Properties

Label 5184.2.a.j.1.1
Level $5184$
Weight $2$
Character 5184.1
Self dual yes
Analytic conductor $41.394$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [5184,2,Mod(1,5184)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5184, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("5184.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5184 = 2^{6} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5184.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: \(41.3944484078\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 2592)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 5184.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{5} -2.00000 q^{7} +O(q^{10})\) \(q-1.00000 q^{5} -2.00000 q^{7} +2.00000 q^{11} -1.00000 q^{13} +3.00000 q^{17} +2.00000 q^{19} -6.00000 q^{23} -4.00000 q^{25} -1.00000 q^{29} +8.00000 q^{31} +2.00000 q^{35} -1.00000 q^{37} -2.00000 q^{41} +10.0000 q^{43} -4.00000 q^{47} -3.00000 q^{49} +10.0000 q^{53} -2.00000 q^{55} +4.00000 q^{59} -9.00000 q^{61} +1.00000 q^{65} -14.0000 q^{67} -10.0000 q^{71} -9.00000 q^{73} -4.00000 q^{77} -10.0000 q^{79} +12.0000 q^{83} -3.00000 q^{85} +11.0000 q^{89} +2.00000 q^{91} -2.00000 q^{95} -2.00000 q^{97} +O(q^{100})\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −1.00000 −0.447214 −0.223607 0.974679i \(-0.571783\pi\)
−0.223607 + 0.974679i \(0.571783\pi\)
\(6\) 0 0
\(7\) −2.00000 −0.755929 −0.377964 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.00000 0.727607 0.363803 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) 0 0
\(19\) 2.00000 0.458831 0.229416 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −6.00000 −1.25109 −0.625543 0.780189i \(-0.715123\pi\)
−0.625543 + 0.780189i \(0.715123\pi\)
\(24\) 0 0
\(25\) −4.00000 −0.800000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −1.00000 −0.185695 −0.0928477 0.995680i \(-0.529597\pi\)
−0.0928477 + 0.995680i \(0.529597\pi\)
\(30\) 0 0
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.00000 0.338062
\(36\) 0 0
\(37\) −1.00000 −0.164399 −0.0821995 0.996616i \(-0.526194\pi\)
−0.0821995 + 0.996616i \(0.526194\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) 10.0000 1.52499 0.762493 0.646997i \(-0.223975\pi\)
0.762493 + 0.646997i \(0.223975\pi\)
\(44\) 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
\(49\) −3.00000 −0.428571
\(50\) 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
\(55\) −2.00000 −0.269680
\(56\) 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
\(61\) −9.00000 −1.15233 −0.576166 0.817333i \(-0.695452\pi\)
−0.576166 + 0.817333i \(0.695452\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.00000 0.124035
\(66\) 0 0
\(67\) −14.0000 −1.71037 −0.855186 0.518321i \(-0.826557\pi\)
−0.855186 + 0.518321i \(0.826557\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −10.0000 −1.18678 −0.593391 0.804914i \(-0.702211\pi\)
−0.593391 + 0.804914i \(0.702211\pi\)
\(72\) 0 0
\(73\) −9.00000 −1.05337 −0.526685 0.850060i \(-0.676565\pi\)
−0.526685 + 0.850060i \(0.676565\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −4.00000 −0.455842
\(78\) 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
\(85\) −3.00000 −0.325396
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 11.0000 1.16600 0.582999 0.812473i \(-0.301879\pi\)
0.582999 + 0.812473i \(0.301879\pi\)
\(90\) 0 0
\(91\) 2.00000 0.209657
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −2.00000 −0.205196
\(96\) 0 0
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 0 0
\(103\) 12.0000 1.18240 0.591198 0.806527i \(-0.298655\pi\)
