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Properties

Label 3528.2.a.m.1.1
Level $3528$
Weight $2$
Character 3528.1
Self dual yes
Analytic conductor $28.171$
Analytic rank $1$
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] = [3528,2,Mod(1,3528)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3528, 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("3528.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3528.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: \(28.1712218331\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1176)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 3528.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+O(q^{10})\) \(q-4.00000 q^{13} +4.00000 q^{17} +4.00000 q^{19} -4.00000 q^{23} -5.00000 q^{25} -2.00000 q^{29} -8.00000 q^{31} -6.00000 q^{37} +12.0000 q^{41} +4.00000 q^{43} -8.00000 q^{47} -6.00000 q^{53} +12.0000 q^{59} -4.00000 q^{61} -4.00000 q^{67} +12.0000 q^{71} -8.00000 q^{73} -16.0000 q^{79} -4.00000 q^{83} +4.00000 q^{89} -16.0000 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) −4.00000 −1.10940 −0.554700 − 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.00000 0.970143 0.485071 − 0.874475i \(-0.338794\pi\)
0.485071 + 0.874475i \(0.338794\pi\)
\(18\) 0 0
\(19\) 4.00000 0.917663 0.458831 − 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 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
\(25\) −5.00000 −1.00000
\(26\) 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
\(31\) −8.00000 −1.43684 −0.718421 − 0.695608i \(-0.755135\pi\)
−0.718421 + 0.695608i \(0.755135\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −6.00000 −0.986394 −0.493197 − 0.869918i \(-0.664172\pi\)
−0.493197 + 0.869918i \(0.664172\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 12.0000 1.87409 0.937043 − 0.349215i \(-0.113552\pi\)
0.937043 + 0.349215i \(0.113552\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 − 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −8.00000 −1.16692 −0.583460 − 0.812142i \(-0.698301\pi\)
−0.583460 + 0.812142i \(0.698301\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −6.00000 −0.824163 −0.412082 − 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 12.0000 1.56227 0.781133 − 0.624364i \(-0.214642\pi\)
0.781133 + 0.624364i \(0.214642\pi\)
\(60\) 0 0
\(61\) −4.00000 −0.512148 −0.256074 − 0.966657i \(-0.582429\pi\)
−0.256074 + 0.966657i \(0.582429\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −4.00000 −0.488678 −0.244339 − 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 − 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 0 0
\(73\) −8.00000 −0.936329 −0.468165 − 0.883641i \(-0.655085\pi\)
−0.468165 + 0.883641i \(0.655085\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −16.0000 −1.80014 −0.900070 − 0.435745i \(-0.856485\pi\)
−0.900070 + 0.435745i \(0.856485\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −4.00000 −0.439057 −0.219529 − 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 4.00000 0.423999 0.212000 − 0.977270i \(-0.432002\pi\)
0.212000 + 0.977270i \(0.432002\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −16.0000 −1.62455 −0.812277 − 0.583272i \(-0.801772\pi\)
−0.812277 + 0.583272i \(0.801772\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −8.00000 −0.796030 −0.398015 − 0.917379i \(-0.630301\pi\)
−0.398015 + 0.917379i \(0.630301\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 − 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −8.00000 −0.773389 −0.386695 − 0.922208i \(-0.626383\pi\)
−0.386695 + 0.922208i \(0.626383\pi\)
\(108\) 0 0
\(109\) −14.0000 −1.34096 −0.670478 − 0.741929i \(-0.733911\pi\)
−0.670478 + 0.741929i \(0.733911\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −2.00000 −0.188144 −0.0940721 − 0.995565i \(-0.529988\pi\)
−0.0940721 + 0.995565i \(0.529988\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 − 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −4.00000 −0.349482 −0.174741 − 0.984614i \(-0.555909\pi\)
−0.174741 + 0.984614i \(0.555909\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −22.0000 −1.87959 −0.939793 − 0.341743i \(-0.888983\pi\)
−0.939793 + 0.341743i \(0.888983\pi\)
\(138\) 0 0
\(139\) 12.0000 1.01783 0.508913 − 0.860818i \(-0.330047\pi\)
0.508913 + 0.860818i \(0.330047\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 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
\(151\) −8.00000 −0.651031 −0.325515 − 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 20.0000 1.59617 0.798087 − 0.602542i \(-0.205846\pi\)
