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Properties

Label 2760.2.a.a.1.1
Level $2760$
Weight $2$
Character 2760.1
Self dual yes
Analytic conductor $22.039$
Analytic rank $0$
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] = [2760,2,Mod(1,2760)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2760, 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("2760.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2760.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: \(22.0387109579\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2760.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{3} -1.00000 q^{5} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} -1.00000 q^{5} +1.00000 q^{9} +4.00000 q^{11} +2.00000 q^{13} +1.00000 q^{15} +2.00000 q^{17} -1.00000 q^{23} +1.00000 q^{25} -1.00000 q^{27} -6.00000 q^{29} -4.00000 q^{33} -6.00000 q^{37} -2.00000 q^{39} +2.00000 q^{41} +12.0000 q^{43} -1.00000 q^{45} -7.00000 q^{49} -2.00000 q^{51} +10.0000 q^{53} -4.00000 q^{55} -12.0000 q^{59} -6.00000 q^{61} -2.00000 q^{65} +12.0000 q^{67} +1.00000 q^{69} -12.0000 q^{71} +2.00000 q^{73} -1.00000 q^{75} +16.0000 q^{79} +1.00000 q^{81} +16.0000 q^{83} -2.00000 q^{85} +6.00000 q^{87} +14.0000 q^{89} +6.00000 q^{97} +4.00000 q^{99} +O(q^{100})\)

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
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 4.00000 1.20605 0.603023 − 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(12\) 0 0
\(13\) 2.00000 0.554700 0.277350 − 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) 0 0
\(17\) 2.00000 0.485071 0.242536 − 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 0 0
\(19\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −6.00000 −1.11417 −0.557086 − 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) −4.00000 −0.696311
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −6.00000 −0.986394 −0.493197 − 0.869918i \(-0.664172\pi\)
−0.493197 + 0.869918i \(0.664172\pi\)
\(38\) 0 0
\(39\) −2.00000 −0.320256
\(40\) 0 0
\(41\) 2.00000 0.312348 0.156174 − 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 0 0
\(43\) 12.0000 1.82998 0.914991 − 0.403473i \(-0.132197\pi\)
0.914991 + 0.403473i \(0.132197\pi\)
\(44\) 0 0
\(45\) −1.00000 −0.149071
\(46\) 0 0
\(47\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) −7.00000 −1.00000
\(50\) 0 0
\(51\) −2.00000 −0.280056
\(52\) 0 0
\(53\) 10.0000 1.37361 0.686803 − 0.726844i \(-0.259014\pi\)
0.686803 + 0.726844i \(0.259014\pi\)
\(54\) 0 0
\(55\) −4.00000 −0.539360
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −12.0000 −1.56227 −0.781133 − 0.624364i \(-0.785358\pi\)
−0.781133 + 0.624364i \(0.785358\pi\)
\(60\) 0 0
\(61\) −6.00000 −0.768221 −0.384111 − 0.923287i \(-0.625492\pi\)
−0.384111 + 0.923287i \(0.625492\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −2.00000 −0.248069
\(66\) 0 0
\(67\) 12.0000 1.46603 0.733017 − 0.680211i \(-0.238112\pi\)
0.733017 + 0.680211i \(0.238112\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) −12.0000 −1.42414 −0.712069 − 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 0 0
\(73\) 2.00000 0.234082 0.117041 − 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 0 0
\(75\) −1.00000 −0.115470
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 16.0000 1.80014 0.900070 − 0.435745i \(-0.143515\pi\)
0.900070 + 0.435745i \(0.143515\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 16.0000 1.75623 0.878114 − 0.478451i \(-0.158802\pi\)
0.878114 + 0.478451i \(0.158802\pi\)
\(84\) 0 0
\(85\) −2.00000 −0.216930
\(86\) 0 0
\(87\) 6.00000 0.643268
\(88\) 0 0
\(89\) 14.0000 1.48400 0.741999 − 0.670402i \(-0.233878\pi\)