0.591198 + 0.806527i \(0.298655\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 16.0000 1.54678 0.773389 0.633932i \(-0.218560\pi\)
0.773389 + 0.633932i \(0.218560\pi\)
\(108\) 0 0
\(109\) −5.00000 −0.478913 −0.239457 0.970907i \(-0.576969\pi\)
−0.239457 + 0.970907i \(0.576969\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −17.0000 −1.59923 −0.799613 0.600516i \(-0.794962\pi\)
−0.799613 + 0.600516i \(0.794962\pi\)
\(114\) 0 0
\(115\) 6.00000 0.559503
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −6.00000 −0.550019
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 9.00000 0.804984
\(126\) 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
\(131\) 14.0000 1.22319 0.611593 0.791173i \(-0.290529\pi\)
0.611593 + 0.791173i \(0.290529\pi\)
\(132\) 0 0
\(133\) −4.00000 −0.346844
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −9.00000 −0.768922 −0.384461 0.923141i \(-0.625613\pi\)
−0.384461 + 0.923141i \(0.625613\pi\)
\(138\) 0 0
\(139\) −20.0000 −1.69638 −0.848189 0.529694i \(-0.822307\pi\)
−0.848189 + 0.529694i \(0.822307\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −2.00000 −0.167248
\(144\) 0 0
\(145\) 1.00000 0.0830455
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −21.0000 −1.72039 −0.860194 0.509968i \(-0.829657\pi\)
−0.860194 + 0.509968i \(0.829657\pi\)
\(150\) 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
\(155\) −8.00000 −0.642575
\(156\) 0 0
\(157\) −17.0000 −1.35675 −0.678374 0.734717i \(-0.737315\pi\)
−0.678374 + 0.734717i \(0.737315\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 12.0000 0.945732
\(162\) 0 0
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2.00000 0.154765 0.0773823 0.997001i \(-0.475344\pi\)
0.0773823 + 0.997001i \(0.475344\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −21.0000 −1.59660 −0.798300 0.602260i \(-0.794267\pi\)
−0.798300 + 0.602260i \(0.794267\pi\)
\(174\) 0 0
\(175\) 8.00000 0.604743
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) −14.0000 −1.04061 −0.520306 0.853980i \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.00000 0.0735215
\(186\) 0 0
\(187\) 6.00000 0.438763
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −18.0000 −1.30243 −0.651217 0.758891i \(-0.725741\pi\)
−0.651217 + 0.758891i \(0.725741\pi\)
\(192\) 0 0
\(193\) −9.00000 −0.647834 −0.323917 0.946085i \(-0.605000\pi\)
−0.323917 + 0.946085i \(0.605000\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 11.0000 0.783718 0.391859 0.920025i \(-0.371832\pi\)
0.391859 + 0.920025i \(0.371832\pi\)
\(198\) 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
\(205\) 2.00000 0.139686
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 4.00000 0.276686
\(210\) 0 0
\(211\) 2.00000 0.137686 0.0688428 0.997628i \(-0.478069\pi\)
0.0688428 + 0.997628i \(0.478069\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −10.0000 −0.681994
\(216\) 0 0
\(217\) −16.0000 −1.08615
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −3.00000 −0.201802
\(222\) 0 0
\(223\) −2.00000 −0.133930 −0.0669650 0.997755i \(-0.521332\pi\)
−0.0669650 + 0.997755i \(0.521332\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 6.00000 0.398234 0.199117 0.979976i \(-0.436193\pi\)
0.199117 + 0.979976i \(0.436193\pi\)
\(228\) 0 0
\(229\) 7.00000 0.462573 0.231287 0.972886i \(-0.425707\pi\)
0.231287 + 0.972886i \(0.425707\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 15.0000 0.982683 0.491341 0.870967i \(-0.336507\pi\)
0.491341 + 0.870967i \(0.336507\pi\)
\(234\) 0 0
\(235\) 4.00000 0.260931
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −12.0000 −0.776215 −0.388108 0.921614i \(-0.626871\pi\)
−0.388108 + 0.921614i \(0.626871\pi\)
\(240\) 0 0
