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Properties

Label 7920.2.a.t.1.1
Level $7920$
Weight $2$
Character 7920.1
Self dual yes
Analytic conductor $63.242$
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] = [7920,2,Mod(1,7920)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7920, 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("7920.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7920 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7920.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: \(63.2415184009\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 330)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 7920.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{5} -4.00000 q^{7} +O(q^{10})\) \(q+1.00000 q^{5} -4.00000 q^{7} -1.00000 q^{11} +2.00000 q^{13} -2.00000 q^{17} -4.00000 q^{19} -4.00000 q^{23} +1.00000 q^{25} -6.00000 q^{29} -4.00000 q^{35} -10.0000 q^{37} +6.00000 q^{41} +12.0000 q^{43} -4.00000 q^{47} +9.00000 q^{49} +6.00000 q^{53} -1.00000 q^{55} -4.00000 q^{59} +10.0000 q^{61} +2.00000 q^{65} +12.0000 q^{67} -4.00000 q^{71} +10.0000 q^{73} +4.00000 q^{77} -4.00000 q^{79} +4.00000 q^{83} -2.00000 q^{85} -10.0000 q^{89} -8.00000 q^{91} -4.00000 q^{95} +18.0000 q^{97} +O(q^{100})\)

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
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −4.00000 −1.51186 −0.755929 − 0.654654i \(-0.772814\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) 2.00000 0.554700 0.277350 − 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.00000 −0.485071 −0.242536 − 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 0 0
\(19\) −4.00000 −0.917663 −0.458831 − 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.00000 −0.834058 −0.417029 − 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 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
\(33\) 0 0
\(34\) 0 0
\(35\) −4.00000 −0.676123
\(36\) 0 0
\(37\) −10.0000 −1.64399 −0.821995 − 0.569495i \(-0.807139\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 6.00000 0.937043 0.468521 − 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) 12.0000 1.82998 0.914991 − 0.403473i \(-0.132197\pi\)
0.914991 + 0.403473i \(0.132197\pi\)
\(44\) 0 0
\(45\) 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
\(49\) 9.00000 1.28571
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 6.00000 0.824163 0.412082 − 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 0 0
\(55\) −1.00000 −0.134840
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −4.00000 −0.520756 −0.260378 − 0.965507i \(-0.583847\pi\)
−0.260378 + 0.965507i \(0.583847\pi\)
\(60\) 0 0
\(61\) 10.0000 1.28037 0.640184 − 0.768221i \(-0.278858\pi\)
0.640184 + 0.768221i \(0.278858\pi\)
\(62\) 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
\(69\) 0 0
\(70\) 0 0
\(71\) −4.00000 −0.474713 −0.237356 − 0.971423i \(-0.576281\pi\)
−0.237356 + 0.971423i \(0.576281\pi\)
\(72\) 0 0
\(73\) 10.0000 1.17041 0.585206 − 0.810885i \(-0.301014\pi\)
0.585206 + 0.810885i \(0.301014\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 4.00000 0.455842
\(78\) 0 0
\(79\) −4.00000 −0.450035 −0.225018 − 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 4.00000 0.439057 0.219529 − 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) 0 0
\(85\) −2.00000 −0.216930
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −10.0000 −1.06000 −0.529999 − 0.847998i \(-0.677808\pi\)
−0.529999 + 0.847998i \(0.677808\pi\)
\(90\) 0 0
\(91\) −8.00000 −0.838628
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −4.00000 −0.410391
\(96\) 0 0
\(97\) 18.0000 1.82762 0.913812 − 0.406138i \(-0.133125\pi\)