0.741999 + 0.670402i \(0.233878\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 6.00000 0.609208 0.304604 − 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) 0 0
\(99\) 4.00000 0.402015
\(100\) 0 0
\(101\) 10.0000 0.995037 0.497519 − 0.867453i \(-0.334245\pi\)
0.497519 + 0.867453i \(0.334245\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 − 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) 10.0000 0.957826 0.478913 − 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) 0 0
\(111\) 6.00000 0.569495
\(112\) 0 0
\(113\) −14.0000 −1.31701 −0.658505 − 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) 0 0
\(115\) 1.00000 0.0932505
\(116\) 0 0
\(117\) 2.00000 0.184900
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 0 0
\(123\) −2.00000 −0.180334
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −4.00000 −0.354943 −0.177471 − 0.984126i \(-0.556792\pi\)
−0.177471 + 0.984126i \(0.556792\pi\)
\(128\) 0 0
\(129\) −12.0000 −1.05654
\(130\) 0 0
\(131\) 20.0000 1.74741 0.873704 − 0.486458i \(-0.161711\pi\)
0.873704 + 0.486458i \(0.161711\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 1.00000 0.0860663
\(136\) 0 0
\(137\) −14.0000 −1.19610 −0.598050 − 0.801459i \(-0.704058\pi\)
−0.598050 + 0.801459i \(0.704058\pi\)
\(138\) 0 0
\(139\) 12.0000 1.01783 0.508913 − 0.860818i \(-0.330047\pi\)
0.508913 + 0.860818i \(0.330047\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 8.00000 0.668994
\(144\) 0 0
\(145\) 6.00000 0.498273
\(146\) 0 0
\(147\) 7.00000 0.577350
\(148\) 0 0
\(149\) −22.0000 −1.80231 −0.901155 − 0.433497i \(-0.857280\pi\)
−0.901155 + 0.433497i \(0.857280\pi\)
\(150\) 0 0
\(151\) 16.0000 1.30206 0.651031 − 0.759051i \(-0.274337\pi\)
0.651031 + 0.759051i \(0.274337\pi\)
\(152\) 0 0
\(153\) 2.00000 0.161690
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 2.00000 0.159617 0.0798087 − 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) 0 0
\(159\) −10.0000 −0.793052
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 20.0000 1.56652 0.783260 − 0.621694i \(-0.213555\pi\)
0.783260 + 0.621694i \(0.213555\pi\)
\(164\) 0 0
\(165\) 4.00000 0.311400
\(166\) 0 0
\(167\) 16.0000 1.23812 0.619059 − 0.785345i \(-0.287514\pi\)
0.619059 + 0.785345i \(0.287514\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 6.00000 0.456172 0.228086 − 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 12.0000 0.901975
\(178\) 0 0
\(179\) −12.0000 −0.896922 −0.448461 − 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 − 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 0 0
\(183\) 6.00000 0.443533
\(184\) 0 0
\(185\) 6.00000 0.441129
\(186\) 0 0
\(187\) 8.00000 0.585018
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −24.0000 −1.73658 −0.868290 − 0.496058i \(-0.834780\pi\)
−0.868290 + 0.496058i \(0.834780\pi\)
\(192\) 0 0
\(193\) 18.0000 1.29567 0.647834 − 0.761781i \(-0.275675\pi\)
0.647834 + 0.761781i \(0.275675\pi\)
\(194\) 0 0
\(195\) 2.00000 0.143223
\(196\) 0 0
\(197\) −2.00000 −0.142494 −0.0712470 − 0.997459i \(-0.522698\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(198\) 0 0
\(199\) 16.0000 1.13421 0.567105 − 0.823646i \(-0.308063\pi\)
0.567105 + 0.823646i \(0.308063\pi\)
\(200\) 0 0
\(201\) −12.0000 −0.846415
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −2.00000 −0.139686
\(206\) 0 0
\(207\) −1.00000 −0.0695048
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 − 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 0 0
\(213\) 12.0000 0.822226
\(214\) 0 0
\(215\) −12.0000 −0.818393
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −2.00000 −0.135147
\(220\) 0 0
\(221\) 4.00000 0.269069
\(222\) 0 0
\(223\) −20.0000 −1.33930 −0.669650 − 0.742677i \(-0.733556\pi\)