\(241\) −5.00000 −0.322078 −0.161039 0.986948i \(-0.551485\pi\)
−0.161039 + 0.986948i \(0.551485\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 3.00000 0.191663
\(246\) 0 0
\(247\) −2.00000 −0.127257
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −18.0000 −1.13615 −0.568075 0.822977i \(-0.692312\pi\)
−0.568075 + 0.822977i \(0.692312\pi\)
\(252\) 0 0
\(253\) −12.0000 −0.754434
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −29.0000 −1.80897 −0.904485 0.426505i \(-0.859745\pi\)
−0.904485 + 0.426505i \(0.859745\pi\)
\(258\) 0 0
\(259\) 2.00000 0.124274
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 12.0000 0.739952 0.369976 0.929041i \(-0.379366\pi\)
0.369976 + 0.929041i \(0.379366\pi\)
\(264\) 0 0
\(265\) −10.0000 −0.614295
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 15.0000 0.914566 0.457283 0.889321i \(-0.348823\pi\)
0.457283 + 0.889321i \(0.348823\pi\)
\(270\) 0 0
\(271\) 6.00000 0.364474 0.182237 0.983255i \(-0.441666\pi\)
0.182237 + 0.983255i \(0.441666\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −8.00000 −0.482418
\(276\) 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
\(281\) −9.00000 −0.536895 −0.268447 0.963294i \(-0.586511\pi\)
−0.268447 + 0.963294i \(0.586511\pi\)
\(282\) 0 0
\(283\) 16.0000 0.951101 0.475551 0.879688i \(-0.342249\pi\)
0.475551 + 0.879688i \(0.342249\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 4.00000 0.236113
\(288\) 0 0
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −21.0000 −1.22683 −0.613417 0.789760i \(-0.710205\pi\)
−0.613417 + 0.789760i \(0.710205\pi\)
\(294\) 0 0
\(295\) −4.00000 −0.232889
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 6.00000 0.346989
\(300\) 0 0
\(301\) −20.0000 −1.15278
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 9.00000 0.515339
\(306\) 0 0
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 7.00000 0.395663 0.197832 0.980236i \(-0.436610\pi\)
0.197832 + 0.980236i \(0.436610\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3.00000 0.168497 0.0842484 0.996445i \(-0.473151\pi\)
0.0842484 + 0.996445i \(0.473151\pi\)
\(318\) 0 0
\(319\) −2.00000 −0.111979
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 6.00000 0.333849
\(324\) 0 0
\(325\) 4.00000 0.221880
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 8.00000 0.441054
\(330\) 0 0
\(331\) −14.0000 −0.769510 −0.384755 0.923019i \(-0.625714\pi\)
−0.384755 + 0.923019i \(0.625714\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 14.0000 0.764902
\(336\) 0 0
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 16.0000 0.866449
\(342\) 0 0
\(343\) 20.0000 1.07990
\(344\) 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
\(349\) −34.0000 −1.81998 −0.909989 0.414632i \(-0.863910\pi\)
−0.909989 + 0.414632i \(0.863910\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2.00000 0.106449 0.0532246 0.998583i \(-0.483050\pi\)
0.0532246 + 0.998583i \(0.483050\pi\)
\(354\) 0 0
\(355\) 10.0000 0.530745
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 34.0000 1.79445 0.897226 0.441572i \(-0.145579\pi\)
0.897226 + 0.441572i \(0.145579\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 9.00000 0.471082
\(366\) 0 0
\(367\) 24.0000 1.25279 0.626395 0.779506i \(-0.284530\pi\)
0.626395 + 0.779506i \(0.284530\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −20.0000 −1.03835
\(372\) 0 0
\(373\) 10.0000 0.517780 0.258890 0.965907i \(-0.416643\pi\)
0.258890 + 0.965907i \(0.416643\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.00000 0.0515026
\(378\) 0 0
\(379\) 8.00000 0.410932 0.205466 0.978664i \(-0.434129\pi\)
