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Properties

Label 9576.2.a.bb.1.1
Level $9576$
Weight $2$
Character 9576.1
Self dual yes
Analytic conductor $76.465$
Analytic rank $0$
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] = [9576,2,Mod(1,9576)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9576, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("9576.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9576 = 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9576.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: \(76.4647449756\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 3192)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 9576.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+4.00000 q^{5} +1.00000 q^{7} +O(q^{10})\) \(q+4.00000 q^{5} +1.00000 q^{7} -2.00000 q^{11} -4.00000 q^{13} -4.00000 q^{17} +1.00000 q^{19} +6.00000 q^{23} +11.0000 q^{25} +2.00000 q^{29} +4.00000 q^{31} +4.00000 q^{35} +2.00000 q^{37} +2.00000 q^{41} -8.00000 q^{43} -4.00000 q^{47} +1.00000 q^{49} +10.0000 q^{53} -8.00000 q^{55} +4.00000 q^{59} +6.00000 q^{61} -16.0000 q^{65} -10.0000 q^{67} +16.0000 q^{71} -6.00000 q^{73} -2.00000 q^{77} -10.0000 q^{79} +12.0000 q^{83} -16.0000 q^{85} -6.00000 q^{89} -4.00000 q^{91} +4.00000 q^{95} +16.0000 q^{97} +O(q^{100})\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) 4.00000 1.78885 0.894427 − 0.447214i \(-0.147584\pi\)
0.894427 + 0.447214i \(0.147584\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.00000 −0.603023 −0.301511 − 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 0 0
\(13\) −4.00000 −1.10940 −0.554700 − 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −4.00000 −0.970143 −0.485071 − 0.874475i \(-0.661206\pi\)
−0.485071 + 0.874475i \(0.661206\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 6.00000 1.25109 0.625543 − 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) 0 0
\(25\) 11.0000 2.20000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2.00000 0.371391 0.185695 − 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 − 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 4.00000 0.676123
\(36\) 0 0
\(37\) 2.00000 0.328798 0.164399 − 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2.00000 0.312348 0.156174 − 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 0 0
\(43\) −8.00000 −1.21999 −0.609994 − 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.00000 −0.583460 −0.291730 − 0.956501i \(-0.594231\pi\)
−0.291730 + 0.956501i \(0.594231\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 10.0000 1.37361 0.686803 − 0.726844i \(-0.259014\pi\)
0.686803 + 0.726844i \(0.259014\pi\)
\(54\) 0 0
\(55\) −8.00000 −1.07872
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 4.00000 0.520756 0.260378 − 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) 0 0
\(61\) 6.00000 0.768221 0.384111 − 0.923287i \(-0.374508\pi\)
0.384111 + 0.923287i \(0.374508\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −16.0000 −1.98456
\(66\) 0 0
\(67\) −10.0000 −1.22169 −0.610847 − 0.791748i \(-0.709171\pi\)
−0.610847 + 0.791748i \(0.709171\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 16.0000 1.89885 0.949425 − 0.313993i \(-0.101667\pi\)
0.949425 + 0.313993i \(0.101667\pi\)
\(72\) 0 0
\(73\) −6.00000 −0.702247 −0.351123 − 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.00000 −0.227921
\(78\) 0 0
\(79\) −10.0000 −1.12509 −0.562544 − 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 12.0000 1.31717 0.658586 − 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 0 0
\(85\) −16.0000 −1.73544