−0.669650 + 0.742677i \(0.733556\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 0 0
\(229\) −14.0000 −0.925146 −0.462573 − 0.886581i \(-0.653074\pi\)
−0.462573 + 0.886581i \(0.653074\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −6.00000 −0.393073 −0.196537 − 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −16.0000 −1.03931
\(238\) 0 0
\(239\) 20.0000 1.29369 0.646846 − 0.762620i \(-0.276088\pi\)
0.646846 + 0.762620i \(0.276088\pi\)
\(240\) 0 0
\(241\) 10.0000 0.644157 0.322078 − 0.946713i \(-0.395619\pi\)
0.322078 + 0.946713i \(0.395619\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 7.00000 0.447214
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −16.0000 −1.01396
\(250\) 0 0
\(251\) −12.0000 −0.757433 −0.378717 − 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 0 0
\(253\) −4.00000 −0.251478
\(254\) 0 0
\(255\) 2.00000 0.125245
\(256\) 0 0
\(257\) 2.00000 0.124757 0.0623783 − 0.998053i \(-0.480131\pi\)
0.0623783 + 0.998053i \(0.480131\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −6.00000 −0.371391
\(262\) 0 0
\(263\) 16.0000 0.986602 0.493301 − 0.869859i \(-0.335790\pi\)
0.493301 + 0.869859i \(0.335790\pi\)
\(264\) 0 0
\(265\) −10.0000 −0.614295
\(266\) 0 0
\(267\) −14.0000 −0.856786
\(268\) 0 0
\(269\) 18.0000 1.09748 0.548740 − 0.835993i \(-0.315108\pi\)
0.548740 + 0.835993i \(0.315108\pi\)
\(270\) 0 0
\(271\) −8.00000 −0.485965 −0.242983 − 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 4.00000 0.241209
\(276\) 0 0
\(277\) 2.00000 0.120168 0.0600842 − 0.998193i \(-0.480863\pi\)
0.0600842 + 0.998193i \(0.480863\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 − 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 0 0
\(283\) 20.0000 1.18888 0.594438 − 0.804141i \(-0.297374\pi\)
0.594438 + 0.804141i \(0.297374\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) −6.00000 −0.351726
\(292\) 0 0
\(293\) 10.0000 0.584206 0.292103 − 0.956387i \(-0.405645\pi\)
0.292103 + 0.956387i \(0.405645\pi\)
\(294\) 0 0
\(295\) 12.0000 0.698667
\(296\) 0 0
\(297\) −4.00000 −0.232104
\(298\) 0 0
\(299\) −2.00000 −0.115663
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −10.0000 −0.574485
\(304\) 0 0
\(305\) 6.00000 0.343559
\(306\) 0 0
\(307\) 12.0000 0.684876 0.342438 − 0.939540i \(-0.388747\pi\)
0.342438 + 0.939540i \(0.388747\pi\)
\(308\) 0 0
\(309\) −8.00000 −0.455104
\(310\) 0 0
\(311\) 12.0000 0.680458 0.340229 − 0.940343i \(-0.389495\pi\)
0.340229 + 0.940343i \(0.389495\pi\)
\(312\) 0 0
\(313\) 22.0000 1.24351 0.621757 − 0.783210i \(-0.286419\pi\)
0.621757 + 0.783210i \(0.286419\pi\)
\(314\) 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
\(319\) −24.0000 −1.34374
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 2.00000 0.110940
\(326\) 0 0
\(327\) −10.0000 −0.553001
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 28.0000 1.53902 0.769510 − 0.638635i \(-0.220501\pi\)
0.769510 + 0.638635i \(0.220501\pi\)
\(332\) 0 0
\(333\) −6.00000 −0.328798
\(334\) 0 0
\(335\) −12.0000 −0.655630
\(336\) 0 0
\(337\) −10.0000 −0.544735 −0.272367 − 0.962193i \(-0.587807\pi\)
−0.272367 + 0.962193i \(0.587807\pi\)
\(338\) 0 0
\(339\) 14.0000 0.760376
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −1.00000 −0.0538382
\(346\) 0 0
\(347\) −4.00000 −0.214731 −0.107366 − 0.994220i \(-0.534242\pi\)
−0.107366 + 0.994220i \(0.534242\pi\)
\(348\) 0 0
\(349\) 14.0000 0.749403 0.374701 − 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 0 0
\(351\) −2.00000 −0.106752
\(352\) 0 0
\(353\) 18.0000 0.958043 0.479022 − 0.877803i \(-0.340992\pi\)
0.479022 + 0.877803i \(0.340992\pi\)
\(354\) 0 0
\(355\) 12.0000 0.636894
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −16.0000 −0.844448 −0.422224 − 0.906492i \(-0.638750\pi\)