0.798087 + 0.602542i \(0.205846\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −12.0000 −0.939913 −0.469956 − 0.882690i \(-0.655730\pi\)
−0.469956 + 0.882690i \(0.655730\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −8.00000 −0.619059 −0.309529 − 0.950890i \(-0.600171\pi\)
−0.309529 + 0.950890i \(0.600171\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 16.0000 1.21646 0.608229 − 0.793762i \(-0.291880\pi\)
0.608229 + 0.793762i \(0.291880\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 24.0000 1.79384 0.896922 − 0.442189i \(-0.145798\pi\)
0.896922 + 0.442189i \(0.145798\pi\)
\(180\) 0 0
\(181\) 12.0000 0.891953 0.445976 − 0.895045i \(-0.352856\pi\)
0.445976 + 0.895045i \(0.352856\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −12.0000 −0.868290 −0.434145 − 0.900843i \(-0.642949\pi\)
−0.434145 + 0.900843i \(0.642949\pi\)
\(192\) 0 0
\(193\) −14.0000 −1.00774 −0.503871 − 0.863779i \(-0.668091\pi\)
−0.503871 + 0.863779i \(0.668091\pi\)
\(194\) 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
\(199\) 8.00000 0.567105 0.283552 − 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 20.0000 1.37686 0.688428 − 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −16.0000 −1.07628
\(222\) 0 0
\(223\) 16.0000 1.07144 0.535720 − 0.844396i \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −20.0000 −1.32745 −0.663723 − 0.747978i \(-0.731025\pi\)
−0.663723 + 0.747978i \(0.731025\pi\)
\(228\) 0 0
\(229\) −20.0000 −1.32164 −0.660819 − 0.750546i \(-0.729791\pi\)
−0.660819 + 0.750546i \(0.729791\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −6.00000 −0.393073 −0.196537 − 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 20.0000 1.29369 0.646846 − 0.762620i \(-0.276088\pi\)
0.646846 + 0.762620i \(0.276088\pi\)
\(240\) 0 0
\(241\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −16.0000 −1.01806
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −12.0000 −0.757433 −0.378717 − 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −12.0000 −0.748539 −0.374270 − 0.927320i \(-0.622107\pi\)
−0.374270 + 0.927320i \(0.622107\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −12.0000 −0.739952 −0.369976 − 0.929041i \(-0.620634\pi\)
−0.369976 + 0.929041i \(0.620634\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −24.0000 −1.46331 −0.731653 − 0.681677i \(-0.761251\pi\)
−0.731653 + 0.681677i \(0.761251\pi\)
\(270\) 0 0
\(271\) −16.0000 −0.971931 −0.485965 − 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −10.0000 −0.600842 −0.300421 − 0.953807i \(-0.597127\pi\)
−0.300421 + 0.953807i \(0.597127\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −22.0000 −1.31241 −0.656205 − 0.754583i \(-0.727839\pi\)
−0.656205 + 0.754583i \(0.727839\pi\)
\(282\) 0 0
\(283\) 4.00000 0.237775 0.118888 − 0.992908i \(-0.462067\pi\)
0.118888 + 0.992908i \(0.462067\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −1.00000 −0.0588235
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −24.0000 −1.40209 −0.701047 − 0.713115i \(-0.747284\pi\)
−0.701047 + 0.713115i \(0.747284\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 16.0000 0.925304
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −12.0000 −0.684876 −0.342438 − 0.939540i \(-0.611253\pi\)
−0.342438 + 0.939540i \(0.611253\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −16.0000 −0.907277 −0.453638 − 0.891186i \(-0.649874\pi\)
−0.453638 + 0.891186i \(0.649874\pi\)
\(312\) 0 0
\(313\) 8.00000 0.452187 0.226093 − 0.974106i \(-0.427405\pi\)
0.226093 + 0.974106i \(0.427405\pi\)
\(314\) 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
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 16.0000 0.890264
\(324\) 0 0
\(325\) 20.0000 1.10940
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 4.00000 0.219860 0.109930 − 0.993939i \(-0.464937\pi\)
0.109930 + 0.993939i \(0.464937\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −18.0000 −0.980522 −0.490261 − 0.871576i \(-0.663099\pi\)
−0.490261 + 0.871576i \(0.663099\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 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
\(349\) 36.0000 1.92704 0.963518 − 0.267644i \(-0.0862451\pi\)
0.963518 + 0.267644i \(0.0862451\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 28.0000 1.49029 0.745145 − 0.666903i \(-0.232380\pi\)
0.745145 + 0.666903i \(0.232380\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −28.0000 −1.47778 −0.738892 − 0.673824i \(-0.764651\pi\)