0.913812 + 0.406138i \(0.133125\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 18.0000 1.79107 0.895533 − 0.444994i \(-0.146794\pi\)
0.895533 + 0.444994i \(0.146794\pi\)
\(102\) 0 0
\(103\) 16.0000 1.57653 0.788263 − 0.615338i \(-0.210980\pi\)
0.788263 + 0.615338i \(0.210980\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −12.0000 −1.16008 −0.580042 − 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) 0 0
\(109\) 2.00000 0.191565 0.0957826 − 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −18.0000 −1.69330 −0.846649 − 0.532152i \(-0.821383\pi\)
−0.846649 + 0.532152i \(0.821383\pi\)
\(114\) 0 0
\(115\) −4.00000 −0.373002
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 8.00000 0.733359
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 0 0
\(124\) 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
\(129\) 0 0
\(130\) 0 0
\(131\) −12.0000 −1.04844 −0.524222 − 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 0 0
\(133\) 16.0000 1.38738
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2.00000 −0.170872 −0.0854358 − 0.996344i \(-0.527228\pi\)
−0.0854358 + 0.996344i \(0.527228\pi\)
\(138\) 0 0
\(139\) 4.00000 0.339276 0.169638 − 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −2.00000 −0.167248
\(144\) 0 0
\(145\) −6.00000 −0.498273
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −6.00000 −0.491539 −0.245770 − 0.969328i \(-0.579041\pi\)
−0.245770 + 0.969328i \(0.579041\pi\)
\(150\) 0 0
\(151\) −12.0000 −0.976546 −0.488273 − 0.872691i \(-0.662373\pi\)
−0.488273 + 0.872691i \(0.662373\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −10.0000 −0.798087 −0.399043 − 0.916932i \(-0.630658\pi\)
−0.399043 + 0.916932i \(0.630658\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 16.0000 1.26098
\(162\) 0 0
\(163\) 20.0000 1.56652 0.783260 − 0.621694i \(-0.213555\pi\)
0.783260 + 0.621694i \(0.213555\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 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 \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) 0 0
\(175\) −4.00000 −0.302372
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 4.00000 0.298974 0.149487 − 0.988764i \(-0.452238\pi\)
0.149487 + 0.988764i \(0.452238\pi\)
\(180\) 0 0
\(181\) 14.0000 1.04061 0.520306 − 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −10.0000 −0.735215
\(186\) 0 0
\(187\) 2.00000 0.146254
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 12.0000 0.868290 0.434145 − 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) 0 0
\(193\) −22.0000 −1.58359 −0.791797 − 0.610784i \(-0.790854\pi\)
−0.791797 + 0.610784i \(0.790854\pi\)
\(194\) 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
\(199\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 24.0000 1.68447
\(204\) 0 0
\(205\) 6.00000 0.419058
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 4.00000 0.276686
\(210\) 0 0
\(211\) −12.0000 −0.826114 −0.413057 − 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 12.0000 0.818393
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −4.00000 −0.269069
\(222\) 0 0
\(223\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 28.0000 1.85843 0.929213 − 0.369546i \(-0.120487\pi\)
0.929213 + 0.369546i \(0.120487\pi\)
\(228\) 0 0
\(229\) −2.00000 −0.132164 −0.0660819 − 0.997814i \(-0.521050\pi\)
−0.0660819 + 0.997814i \(0.521050\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 22.0000 1.44127 0.720634 − 0.693316i \(-0.243851\pi\)
0.720634 + 0.693316i \(0.243851\pi\)
\(234\) 0 0
\(235\) −4.00000 −0.260931
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 24.0000 1.55243 0.776215 − 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 0 0