−0.422224 + 0.906492i \(0.638750\pi\)
\(360\) 0 0
\(361\) −19.0000 −1.00000
\(362\) 0 0
\(363\) −5.00000 −0.262432
\(364\) 0 0
\(365\) −2.00000 −0.104685
\(366\) 0 0
\(367\) −8.00000 −0.417597 −0.208798 − 0.977959i \(-0.566955\pi\)
−0.208798 + 0.977959i \(0.566955\pi\)
\(368\) 0 0
\(369\) 2.00000 0.104116
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 10.0000 0.517780 0.258890 − 0.965907i \(-0.416643\pi\)
0.258890 + 0.965907i \(0.416643\pi\)
\(374\) 0 0
\(375\) 1.00000 0.0516398
\(376\) 0 0
\(377\) −12.0000 −0.618031
\(378\) 0 0
\(379\) 16.0000 0.821865 0.410932 − 0.911666i \(-0.365203\pi\)
0.410932 + 0.911666i \(0.365203\pi\)
\(380\) 0 0
\(381\) 4.00000 0.204926
\(382\) 0 0
\(383\) −24.0000 −1.22634 −0.613171 − 0.789950i \(-0.710106\pi\)
−0.613171 + 0.789950i \(0.710106\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 12.0000 0.609994
\(388\) 0 0
\(389\) 10.0000 0.507020 0.253510 − 0.967333i \(-0.418415\pi\)
0.253510 + 0.967333i \(0.418415\pi\)
\(390\) 0 0
\(391\) −2.00000 −0.101144
\(392\) 0 0
\(393\) −20.0000 −1.00887
\(394\) 0 0
\(395\) −16.0000 −0.805047
\(396\) 0 0
\(397\) 2.00000 0.100377 0.0501886 − 0.998740i \(-0.484018\pi\)
0.0501886 + 0.998740i \(0.484018\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −10.0000 −0.499376 −0.249688 − 0.968326i \(-0.580328\pi\)
−0.249688 + 0.968326i \(0.580328\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) −24.0000 −1.18964
\(408\) 0 0
\(409\) −38.0000 −1.87898 −0.939490 − 0.342578i \(-0.888700\pi\)
−0.939490 + 0.342578i \(0.888700\pi\)
\(410\) 0 0
\(411\) 14.0000 0.690569
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −16.0000 −0.785409
\(416\) 0 0
\(417\) −12.0000 −0.587643
\(418\) 0 0
\(419\) −12.0000 −0.586238 −0.293119 − 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) 26.0000 1.26716 0.633581 − 0.773676i \(-0.281584\pi\)
0.633581 + 0.773676i \(0.281584\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 2.00000 0.0970143
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −8.00000 −0.386244
\(430\) 0 0
\(431\) 40.0000 1.92673 0.963366 − 0.268190i \(-0.0864254\pi\)
0.963366 + 0.268190i \(0.0864254\pi\)
\(432\) 0 0
\(433\) 22.0000 1.05725 0.528626 − 0.848855i \(-0.322707\pi\)
0.528626 + 0.848855i \(0.322707\pi\)
\(434\) 0 0
\(435\) −6.00000 −0.287678
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −24.0000 −1.14546 −0.572729 − 0.819745i \(-0.694115\pi\)
−0.572729 + 0.819745i \(0.694115\pi\)
\(440\) 0 0
\(441\) −7.00000 −0.333333
\(442\) 0 0
\(443\) 12.0000 0.570137 0.285069 − 0.958507i \(-0.407984\pi\)
0.285069 + 0.958507i \(0.407984\pi\)
\(444\) 0 0
\(445\) −14.0000 −0.663664
\(446\) 0 0
\(447\) 22.0000 1.04056
\(448\) 0 0
\(449\) −22.0000 −1.03824 −0.519122 − 0.854700i \(-0.673741\pi\)
−0.519122 + 0.854700i \(0.673741\pi\)
\(450\) 0 0
\(451\) 8.00000 0.376705
\(452\) 0 0
\(453\) −16.0000 −0.751746
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 14.0000 0.654892 0.327446 − 0.944870i \(-0.393812\pi\)
0.327446 + 0.944870i \(0.393812\pi\)
\(458\) 0 0
\(459\) −2.00000 −0.0933520
\(460\) 0 0
\(461\) −22.0000 −1.02464 −0.512321 − 0.858794i \(-0.671214\pi\)
−0.512321 + 0.858794i \(0.671214\pi\)
\(462\) 0 0
\(463\) −28.0000 −1.30127 −0.650635 − 0.759390i \(-0.725497\pi\)
−0.650635 + 0.759390i \(0.725497\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 16.0000 0.740392 0.370196 − 0.928954i \(-0.379291\pi\)
0.370196 + 0.928954i \(0.379291\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −2.00000 −0.0921551
\(472\) 0 0
\(473\) 48.0000 2.20704
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 10.0000 0.457869
\(478\) 0 0
\(479\) −16.0000 −0.731059 −0.365529 − 0.930800i \(-0.619112\pi\)