0.205466 + 0.978664i \(0.434129\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 14.0000 0.715367 0.357683 0.933843i \(-0.383567\pi\)
0.357683 + 0.933843i \(0.383567\pi\)
\(384\) 0 0
\(385\) 4.00000 0.203859
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 18.0000 0.912636 0.456318 0.889817i \(-0.349168\pi\)
0.456318 + 0.889817i \(0.349168\pi\)
\(390\) 0 0
\(391\) −18.0000 −0.910299
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 10.0000 0.503155
\(396\) 0 0
\(397\) −13.0000 −0.652451 −0.326226 0.945292i \(-0.605777\pi\)
−0.326226 + 0.945292i \(0.605777\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −25.0000 −1.24844 −0.624220 0.781248i \(-0.714583\pi\)
−0.624220 + 0.781248i \(0.714583\pi\)
\(402\) 0 0
\(403\) −8.00000 −0.398508
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −2.00000 −0.0991363
\(408\) 0 0
\(409\) −29.0000 −1.43396 −0.716979 0.697095i \(-0.754476\pi\)
−0.716979 + 0.697095i \(0.754476\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −8.00000 −0.393654
\(414\) 0 0
\(415\) −12.0000 −0.589057
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −40.0000 −1.95413 −0.977064 0.212946i \(-0.931694\pi\)
−0.977064 + 0.212946i \(0.931694\pi\)
\(420\) 0 0
\(421\) 7.00000 0.341159 0.170580 0.985344i \(-0.445436\pi\)
0.170580 + 0.985344i \(0.445436\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −12.0000 −0.582086
\(426\) 0 0
\(427\) 18.0000 0.871081
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −12.0000 −0.578020 −0.289010 0.957326i \(-0.593326\pi\)
−0.289010 + 0.957326i \(0.593326\pi\)
\(432\) 0 0
\(433\) 19.0000 0.913082 0.456541 0.889702i \(-0.349088\pi\)
0.456541 + 0.889702i \(0.349088\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −12.0000 −0.574038
\(438\) 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
\(443\) 12.0000 0.570137 0.285069 0.958507i \(-0.407984\pi\)
0.285069 + 0.958507i \(0.407984\pi\)
\(444\) 0 0
\(445\) −11.0000 −0.521450
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 14.0000 0.660701 0.330350 0.943858i \(-0.392833\pi\)
0.330350 + 0.943858i \(0.392833\pi\)
\(450\) 0 0
\(451\) −4.00000 −0.188353
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −2.00000 −0.0937614
\(456\) 0 0
\(457\) −37.0000 −1.73079 −0.865393 0.501093i \(-0.832931\pi\)
−0.865393 + 0.501093i \(0.832931\pi\)
\(458\) 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
\(463\) −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
\(467\) −28.0000 −1.29569 −0.647843 0.761774i \(-0.724329\pi\)
−0.647843 + 0.761774i \(0.724329\pi\)
\(468\) 0 0
\(469\) 28.0000 1.29292
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 20.0000 0.919601
\(474\) 0 0
\(475\) −8.00000 −0.367065
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 42.0000 1.91903 0.959514 0.281659i \(-0.0908848\pi\)
0.959514 + 0.281659i \(0.0908848\pi\)
\(480\) 0 0
\(481\) 1.00000 0.0455961
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2.00000 0.0908153
\(486\) 0 0
\(487\) 16.0000 0.725029 0.362515 0.931978i \(-0.381918\pi\)
0.362515 + 0.931978i \(0.381918\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −34.0000 −1.53440 −0.767199 0.641409i \(-0.778350\pi\)
−0.767199 + 0.641409i \(0.778350\pi\)
\(492\) 0 0
\(493\) −3.00000 −0.135113
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 20.0000 0.897123
\(498\) 0 0
\(499\) 6.00000 0.268597 0.134298 0.990941i \(-0.457122\pi\)
0.134298 + 0.990941i \(0.457122\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) −6.00000 −0.266996
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 18.0000 0.797836 0.398918 0.916987i \(-0.369386\pi\)
0.398918 + 0.916987i \(0.369386\pi\)
\(510\) 0 0
\(511\) 18.0000 0.796273