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −6.00000 −0.635999 −0.317999 − 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 0 0
\(91\) −4.00000 −0.419314
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 4.00000 0.410391
\(96\) 0 0
\(97\) 16.0000 1.62455 0.812277 − 0.583272i \(-0.198228\pi\)
0.812277 + 0.583272i \(0.198228\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 12.0000 1.19404 0.597022 − 0.802225i \(-0.296350\pi\)
0.597022 + 0.802225i \(0.296350\pi\)
\(102\) 0 0
\(103\) 4.00000 0.394132 0.197066 − 0.980390i \(-0.436859\pi\)
0.197066 + 0.980390i \(0.436859\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −8.00000 −0.773389 −0.386695 − 0.922208i \(-0.626383\pi\)
−0.386695 + 0.922208i \(0.626383\pi\)
\(108\) 0 0
\(109\) 10.0000 0.957826 0.478913 − 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 18.0000 1.69330 0.846649 − 0.532152i \(-0.178617\pi\)
0.846649 + 0.532152i \(0.178617\pi\)
\(114\) 0 0
\(115\) 24.0000 2.23801
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −4.00000 −0.366679
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 24.0000 2.14663
\(126\) 0 0
\(127\) 2.00000 0.177471 0.0887357 − 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 1.00000 0.0867110
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2.00000 0.170872 0.0854358 − 0.996344i \(-0.472772\pi\)
0.0854358 + 0.996344i \(0.472772\pi\)
\(138\) 0 0
\(139\) 20.0000 1.69638 0.848189 − 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 8.00000 0.668994
\(144\) 0 0
\(145\) 8.00000 0.664364
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 18.0000 1.47462 0.737309 − 0.675556i \(-0.236096\pi\)
0.737309 + 0.675556i \(0.236096\pi\)
\(150\) 0 0
\(151\) −2.00000 −0.162758 −0.0813788 − 0.996683i \(-0.525932\pi\)
−0.0813788 + 0.996683i \(0.525932\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 16.0000 1.28515
\(156\) 0 0
\(157\) −22.0000 −1.75579 −0.877896 − 0.478852i \(-0.841053\pi\)
−0.877896 + 0.478852i \(0.841053\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 6.00000 0.472866
\(162\) 0 0
\(163\) −24.0000 −1.87983 −0.939913 − 0.341415i \(-0.889094\pi\)
−0.939913 + 0.341415i \(0.889094\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 22.0000 1.67263 0.836315 − 0.548250i \(-0.184706\pi\)
0.836315 + 0.548250i \(0.184706\pi\)
\(174\) 0 0
\(175\) 11.0000 0.831522
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −8.00000 −0.597948 −0.298974 − 0.954261i \(-0.596644\pi\)
−0.298974 + 0.954261i \(0.596644\pi\)
\(180\) 0 0
\(181\) 16.0000 1.18927 0.594635 − 0.803996i \(-0.297296\pi\)
0.594635 + 0.803996i \(0.297296\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 8.00000 0.588172
\(186\) 0 0
\(187\) 8.00000 0.585018
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 6.00000 0.434145 0.217072 − 0.976156i \(-0.430349\pi\)
0.217072 + 0.976156i \(0.430349\pi\)
\(192\) 0 0
\(193\) 2.00000 0.143963 0.0719816 − 0.997406i \(-0.477068\pi\)
0.0719816 + 0.997406i \(0.477068\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 18.0000 1.28245 0.641223 − 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) −16.0000 −1.13421 −0.567105 − 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 2.00000 0.140372
\(204\) 0 0
\(205\) 8.00000 0.558744
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2.00000 −0.138343
\(210\) 0 0
\(211\) −2.00000 −0.137686 −0.0688428 − 0.997628i \(-0.521931\pi\)
−0.0688428 + 0.997628i \(0.521931\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −32.0000 −2.18238
\(216\) 0 0
\(217\) 4.00000 0.271538
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 16.0000 1.07628
\(222\) 0 0
\(223\) 16.0000 1.07144 0.535720 − 0.844396i \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −4.00000 −0.265489 −0.132745 − 0.991150i \(-0.542379\pi\)
