(0.547980\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 8724.00 0.864451 0.432225 − 0.901766i \(-0.357728\pi\)
0.432225 + 0.901766i \(0.357728\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 6192.00 0.601921
\(474\) 0 0
\(475\) −6764.00 −0.653376
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 9744.00 0.929467 0.464734 − 0.885451i \(-0.346150\pi\)
0.464734 + 0.885451i \(0.346150\pi\)
\(480\) 0 0
\(481\) 11036.0 1.04615
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −6060.00 −0.567362
\(486\) 0 0
\(487\) 4136.00 0.384846 0.192423 − 0.981312i \(-0.438365\pi\)
0.192423 + 0.981312i \(0.438365\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −16212.0 −1.49010 −0.745048 − 0.667011i \(-0.767574\pi\)
−0.745048 + 0.667011i \(0.767574\pi\)
\(492\) 0 0
\(493\) −6156.00 −0.562378
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 2396.00 0.214949 0.107475 − 0.994208i \(-0.465724\pi\)
0.107475 + 0.994208i \(0.465724\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 13128.0 1.16371 0.581857 − 0.813291i \(-0.302326\pi\)
0.581857 + 0.813291i \(0.302326\pi\)
\(504\) 0 0
\(505\) 36.0000 0.00317224
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 12798.0 1.11446 0.557231 − 0.830357i \(-0.311864\pi\)
0.557231 + 0.830357i \(0.311864\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 2832.00 0.242316
\(516\) 0 0
\(517\) 6912.00 0.587987
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 7386.00 0.621087 0.310544 − 0.950559i \(-0.399489\pi\)
0.310544 + 0.950559i \(0.399489\pi\)
\(522\) 0 0
\(523\) −5180.00 −0.433089 −0.216545 − 0.976273i \(-0.569479\pi\)
−0.216545 + 0.976273i \(0.569479\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 12768.0 1.05538
\(528\) 0 0
\(529\) −11591.0 −0.952659
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −23436.0 −1.90455
\(534\) 0 0
\(535\) 5832.00 0.471288
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 4070.00 0.323444 0.161722 − 0.986836i \(-0.448295\pi\)
0.161722 + 0.986836i \(0.448295\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −10716.0 −0.842244
\(546\) 0 0
\(547\) 14780.0 1.15530 0.577648 − 0.816286i \(-0.303971\pi\)
0.577648 + 0.816286i \(0.303971\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −4104.00 −0.317307
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 6858.00 0.521693 0.260846 − 0.965380i \(-0.415998\pi\)
0.260846 + 0.965380i \(0.415998\pi\)
\(558\) 0 0
\(559\) 10664.0 0.806868
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 6660.00 0.498553 0.249277 − 0.968432i \(-0.419807\pi\)
0.249277 + 0.968432i \(0.419807\pi\)
\(564\) 0 0
\(565\) 13716.0 1.02130
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 150.000 0.0110515 0.00552577 − 0.999985i \(-0.498241\pi\)
0.00552577 + 0.999985i \(0.498241\pi\)
\(570\) 0 0
\(571\) −8188.00 −0.600100 −0.300050 − 0.953923i \(-0.597003\pi\)
−0.300050 + 0.953923i \(0.597003\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −2136.00 −0.154917
\(576\) 0 0
\(577\) 5854.00 0.422366 0.211183 − 0.977447i \(-0.432268\pi\)
0.211183 + 0.977447i \(0.432268\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −14472.0 −1.02808
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 17580.0 1.23612 0.618062 − 0.786130i \(-0.287918\pi\)
0.618062 + 0.786130i \(0.287918\pi\)
\(588\) 0 0
\(589\) 8512.00 0.595468
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 17154.0 1.18791 0.593955 − 0.804498i \(-0.297566\pi\)
0.593955 + 0.804498i \(0.297566\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 18120.0 1.23600 0.617999 − 0.786179i \(-0.287943\pi\)
0.617999 + 0.786179i \(0.287943\pi\)
\(600\) 0 0
\(601\) −17546.0 −1.19088 −0.595438 − 0.803401i \(-0.703021\pi\)
−0.595438 + 0.803401i \(0.703021\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −210.000 −0.0141119
\(606\) 0 0
\(607\) 14560.0 0.973595 0.486798 − 0.873515i \(-0.338165\pi\)
0.486798 + 0.873515i \(0.338165\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 11904.0 0.788190