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −12.0000 −0.528783
\(516\) 0 0
\(517\) −8.00000 −0.351840
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −18.0000 −0.788594 −0.394297 0.918983i \(-0.629012\pi\)
−0.394297 + 0.918983i \(0.629012\pi\)
\(522\) 0 0
\(523\) −30.0000 −1.31181 −0.655904 0.754844i \(-0.727712\pi\)
−0.655904 + 0.754844i \(0.727712\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 24.0000 1.04546
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 2.00000 0.0866296
\(534\) 0 0
\(535\) −16.0000 −0.691740
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −6.00000 −0.258438
\(540\) 0 0
\(541\) −13.0000 −0.558914 −0.279457 0.960158i \(-0.590154\pi\)
−0.279457 + 0.960158i \(0.590154\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 5.00000 0.214176
\(546\) 0 0
\(547\) −12.0000 −0.513083 −0.256541 0.966533i \(-0.582583\pi\)
−0.256541 + 0.966533i \(0.582583\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −2.00000 −0.0852029
\(552\) 0 0
\(553\) 20.0000 0.850487
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 11.0000 0.466085 0.233042 0.972467i \(-0.425132\pi\)
0.233042 + 0.972467i \(0.425132\pi\)
\(558\) 0 0
\(559\) −10.0000 −0.422955
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 36.0000 1.51722 0.758610 0.651546i \(-0.225879\pi\)
0.758610 + 0.651546i \(0.225879\pi\)
\(564\) 0 0
\(565\) 17.0000 0.715195
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −5.00000 −0.209611 −0.104805 0.994493i \(-0.533422\pi\)
−0.104805 + 0.994493i \(0.533422\pi\)
\(570\) 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
\(575\) 24.0000 1.00087
\(576\) 0 0
\(577\) 27.0000 1.12402 0.562012 0.827129i \(-0.310027\pi\)
0.562012 + 0.827129i \(0.310027\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −24.0000 −0.995688
\(582\) 0 0
\(583\) 20.0000 0.828315
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −30.0000 −1.23823 −0.619116 0.785299i \(-0.712509\pi\)
−0.619116 + 0.785299i \(0.712509\pi\)
\(588\) 0 0
\(589\) 16.0000 0.659269
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 15.0000 0.615976 0.307988 0.951390i \(-0.400344\pi\)
0.307988 + 0.951390i \(0.400344\pi\)
\(594\) 0 0
\(595\) 6.00000 0.245976
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 32.0000 1.30748 0.653742 0.756717i \(-0.273198\pi\)
0.653742 + 0.756717i \(0.273198\pi\)
\(600\) 0 0
\(601\) −17.0000 −0.693444 −0.346722 0.937968i \(-0.612705\pi\)
−0.346722 + 0.937968i \(0.612705\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 7.00000 0.284590
\(606\) 0 0
\(607\) −22.0000 −0.892952 −0.446476 0.894795i \(-0.647321\pi\)
−0.446476 + 0.894795i \(0.647321\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 4.00000 0.161823
\(612\) 0 0
\(613\) −6.00000 −0.242338 −0.121169 0.992632i \(-0.538664\pi\)
−0.121169 + 0.992632i \(0.538664\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 15.0000 0.603877 0.301939 0.953327i \(-0.402366\pi\)
0.301939 + 0.953327i \(0.402366\pi\)
\(618\) 0 0
\(619\) −48.0000 −1.92928 −0.964641 0.263566i \(-0.915101\pi\)
−0.964641 + 0.263566i \(0.915101\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −22.0000 −0.881411
\(624\) 0 0
\(625\) 11.0000 0.440000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −3.00000 −0.119618
\(630\) 0 0
\(631\) 20.0000 0.796187 0.398094 0.917345i \(-0.369672\pi\)
0.398094 + 0.917345i \(0.369672\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −2.00000 −0.0793676
\(636\) 0 0
\(637\) 3.00000 0.118864
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 35.0000 1.38242 0.691208 0.722655i \(-0.257079\pi\)
0.691208 + 0.722655i \(0.257079\pi\)
\(642\) 0 0