\(241\) −6.00000 −0.386494 −0.193247 − 0.981150i \(-0.561902\pi\)
−0.193247 + 0.981150i \(0.561902\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 9.00000 0.574989
\(246\) 0 0
\(247\) −8.00000 −0.509028
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 12.0000 0.757433 0.378717 − 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 4.00000 0.251478
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −18.0000 −1.12281 −0.561405 − 0.827541i \(-0.689739\pi\)
−0.561405 + 0.827541i \(0.689739\pi\)
\(258\) 0 0
\(259\) 40.0000 2.48548
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −24.0000 −1.47990 −0.739952 − 0.672660i \(-0.765152\pi\)
−0.739952 + 0.672660i \(0.765152\pi\)
\(264\) 0 0
\(265\) 6.00000 0.368577
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −18.0000 −1.09748 −0.548740 − 0.835993i \(-0.684892\pi\)
−0.548740 + 0.835993i \(0.684892\pi\)
\(270\) 0 0
\(271\) 20.0000 1.21491 0.607457 − 0.794353i \(-0.292190\pi\)
0.607457 + 0.794353i \(0.292190\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.00000 −0.0603023
\(276\) 0 0
\(277\) 18.0000 1.08152 0.540758 − 0.841178i \(-0.318138\pi\)
0.540758 + 0.841178i \(0.318138\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 22.0000 1.31241 0.656205 − 0.754583i \(-0.272161\pi\)
0.656205 + 0.754583i \(0.272161\pi\)
\(282\) 0 0
\(283\) 12.0000 0.713326 0.356663 − 0.934233i \(-0.383914\pi\)
0.356663 + 0.934233i \(0.383914\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −24.0000 −1.41668
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 10.0000 0.584206 0.292103 − 0.956387i \(-0.405645\pi\)
0.292103 + 0.956387i \(0.405645\pi\)
\(294\) 0 0
\(295\) −4.00000 −0.232889
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −8.00000 −0.462652
\(300\) 0 0
\(301\) −48.0000 −2.76667
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 10.0000 0.572598
\(306\) 0 0
\(307\) 28.0000 1.59804 0.799022 − 0.601302i \(-0.205351\pi\)
0.799022 + 0.601302i \(0.205351\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 12.0000 0.680458 0.340229 − 0.940343i \(-0.389495\pi\)
0.340229 + 0.940343i \(0.389495\pi\)
\(312\) 0 0
\(313\) −6.00000 −0.339140 −0.169570 − 0.985518i \(-0.554238\pi\)
−0.169570 + 0.985518i \(0.554238\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −26.0000 −1.46031 −0.730153 − 0.683284i \(-0.760551\pi\)
−0.730153 + 0.683284i \(0.760551\pi\)
\(318\) 0 0
\(319\) 6.00000 0.335936
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 8.00000 0.445132
\(324\) 0 0
\(325\) 2.00000 0.110940
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 16.0000 0.882109
\(330\) 0 0
\(331\) 28.0000 1.53902 0.769510 − 0.638635i \(-0.220501\pi\)
0.769510 + 0.638635i \(0.220501\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 12.0000 0.655630
\(336\) 0 0
\(337\) 2.00000 0.108947 0.0544735 − 0.998515i \(-0.482652\pi\)
0.0544735 + 0.998515i \(0.482652\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −8.00000 −0.431959
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 28.0000 1.50312 0.751559 − 0.659665i \(-0.229302\pi\)
0.751559 + 0.659665i \(0.229302\pi\)
\(348\) 0 0
\(349\) 2.00000 0.107058 0.0535288 − 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 30.0000 1.59674 0.798369 − 0.602168i \(-0.205696\pi\)
0.798369 + 0.602168i \(0.205696\pi\)
\(354\) 0 0
\(355\) −4.00000 −0.212298
\(356\) 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
\(361\) −3.00000 −0.157895
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 10.0000 0.523424
\(366\) 0 0
\(367\) −16.0000 −0.835193 −0.417597 − 0.908633i \(-0.637127\pi\)