−0.132745 + 0.991150i \(0.542379\pi\)
\(228\) 0 0
\(229\) 22.0000 1.45380 0.726900 − 0.686743i \(-0.240960\pi\)
0.726900 + 0.686743i \(0.240960\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 18.0000 1.17922 0.589610 − 0.807688i \(-0.299282\pi\)
0.589610 + 0.807688i \(0.299282\pi\)
\(234\) 0 0
\(235\) −16.0000 −1.04372
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 6.00000 0.388108 0.194054 − 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) 0 0
\(241\) −4.00000 −0.257663 −0.128831 − 0.991667i \(-0.541123\pi\)
−0.128831 + 0.991667i \(0.541123\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 4.00000 0.255551
\(246\) 0 0
\(247\) −4.00000 −0.254514
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 8.00000 0.504956 0.252478 − 0.967603i \(-0.418755\pi\)
0.252478 + 0.967603i \(0.418755\pi\)
\(252\) 0 0
\(253\) −12.0000 −0.754434
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −10.0000 −0.623783 −0.311891 − 0.950118i \(-0.600963\pi\)
−0.311891 + 0.950118i \(0.600963\pi\)
\(258\) 0 0
\(259\) 2.00000 0.124274
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −30.0000 −1.84988 −0.924940 − 0.380114i \(-0.875885\pi\)
−0.924940 + 0.380114i \(0.875885\pi\)
\(264\) 0 0
\(265\) 40.0000 2.45718
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 6.00000 0.365826 0.182913 − 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(270\) 0 0
\(271\) 8.00000 0.485965 0.242983 − 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −22.0000 −1.32665
\(276\) 0 0
\(277\) 22.0000 1.32185 0.660926 − 0.750451i \(-0.270164\pi\)
0.660926 + 0.750451i \(0.270164\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −6.00000 −0.357930 −0.178965 − 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) 0 0
\(283\) −4.00000 −0.237775 −0.118888 − 0.992908i \(-0.537933\pi\)
−0.118888 + 0.992908i \(0.537933\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2.00000 0.118056
\(288\) 0 0
\(289\) −1.00000 −0.0588235
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −10.0000 −0.584206 −0.292103 − 0.956387i \(-0.594355\pi\)
−0.292103 + 0.956387i \(0.594355\pi\)
\(294\) 0 0
\(295\) 16.0000 0.931556
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −24.0000 −1.38796
\(300\) 0 0
\(301\) −8.00000 −0.461112
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 24.0000 1.37424
\(306\) 0 0
\(307\) −32.0000 −1.82634 −0.913168 − 0.407583i \(-0.866372\pi\)
−0.913168 + 0.407583i \(0.866372\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −32.0000 −1.81455 −0.907277 − 0.420534i \(-0.861843\pi\)
−0.907277 + 0.420534i \(0.861843\pi\)
\(312\) 0 0
\(313\) −22.0000 −1.24351 −0.621757 − 0.783210i \(-0.713581\pi\)
−0.621757 + 0.783210i \(0.713581\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −18.0000 −1.01098 −0.505490 − 0.862832i \(-0.668688\pi\)
−0.505490 + 0.862832i \(0.668688\pi\)
\(318\) 0 0
\(319\) −4.00000 −0.223957
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −4.00000 −0.222566
\(324\) 0 0
\(325\) −44.0000 −2.44068
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −4.00000 −0.220527
\(330\) 0 0
\(331\) 10.0000 0.549650 0.274825 − 0.961494i \(-0.411380\pi\)
0.274825 + 0.961494i \(0.411380\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −40.0000 −2.18543
\(336\) 0 0
\(337\) −18.0000 −0.980522 −0.490261 − 0.871576i \(-0.663099\pi\)
−0.490261 + 0.871576i \(0.663099\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −8.00000 −0.433224
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 10.0000 0.536828 0.268414 − 0.963304i \(-0.413500\pi\)
0.268414 + 0.963304i \(0.413500\pi\)