−0.365529 + 0.930800i \(0.619112\pi\)
\(480\) 0 0
\(481\) −12.0000 −0.547153
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −6.00000 −0.272446
\(486\) 0 0
\(487\) −4.00000 −0.181257 −0.0906287 − 0.995885i \(-0.528888\pi\)
−0.0906287 + 0.995885i \(0.528888\pi\)
\(488\) 0 0
\(489\) −20.0000 −0.904431
\(490\) 0 0
\(491\) 20.0000 0.902587 0.451294 − 0.892375i \(-0.350963\pi\)
0.451294 + 0.892375i \(0.350963\pi\)
\(492\) 0 0
\(493\) −12.0000 −0.540453
\(494\) 0 0
\(495\) −4.00000 −0.179787
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −4.00000 −0.179065 −0.0895323 − 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) 0 0
\(501\) −16.0000 −0.714827
\(502\) 0 0
\(503\) −32.0000 −1.42681 −0.713405 − 0.700752i \(-0.752848\pi\)
−0.713405 + 0.700752i \(0.752848\pi\)
\(504\) 0 0
\(505\) −10.0000 −0.444994
\(506\) 0 0
\(507\) 9.00000 0.399704
\(508\) 0 0
\(509\) 26.0000 1.15243 0.576215 − 0.817298i \(-0.304529\pi\)
0.576215 + 0.817298i \(0.304529\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −8.00000 −0.352522
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −6.00000 −0.263371
\(520\) 0 0
\(521\) −26.0000 −1.13908 −0.569540 − 0.821963i \(-0.692879\pi\)
−0.569540 + 0.821963i \(0.692879\pi\)
\(522\) 0 0
\(523\) −20.0000 −0.874539 −0.437269 − 0.899331i \(-0.644054\pi\)
−0.437269 + 0.899331i \(0.644054\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −12.0000 −0.520756
\(532\) 0 0
\(533\) 4.00000 0.173259
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 12.0000 0.517838
\(538\) 0 0
\(539\) −28.0000 −1.20605
\(540\) 0 0
\(541\) 14.0000 0.601907 0.300954 − 0.953639i \(-0.402695\pi\)
0.300954 + 0.953639i \(0.402695\pi\)
\(542\) 0 0
\(543\) −2.00000 −0.0858282
\(544\) 0 0
\(545\) −10.0000 −0.428353
\(546\) 0 0
\(547\) 36.0000 1.53925 0.769624 − 0.638497i \(-0.220443\pi\)
0.769624 + 0.638497i \(0.220443\pi\)
\(548\) 0 0
\(549\) −6.00000 −0.256074
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −6.00000 −0.254686
\(556\) 0 0
\(557\) −22.0000 −0.932170 −0.466085 − 0.884740i \(-0.654336\pi\)
−0.466085 + 0.884740i \(0.654336\pi\)
\(558\) 0 0
\(559\) 24.0000 1.01509
\(560\) 0 0
\(561\) −8.00000 −0.337760
\(562\) 0 0
\(563\) −24.0000 −1.01148 −0.505740 − 0.862686i \(-0.668780\pi\)
−0.505740 + 0.862686i \(0.668780\pi\)
\(564\) 0 0
\(565\) 14.0000 0.588984
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −34.0000 −1.42535 −0.712677 − 0.701492i \(-0.752517\pi\)
−0.712677 + 0.701492i \(0.752517\pi\)
\(570\) 0 0
\(571\) −32.0000 −1.33916 −0.669579 − 0.742741i \(-0.733526\pi\)
−0.669579 + 0.742741i \(0.733526\pi\)
\(572\) 0 0
\(573\) 24.0000 1.00261
\(574\) 0 0
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) −22.0000 −0.915872 −0.457936 − 0.888985i \(-0.651411\pi\)
−0.457936 + 0.888985i \(0.651411\pi\)
\(578\) 0 0
\(579\) −18.0000 −0.748054
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 40.0000 1.65663
\(584\) 0 0
\(585\) −2.00000 −0.0826898
\(586\) 0 0
\(587\) −28.0000 −1.15568 −0.577842 − 0.816149i \(-0.696105\pi\)
−0.577842 + 0.816149i \(0.696105\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 2.00000 0.0822690
\(592\) 0 0
\(593\) 18.0000 0.739171 0.369586 − 0.929197i \(-0.379500\pi\)
0.369586 + 0.929197i \(0.379500\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −16.0000 −0.654836
\(598\) 0 0
\(599\) −28.0000 −1.14405 −0.572024 − 0.820237i \(-0.693842\pi\)
−0.572024 + 0.820237i \(0.693842\pi\)
\(600\) 0 0
\(601\) 42.0000 1.71322 0.856608 − 0.515968i \(-0.172568\pi\)
0.856608 + 0.515968i \(0.172568\pi\)
\(602\) 0 0
\(603\) 12.0000 0.488678
\(604\) 0 0
\(605\) −5.00000 −0.203279
\(606\) 0 0
\(607\) 28.0000 1.13648 0.568242 − 0.822861i \(-0.307624\pi\)