−0.417597 + 0.908633i \(0.637127\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −24.0000 −1.24602
\(372\) 0 0
\(373\) −6.00000 −0.310668 −0.155334 − 0.987862i \(-0.549645\pi\)
−0.155334 + 0.987862i \(0.549645\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −12.0000 −0.618031
\(378\) 0 0
\(379\) −20.0000 −1.02733 −0.513665 − 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 20.0000 1.02195 0.510976 − 0.859595i \(-0.329284\pi\)
0.510976 + 0.859595i \(0.329284\pi\)
\(384\) 0 0
\(385\) 4.00000 0.203859
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −26.0000 −1.31825 −0.659126 − 0.752032i \(-0.729074\pi\)
−0.659126 + 0.752032i \(0.729074\pi\)
\(390\) 0 0
\(391\) 8.00000 0.404577
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −4.00000 −0.201262
\(396\) 0 0
\(397\) 22.0000 1.10415 0.552074 − 0.833795i \(-0.313837\pi\)
0.552074 + 0.833795i \(0.313837\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 22.0000 1.09863 0.549314 − 0.835616i \(-0.314889\pi\)
0.549314 + 0.835616i \(0.314889\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 10.0000 0.495682
\(408\) 0 0
\(409\) 2.00000 0.0988936 0.0494468 − 0.998777i \(-0.484254\pi\)
0.0494468 + 0.998777i \(0.484254\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 16.0000 0.787309
\(414\) 0 0
\(415\) 4.00000 0.196352
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −28.0000 −1.36789 −0.683945 − 0.729534i \(-0.739737\pi\)
−0.683945 + 0.729534i \(0.739737\pi\)
\(420\) 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
\(425\) −2.00000 −0.0970143
\(426\) 0 0
\(427\) −40.0000 −1.93574
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 34.0000 1.63394 0.816968 − 0.576683i \(-0.195653\pi\)
0.816968 + 0.576683i \(0.195653\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 16.0000 0.765384
\(438\) 0 0
\(439\) −12.0000 −0.572729 −0.286364 − 0.958121i \(-0.592447\pi\)
−0.286364 + 0.958121i \(0.592447\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 12.0000 0.570137 0.285069 − 0.958507i \(-0.407984\pi\)
0.285069 + 0.958507i \(0.407984\pi\)
\(444\) 0 0
\(445\) −10.0000 −0.474045
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 6.00000 0.283158 0.141579 − 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) 0 0
\(451\) −6.00000 −0.282529
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −8.00000 −0.375046
\(456\) 0 0
\(457\) 34.0000 1.59045 0.795226 − 0.606313i \(-0.207352\pi\)
0.795226 + 0.606313i \(0.207352\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −30.0000 −1.39724 −0.698620 − 0.715493i \(-0.746202\pi\)
−0.698620 + 0.715493i \(0.746202\pi\)
\(462\) 0 0
\(463\) −24.0000 −1.11537 −0.557687 − 0.830051i \(-0.688311\pi\)
−0.557687 + 0.830051i \(0.688311\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −20.0000 −0.925490 −0.462745 − 0.886492i \(-0.653135\pi\)
−0.462745 + 0.886492i \(0.653135\pi\)
\(468\) 0 0
\(469\) −48.0000 −2.21643
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −12.0000 −0.551761
\(474\) 0 0
\(475\) −4.00000 −0.183533
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) −20.0000 −0.911922
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 18.0000 0.817338
\(486\) 0 0
\(487\) 32.0000 1.45006 0.725029 − 0.688718i \(-0.241826\pi\)
0.725029 + 0.688718i \(0.241826\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 36.0000 1.62466 0.812329 − 0.583200i \(-0.198200\pi\)
0.812329 + 0.583200i \(0.198200\pi\)
\(492\) 0 0
\(493\) 12.0000 0.540453
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 16.0000 0.717698
\(498\) 0 0
\(499\) −12.0000 −0.537194 −0.268597 − 0.963253i \(-0.586560\pi\)
−0.268597 + 0.963253i \(0.586560\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 16.0000 0.713405 0.356702 − 0.934218i \(-0.383901\pi\)