\(348\) 0 0
\(349\) 10.0000 0.535288 0.267644 − 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −12.0000 −0.638696 −0.319348 − 0.947638i \(-0.603464\pi\)
−0.319348 + 0.947638i \(0.603464\pi\)
\(354\) 0 0
\(355\) 64.0000 3.39677
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −22.0000 −1.16112 −0.580558 − 0.814219i \(-0.697165\pi\)
−0.580558 + 0.814219i \(0.697165\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −24.0000 −1.25622
\(366\) 0 0
\(367\) 8.00000 0.417597 0.208798 − 0.977959i \(-0.433045\pi\)
0.208798 + 0.977959i \(0.433045\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 10.0000 0.519174
\(372\) 0 0
\(373\) 22.0000 1.13912 0.569558 − 0.821951i \(-0.307114\pi\)
0.569558 + 0.821951i \(0.307114\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −8.00000 −0.412021
\(378\) 0 0
\(379\) −14.0000 −0.719132 −0.359566 − 0.933120i \(-0.617075\pi\)
−0.359566 + 0.933120i \(0.617075\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) −8.00000 −0.407718
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 6.00000 0.304212 0.152106 − 0.988364i \(-0.451394\pi\)
0.152106 + 0.988364i \(0.451394\pi\)
\(390\) 0 0
\(391\) −24.0000 −1.21373
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −40.0000 −2.01262
\(396\) 0 0
\(397\) −30.0000 −1.50566 −0.752828 − 0.658217i \(-0.771311\pi\)
−0.752828 + 0.658217i \(0.771311\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 6.00000 0.299626 0.149813 − 0.988714i \(-0.452133\pi\)
0.149813 + 0.988714i \(0.452133\pi\)
\(402\) 0 0
\(403\) −16.0000 −0.797017
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −4.00000 −0.198273
\(408\) 0 0
\(409\) −24.0000 −1.18672 −0.593362 − 0.804936i \(-0.702200\pi\)
−0.593362 + 0.804936i \(0.702200\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 4.00000 0.196827
\(414\) 0 0
\(415\) 48.0000 2.35623
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 24.0000 1.17248 0.586238 − 0.810139i \(-0.300608\pi\)
0.586238 + 0.810139i \(0.300608\pi\)
\(420\) 0 0
\(421\) 22.0000 1.07221 0.536107 − 0.844150i \(-0.319894\pi\)
0.536107 + 0.844150i \(0.319894\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −44.0000 −2.13431
\(426\) 0 0
\(427\) 6.00000 0.290360
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 16.0000 0.768911 0.384455 − 0.923144i \(-0.374389\pi\)
0.384455 + 0.923144i \(0.374389\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 6.00000 0.287019
\(438\) 0 0
\(439\) 28.0000 1.33637 0.668184 − 0.743996i \(-0.267072\pi\)
0.668184 + 0.743996i \(0.267072\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −18.0000 −0.855206 −0.427603 − 0.903967i \(-0.640642\pi\)
−0.427603 + 0.903967i \(0.640642\pi\)
\(444\) 0 0
\(445\) −24.0000 −1.13771
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 10.0000 0.471929 0.235965 − 0.971762i \(-0.424175\pi\)
0.235965 + 0.971762i \(0.424175\pi\)
\(450\) 0 0
\(451\) −4.00000 −0.188353
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −16.0000 −0.750092
\(456\) 0 0
\(457\) 6.00000 0.280668 0.140334 − 0.990104i \(-0.455182\pi\)
0.140334 + 0.990104i \(0.455182\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 12.0000 0.558896 0.279448 − 0.960161i \(-0.409849\pi\)
0.279448 + 0.960161i \(0.409849\pi\)
\(462\) 0 0
\(463\) 8.00000 0.371792 0.185896 − 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −12.0000 −0.555294 −0.277647 − 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) 0 0
\(469\) −10.0000 −0.461757
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 16.0000 0.735681
\(474\) 0 0
\(475\) 11.0000 0.504715
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) −8.00000 −0.364769
