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Properties

Label 9072.2.a.n.1.1
Level $9072$
Weight $2$
Character 9072.1
Self dual yes
Analytic conductor $72.440$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [9072,2,Mod(1,9072)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9072, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("9072.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9072 = 2^{4} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9072.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: \(72.4402847137\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 504)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 9072.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{5} -1.00000 q^{7} +O(q^{10})\) \(q+1.00000 q^{5} -1.00000 q^{7} -6.00000 q^{11} +6.00000 q^{13} +2.00000 q^{17} -7.00000 q^{19} -1.00000 q^{23} -4.00000 q^{25} -2.00000 q^{29} -10.0000 q^{31} -1.00000 q^{35} -6.00000 q^{37} +8.00000 q^{41} +10.0000 q^{43} +8.00000 q^{47} +1.00000 q^{49} -2.00000 q^{53} -6.00000 q^{55} +7.00000 q^{61} +6.00000 q^{65} +12.0000 q^{67} +15.0000 q^{71} -2.00000 q^{73} +6.00000 q^{77} -1.00000 q^{79} +12.0000 q^{83} +2.00000 q^{85} -4.00000 q^{89} -6.00000 q^{91} -7.00000 q^{95} -2.00000 q^{97} +O(q^{100})\)

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 0.223607 − 0.974679i \(-0.428217\pi\)
0.223607 + 0.974679i \(0.428217\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −6.00000 −1.80907 −0.904534 − 0.426401i \(-0.859781\pi\)
−0.904534 + 0.426401i \(0.859781\pi\)
\(12\) 0 0
\(13\) 6.00000 1.66410 0.832050 − 0.554700i \(-0.187167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.00000 0.485071 0.242536 − 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 0 0
\(19\) −7.00000 −1.60591 −0.802955 − 0.596040i \(-0.796740\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.00000 −0.208514 −0.104257 − 0.994550i \(-0.533247\pi\)
−0.104257 + 0.994550i \(0.533247\pi\)
\(24\) 0 0
\(25\) −4.00000 −0.800000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −2.00000 −0.371391 −0.185695 − 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0 0
\(31\) −10.0000 −1.79605 −0.898027 − 0.439941i \(-0.854999\pi\)
−0.898027 + 0.439941i \(0.854999\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.00000 −0.169031
\(36\) 0 0
\(37\) −6.00000 −0.986394 −0.493197 − 0.869918i \(-0.664172\pi\)
−0.493197 + 0.869918i \(0.664172\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 8.00000 1.24939 0.624695 − 0.780869i \(-0.285223\pi\)
0.624695 + 0.780869i \(0.285223\pi\)
\(42\) 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
\(47\) 8.00000 1.16692 0.583460 − 0.812142i \(-0.301699\pi\)
0.583460 + 0.812142i \(0.301699\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −2.00000 −0.274721 −0.137361 − 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(54\) 0 0
\(55\) −6.00000 −0.809040
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 7.00000 0.896258 0.448129 − 0.893969i \(-0.352090\pi\)
0.448129 + 0.893969i \(0.352090\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 6.00000 0.744208
\(66\) 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
\(71\) 15.0000 1.78017 0.890086 − 0.455792i \(-0.150644\pi\)
0.890086 + 0.455792i \(0.150644\pi\)
\(72\) 0 0
\(73\) −2.00000 −0.234082 −0.117041 − 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 6.00000 0.683763
\(78\) 0 0
\(79\) −1.00000 −0.112509 −0.0562544 − 0.998416i \(-0.517916\pi\)
−0.0562544 + 0.998416i \(0.517916\pi\)
\(80\) 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
\(85\) 2.00000 0.216930
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −4.00000 −0.423999 −0.212000 − 0.977270i \(-0.567998\pi\)
−0.212000 + 0.977270i \(0.567998\pi\)