0.568242 + 0.822861i \(0.307624\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 26.0000 1.05013 0.525065 − 0.851062i \(-0.324041\pi\)
0.525065 + 0.851062i \(0.324041\pi\)
\(614\) 0 0
\(615\) 2.00000 0.0806478
\(616\) 0 0
\(617\) −30.0000 −1.20775 −0.603877 − 0.797077i \(-0.706378\pi\)
−0.603877 + 0.797077i \(0.706378\pi\)
\(618\) 0 0
\(619\) −32.0000 −1.28619 −0.643094 − 0.765787i \(-0.722350\pi\)
−0.643094 + 0.765787i \(0.722350\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −12.0000 −0.478471
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 − 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) 0 0
\(633\) −4.00000 −0.158986
\(634\) 0 0
\(635\) 4.00000 0.158735
\(636\) 0 0
\(637\) −14.0000 −0.554700
\(638\) 0 0
\(639\) −12.0000 −0.474713
\(640\) 0 0
\(641\) 30.0000 1.18493 0.592464 − 0.805597i \(-0.298155\pi\)
0.592464 + 0.805597i \(0.298155\pi\)
\(642\) 0 0
\(643\) −20.0000 −0.788723 −0.394362 − 0.918955i \(-0.629034\pi\)
−0.394362 + 0.918955i \(0.629034\pi\)
\(644\) 0 0
\(645\) 12.0000 0.472500
\(646\) 0 0
\(647\) −32.0000 −1.25805 −0.629025 − 0.777385i \(-0.716546\pi\)
−0.629025 + 0.777385i \(0.716546\pi\)
\(648\) 0 0
\(649\) −48.0000 −1.88416
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 38.0000 1.48705 0.743527 − 0.668705i \(-0.233151\pi\)
0.743527 + 0.668705i \(0.233151\pi\)
\(654\) 0 0
\(655\) −20.0000 −0.781465
\(656\) 0 0
\(657\) 2.00000 0.0780274
\(658\) 0 0
\(659\) 36.0000 1.40236 0.701180 − 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) 0 0
\(661\) −14.0000 −0.544537 −0.272268 − 0.962221i \(-0.587774\pi\)
−0.272268 + 0.962221i \(0.587774\pi\)
\(662\) 0 0
\(663\) −4.00000 −0.155347
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 6.00000 0.232321
\(668\) 0 0
\(669\) 20.0000 0.773245
\(670\) 0 0
\(671\) −24.0000 −0.926510
\(672\) 0 0
\(673\) −38.0000 −1.46479 −0.732396 − 0.680879i \(-0.761598\pi\)
−0.732396 + 0.680879i \(0.761598\pi\)
\(674\) 0 0
\(675\) −1.00000 −0.0384900
\(676\) 0 0
\(677\) −6.00000 −0.230599 −0.115299 − 0.993331i \(-0.536783\pi\)
−0.115299 + 0.993331i \(0.536783\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 20.0000 0.765279 0.382639 − 0.923898i \(-0.375015\pi\)
0.382639 + 0.923898i \(0.375015\pi\)
\(684\) 0 0
\(685\) 14.0000 0.534913
\(686\) 0 0
\(687\) 14.0000 0.534133
\(688\) 0 0
\(689\) 20.0000 0.761939
\(690\) 0 0
\(691\) 12.0000 0.456502 0.228251 − 0.973602i \(-0.426699\pi\)
0.228251 + 0.973602i \(0.426699\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −12.0000 −0.455186
\(696\) 0 0
\(697\) 4.00000 0.151511
\(698\) 0 0
\(699\) 6.00000 0.226941
\(700\) 0 0
\(701\) 18.0000 0.679851 0.339925 − 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −38.0000 −1.42712 −0.713560 − 0.700594i \(-0.752918\pi\)
−0.713560 + 0.700594i \(0.752918\pi\)
\(710\) 0 0
\(711\) 16.0000 0.600047
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −8.00000 −0.299183
\(716\) 0 0
\(717\) −20.0000 −0.746914
\(718\) 0 0
\(719\) −36.0000 −1.34257 −0.671287 − 0.741198i \(-0.734258\pi\)
−0.671287 + 0.741198i \(0.734258\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −10.0000 −0.371904
\(724\) 0 0
\(725\) −6.00000 −0.222834
\(726\) 0 0
\(727\) 8.00000 0.296704 0.148352 − 0.988935i \(-0.452603\pi\)
0.148352 + 0.988935i \(0.452603\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 24.0000 0.887672
\(732\) 0 0
\(733\) 34.0000 1.25582 0.627909 − 0.778287i \(-0.283911\pi\)
0.627909 + 0.778287i \(0.283911\pi\)
\(734\) 0 0
\(735\) −7.00000 −0.258199
\(736\) 0 0
\(737\) 48.0000 1.76810
\(738\) 0 0
\(739\) −28.0000 −1.03000 −0.514998 − 0.857191i \(-0.672207\pi\)
−0.514998 + 0.857191i \(0.672207\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) 22.0000 0.806018