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 64.0000 2.90609
\(486\) 0 0
\(487\) 10.0000 0.453143 0.226572 − 0.973995i \(-0.427248\pi\)
0.226572 + 0.973995i \(0.427248\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −30.0000 −1.35388 −0.676941 − 0.736038i \(-0.736695\pi\)
−0.676941 + 0.736038i \(0.736695\pi\)
\(492\) 0 0
\(493\) −8.00000 −0.360302
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 16.0000 0.717698
\(498\) 0 0
\(499\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 24.0000 1.07011 0.535054 − 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 0 0
\(505\) 48.0000 2.13597
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 30.0000 1.32973 0.664863 − 0.746965i \(-0.268490\pi\)
0.664863 + 0.746965i \(0.268490\pi\)
\(510\) 0 0
\(511\) −6.00000 −0.265424
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 16.0000 0.705044
\(516\) 0 0
\(517\) 8.00000 0.351840
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −6.00000 −0.262865 −0.131432 − 0.991325i \(-0.541958\pi\)
−0.131432 + 0.991325i \(0.541958\pi\)
\(522\) 0 0
\(523\) −16.0000 −0.699631 −0.349816 − 0.936819i \(-0.613756\pi\)
−0.349816 + 0.936819i \(0.613756\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −16.0000 −0.696971
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −8.00000 −0.346518
\(534\) 0 0
\(535\) −32.0000 −1.38348
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −2.00000 −0.0861461
\(540\) 0 0
\(541\) −46.0000 −1.97769 −0.988847 − 0.148933i \(-0.952416\pi\)
−0.988847 + 0.148933i \(0.952416\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 40.0000 1.71341
\(546\) 0 0
\(547\) −18.0000 −0.769624 −0.384812 − 0.922995i \(-0.625734\pi\)
−0.384812 + 0.922995i \(0.625734\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 2.00000 0.0852029
\(552\) 0 0
\(553\) −10.0000 −0.425243
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 18.0000 0.762684 0.381342 − 0.924434i \(-0.375462\pi\)
0.381342 + 0.924434i \(0.375462\pi\)
\(558\) 0 0
\(559\) 32.0000 1.35346
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −36.0000 −1.51722 −0.758610 − 0.651546i \(-0.774121\pi\)
−0.758610 + 0.651546i \(0.774121\pi\)
\(564\) 0 0
\(565\) 72.0000 3.02906
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −26.0000 −1.08998 −0.544988 − 0.838444i \(-0.683466\pi\)
−0.544988 + 0.838444i \(0.683466\pi\)
\(570\) 0 0
\(571\) 20.0000 0.836974 0.418487 − 0.908223i \(-0.362561\pi\)
0.418487 + 0.908223i \(0.362561\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 66.0000 2.75239
\(576\) 0 0
\(577\) −30.0000 −1.24892 −0.624458 − 0.781058i \(-0.714680\pi\)
−0.624458 + 0.781058i \(0.714680\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 12.0000 0.497844
\(582\) 0 0
\(583\) −20.0000 −0.828315
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 12.0000 0.495293 0.247647 − 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) 0 0
\(589\) 4.00000 0.164817
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −24.0000 −0.985562 −0.492781 − 0.870153i \(-0.664020\pi\)
−0.492781 + 0.870153i \(0.664020\pi\)
\(594\) 0 0
\(595\) −16.0000 −0.655936
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 40.0000 1.63436 0.817178 − 0.576386i \(-0.195537\pi\)
0.817178 + 0.576386i \(0.195537\pi\)
\(600\) 0 0
\(601\) 24.0000 0.978980 0.489490 − 0.872009i \(-0.337183\pi\)
0.489490 + 0.872009i \(0.337183\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −28.0000 −1.13836
\(606\) 0 0
\(607\) 32.0000 1.29884 0.649420 − 0.760430i \(-0.275012\pi\)
0.649420 + 0.760430i \(0.275012\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 16.0000 0.647291
\(612\) 0 0
\(613\) 14.0000 0.565455 0.282727 − 0.959200i \(-0.408761\pi\)