\(643\) 36.0000 1.41970 0.709851 0.704352i \(-0.248762\pi\)
0.709851 + 0.704352i \(0.248762\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −6.00000 −0.235884 −0.117942 0.993020i \(-0.537630\pi\)
−0.117942 + 0.993020i \(0.537630\pi\)
\(648\) 0 0
\(649\) 8.00000 0.314027
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 34.0000 1.33052 0.665261 0.746611i \(-0.268320\pi\)
0.665261 + 0.746611i \(0.268320\pi\)
\(654\) 0 0
\(655\) −14.0000 −0.547025
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −30.0000 −1.16863 −0.584317 0.811525i \(-0.698638\pi\)
−0.584317 + 0.811525i \(0.698638\pi\)
\(660\) 0 0
\(661\) 31.0000 1.20576 0.602880 0.797832i \(-0.294020\pi\)
0.602880 + 0.797832i \(0.294020\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 4.00000 0.155113
\(666\) 0 0
\(667\) 6.00000 0.232321
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −18.0000 −0.694882
\(672\) 0 0
\(673\) 23.0000 0.886585 0.443292 0.896377i \(-0.353810\pi\)
0.443292 + 0.896377i \(0.353810\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 34.0000 1.30673 0.653363 0.757045i \(-0.273358\pi\)
0.653363 + 0.757045i \(0.273358\pi\)
\(678\) 0 0
\(679\) 4.00000 0.153506
\(680\) 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
\(685\) 9.00000 0.343872
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −10.0000 −0.380970
\(690\) 0 0
\(691\) −10.0000 −0.380418 −0.190209 0.981744i \(-0.560917\pi\)
−0.190209 + 0.981744i \(0.560917\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 20.0000 0.758643
\(696\) 0 0
\(697\) −6.00000 −0.227266
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −45.0000 −1.69963 −0.849813 0.527084i \(-0.823285\pi\)
−0.849813 + 0.527084i \(0.823285\pi\)
\(702\) 0 0
\(703\) −2.00000 −0.0754314
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −12.0000 −0.451306
\(708\) 0 0
\(709\) −1.00000 −0.0375558 −0.0187779 0.999824i \(-0.505978\pi\)
−0.0187779 + 0.999824i \(0.505978\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −48.0000 −1.79761
\(714\) 0 0
\(715\) 2.00000 0.0747958
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 14.0000 0.522112 0.261056 0.965324i \(-0.415929\pi\)
0.261056 + 0.965324i \(0.415929\pi\)
\(720\) 0 0
\(721\) −24.0000 −0.893807
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 4.00000 0.148556
\(726\) 0 0
\(727\) −6.00000 −0.222528 −0.111264 0.993791i \(-0.535490\pi\)
−0.111264 + 0.993791i \(0.535490\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 30.0000 1.10959
\(732\) 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
\(737\) −28.0000 −1.03139
\(738\) 0 0
\(739\) 8.00000 0.294285 0.147142 0.989115i \(-0.452992\pi\)
0.147142 + 0.989115i \(0.452992\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 24.0000 0.880475 0.440237 0.897881i \(-0.354894\pi\)
0.440237 + 0.897881i \(0.354894\pi\)
\(744\) 0 0
\(745\) 21.0000 0.769380
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −32.0000 −1.16925
\(750\) 0 0
\(751\) −22.0000 −0.802791 −0.401396 0.915905i \(-0.631475\pi\)
−0.401396 + 0.915905i \(0.631475\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 12.0000 0.436725
\(756\) 0 0
\(757\) 42.0000 1.52652 0.763258 0.646094i \(-0.223599\pi\)
0.763258 + 0.646094i \(0.223599\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 39.0000 1.41375 0.706874 0.707339i \(-0.250105\pi\)
0.706874 + 0.707339i \(0.250105\pi\)
\(762\) 0 0
\(763\) 10.0000 0.362024
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −4.00000 −0.144432
\(768\) 0 0
\(769\) 31.0000 1.11789 0.558944 0.829205i \(-0.311207\pi\)
0.558944 + 0.829205i \(0.311207\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −9.00000 −0.323708 −0.161854 0.986815i \(-0.551747\pi\)