\(746\) 0 0
\(747\) 16.0000 0.585409
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 32.0000 1.16770 0.583848 − 0.811863i \(-0.301546\pi\)
0.583848 + 0.811863i \(0.301546\pi\)
\(752\) 0 0
\(753\) 12.0000 0.437304
\(754\) 0 0
\(755\) −16.0000 −0.582300
\(756\) 0 0
\(757\) 26.0000 0.944986 0.472493 − 0.881334i \(-0.343354\pi\)
0.472493 + 0.881334i \(0.343354\pi\)
\(758\) 0 0
\(759\) 4.00000 0.145191
\(760\) 0 0
\(761\) 10.0000 0.362500 0.181250 − 0.983437i \(-0.441986\pi\)
0.181250 + 0.983437i \(0.441986\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −2.00000 −0.0723102
\(766\) 0 0
\(767\) −24.0000 −0.866590
\(768\) 0 0
\(769\) −14.0000 −0.504853 −0.252426 − 0.967616i \(-0.581229\pi\)
−0.252426 + 0.967616i \(0.581229\pi\)
\(770\) 0 0
\(771\) −2.00000 −0.0720282
\(772\) 0 0
\(773\) −46.0000 −1.65451 −0.827253 − 0.561830i \(-0.810097\pi\)
−0.827253 + 0.561830i \(0.810097\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) −48.0000 −1.71758
\(782\) 0 0
\(783\) 6.00000 0.214423
\(784\) 0 0
\(785\) −2.00000 −0.0713831
\(786\) 0 0
\(787\) 44.0000 1.56843 0.784215 − 0.620489i \(-0.213066\pi\)
0.784215 + 0.620489i \(0.213066\pi\)
\(788\) 0 0
\(789\) −16.0000 −0.569615
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −12.0000 −0.426132
\(794\) 0 0
\(795\) 10.0000 0.354663
\(796\) 0 0
\(797\) −38.0000 −1.34603 −0.673015 − 0.739629i \(-0.735001\pi\)
−0.673015 + 0.739629i \(0.735001\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 14.0000 0.494666
\(802\) 0 0
\(803\) 8.00000 0.282314
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −18.0000 −0.633630
\(808\) 0 0
\(809\) 10.0000 0.351581 0.175791 − 0.984428i \(-0.443752\pi\)
0.175791 + 0.984428i \(0.443752\pi\)
\(810\) 0 0
\(811\) 20.0000 0.702295 0.351147 − 0.936320i \(-0.385792\pi\)
0.351147 + 0.936320i \(0.385792\pi\)
\(812\) 0 0
\(813\) 8.00000 0.280572
\(814\) 0 0
\(815\) −20.0000 −0.700569
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −30.0000 −1.04701 −0.523504 − 0.852023i \(-0.675375\pi\)
−0.523504 + 0.852023i \(0.675375\pi\)
\(822\) 0 0
\(823\) −4.00000 −0.139431 −0.0697156 − 0.997567i \(-0.522209\pi\)
−0.0697156 + 0.997567i \(0.522209\pi\)
\(824\) 0 0
\(825\) −4.00000 −0.139262
\(826\) 0 0
\(827\) −48.0000 −1.66912 −0.834562 − 0.550914i \(-0.814279\pi\)
−0.834562 + 0.550914i \(0.814279\pi\)
\(828\) 0 0
\(829\) −34.0000 −1.18087 −0.590434 − 0.807086i \(-0.701044\pi\)
−0.590434 + 0.807086i \(0.701044\pi\)
\(830\) 0 0
\(831\) −2.00000 −0.0693792
\(832\) 0 0
\(833\) −14.0000 −0.485071
\(834\) 0 0
\(835\) −16.0000 −0.553703
\(836\) 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
\(841\) 7.00000 0.241379
\(842\) 0 0
\(843\) 18.0000 0.619953
\(844\) 0 0
\(845\) 9.00000 0.309609
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −20.0000 −0.686398
\(850\) 0 0
\(851\) 6.00000 0.205677
\(852\) 0 0
\(853\) 42.0000 1.43805 0.719026 − 0.694983i \(-0.244588\pi\)
0.719026 + 0.694983i \(0.244588\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 42.0000 1.43469 0.717346 − 0.696717i \(-0.245357\pi\)
0.717346 + 0.696717i \(0.245357\pi\)
\(858\) 0 0
\(859\) −20.0000 −0.682391 −0.341196 − 0.939992i \(-0.610832\pi\)
−0.341196 + 0.939992i \(0.610832\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −40.0000 −1.36162 −0.680808 − 0.732462i \(-0.738371\pi\)
−0.680808 + 0.732462i \(0.738371\pi\)
\(864\) 0 0
\(865\) −6.00000 −0.204006
\(866\) 0 0
\(867\) 13.0000 0.441503
\(868\) 0 0
\(869\) 64.0000 2.17105
\(870\) 0 0
\(871\) 24.0000 0.813209
\(872\) 0 0
\(873\) 6.00000 0.203069
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 10.0000 0.337676 0.168838 − 0.985644i \(-0.445999\pi\)
0.168838 + 0.985644i \(0.445999\pi\)
\(878\) 0 0