\(90\) 0 0
\(91\) −6.00000 −0.628971
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −7.00000 −0.718185
\(96\) 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
\(101\) −3.00000 −0.298511 −0.149256 − 0.988799i \(-0.547688\pi\)
−0.149256 + 0.988799i \(0.547688\pi\)
\(102\) 0 0
\(103\) −6.00000 −0.591198 −0.295599 − 0.955312i \(-0.595519\pi\)
−0.295599 + 0.955312i \(0.595519\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 12.0000 1.16008 0.580042 − 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 0 0
\(109\) 10.0000 0.957826 0.478913 − 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 9.00000 0.846649 0.423324 − 0.905978i \(-0.360863\pi\)
0.423324 + 0.905978i \(0.360863\pi\)
\(114\) 0 0
\(115\) −1.00000 −0.0932505
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2.00000 −0.183340
\(120\) 0 0
\(121\) 25.0000 2.27273
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −9.00000 −0.804984
\(126\) 0 0
\(127\) −5.00000 −0.443678 −0.221839 − 0.975083i \(-0.571206\pi\)
−0.221839 + 0.975083i \(0.571206\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 17.0000 1.48530 0.742648 − 0.669681i \(-0.233569\pi\)
0.742648 + 0.669681i \(0.233569\pi\)
\(132\) 0 0
\(133\) 7.00000 0.606977
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −14.0000 −1.19610 −0.598050 − 0.801459i \(-0.704058\pi\)
−0.598050 + 0.801459i \(0.704058\pi\)
\(138\) 0 0
\(139\) −3.00000 −0.254457 −0.127228 − 0.991873i \(-0.540608\pi\)
−0.127228 + 0.991873i \(0.540608\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −36.0000 −3.01047
\(144\) 0 0
\(145\) −2.00000 −0.166091
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 14.0000 1.14692 0.573462 − 0.819232i \(-0.305600\pi\)
0.573462 + 0.819232i \(0.305600\pi\)
\(150\) 0 0
\(151\) 5.00000 0.406894 0.203447 − 0.979086i \(-0.434786\pi\)
0.203447 + 0.979086i \(0.434786\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −10.0000 −0.803219
\(156\) 0 0
\(157\) −15.0000 −1.19713 −0.598565 − 0.801074i \(-0.704262\pi\)
−0.598565 + 0.801074i \(0.704262\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1.00000 0.0788110
\(162\) 0 0
\(163\) −10.0000 −0.783260 −0.391630 − 0.920123i \(-0.628089\pi\)
−0.391630 + 0.920123i \(0.628089\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 12.0000 0.928588 0.464294 − 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) 0 0
\(169\) 23.0000 1.76923
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −14.0000 −1.06440 −0.532200 − 0.846619i \(-0.678635\pi\)
−0.532200 + 0.846619i \(0.678635\pi\)
\(174\) 0 0
\(175\) 4.00000 0.302372
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −10.0000 −0.747435 −0.373718 − 0.927543i \(-0.621917\pi\)
−0.373718 + 0.927543i \(0.621917\pi\)
\(180\) 0 0
\(181\) 5.00000 0.371647 0.185824 − 0.982583i \(-0.440505\pi\)
0.185824 + 0.982583i \(0.440505\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −6.00000 −0.441129
\(186\) 0 0
\(187\) −12.0000 −0.877527
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −5.00000 −0.361787 −0.180894 − 0.983503i \(-0.557899\pi\)
−0.180894 + 0.983503i \(0.557899\pi\)
\(192\) 0 0
\(193\) 9.00000 0.647834 0.323917 − 0.946085i \(-0.395000\pi\)
0.323917 + 0.946085i \(0.395000\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −6.00000 −0.427482 −0.213741 − 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 0 0
\(199\) −2.00000 −0.141776 −0.0708881 − 0.997484i \(-0.522583\pi\)
−0.0708881 + 0.997484i \(0.522583\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 2.00000 0.140372
\(204\) 0 0
\(205\) 8.00000 0.558744
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 42.0000 2.90520
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 − 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 10.0000 0.681994