−0.161854 + 0.986815i \(0.551747\pi\)
\(774\) 0 0
\(775\) −32.0000 −1.14947
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −4.00000 −0.143315
\(780\) 0 0
\(781\) −20.0000 −0.715656
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 17.0000 0.606756
\(786\) 0 0
\(787\) 18.0000 0.641631 0.320815 0.947142i \(-0.396043\pi\)
0.320815 + 0.947142i \(0.396043\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 34.0000 1.20890
\(792\) 0 0
\(793\) 9.00000 0.319599
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 39.0000 1.38145 0.690725 0.723117i \(-0.257291\pi\)
0.690725 + 0.723117i \(0.257291\pi\)
\(798\) 0 0
\(799\) −12.0000 −0.424529
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −18.0000 −0.635206
\(804\) 0 0
\(805\) −12.0000 −0.422944
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −37.0000 −1.30085 −0.650425 0.759570i \(-0.725409\pi\)
−0.650425 + 0.759570i \(0.725409\pi\)
\(810\) 0 0
\(811\) −16.0000 −0.561836 −0.280918 0.959732i \(-0.590639\pi\)
−0.280918 + 0.959732i \(0.590639\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 4.00000 0.140114
\(816\) 0 0
\(817\) 20.0000 0.699711
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 23.0000 0.802706 0.401353 0.915924i \(-0.368540\pi\)
0.401353 + 0.915924i \(0.368540\pi\)
\(822\) 0 0
\(823\) −8.00000 −0.278862 −0.139431 0.990232i \(-0.544527\pi\)
−0.139431 + 0.990232i \(0.544527\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −22.0000 −0.765015 −0.382507 0.923952i \(-0.624939\pi\)
−0.382507 + 0.923952i \(0.624939\pi\)
\(828\) 0 0
\(829\) −38.0000 −1.31979 −0.659897 0.751356i \(-0.729400\pi\)
−0.659897 + 0.751356i \(0.729400\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −9.00000 −0.311832
\(834\) 0 0
\(835\) −2.00000 −0.0692129
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −22.0000 −0.759524 −0.379762 0.925084i \(-0.623994\pi\)
−0.379762 + 0.925084i \(0.623994\pi\)
\(840\) 0 0
\(841\) −28.0000 −0.965517
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 12.0000 0.412813
\(846\) 0 0
\(847\) 14.0000 0.481046
\(848\) 0 0
\(849\) 0 0
\(850\) 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
\(857\) −13.0000 −0.444072 −0.222036 0.975039i \(-0.571270\pi\)
−0.222036 + 0.975039i \(0.571270\pi\)
\(858\) 0 0
\(859\) −44.0000 −1.50126 −0.750630 0.660722i \(-0.770250\pi\)
−0.750630 + 0.660722i \(0.770250\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −46.0000 −1.56586 −0.782929 0.622111i \(-0.786275\pi\)
−0.782929 + 0.622111i \(0.786275\pi\)
\(864\) 0 0
\(865\) 21.0000 0.714021
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −20.0000 −0.678454
\(870\) 0 0
\(871\) 14.0000 0.474372
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −18.0000 −0.608511
\(876\) 0 0
\(877\) 35.0000 1.18187 0.590933 0.806721i \(-0.298760\pi\)
0.590933 + 0.806721i \(0.298760\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −42.0000 −1.41502 −0.707508 0.706705i \(-0.750181\pi\)
−0.707508 + 0.706705i \(0.750181\pi\)
\(882\) 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
\(887\) −54.0000 −1.81314 −0.906571 0.422053i \(-0.861310\pi\)
−0.906571 + 0.422053i \(0.861310\pi\)
\(888\) 0 0
\(889\) −4.00000 −0.134156
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −8.00000 −0.267710
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −8.00000 −0.266815
\(900\) 0 0
\(901\) 30.0000 0.999445
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 14.0000 0.465376
\(906\) 0 0
\(907\) 8.00000 0.265636 0.132818 0.991140i \(-0.457597\pi\)
0.132818 + 0.991140i \(0.457597\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 30.0000 0.993944 0.496972 0.867766i \(-0.334445\pi\)