\(612\) 0 0
\(613\) −4498.00 −0.296366 −0.148183 − 0.988960i \(-0.547343\pi\)
−0.148183 + 0.988960i \(0.547343\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 5478.00 0.357433 0.178716 − 0.983901i \(-0.442806\pi\)
0.178716 + 0.983901i \(0.442806\pi\)
\(618\) 0 0
\(619\) −6044.00 −0.392454 −0.196227 − 0.980559i \(-0.562869\pi\)
−0.196227 + 0.980559i \(0.562869\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 3421.00 0.218944
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −20292.0 −1.28632
\(630\) 0 0
\(631\) −15352.0 −0.968547 −0.484274 − 0.874917i \(-0.660916\pi\)
−0.484274 + 0.874917i \(0.660916\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 7968.00 0.497953
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 22398.0 1.38014 0.690068 − 0.723744i \(-0.257580\pi\)
0.690068 + 0.723744i \(0.257580\pi\)
\(642\) 0 0
\(643\) −3764.00 −0.230852 −0.115426 − 0.993316i \(-0.536823\pi\)
−0.115426 + 0.993316i \(0.536823\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −17688.0 −1.07479 −0.537393 − 0.843332i \(-0.680591\pi\)
−0.537393 + 0.843332i \(0.680591\pi\)
\(648\) 0 0
\(649\) −14256.0 −0.862245
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −19878.0 −1.19125 −0.595625 − 0.803263i \(-0.703096\pi\)
−0.595625 + 0.803263i \(0.703096\pi\)
\(654\) 0 0
\(655\) −7272.00 −0.433802
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 20004.0 1.18247 0.591233 − 0.806501i \(-0.298641\pi\)
0.591233 + 0.806501i \(0.298641\pi\)
\(660\) 0 0
\(661\) 1306.00 0.0768495 0.0384247 − 0.999261i \(-0.487766\pi\)
0.0384247 + 0.999261i \(0.487766\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −1296.00 −0.0752344
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 9144.00 0.526081
\(672\) 0 0
\(673\) −13054.0 −0.747689 −0.373845 − 0.927491i \(-0.621961\pi\)
−0.373845 + 0.927491i \(0.621961\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 5046.00 0.286460 0.143230 − 0.989689i \(-0.454251\pi\)
0.143230 + 0.989689i \(0.454251\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −12468.0 −0.698499 −0.349249 − 0.937030i \(-0.613563\pi\)
−0.349249 + 0.937030i \(0.613563\pi\)
\(684\) 0 0
\(685\) 7524.00 0.419675
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −24924.0 −1.37813
\(690\) 0 0
\(691\) 23212.0 1.27790 0.638948 − 0.769250i \(-0.279370\pi\)
0.638948 + 0.769250i \(0.279370\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 2040.00 0.111340
\(696\) 0 0
\(697\) 43092.0 2.34179
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −35958.0 −1.93740 −0.968698 − 0.248241i \(-0.920147\pi\)
−0.968698 + 0.248241i \(0.920147\pi\)
\(702\) 0 0
\(703\) −13528.0 −0.725773
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 6446.00 0.341445 0.170723 − 0.985319i \(-0.445390\pi\)
0.170723 + 0.985319i \(0.445390\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2688.00 0.141187
\(714\) 0 0
\(715\) 13392.0 0.700465
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −4704.00 −0.243991 −0.121996 − 0.992531i \(-0.538929\pi\)
−0.121996 + 0.992531i \(0.538929\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 4806.00 0.246194
\(726\) 0 0
\(727\) 10600.0 0.540760 0.270380 − 0.962754i \(-0.412851\pi\)
0.270380 + 0.962754i \(0.412851\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −19608.0 −0.992104
\(732\) 0 0
\(733\) −12542.0 −0.631991 −0.315995 − 0.948761i \(-0.602338\pi\)
−0.315995 + 0.948761i \(0.602338\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 36432.0 1.82088
\(738\) 0 0
\(739\) 23324.0 1.16101 0.580506 − 0.814256i \(-0.302855\pi\)
0.580506 + 0.814256i \(0.302855\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 6312.00 0.311662 0.155831 − 0.987784i \(-0.450194\pi\)
0.155831 + 0.987784i \(0.450194\pi\)
\(744\) 0 0
\(745\) −6228.00 −0.306277
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 35840.0 1.74144 0.870719 − 0.491781i \(-0.163654\pi\)
0.870719 + 0.491781i \(0.163654\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 17616.0 0.849155