\(216\) 0 0
\(217\) 10.0000 0.678844
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 12.0000 0.807207
\(222\) 0 0
\(223\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1.00000 −0.0663723 −0.0331862 − 0.999449i \(-0.510565\pi\)
−0.0331862 + 0.999449i \(0.510565\pi\)
\(228\) 0 0
\(229\) 5.00000 0.330409 0.165205 − 0.986259i \(-0.447172\pi\)
0.165205 + 0.986259i \(0.447172\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 7.00000 0.458585 0.229293 − 0.973358i \(-0.426359\pi\)
0.229293 + 0.973358i \(0.426359\pi\)
\(234\) 0 0
\(235\) 8.00000 0.521862
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 5.00000 0.323423 0.161712 − 0.986838i \(-0.448299\pi\)
0.161712 + 0.986838i \(0.448299\pi\)
\(240\) 0 0
\(241\) 4.00000 0.257663 0.128831 − 0.991667i \(-0.458877\pi\)
0.128831 + 0.991667i \(0.458877\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1.00000 0.0638877
\(246\) 0 0
\(247\) −42.0000 −2.67240
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 13.0000 0.820553 0.410276 − 0.911961i \(-0.365432\pi\)
0.410276 + 0.911961i \(0.365432\pi\)
\(252\) 0 0
\(253\) 6.00000 0.377217
\(254\) 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
\(259\) 6.00000 0.372822
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 15.0000 0.924940 0.462470 − 0.886635i \(-0.346963\pi\)
0.462470 + 0.886635i \(0.346963\pi\)
\(264\) 0 0
\(265\) −2.00000 −0.122859
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3.00000 0.182913 0.0914566 − 0.995809i \(-0.470848\pi\)
0.0914566 + 0.995809i \(0.470848\pi\)
\(270\) 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
\(275\) 24.0000 1.44725
\(276\) 0 0
\(277\) 4.00000 0.240337 0.120168 − 0.992754i \(-0.461657\pi\)
0.120168 + 0.992754i \(0.461657\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 3.00000 0.178965 0.0894825 − 0.995988i \(-0.471479\pi\)
0.0894825 + 0.995988i \(0.471479\pi\)
\(282\) 0 0
\(283\) 13.0000 0.772770 0.386385 − 0.922338i \(-0.373724\pi\)
0.386385 + 0.922338i \(0.373724\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −8.00000 −0.472225
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 9.00000 0.525786 0.262893 − 0.964825i \(-0.415323\pi\)
0.262893 + 0.964825i \(0.415323\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −6.00000 −0.346989
\(300\) 0 0
\(301\) −10.0000 −0.576390
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 7.00000 0.400819
\(306\) 0 0
\(307\) 23.0000 1.31268 0.656340 − 0.754466i \(-0.272104\pi\)
0.656340 + 0.754466i \(0.272104\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 24.0000 1.36092 0.680458 − 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 0 0
\(313\) 2.00000 0.113047 0.0565233 − 0.998401i \(-0.481998\pi\)
0.0565233 + 0.998401i \(0.481998\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 18.0000 1.01098 0.505490 − 0.862832i \(-0.331312\pi\)
0.505490 + 0.862832i \(0.331312\pi\)
\(318\) 0 0
\(319\) 12.0000 0.671871
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −14.0000 −0.778981
\(324\) 0 0
\(325\) −24.0000 −1.33128
\(326\) 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
\(335\) 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
\(341\) 60.0000 3.24918
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 24.0000 1.28839 0.644194 − 0.764862i \(-0.277193\pi\)
0.644194 + 0.764862i \(0.277193\pi\)
\(348\) 0 0
\(349\) −10.0000 −0.535288 −0.267644 − 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −6.00000 −0.319348 −0.159674 − 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) 0 0
\(355\) 15.0000 0.796117
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 33.0000 1.74167 0.870837 − 0.491572i \(-0.163578\pi\)
0.870837 + 0.491572i \(0.163578\pi\)
\(360\) 0 0