0.356702 + 0.934218i \(0.383901\pi\)
\(504\) 0 0
\(505\) 18.0000 0.800989
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −34.0000 −1.50702 −0.753512 − 0.657434i \(-0.771642\pi\)
−0.753512 + 0.657434i \(0.771642\pi\)
\(510\) 0 0
\(511\) −40.0000 −1.76950
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 16.0000 0.705044
\(516\) 0 0
\(517\) 4.00000 0.175920
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 30.0000 1.31432 0.657162 − 0.753749i \(-0.271757\pi\)
0.657162 + 0.753749i \(0.271757\pi\)
\(522\) 0 0
\(523\) 28.0000 1.22435 0.612177 − 0.790721i \(-0.290294\pi\)
0.612177 + 0.790721i \(0.290294\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 12.0000 0.519778
\(534\) 0 0
\(535\) −12.0000 −0.518805
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −9.00000 −0.387657
\(540\) 0 0
\(541\) 2.00000 0.0859867 0.0429934 − 0.999075i \(-0.486311\pi\)
0.0429934 + 0.999075i \(0.486311\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2.00000 0.0856706
\(546\) 0 0
\(547\) −4.00000 −0.171028 −0.0855138 − 0.996337i \(-0.527253\pi\)
−0.0855138 + 0.996337i \(0.527253\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 24.0000 1.02243
\(552\) 0 0
\(553\) 16.0000 0.680389
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −30.0000 −1.27114 −0.635570 − 0.772043i \(-0.719235\pi\)
−0.635570 + 0.772043i \(0.719235\pi\)
\(558\) 0 0
\(559\) 24.0000 1.01509
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −4.00000 −0.168580 −0.0842900 − 0.996441i \(-0.526862\pi\)
−0.0842900 + 0.996441i \(0.526862\pi\)
\(564\) 0 0
\(565\) −18.0000 −0.757266
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 22.0000 0.922288 0.461144 − 0.887325i \(-0.347439\pi\)
0.461144 + 0.887325i \(0.347439\pi\)
\(570\) 0 0
\(571\) −44.0000 −1.84134 −0.920671 − 0.390339i \(-0.872358\pi\)
−0.920671 + 0.390339i \(0.872358\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −4.00000 −0.166812
\(576\) 0 0
\(577\) −14.0000 −0.582828 −0.291414 − 0.956597i \(-0.594126\pi\)
−0.291414 + 0.956597i \(0.594126\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −16.0000 −0.663792
\(582\) 0 0
\(583\) −6.00000 −0.248495
\(584\) 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
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −2.00000 −0.0821302 −0.0410651 − 0.999156i \(-0.513075\pi\)
−0.0410651 + 0.999156i \(0.513075\pi\)
\(594\) 0 0
\(595\) 8.00000 0.327968
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 12.0000 0.490307 0.245153 − 0.969484i \(-0.421162\pi\)
0.245153 + 0.969484i \(0.421162\pi\)
\(600\) 0 0
\(601\) 10.0000 0.407909 0.203954 − 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.00000 0.0406558
\(606\) 0 0
\(607\) −20.0000 −0.811775 −0.405887 − 0.913923i \(-0.633038\pi\)
−0.405887 + 0.913923i \(0.633038\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −8.00000 −0.323645
\(612\) 0 0
\(613\) −14.0000 −0.565455 −0.282727 − 0.959200i \(-0.591239\pi\)
−0.282727 + 0.959200i \(0.591239\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 6.00000 0.241551 0.120775 − 0.992680i \(-0.461462\pi\)
0.120775 + 0.992680i \(0.461462\pi\)
\(618\) 0 0
\(619\) 36.0000 1.44696 0.723481 − 0.690344i \(-0.242541\pi\)
0.723481 + 0.690344i \(0.242541\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 40.0000 1.60257
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 20.0000 0.797452
\(630\) 0 0
\(631\) −24.0000 −0.955425 −0.477712 − 0.878516i \(-0.658534\pi\)
−0.477712 + 0.878516i \(0.658534\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −4.00000 −0.158735
\(636\) 0 0
\(637\) 18.0000 0.713186