0.282727 + 0.959200i \(0.408761\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −14.0000 −0.563619 −0.281809 − 0.959470i \(-0.590935\pi\)
−0.281809 + 0.959470i \(0.590935\pi\)
\(618\) 0 0
\(619\) −4.00000 −0.160774 −0.0803868 − 0.996764i \(-0.525616\pi\)
−0.0803868 + 0.996764i \(0.525616\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −6.00000 −0.240385
\(624\) 0 0
\(625\) 41.0000 1.64000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −8.00000 −0.318981
\(630\) 0 0
\(631\) −20.0000 −0.796187 −0.398094 − 0.917345i \(-0.630328\pi\)
−0.398094 + 0.917345i \(0.630328\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 8.00000 0.317470
\(636\) 0 0
\(637\) −4.00000 −0.158486
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 34.0000 1.34292 0.671460 − 0.741041i \(-0.265668\pi\)
0.671460 + 0.741041i \(0.265668\pi\)
\(642\) 0 0
\(643\) −4.00000 −0.157745 −0.0788723 − 0.996885i \(-0.525132\pi\)
−0.0788723 + 0.996885i \(0.525132\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 32.0000 1.25805 0.629025 − 0.777385i \(-0.283454\pi\)
0.629025 + 0.777385i \(0.283454\pi\)
\(648\) 0 0
\(649\) −8.00000 −0.314027
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −42.0000 −1.64359 −0.821794 − 0.569785i \(-0.807026\pi\)
−0.821794 + 0.569785i \(0.807026\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −40.0000 −1.55818 −0.779089 − 0.626913i \(-0.784318\pi\)
−0.779089 + 0.626913i \(0.784318\pi\)
\(660\) 0 0
\(661\) −16.0000 −0.622328 −0.311164 − 0.950356i \(-0.600719\pi\)
−0.311164 + 0.950356i \(0.600719\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 4.00000 0.155113
\(666\) 0 0
\(667\) 12.0000 0.464642
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −12.0000 −0.463255
\(672\) 0 0
\(673\) 30.0000 1.15642 0.578208 − 0.815890i \(-0.303752\pi\)
0.578208 + 0.815890i \(0.303752\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 26.0000 0.999261 0.499631 − 0.866239i \(-0.333469\pi\)
0.499631 + 0.866239i \(0.333469\pi\)
\(678\) 0 0
\(679\) 16.0000 0.614024
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −36.0000 −1.37750 −0.688751 − 0.724998i \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) 0 0
\(685\) 8.00000 0.305664
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −40.0000 −1.52388
\(690\) 0 0
\(691\) 4.00000 0.152167 0.0760836 − 0.997101i \(-0.475758\pi\)
0.0760836 + 0.997101i \(0.475758\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 80.0000 3.03457
\(696\) 0 0
\(697\) −8.00000 −0.303022
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −34.0000 −1.28416 −0.642081 − 0.766637i \(-0.721929\pi\)
−0.642081 + 0.766637i \(0.721929\pi\)
\(702\) 0 0
\(703\) 2.00000 0.0754314
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 12.0000 0.451306
\(708\) 0 0
\(709\) 10.0000 0.375558 0.187779 − 0.982211i \(-0.439871\pi\)
0.187779 + 0.982211i \(0.439871\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 24.0000 0.898807
\(714\) 0 0
\(715\) 32.0000 1.19673
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −48.0000 −1.79010 −0.895049 − 0.445968i \(-0.852860\pi\)
−0.895049 + 0.445968i \(0.852860\pi\)
\(720\) 0 0
\(721\) 4.00000 0.148968
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 22.0000 0.817059
\(726\) 0 0
\(727\) 16.0000 0.593407 0.296704 − 0.954970i \(-0.404113\pi\)
0.296704 + 0.954970i \(0.404113\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 32.0000 1.18356
\(732\) 0 0
\(733\) −46.0000 −1.69905 −0.849524 − 0.527549i \(-0.823111\pi\)
−0.849524 + 0.527549i \(0.823111\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 20.0000 0.736709
\(738\) 0 0
\(739\) 44.0000 1.61857 0.809283 − 0.587419i \(-0.199856\pi\)