\(361\) 30.0000 1.57895
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2.00000 −0.104685
\(366\) 0 0
\(367\) −32.0000 −1.67039 −0.835193 − 0.549957i \(-0.814644\pi\)
−0.835193 + 0.549957i \(0.814644\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 2.00000 0.103835
\(372\) 0 0
\(373\) 2.00000 0.103556 0.0517780 − 0.998659i \(-0.483511\pi\)
0.0517780 + 0.998659i \(0.483511\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −12.0000 −0.618031
\(378\) 0 0
\(379\) −6.00000 −0.308199 −0.154100 − 0.988055i \(-0.549248\pi\)
−0.154100 + 0.988055i \(0.549248\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −6.00000 −0.306586 −0.153293 − 0.988181i \(-0.548988\pi\)
−0.153293 + 0.988181i \(0.548988\pi\)
\(384\) 0 0
\(385\) 6.00000 0.305788
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 20.0000 1.01404 0.507020 − 0.861934i \(-0.330747\pi\)
0.507020 + 0.861934i \(0.330747\pi\)
\(390\) 0 0
\(391\) −2.00000 −0.101144
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1.00000 −0.0503155
\(396\) 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
\(401\) 21.0000 1.04869 0.524345 − 0.851506i \(-0.324310\pi\)
0.524345 + 0.851506i \(0.324310\pi\)
\(402\) 0 0
\(403\) −60.0000 −2.98881
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 36.0000 1.78445
\(408\) 0 0
\(409\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 12.0000 0.589057
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −7.00000 −0.341972 −0.170986 − 0.985273i \(-0.554695\pi\)
−0.170986 + 0.985273i \(0.554695\pi\)
\(420\) 0 0
\(421\) 10.0000 0.487370 0.243685 − 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −8.00000 −0.388057
\(426\) 0 0
\(427\) −7.00000 −0.338754
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 36.0000 1.73406 0.867029 − 0.498257i \(-0.166026\pi\)
0.867029 + 0.498257i \(0.166026\pi\)
\(432\) 0 0
\(433\) −26.0000 −1.24948 −0.624740 − 0.780833i \(-0.714795\pi\)
−0.624740 + 0.780833i \(0.714795\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 7.00000 0.334855
\(438\) 0 0
\(439\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −34.0000 −1.61539 −0.807694 − 0.589601i \(-0.799285\pi\)
−0.807694 + 0.589601i \(0.799285\pi\)
\(444\) 0 0
\(445\) −4.00000 −0.189618
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1.00000 −0.0471929 −0.0235965 − 0.999722i \(-0.507512\pi\)
−0.0235965 + 0.999722i \(0.507512\pi\)
\(450\) 0 0
\(451\) −48.0000 −2.26023
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −6.00000 −0.281284
\(456\) 0 0
\(457\) −11.0000 −0.514558 −0.257279 − 0.966337i \(-0.582826\pi\)
−0.257279 + 0.966337i \(0.582826\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 3.00000 0.139724 0.0698620 − 0.997557i \(-0.477744\pi\)
0.0698620 + 0.997557i \(0.477744\pi\)
\(462\) 0 0
\(463\) −23.0000 −1.06890 −0.534450 − 0.845200i \(-0.679481\pi\)
−0.534450 + 0.845200i \(0.679481\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 12.0000 0.555294 0.277647 − 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) 0 0
\(469\) −12.0000 −0.554109
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −60.0000 −2.75880
\(474\) 0 0
\(475\) 28.0000 1.28473
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 34.0000 1.55350 0.776750 − 0.629809i \(-0.216867\pi\)
0.776750 + 0.629809i \(0.216867\pi\)
\(480\) 0 0
\(481\) −36.0000 −1.64146
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2.00000 −0.0908153
\(486\) 0 0
\(487\) −1.00000 −0.0453143 −0.0226572 − 0.999743i \(-0.507213\pi\)
−0.0226572 + 0.999743i \(0.507213\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −6.00000 −0.270776 −0.135388 − 0.990793i \(-0.543228\pi\)
−0.135388 + 0.990793i \(0.543228\pi\)
\(492\) 0 0
\(493\) −4.00000 −0.180151