0.496972 + 0.867766i \(0.334445\pi\)
\(912\) 0 0
\(913\) 24.0000 0.794284
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −28.0000 −0.924641
\(918\) 0 0
\(919\) −42.0000 −1.38545 −0.692726 0.721201i \(-0.743591\pi\)
−0.692726 + 0.721201i \(0.743591\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 10.0000 0.329154
\(924\) 0 0
\(925\) 4.00000 0.131519
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 27.0000 0.885841 0.442921 0.896561i \(-0.353942\pi\)
0.442921 + 0.896561i \(0.353942\pi\)
\(930\) 0 0
\(931\) −6.00000 −0.196642
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −6.00000 −0.196221
\(936\) 0 0
\(937\) −25.0000 −0.816714 −0.408357 0.912822i \(-0.633898\pi\)
−0.408357 + 0.912822i \(0.633898\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 43.0000 1.40176 0.700880 0.713279i \(-0.252791\pi\)
0.700880 + 0.713279i \(0.252791\pi\)
\(942\) 0 0
\(943\) 12.0000 0.390774
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 54.0000 1.75476 0.877382 0.479792i \(-0.159288\pi\)
0.877382 + 0.479792i \(0.159288\pi\)
\(948\) 0 0
\(949\) 9.00000 0.292152
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −21.0000 −0.680257 −0.340128 0.940379i \(-0.610471\pi\)
−0.340128 + 0.940379i \(0.610471\pi\)
\(954\) 0 0
\(955\) 18.0000 0.582466
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 18.0000 0.581250
\(960\) 0 0
\(961\) 33.0000 1.06452
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 9.00000 0.289720
\(966\) 0 0
\(967\) 18.0000 0.578841 0.289420 0.957202i \(-0.406537\pi\)
0.289420 + 0.957202i \(0.406537\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 38.0000 1.21948 0.609739 0.792602i \(-0.291274\pi\)
0.609739 + 0.792602i \(0.291274\pi\)
\(972\) 0 0
\(973\) 40.0000 1.28234
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −2.00000 −0.0639857 −0.0319928 0.999488i \(-0.510185\pi\)
−0.0319928 + 0.999488i \(0.510185\pi\)
\(978\) 0 0
\(979\) 22.0000 0.703123
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −24.0000 −0.765481 −0.382741 0.923856i \(-0.625020\pi\)
−0.382741 + 0.923856i \(0.625020\pi\)
\(984\) 0 0
\(985\) −11.0000 −0.350489
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −60.0000 −1.90789
\(990\) 0 0
\(991\) 38.0000 1.20711 0.603555 0.797321i \(-0.293750\pi\)
0.603555 + 0.797321i \(0.293750\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 16.0000 0.507234
\(996\) 0 0
\(997\) 15.0000 0.475055 0.237527 0.971381i \(-0.423663\pi\)
0.237527 + 0.971381i \(0.423663\pi\)
\(998\) 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 5184.2.a.j.1.1 1
3.2 odd 2 5184.2.a.t.1.1 1
4.3 odd 2 5184.2.a.m.1.1 1
8.3 odd 2 2592.2.a.f.1.1 yes 1
8.5 even 2 2592.2.a.e.1.1 yes 1
12.11 even 2 5184.2.a.w.1.1 1
24.5 odd 2 2592.2.a.c.1.1 1
24.11 even 2 2592.2.a.d.1.1 yes 1
72.5 odd 6 2592.2.i.o.865.1 2
72.11 even 6 2592.2.i.n.1729.1 2
72.13 even 6 2592.2.i.k.865.1 2
72.29 odd 6 2592.2.i.o.1729.1 2
72.43 odd 6 2592.2.i.j.1729.1 2
72.59 even 6 2592.2.i.n.865.1 2
72.61 even 6 2592.2.i.k.1729.1 2
72.67 odd 6 2592.2.i.j.865.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2592.2.a.c.1.1 1 24.5 odd 2
2592.2.a.d.1.1 yes 1 24.11 even 2
2592.2.a.e.1.1 yes 1 8.5 even 2
2592.2.a.f.1.1 yes 1 8.3 odd 2
2592.2.i.j.865.1 2 72.67 odd 6
2592.2.i.j.1729.1 2 72.43 odd 6
2592.2.i.k.865.1 2 72.13 even 6
2592.2.i.k.1729.1 2 72.61 even 6
2592.2.i.n.865.1 2 72.59 even 6
2592.2.i.n.1729.1 2 72.11 even 6
2592.2.i.o.865.1 2 72.5 odd 6
2592.2.i.o.1729.1 2 72.29 odd 6
5184.2.a.j.1.1 1 1.1 even 1 trivial
5184.2.a.m.1.1 1 4.3 odd 2
5184.2.a.t.1.1 1 3.2 odd 2
5184.2.a.w.1.1 1 12.11 even 2