0.809283 + 0.587419i \(0.199856\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 36.0000 1.32071 0.660356 − 0.750953i \(-0.270405\pi\)
0.660356 + 0.750953i \(0.270405\pi\)
\(744\) 0 0
\(745\) 72.0000 2.63788
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −8.00000 −0.292314
\(750\) 0 0
\(751\) 26.0000 0.948753 0.474377 − 0.880322i \(-0.342673\pi\)
0.474377 + 0.880322i \(0.342673\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −8.00000 −0.291150
\(756\) 0 0
\(757\) 30.0000 1.09037 0.545184 − 0.838316i \(-0.316460\pi\)
0.545184 + 0.838316i \(0.316460\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −24.0000 −0.869999 −0.435000 − 0.900431i \(-0.643252\pi\)
−0.435000 + 0.900431i \(0.643252\pi\)
\(762\) 0 0
\(763\) 10.0000 0.362024
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −16.0000 −0.577727
\(768\) 0 0
\(769\) −22.0000 −0.793340 −0.396670 − 0.917961i \(-0.629834\pi\)
−0.396670 + 0.917961i \(0.629834\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 38.0000 1.36677 0.683383 − 0.730061i \(-0.260508\pi\)
0.683383 + 0.730061i \(0.260508\pi\)
\(774\) 0 0
\(775\) 44.0000 1.58053
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 2.00000 0.0716574
\(780\) 0 0
\(781\) −32.0000 −1.14505
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −88.0000 −3.14085
\(786\) 0 0
\(787\) −48.0000 −1.71102 −0.855508 − 0.517790i \(-0.826755\pi\)
−0.855508 + 0.517790i \(0.826755\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 18.0000 0.640006
\(792\) 0 0
\(793\) −24.0000 −0.852265
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −42.0000 −1.48772 −0.743858 − 0.668338i \(-0.767006\pi\)
−0.743858 + 0.668338i \(0.767006\pi\)
\(798\) 0 0
\(799\) 16.0000 0.566039
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 12.0000 0.423471
\(804\) 0 0
\(805\) 24.0000 0.845889
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −34.0000 −1.19538 −0.597688 − 0.801729i \(-0.703914\pi\)
−0.597688 + 0.801729i \(0.703914\pi\)
\(810\) 0 0
\(811\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −96.0000 −3.36273
\(816\) 0 0
\(817\) −8.00000 −0.279885
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −6.00000 −0.209401 −0.104701 − 0.994504i \(-0.533388\pi\)
−0.104701 + 0.994504i \(0.533388\pi\)
\(822\) 0 0
\(823\) −16.0000 −0.557725 −0.278862 − 0.960331i \(-0.589957\pi\)
−0.278862 + 0.960331i \(0.589957\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) 0 0
\(829\) 36.0000 1.25033 0.625166 − 0.780492i \(-0.285031\pi\)
0.625166 + 0.780492i \(0.285031\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −4.00000 −0.138592
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 16.0000 0.552381 0.276191 − 0.961103i \(-0.410928\pi\)
0.276191 + 0.961103i \(0.410928\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 12.0000 0.412813
\(846\) 0 0
\(847\) −7.00000 −0.240523
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 12.0000 0.411355
\(852\) 0 0
\(853\) −26.0000 −0.890223 −0.445112 − 0.895475i \(-0.646836\pi\)
−0.445112 + 0.895475i \(0.646836\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 18.0000 0.614868 0.307434 − 0.951569i \(-0.400530\pi\)
0.307434 + 0.951569i \(0.400530\pi\)
\(858\) 0 0
\(859\) −36.0000 −1.22830 −0.614152 − 0.789188i \(-0.710502\pi\)
−0.614152 + 0.789188i \(0.710502\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −4.00000 −0.136162 −0.0680808 − 0.997680i \(-0.521688\pi\)
−0.0680808 + 0.997680i \(0.521688\pi\)
\(864\) 0 0
\(865\) 88.0000 2.99209
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 20.0000 0.678454
\(870\) 0 0
\(871\) 40.0000 1.35535
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 24.0000 0.811348