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −15.0000 −0.672842
\(498\) 0 0
\(499\) −16.0000 −0.716258 −0.358129 − 0.933672i \(-0.616585\pi\)
−0.358129 + 0.933672i \(0.616585\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −32.0000 −1.42681 −0.713405 − 0.700752i \(-0.752848\pi\)
−0.713405 + 0.700752i \(0.752848\pi\)
\(504\) 0 0
\(505\) −3.00000 −0.133498
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 30.0000 1.32973 0.664863 − 0.746965i \(-0.268490\pi\)
0.664863 + 0.746965i \(0.268490\pi\)
\(510\) 0 0
\(511\) 2.00000 0.0884748
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −6.00000 −0.264392
\(516\) 0 0
\(517\) −48.0000 −2.11104
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 12.0000 0.525730 0.262865 − 0.964833i \(-0.415333\pi\)
0.262865 + 0.964833i \(0.415333\pi\)
\(522\) 0 0
\(523\) −29.0000 −1.26808 −0.634041 − 0.773300i \(-0.718605\pi\)
−0.634041 + 0.773300i \(0.718605\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −20.0000 −0.871214
\(528\) 0 0
\(529\) −22.0000 −0.956522
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 48.0000 2.07911
\(534\) 0 0
\(535\) 12.0000 0.518805
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −6.00000 −0.258438
\(540\) 0 0
\(541\) −14.0000 −0.601907 −0.300954 − 0.953639i \(-0.597305\pi\)
−0.300954 + 0.953639i \(0.597305\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 10.0000 0.428353
\(546\) 0 0
\(547\) 8.00000 0.342055 0.171028 − 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 14.0000 0.596420
\(552\) 0 0
\(553\) 1.00000 0.0425243
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 44.0000 1.86434 0.932170 − 0.362021i \(-0.117913\pi\)
0.932170 + 0.362021i \(0.117913\pi\)
\(558\) 0 0
\(559\) 60.0000 2.53773
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −23.0000 −0.969334 −0.484667 − 0.874699i \(-0.661059\pi\)
−0.484667 + 0.874699i \(0.661059\pi\)
\(564\) 0 0
\(565\) 9.00000 0.378633
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −30.0000 −1.25767 −0.628833 − 0.777541i \(-0.716467\pi\)
−0.628833 + 0.777541i \(0.716467\pi\)
\(570\) 0 0
\(571\) 40.0000 1.67395 0.836974 − 0.547243i \(-0.184323\pi\)
0.836974 + 0.547243i \(0.184323\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 4.00000 0.166812
\(576\) 0 0
\(577\) 36.0000 1.49870 0.749350 − 0.662174i \(-0.230366\pi\)
0.749350 + 0.662174i \(0.230366\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −12.0000 −0.497844
\(582\) 0 0
\(583\) 12.0000 0.496989
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −5.00000 −0.206372 −0.103186 − 0.994662i \(-0.532904\pi\)
−0.103186 + 0.994662i \(0.532904\pi\)
\(588\) 0 0
\(589\) 70.0000 2.88430
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 12.0000 0.492781 0.246390 − 0.969171i \(-0.420755\pi\)
0.246390 + 0.969171i \(0.420755\pi\)
\(594\) 0 0
\(595\) −2.00000 −0.0819920
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −32.0000 −1.30748 −0.653742 − 0.756717i \(-0.726802\pi\)
−0.653742 + 0.756717i \(0.726802\pi\)
\(600\) 0 0
\(601\) −14.0000 −0.571072 −0.285536 − 0.958368i \(-0.592172\pi\)
−0.285536 + 0.958368i \(0.592172\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 25.0000 1.01639
\(606\) 0 0
\(607\) 2.00000 0.0811775 0.0405887 − 0.999176i \(-0.487077\pi\)
0.0405887 + 0.999176i \(0.487077\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 48.0000 1.94187
\(612\) 0 0
\(613\) −20.0000 −0.807792 −0.403896 − 0.914805i \(-0.632344\pi\)
−0.403896 + 0.914805i \(0.632344\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 30.0000 1.20775 0.603877 − 0.797077i \(-0.293622\pi\)
0.603877 + 0.797077i \(0.293622\pi\)
\(618\) 0 0
\(619\) 33.0000 1.32638 0.663191 − 0.748450i \(-0.269202\pi\)
0.663191 + 0.748450i \(0.269202\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 4.00000 0.160257