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −26.0000 −1.02694 −0.513469 − 0.858108i \(-0.671640\pi\)
−0.513469 + 0.858108i \(0.671640\pi\)
\(642\) 0 0
\(643\) −20.0000 −0.788723 −0.394362 − 0.918955i \(-0.629034\pi\)
−0.394362 + 0.918955i \(0.629034\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −36.0000 −1.41531 −0.707653 − 0.706560i \(-0.750246\pi\)
−0.707653 + 0.706560i \(0.750246\pi\)
\(648\) 0 0
\(649\) 4.00000 0.157014
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −26.0000 −1.01746 −0.508729 − 0.860927i \(-0.669885\pi\)
−0.508729 + 0.860927i \(0.669885\pi\)
\(654\) 0 0
\(655\) −12.0000 −0.468879
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 28.0000 1.09073 0.545363 − 0.838200i \(-0.316392\pi\)
0.545363 + 0.838200i \(0.316392\pi\)
\(660\) 0 0
\(661\) −34.0000 −1.32245 −0.661223 − 0.750189i \(-0.729962\pi\)
−0.661223 + 0.750189i \(0.729962\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 16.0000 0.620453
\(666\) 0 0
\(667\) 24.0000 0.929284
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −10.0000 −0.386046
\(672\) 0 0
\(673\) 26.0000 1.00223 0.501113 − 0.865382i \(-0.332924\pi\)
0.501113 + 0.865382i \(0.332924\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −30.0000 −1.15299 −0.576497 − 0.817099i \(-0.695581\pi\)
−0.576497 + 0.817099i \(0.695581\pi\)
\(678\) 0 0
\(679\) −72.0000 −2.76311
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −4.00000 −0.153056 −0.0765279 − 0.997067i \(-0.524383\pi\)
−0.0765279 + 0.997067i \(0.524383\pi\)
\(684\) 0 0
\(685\) −2.00000 −0.0764161
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 12.0000 0.457164
\(690\) 0 0
\(691\) −20.0000 −0.760836 −0.380418 − 0.924815i \(-0.624220\pi\)
−0.380418 + 0.924815i \(0.624220\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 4.00000 0.151729
\(696\) 0 0
\(697\) −12.0000 −0.454532
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 18.0000 0.679851 0.339925 − 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) 0 0
\(703\) 40.0000 1.50863
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −72.0000 −2.70784
\(708\) 0 0
\(709\) −34.0000 −1.27690 −0.638448 − 0.769665i \(-0.720423\pi\)
−0.638448 + 0.769665i \(0.720423\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −2.00000 −0.0747958
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 20.0000 0.745874 0.372937 − 0.927857i \(-0.378351\pi\)
0.372937 + 0.927857i \(0.378351\pi\)
\(720\) 0 0
\(721\) −64.0000 −2.38348
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −6.00000 −0.222834
\(726\) 0 0
\(727\) −16.0000 −0.593407 −0.296704 − 0.954970i \(-0.595887\pi\)
−0.296704 + 0.954970i \(0.595887\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −24.0000 −0.887672
\(732\) 0 0
\(733\) −14.0000 −0.517102 −0.258551 − 0.965998i \(-0.583245\pi\)
−0.258551 + 0.965998i \(0.583245\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −12.0000 −0.442026
\(738\) 0 0
\(739\) 36.0000 1.32428 0.662141 − 0.749380i \(-0.269648\pi\)
0.662141 + 0.749380i \(0.269648\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 16.0000 0.586983 0.293492 − 0.955962i \(-0.405183\pi\)
0.293492 + 0.955962i \(0.405183\pi\)
\(744\) 0 0
\(745\) −6.00000 −0.219823
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 48.0000 1.75388
\(750\) 0 0
\(751\) 32.0000 1.16770 0.583848 − 0.811863i \(-0.301546\pi\)
0.583848 + 0.811863i \(0.301546\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −12.0000 −0.436725
\(756\) 0 0
\(757\) 22.0000 0.799604 0.399802 − 0.916602i \(-0.369079\pi\)
0.399802 + 0.916602i \(0.369079\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −10.0000 −0.362500 −0.181250 − 0.983437i \(-0.558014\pi\)