\(876\) 0 0
\(877\) 18.0000 0.607817 0.303908 − 0.952701i \(-0.401708\pi\)
0.303908 + 0.952701i \(0.401708\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 44.0000 1.48240 0.741199 − 0.671286i \(-0.234258\pi\)
0.741199 + 0.671286i \(0.234258\pi\)
\(882\) 0 0
\(883\) 40.0000 1.34611 0.673054 − 0.739594i \(-0.264982\pi\)
0.673054 + 0.739594i \(0.264982\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 32.0000 1.07445 0.537227 − 0.843437i \(-0.319472\pi\)
0.537227 + 0.843437i \(0.319472\pi\)
\(888\) 0 0
\(889\) 2.00000 0.0670778
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −4.00000 −0.133855
\(894\) 0 0
\(895\) −32.0000 −1.06964
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 8.00000 0.266815
\(900\) 0 0
\(901\) −40.0000 −1.33259
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 64.0000 2.12743
\(906\) 0 0
\(907\) −30.0000 −0.996134 −0.498067 − 0.867139i \(-0.665957\pi\)
−0.498067 + 0.867139i \(0.665957\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 56.0000 1.85536 0.927681 − 0.373373i \(-0.121799\pi\)
0.927681 + 0.373373i \(0.121799\pi\)
\(912\) 0 0
\(913\) −24.0000 −0.794284
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −48.0000 −1.58337 −0.791687 − 0.610927i \(-0.790797\pi\)
−0.791687 + 0.610927i \(0.790797\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −64.0000 −2.10659
\(924\) 0 0
\(925\) 22.0000 0.723356
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −20.0000 −0.656179 −0.328089 − 0.944647i \(-0.606405\pi\)
−0.328089 + 0.944647i \(0.606405\pi\)
\(930\) 0 0
\(931\) 1.00000 0.0327737
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 32.0000 1.04651
\(936\) 0 0
\(937\) 22.0000 0.718709 0.359354 − 0.933201i \(-0.382997\pi\)
0.359354 + 0.933201i \(0.382997\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 22.0000 0.717180 0.358590 − 0.933495i \(-0.383258\pi\)
0.358590 + 0.933495i \(0.383258\pi\)
\(942\) 0 0
\(943\) 12.0000 0.390774
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 42.0000 1.36482 0.682408 − 0.730971i \(-0.260933\pi\)
0.682408 + 0.730971i \(0.260933\pi\)
\(948\) 0 0
\(949\) 24.0000 0.779073
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 2.00000 0.0647864 0.0323932 − 0.999475i \(-0.489687\pi\)
0.0323932 + 0.999475i \(0.489687\pi\)
\(954\) 0 0
\(955\) 24.0000 0.776622
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 2.00000 0.0645834
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 8.00000 0.257529
\(966\) 0 0
\(967\) −28.0000 −0.900419 −0.450210 − 0.892923i \(-0.648651\pi\)
−0.450210 + 0.892923i \(0.648651\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −36.0000 −1.15529 −0.577647 − 0.816286i \(-0.696029\pi\)
−0.577647 + 0.816286i \(0.696029\pi\)
\(972\) 0 0
\(973\) 20.0000 0.641171
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −42.0000 −1.34370 −0.671850 − 0.740688i \(-0.734500\pi\)
−0.671850 + 0.740688i \(0.734500\pi\)
\(978\) 0 0
\(979\) 12.0000 0.383522
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 0 0
\(985\) 72.0000 2.29411
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −48.0000 −1.52631
\(990\) 0 0
\(991\) 22.0000 0.698853 0.349427 − 0.936964i \(-0.386376\pi\)
0.349427 + 0.936964i \(0.386376\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −64.0000 −2.02894
\(996\) 0 0
\(997\) 34.0000 1.07679 0.538395 − 0.842692i \(-0.319031\pi\)
0.538395 + 0.842692i \(0.319031\pi\)
\(998\) 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 9576.2.a.bb.1.1 1
3.2 odd 2 3192.2.a.l.1.1 ✓ 1
12.11 even 2 6384.2.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3192.2.a.l.1.1 ✓ 1 3.2 odd 2
6384.2.a.a.1.1 1 12.11 even 2
9576.2.a.bb.1.1 1 1.1 even 1 trivial