\(624\) 0 0
\(625\) 11.0000 0.440000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −12.0000 −0.478471
\(630\) 0 0
\(631\) −5.00000 −0.199047 −0.0995234 − 0.995035i \(-0.531732\pi\)
−0.0995234 + 0.995035i \(0.531732\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −5.00000 −0.198419
\(636\) 0 0
\(637\) 6.00000 0.237729
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −43.0000 −1.69840 −0.849199 − 0.528073i \(-0.822915\pi\)
−0.849199 + 0.528073i \(0.822915\pi\)
\(642\) 0 0
\(643\) −4.00000 −0.157745 −0.0788723 − 0.996885i \(-0.525132\pi\)
−0.0788723 + 0.996885i \(0.525132\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 12.0000 0.471769 0.235884 − 0.971781i \(-0.424201\pi\)
0.235884 + 0.971781i \(0.424201\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −44.0000 −1.72185 −0.860927 − 0.508729i \(-0.830115\pi\)
−0.860927 + 0.508729i \(0.830115\pi\)
\(654\) 0 0
\(655\) 17.0000 0.664245
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −34.0000 −1.32445 −0.662226 − 0.749304i \(-0.730388\pi\)
−0.662226 + 0.749304i \(0.730388\pi\)
\(660\) 0 0
\(661\) −25.0000 −0.972387 −0.486194 − 0.873851i \(-0.661615\pi\)
−0.486194 + 0.873851i \(0.661615\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 7.00000 0.271448
\(666\) 0 0
\(667\) 2.00000 0.0774403
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −42.0000 −1.62139
\(672\) 0 0
\(673\) 19.0000 0.732396 0.366198 − 0.930537i \(-0.380659\pi\)
0.366198 + 0.930537i \(0.380659\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 42.0000 1.61419 0.807096 − 0.590421i \(-0.201038\pi\)
0.807096 + 0.590421i \(0.201038\pi\)
\(678\) 0 0
\(679\) 2.00000 0.0767530
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 18.0000 0.688751 0.344375 − 0.938832i \(-0.388091\pi\)
0.344375 + 0.938832i \(0.388091\pi\)
\(684\) 0 0
\(685\) −14.0000 −0.534913
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −12.0000 −0.457164
\(690\) 0 0
\(691\) −41.0000 −1.55971 −0.779857 − 0.625958i \(-0.784708\pi\)
−0.779857 + 0.625958i \(0.784708\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −3.00000 −0.113796
\(696\) 0 0
\(697\) 16.0000 0.606043
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 26.0000 0.982006 0.491003 − 0.871158i \(-0.336630\pi\)
0.491003 + 0.871158i \(0.336630\pi\)
\(702\) 0 0
\(703\) 42.0000 1.58406
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 3.00000 0.112827
\(708\) 0 0
\(709\) −44.0000 −1.65245 −0.826227 − 0.563337i \(-0.809517\pi\)
−0.826227 + 0.563337i \(0.809517\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 10.0000 0.374503
\(714\) 0 0
\(715\) −36.0000 −1.34632
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −12.0000 −0.447524 −0.223762 − 0.974644i \(-0.571834\pi\)
−0.223762 + 0.974644i \(0.571834\pi\)
\(720\) 0 0
\(721\) 6.00000 0.223452
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 8.00000 0.297113
\(726\) 0 0
\(727\) 28.0000 1.03846 0.519231 − 0.854634i \(-0.326218\pi\)
0.519231 + 0.854634i \(0.326218\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 20.0000 0.739727
\(732\) 0 0
\(733\) 31.0000 1.14501 0.572506 − 0.819901i \(-0.305971\pi\)
0.572506 + 0.819901i \(0.305971\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −72.0000 −2.65215
\(738\) 0 0
\(739\) 38.0000 1.39785 0.698926 − 0.715194i \(-0.253662\pi\)
0.698926 + 0.715194i \(0.253662\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 44.0000 1.61420 0.807102 − 0.590412i \(-0.201035\pi\)
0.807102 + 0.590412i \(0.201035\pi\)
\(744\) 0 0
\(745\) 14.0000 0.512920
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −12.0000 −0.438470
\(750\) 0 0
\(751\) −5.00000 −0.182453 −0.0912263 − 0.995830i \(-0.529079\pi\)