\(756\) 0 0
\(757\) −34594.0 −1.66095 −0.830476 − 0.557055i \(-0.811931\pi\)
−0.830476 + 0.557055i \(0.811931\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 23946.0 1.14066 0.570330 − 0.821416i \(-0.306815\pi\)
0.570330 + 0.821416i \(0.306815\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −24552.0 −1.15583
\(768\) 0 0
\(769\) −18770.0 −0.880187 −0.440093 − 0.897952i \(-0.645055\pi\)
−0.440093 + 0.897952i \(0.645055\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 30342.0 1.41181 0.705903 − 0.708309i \(-0.250541\pi\)
0.705903 + 0.708309i \(0.250541\pi\)
\(774\) 0 0
\(775\) −9968.00 −0.462014
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 28728.0 1.32129
\(780\) 0 0
\(781\) 30240.0 1.38550
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 7980.00 0.362826
\(786\) 0 0
\(787\) 26188.0 1.18615 0.593076 − 0.805147i \(-0.297913\pi\)
0.593076 + 0.805147i \(0.297913\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 15748.0 0.705205
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −34818.0 −1.54745 −0.773724 − 0.633522i \(-0.781609\pi\)
−0.773724 + 0.633522i \(0.781609\pi\)
\(798\) 0 0
\(799\) −21888.0 −0.969139
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 32040.0 1.40805
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 21702.0 0.943142 0.471571 − 0.881828i \(-0.343687\pi\)
0.471571 + 0.881828i \(0.343687\pi\)
\(810\) 0 0
\(811\) 20356.0 0.881376 0.440688 − 0.897660i \(-0.354735\pi\)
0.440688 + 0.897660i \(0.354735\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −20184.0 −0.867503
\(816\) 0 0
\(817\) −13072.0 −0.559769
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 19890.0 0.845513 0.422756 − 0.906243i \(-0.361063\pi\)
0.422756 + 0.906243i \(0.361063\pi\)
\(822\) 0 0
\(823\) 4232.00 0.179245 0.0896223 − 0.995976i \(-0.471434\pi\)
0.0896223 + 0.995976i \(0.471434\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −9636.00 −0.405171 −0.202586 − 0.979265i \(-0.564934\pi\)
−0.202586 + 0.979265i \(0.564934\pi\)
\(828\) 0 0
\(829\) −35294.0 −1.47866 −0.739331 − 0.673342i \(-0.764858\pi\)
−0.739331 + 0.673342i \(0.764858\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 18288.0 0.757943
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −3768.00 −0.155049 −0.0775243 − 0.996990i \(-0.524702\pi\)
−0.0775243 + 0.996990i \(0.524702\pi\)
\(840\) 0 0
\(841\) −21473.0 −0.880438
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 9882.00 0.402309
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −4272.00 −0.172083
\(852\) 0 0
\(853\) 39466.0 1.58416 0.792081 − 0.610416i \(-0.208998\pi\)
0.792081 + 0.610416i \(0.208998\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −34038.0 −1.35673 −0.678364 − 0.734726i \(-0.737311\pi\)
−0.678364 + 0.734726i \(0.737311\pi\)
\(858\) 0 0
\(859\) 3364.00 0.133618 0.0668092 − 0.997766i \(-0.478718\pi\)
0.0668092 + 0.997766i \(0.478718\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −13104.0 −0.516878 −0.258439 − 0.966028i \(-0.583208\pi\)
−0.258439 + 0.966028i \(0.583208\pi\)
\(864\) 0 0
\(865\) −16236.0 −0.638197
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −2880.00 −0.112425
\(870\) 0 0
\(871\) 62744.0 2.44087
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −40858.0 −1.57318 −0.786589 − 0.617477i \(-0.788155\pi\)
−0.786589 + 0.617477i \(0.788155\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −37374.0 −1.42924 −0.714621 − 0.699512i \(-0.753401\pi\)
−0.714621 + 0.699512i \(0.753401\pi\)
\(882\) 0 0
\(883\) 9788.00 0.373038 0.186519 − 0.982451i \(-0.440279\pi\)
0.186519 + 0.982451i \(0.440279\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 50424.0 1.90876 0.954381 − 0.298591i \(-0.0965166\pi\)
0.954381 + 0.298591i \(0.0965166\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −14592.0 −0.546811
\(894\) 0 0
\(895\) −28296.0 −1.05679
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −6048.00 −0.224374
\(900\) 0 0
\(901\) 45828.0 1.69451