−0.181250 + 0.983437i \(0.558014\pi\)
\(762\) 0 0
\(763\) −8.00000 −0.289619
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −8.00000 −0.288863
\(768\) 0 0
\(769\) 26.0000 0.937584 0.468792 − 0.883309i \(-0.344689\pi\)
0.468792 + 0.883309i \(0.344689\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −10.0000 −0.359675 −0.179838 − 0.983696i \(-0.557557\pi\)
−0.179838 + 0.983696i \(0.557557\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −24.0000 −0.859889
\(780\) 0 0
\(781\) 4.00000 0.143131
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −10.0000 −0.356915
\(786\) 0 0
\(787\) 36.0000 1.28326 0.641631 − 0.767014i \(-0.278258\pi\)
0.641631 + 0.767014i \(0.278258\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 72.0000 2.56003
\(792\) 0 0
\(793\) 20.0000 0.710221
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 30.0000 1.06265 0.531327 − 0.847167i \(-0.321693\pi\)
0.531327 + 0.847167i \(0.321693\pi\)
\(798\) 0 0
\(799\) 8.00000 0.283020
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −10.0000 −0.352892
\(804\) 0 0
\(805\) 16.0000 0.563926
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 22.0000 0.773479 0.386739 − 0.922189i \(-0.373601\pi\)
0.386739 + 0.922189i \(0.373601\pi\)
\(810\) 0 0
\(811\) −52.0000 −1.82597 −0.912983 − 0.407997i \(-0.866228\pi\)
−0.912983 + 0.407997i \(0.866228\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 20.0000 0.700569
\(816\) 0 0
\(817\) −48.0000 −1.67931
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 2.00000 0.0698005 0.0349002 − 0.999391i \(-0.488889\pi\)
0.0349002 + 0.999391i \(0.488889\pi\)
\(822\) 0 0
\(823\) 40.0000 1.39431 0.697156 − 0.716919i \(-0.254448\pi\)
0.697156 + 0.716919i \(0.254448\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 12.0000 0.417281 0.208640 − 0.977992i \(-0.433096\pi\)
0.208640 + 0.977992i \(0.433096\pi\)
\(828\) 0 0
\(829\) 46.0000 1.59765 0.798823 − 0.601566i \(-0.205456\pi\)
0.798823 + 0.601566i \(0.205456\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −18.0000 −0.623663
\(834\) 0 0
\(835\) 16.0000 0.553703
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 36.0000 1.24286 0.621429 − 0.783470i \(-0.286552\pi\)
0.621429 + 0.783470i \(0.286552\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −9.00000 −0.309609
\(846\) 0 0
\(847\) −4.00000 −0.137442
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 40.0000 1.37118
\(852\) 0 0
\(853\) 18.0000 0.616308 0.308154 − 0.951336i \(-0.400289\pi\)
0.308154 + 0.951336i \(0.400289\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 38.0000 1.29806 0.649028 − 0.760765i \(-0.275176\pi\)
0.649028 + 0.760765i \(0.275176\pi\)
\(858\) 0 0
\(859\) 44.0000 1.50126 0.750630 − 0.660722i \(-0.229750\pi\)
0.750630 + 0.660722i \(0.229750\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −36.0000 −1.22545 −0.612727 − 0.790295i \(-0.709928\pi\)
−0.612727 + 0.790295i \(0.709928\pi\)
\(864\) 0 0
\(865\) −6.00000 −0.204006
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 4.00000 0.135691
\(870\) 0 0
\(871\) 24.0000 0.813209
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −4.00000 −0.135225
\(876\) 0 0
\(877\) −14.0000 −0.472746 −0.236373 − 0.971662i \(-0.575959\pi\)
−0.236373 + 0.971662i \(0.575959\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −18.0000 −0.606435 −0.303218 − 0.952921i \(-0.598061\pi\)
−0.303218 + 0.952921i \(0.598061\pi\)
\(882\) 0 0
\(883\) −20.0000 −0.673054 −0.336527 − 0.941674i \(-0.609252\pi\)
−0.336527 + 0.941674i \(0.609252\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 48.0000 1.61168 0.805841 − 0.592132i \(-0.201714\pi\)
0.805841 + 0.592132i \(0.201714\pi\)