−0.0912263 + 0.995830i \(0.529079\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 5.00000 0.181969
\(756\) 0 0
\(757\) 34.0000 1.23575 0.617876 − 0.786276i \(-0.287994\pi\)
0.617876 + 0.786276i \(0.287994\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −6.00000 −0.217500 −0.108750 − 0.994069i \(-0.534685\pi\)
−0.108750 + 0.994069i \(0.534685\pi\)
\(762\) 0 0
\(763\) −10.0000 −0.362024
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 10.0000 0.360609 0.180305 − 0.983611i \(-0.442292\pi\)
0.180305 + 0.983611i \(0.442292\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −31.0000 −1.11499 −0.557496 − 0.830179i \(-0.688238\pi\)
−0.557496 + 0.830179i \(0.688238\pi\)
\(774\) 0 0
\(775\) 40.0000 1.43684
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −56.0000 −2.00641
\(780\) 0 0
\(781\) −90.0000 −3.22045
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −15.0000 −0.535373
\(786\) 0 0
\(787\) 20.0000 0.712923 0.356462 − 0.934310i \(-0.383983\pi\)
0.356462 + 0.934310i \(0.383983\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −9.00000 −0.320003
\(792\) 0 0
\(793\) 42.0000 1.49146
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −9.00000 −0.318796 −0.159398 − 0.987214i \(-0.550955\pi\)
−0.159398 + 0.987214i \(0.550955\pi\)
\(798\) 0 0
\(799\) 16.0000 0.566039
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 12.0000 0.423471
\(804\) 0 0
\(805\) 1.00000 0.0352454
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 6.00000 0.210949 0.105474 − 0.994422i \(-0.466364\pi\)
0.105474 + 0.994422i \(0.466364\pi\)
\(810\) 0 0
\(811\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −10.0000 −0.350285
\(816\) 0 0
\(817\) −70.0000 −2.44899
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(822\) 0 0
\(823\) 16.0000 0.557725 0.278862 − 0.960331i \(-0.410043\pi\)
0.278862 + 0.960331i \(0.410043\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) 0 0
\(829\) 50.0000 1.73657 0.868286 − 0.496064i \(-0.165222\pi\)
0.868286 + 0.496064i \(0.165222\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 2.00000 0.0692959
\(834\) 0 0
\(835\) 12.0000 0.415277
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −12.0000 −0.414286 −0.207143 − 0.978311i \(-0.566417\pi\)
−0.207143 + 0.978311i \(0.566417\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 23.0000 0.791224
\(846\) 0 0
\(847\) −25.0000 −0.859010
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 6.00000 0.205677
\(852\) 0 0
\(853\) −23.0000 −0.787505 −0.393753 − 0.919216i \(-0.628823\pi\)
−0.393753 + 0.919216i \(0.628823\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 6.00000 0.204956 0.102478 − 0.994735i \(-0.467323\pi\)
0.102478 + 0.994735i \(0.467323\pi\)
\(858\) 0 0
\(859\) 20.0000 0.682391 0.341196 − 0.939992i \(-0.389168\pi\)
0.341196 + 0.939992i \(0.389168\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −43.0000 −1.46374 −0.731869 − 0.681446i \(-0.761351\pi\)
−0.731869 + 0.681446i \(0.761351\pi\)
\(864\) 0 0
\(865\) −14.0000 −0.476014
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 6.00000 0.203536
\(870\) 0 0
\(871\) 72.0000 2.43963
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 9.00000 0.304256
\(876\) 0 0
\(877\) 14.0000 0.472746 0.236373 − 0.971662i \(-0.424041\pi\)
0.236373 + 0.971662i \(0.424041\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −40.0000 −1.34763 −0.673817 − 0.738898i \(-0.735346\pi\)
−0.673817 + 0.738898i \(0.735346\pi\)
\(882\) 0 0
\(883\) 26.0000 0.874970 0.437485 − 0.899226i \(-0.355869\pi\)
0.437485 + 0.899226i \(0.355869\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 0 0
\(889\) 5.00000 0.167695
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −56.0000 −1.87397
\(894\) 0 0
\(895\) −10.0000 −0.334263