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −11460.0 −0.420932
\(906\) 0 0
\(907\) −12412.0 −0.454392 −0.227196 − 0.973849i \(-0.572956\pi\)
−0.227196 + 0.973849i \(0.572956\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −6576.00 −0.239158 −0.119579 − 0.992825i \(-0.538154\pi\)
−0.119579 + 0.992825i \(0.538154\pi\)
\(912\) 0 0
\(913\) 3888.00 0.140935
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 8264.00 0.296631 0.148316 − 0.988940i \(-0.452615\pi\)
0.148316 + 0.988940i \(0.452615\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 52080.0 1.85724
\(924\) 0 0
\(925\) 15842.0 0.563115
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 39426.0 1.39238 0.696192 − 0.717855i \(-0.254876\pi\)
0.696192 + 0.717855i \(0.254876\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −24624.0 −0.861274
\(936\) 0 0
\(937\) 4678.00 0.163099 0.0815494 − 0.996669i \(-0.474013\pi\)
0.0815494 + 0.996669i \(0.474013\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −17346.0 −0.600918 −0.300459 − 0.953795i \(-0.597140\pi\)
−0.300459 + 0.953795i \(0.597140\pi\)
\(942\) 0 0
\(943\) 9072.00 0.313282
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −19452.0 −0.667482 −0.333741 − 0.942665i \(-0.608311\pi\)
−0.333741 + 0.942665i \(0.608311\pi\)
\(948\) 0 0
\(949\) 55180.0 1.88748
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −4458.00 −0.151531 −0.0757654 − 0.997126i \(-0.524140\pi\)
−0.0757654 + 0.997126i \(0.524140\pi\)
\(954\) 0 0
\(955\) −24480.0 −0.829481
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −17247.0 −0.578933
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −16116.0 −0.537609
\(966\) 0 0
\(967\) 52520.0 1.74657 0.873283 − 0.487213i \(-0.161987\pi\)
0.873283 + 0.487213i \(0.161987\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −10404.0 −0.343852 −0.171926 − 0.985110i \(-0.554999\pi\)
−0.171926 + 0.985110i \(0.554999\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 7566.00 0.247756 0.123878 − 0.992297i \(-0.460467\pi\)
0.123878 + 0.992297i \(0.460467\pi\)
\(978\) 0 0
\(979\) 58968.0 1.92505
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 44376.0 1.43985 0.719926 − 0.694051i \(-0.244176\pi\)
0.719926 + 0.694051i \(0.244176\pi\)
\(984\) 0 0
\(985\) −3060.00 −0.0989845
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −4128.00 −0.132723
\(990\) 0 0
\(991\) −27328.0 −0.875986 −0.437993 − 0.898978i \(-0.644311\pi\)
−0.437993 + 0.898978i \(0.644311\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −8112.00 −0.258460
\(996\) 0 0
\(997\) −2774.00 −0.0881178 −0.0440589 − 0.999029i \(-0.514029\pi\)
−0.0440589 + 0.999029i \(0.514029\pi\)
\(998\) 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 1764.4.a.j.1.1 1
3.2 odd 2 588.4.a.d.1.1 1
7.2 even 3 1764.4.k.f.361.1 2
7.3 odd 6 1764.4.k.l.1549.1 2
7.4 even 3 1764.4.k.f.1549.1 2
7.5 odd 6 1764.4.k.l.361.1 2
7.6 odd 2 252.4.a.b.1.1 1
12.11 even 2 2352.4.a.d.1.1 1
21.2 odd 6 588.4.i.c.361.1 2
21.5 even 6 588.4.i.f.361.1 2
21.11 odd 6 588.4.i.c.373.1 2
21.17 even 6 588.4.i.f.373.1 2
21.20 even 2 84.4.a.a.1.1 ✓ 1
28.27 even 2 1008.4.a.h.1.1 1
84.83 odd 2 336.4.a.k.1.1 1
105.62 odd 4 2100.4.k.j.1849.2 2
105.83 odd 4 2100.4.k.j.1849.1 2
105.104 even 2 2100.4.a.l.1.1 1
168.83 odd 2 1344.4.a.d.1.1 1
168.125 even 2 1344.4.a.q.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.4.a.a.1.1 ✓ 1 21.20 even 2
252.4.a.b.1.1 1 7.6 odd 2
336.4.a.k.1.1 1 84.83 odd 2
588.4.a.d.1.1 1 3.2 odd 2
588.4.i.c.361.1 2 21.2 odd 6
588.4.i.c.373.1 2 21.11 odd 6
588.4.i.f.361.1 2 21.5 even 6
588.4.i.f.373.1 2 21.17 even 6
1008.4.a.h.1.1 1 28.27 even 2
1344.4.a.d.1.1 1 168.83 odd 2
1344.4.a.q.1.1 1 168.125 even 2
1764.4.a.j.1.1 1 1.1 even 1 trivial
1764.4.k.f.361.1 2 7.2 even 3
1764.4.k.f.1549.1 2 7.4 even 3
1764.4.k.l.361.1 2 7.5 odd 6
1764.4.k.l.1549.1 2 7.3 odd 6
2100.4.a.l.1.1 1 105.104 even 2
2100.4.k.j.1849.1 2 105.83 odd 4
2100.4.k.j.1849.2 2 105.62 odd 4
2352.4.a.d.1.1 1 12.11 even 2