\(879\) −10.0000 −0.337292
\(880\) 0 0
\(881\) 54.0000 1.81931 0.909653 − 0.415369i \(-0.136347\pi\)
0.909653 + 0.415369i \(0.136347\pi\)
\(882\) 0 0
\(883\) −20.0000 −0.673054 −0.336527 − 0.941674i \(-0.609252\pi\)
−0.336527 + 0.941674i \(0.609252\pi\)
\(884\) 0 0
\(885\) −12.0000 −0.403376
\(886\) 0 0
\(887\) 8.00000 0.268614 0.134307 − 0.990940i \(-0.457119\pi\)
0.134307 + 0.990940i \(0.457119\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 4.00000 0.134005
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 12.0000 0.401116
\(896\) 0 0
\(897\) 2.00000 0.0667781
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 20.0000 0.666297
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −2.00000 −0.0664822
\(906\) 0 0
\(907\) 44.0000 1.46100 0.730498 − 0.682915i \(-0.239288\pi\)
0.730498 + 0.682915i \(0.239288\pi\)
\(908\) 0 0
\(909\) 10.0000 0.331679
\(910\) 0 0
\(911\) −48.0000 −1.59031 −0.795155 − 0.606406i \(-0.792611\pi\)
−0.795155 + 0.606406i \(0.792611\pi\)
\(912\) 0 0
\(913\) 64.0000 2.11809
\(914\) 0 0
\(915\) −6.00000 −0.198354
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −16.0000 −0.527791 −0.263896 − 0.964551i \(-0.585007\pi\)
−0.263896 + 0.964551i \(0.585007\pi\)
\(920\) 0 0
\(921\) −12.0000 −0.395413
\(922\) 0 0
\(923\) −24.0000 −0.789970
\(924\) 0 0
\(925\) −6.00000 −0.197279
\(926\) 0 0
\(927\) 8.00000 0.262754
\(928\) 0 0
\(929\) 42.0000 1.37798 0.688988 − 0.724773i \(-0.258055\pi\)
0.688988 + 0.724773i \(0.258055\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −12.0000 −0.392862
\(934\) 0 0
\(935\) −8.00000 −0.261628
\(936\) 0 0
\(937\) 22.0000 0.718709 0.359354 − 0.933201i \(-0.382997\pi\)
0.359354 + 0.933201i \(0.382997\pi\)
\(938\) 0 0
\(939\) −22.0000 −0.717943
\(940\) 0 0
\(941\) −14.0000 −0.456387 −0.228193 − 0.973616i \(-0.573282\pi\)
−0.228193 + 0.973616i \(0.573282\pi\)
\(942\) 0 0
\(943\) −2.00000 −0.0651290
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 12.0000 0.389948 0.194974 − 0.980808i \(-0.437538\pi\)
0.194974 + 0.980808i \(0.437538\pi\)
\(948\) 0 0
\(949\) 4.00000 0.129845
\(950\) 0 0
\(951\) 18.0000 0.583690
\(952\) 0 0
\(953\) −14.0000 −0.453504 −0.226752 − 0.973952i \(-0.572811\pi\)
−0.226752 + 0.973952i \(0.572811\pi\)
\(954\) 0 0
\(955\) 24.0000 0.776622
\(956\) 0 0
\(957\) 24.0000 0.775810
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −31.0000 −1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −18.0000 −0.579441
\(966\) 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
\(971\) −20.0000 −0.641831 −0.320915 − 0.947108i \(-0.603990\pi\)
−0.320915 + 0.947108i \(0.603990\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −2.00000 −0.0640513
\(976\) 0 0
\(977\) −30.0000 −0.959785 −0.479893 − 0.877327i \(-0.659324\pi\)
−0.479893 + 0.877327i \(0.659324\pi\)
\(978\) 0 0
\(979\) 56.0000 1.78977
\(980\) 0 0
\(981\) 10.0000 0.319275
\(982\) 0 0
\(983\) 24.0000 0.765481 0.382741 − 0.923856i \(-0.374980\pi\)
0.382741 + 0.923856i \(0.374980\pi\)
\(984\) 0 0
\(985\) 2.00000 0.0637253
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −12.0000 −0.381578
\(990\) 0 0
\(991\) 8.00000 0.254128 0.127064 − 0.991894i \(-0.459445\pi\)
0.127064 + 0.991894i \(0.459445\pi\)
\(992\) 0 0
\(993\) −28.0000 −0.888553
\(994\) 0 0
\(995\) −16.0000 −0.507234
\(996\) 0 0
\(997\) −46.0000 −1.45683 −0.728417 − 0.685134i \(-0.759744\pi\)
−0.728417 + 0.685134i \(0.759744\pi\)
\(998\) 0 0
\(999\) 6.00000 0.189832
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 2760.2.a.a.1.1 ✓ 1
3.2 odd 2 8280.2.a.p.1.1 1
4.3 odd 2 5520.2.a.v.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2760.2.a.a.1.1 ✓ 1 1.1 even 1 trivial
5520.2.a.v.1.1 1 4.3 odd 2
8280.2.a.p.1.1 1 3.2 odd 2