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 20.0000 0.667037
\(900\) 0 0
\(901\) −4.00000 −0.133259
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 5.00000 0.166206
\(906\) 0 0
\(907\) 28.0000 0.929725 0.464862 − 0.885383i \(-0.346104\pi\)
0.464862 + 0.885383i \(0.346104\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 19.0000 0.629498 0.314749 − 0.949175i \(-0.398080\pi\)
0.314749 + 0.949175i \(0.398080\pi\)
\(912\) 0 0
\(913\) −72.0000 −2.38285
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −17.0000 −0.561389
\(918\) 0 0
\(919\) 17.0000 0.560778 0.280389 − 0.959886i \(-0.409536\pi\)
0.280389 + 0.959886i \(0.409536\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 90.0000 2.96239
\(924\) 0 0
\(925\) 24.0000 0.789115
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −4.00000 −0.131236 −0.0656179 − 0.997845i \(-0.520902\pi\)
−0.0656179 + 0.997845i \(0.520902\pi\)
\(930\) 0 0
\(931\) −7.00000 −0.229416
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −12.0000 −0.392442
\(936\) 0 0
\(937\) −42.0000 −1.37208 −0.686040 − 0.727564i \(-0.740653\pi\)
−0.686040 + 0.727564i \(0.740653\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 33.0000 1.07577 0.537885 − 0.843018i \(-0.319224\pi\)
0.537885 + 0.843018i \(0.319224\pi\)
\(942\) 0 0
\(943\) −8.00000 −0.260516
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 28.0000 0.909878 0.454939 − 0.890523i \(-0.349661\pi\)
0.454939 + 0.890523i \(0.349661\pi\)
\(948\) 0 0
\(949\) −12.0000 −0.389536
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 14.0000 0.453504 0.226752 − 0.973952i \(-0.427189\pi\)
0.226752 + 0.973952i \(0.427189\pi\)
\(954\) 0 0
\(955\) −5.00000 −0.161796
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 14.0000 0.452084
\(960\) 0 0
\(961\) 69.0000 2.22581
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 9.00000 0.289720
\(966\) 0 0
\(967\) 3.00000 0.0964735 0.0482367 − 0.998836i \(-0.484640\pi\)
0.0482367 + 0.998836i \(0.484640\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 55.0000 1.76503 0.882517 − 0.470281i \(-0.155847\pi\)
0.882517 + 0.470281i \(0.155847\pi\)
\(972\) 0 0
\(973\) 3.00000 0.0961756
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −6.00000 −0.191957 −0.0959785 − 0.995383i \(-0.530598\pi\)
−0.0959785 + 0.995383i \(0.530598\pi\)
\(978\) 0 0
\(979\) 24.0000 0.767043
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 18.0000 0.574111 0.287055 − 0.957914i \(-0.407324\pi\)
0.287055 + 0.957914i \(0.407324\pi\)
\(984\) 0 0
\(985\) −6.00000 −0.191176
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −10.0000 −0.317982
\(990\) 0 0
\(991\) 48.0000 1.52477 0.762385 − 0.647124i \(-0.224028\pi\)
0.762385 + 0.647124i \(0.224028\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −2.00000 −0.0634043
\(996\) 0 0
\(997\) 19.0000 0.601736 0.300868 − 0.953666i \(-0.402724\pi\)
0.300868 + 0.953666i \(0.402724\pi\)
\(998\) 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 9072.2.a.n.1.1 1
3.2 odd 2 9072.2.a.i.1.1 1
4.3 odd 2 4536.2.a.g.1.1 1
9.2 odd 6 1008.2.r.c.337.1 2
9.4 even 3 3024.2.r.b.2017.1 2
9.5 odd 6 1008.2.r.c.673.1 2
9.7 even 3 3024.2.r.b.1009.1 2
12.11 even 2 4536.2.a.d.1.1 1
36.7 odd 6 1512.2.r.a.1009.1 2
36.11 even 6 504.2.r.a.337.1 yes 2
36.23 even 6 504.2.r.a.169.1 ✓ 2
36.31 odd 6 1512.2.r.a.505.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.r.a.169.1 ✓ 2 36.23 even 6
504.2.r.a.337.1 yes 2 36.11 even 6
1008.2.r.c.337.1 2 9.2 odd 6
1008.2.r.c.673.1 2 9.5 odd 6
1512.2.r.a.505.1 2 36.31 odd 6
1512.2.r.a.1009.1 2 36.7 odd 6
3024.2.r.b.1009.1 2 9.7 even 3
3024.2.r.b.2017.1 2 9.4 even 3
4536.2.a.d.1.1 1 12.11 even 2
4536.2.a.g.1.1 1 4.3 odd 2
9072.2.a.i.1.1 1 3.2 odd 2
9072.2.a.n.1.1 1 1.1 even 1 trivial