\(888\) 0 0
\(889\) 16.0000 0.536623
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 16.0000 0.535420
\(894\) 0 0
\(895\) 4.00000 0.133705
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) −12.0000 −0.399778
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 14.0000 0.465376
\(906\) 0 0
\(907\) 52.0000 1.72663 0.863316 − 0.504664i \(-0.168384\pi\)
0.863316 + 0.504664i \(0.168384\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −12.0000 −0.397578 −0.198789 − 0.980042i \(-0.563701\pi\)
−0.198789 + 0.980042i \(0.563701\pi\)
\(912\) 0 0
\(913\) −4.00000 −0.132381
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 48.0000 1.58510
\(918\) 0 0
\(919\) 12.0000 0.395843 0.197922 − 0.980218i \(-0.436581\pi\)
0.197922 + 0.980218i \(0.436581\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −8.00000 −0.263323
\(924\) 0 0
\(925\) −10.0000 −0.328798
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 6.00000 0.196854 0.0984268 − 0.995144i \(-0.468619\pi\)
0.0984268 + 0.995144i \(0.468619\pi\)
\(930\) 0 0
\(931\) −36.0000 −1.17985
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 2.00000 0.0654070
\(936\) 0 0
\(937\) −22.0000 −0.718709 −0.359354 − 0.933201i \(-0.617003\pi\)
−0.359354 + 0.933201i \(0.617003\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −22.0000 −0.717180 −0.358590 − 0.933495i \(-0.616742\pi\)
−0.358590 + 0.933495i \(0.616742\pi\)
\(942\) 0 0
\(943\) −24.0000 −0.781548
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −52.0000 −1.68977 −0.844886 − 0.534946i \(-0.820332\pi\)
−0.844886 + 0.534946i \(0.820332\pi\)
\(948\) 0 0
\(949\) 20.0000 0.649227
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 6.00000 0.194359 0.0971795 − 0.995267i \(-0.469018\pi\)
0.0971795 + 0.995267i \(0.469018\pi\)
\(954\) 0 0
\(955\) 12.0000 0.388311
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 8.00000 0.258333
\(960\) 0 0
\(961\) −31.0000 −1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −22.0000 −0.708205
\(966\) 0 0
\(967\) −12.0000 −0.385894 −0.192947 − 0.981209i \(-0.561805\pi\)
−0.192947 + 0.981209i \(0.561805\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −4.00000 −0.128366 −0.0641831 − 0.997938i \(-0.520444\pi\)
−0.0641831 + 0.997938i \(0.520444\pi\)
\(972\) 0 0
\(973\) −16.0000 −0.512936
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 38.0000 1.21573 0.607864 − 0.794041i \(-0.292027\pi\)
0.607864 + 0.794041i \(0.292027\pi\)
\(978\) 0 0
\(979\) 10.0000 0.319601
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 28.0000 0.893061 0.446531 − 0.894768i \(-0.352659\pi\)
0.446531 + 0.894768i \(0.352659\pi\)
\(984\) 0 0
\(985\) 18.0000 0.573528
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −48.0000 −1.52631
\(990\) 0 0
\(991\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −38.0000 −1.20347 −0.601736 − 0.798695i \(-0.705524\pi\)
−0.601736 + 0.798695i \(0.705524\pi\)
\(998\) 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 7920.2.a.t.1.1 1
3.2 odd 2 2640.2.a.j.1.1 1
4.3 odd 2 990.2.a.g.1.1 1
12.11 even 2 330.2.a.c.1.1 ✓ 1
20.3 even 4 4950.2.c.y.199.2 2
20.7 even 4 4950.2.c.y.199.1 2
20.19 odd 2 4950.2.a.x.1.1 1
60.23 odd 4 1650.2.c.a.199.1 2
60.47 odd 4 1650.2.c.a.199.2 2
60.59 even 2 1650.2.a.e.1.1 1
132.131 odd 2 3630.2.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
330.2.a.c.1.1 ✓ 1 12.11 even 2
990.2.a.g.1.1 1 4.3 odd 2
1650.2.a.e.1.1 1 60.59 even 2
1650.2.c.a.199.1 2 60.23 odd 4
1650.2.c.a.199.2 2 60.47 odd 4
2640.2.a.j.1.1 1 3.2 odd 2
3630.2.a.a.1.1 1 132.131 odd 2
4950.2.a.x.1.1 1 20.19 odd 2
4950.2.c.y.199.1 2 20.7 even 4
4950.2.c.y.199.2 2 20.3 even 4
7920.2.a.t.1.1 1 1.1 even 1 trivial