−0.738892 + 0.673824i \(0.764651\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 16.0000 0.835193 0.417597 − 0.908633i \(-0.362873\pi\)
0.417597 + 0.908633i \(0.362873\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −10.0000 −0.517780 −0.258890 − 0.965907i \(-0.583357\pi\)
−0.258890 + 0.965907i \(0.583357\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 8.00000 0.412021
\(378\) 0 0
\(379\) −12.0000 −0.616399 −0.308199 − 0.951322i \(-0.599726\pi\)
−0.308199 + 0.951322i \(0.599726\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 24.0000 1.22634 0.613171 − 0.789950i \(-0.289894\pi\)
0.613171 + 0.789950i \(0.289894\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 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
\(391\) −16.0000 −0.809155
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 20.0000 1.00377 0.501886 − 0.864934i \(-0.332640\pi\)
0.501886 + 0.864934i \(0.332640\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 18.0000 0.898877 0.449439 − 0.893311i \(-0.351624\pi\)
0.449439 + 0.893311i \(0.351624\pi\)
\(402\) 0 0
\(403\) 32.0000 1.59403
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −32.0000 −1.58230 −0.791149 − 0.611623i \(-0.790517\pi\)
−0.791149 + 0.611623i \(0.790517\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 20.0000 0.977064 0.488532 − 0.872546i \(-0.337533\pi\)
0.488532 + 0.872546i \(0.337533\pi\)
\(420\) 0 0
\(421\) 6.00000 0.292422 0.146211 − 0.989253i \(-0.453292\pi\)
0.146211 + 0.989253i \(0.453292\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −20.0000 −0.970143
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 12.0000 0.578020 0.289010 − 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(432\) 0 0
\(433\) −8.00000 −0.384455 −0.192228 − 0.981350i \(-0.561571\pi\)
−0.192228 + 0.981350i \(0.561571\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −16.0000 −0.765384
\(438\) 0 0
\(439\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 32.0000 1.52037 0.760183 − 0.649709i \(-0.225109\pi\)
0.760183 + 0.649709i \(0.225109\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 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
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 10.0000 0.467780 0.233890 − 0.972263i \(-0.424854\pi\)
0.233890 + 0.972263i \(0.424854\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −16.0000 −0.745194 −0.372597 − 0.927993i \(-0.621533\pi\)
−0.372597 + 0.927993i \(0.621533\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 − 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) 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
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −20.0000 −0.917663
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 40.0000 1.82765 0.913823 − 0.406112i \(-0.133116\pi\)
0.913823 + 0.406112i \(0.133116\pi\)
\(480\) 0 0
\(481\) 24.0000 1.09431
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 8.00000 0.362515 0.181257 − 0.983436i \(-0.441983\pi\)
0.181257 + 0.983436i \(0.441983\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) −8.00000 −0.360302
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 36.0000 1.61158 0.805791 − 0.592200i \(-0.201741\pi\)
0.805791 + 0.592200i \(0.201741\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 32.0000 1.42681 0.713405 − 0.700752i \(-0.247152\pi\)
0.713405 + 0.700752i \(0.247152\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 8.00000 0.354594 0.177297 − 0.984157i \(-0.443265\pi\)
0.177297 + 0.984157i \(0.443265\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 36.0000 1.57719 0.788594 − 0.614914i \(-0.210809\pi\)
0.788594 + 0.614914i \(0.210809\pi\)
\(522\) 0 0
\(523\) −28.0000 −1.22435 −0.612177 − 0.790721i \(-0.709706\pi\)
−0.612177 + 0.790721i \(0.709706\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −32.0000 −1.39394
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −48.0000 −2.07911
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 30.0000 1.28980 0.644900 − 0.764267i \(-0.276899\pi\)
0.644900 + 0.764267i \(0.276899\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 − 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −8.00000 −0.340811
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 34.0000 1.44063 0.720313 − 0.693649i \(-0.243998\pi\)
0.720313 + 0.693649i \(0.243998\pi\)
\(558\) 0 0
\(559\) −16.0000 −0.676728
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −12.0000 −0.505740 −0.252870 − 0.967500i \(-0.581374\pi\)
−0.252870 + 0.967500i \(0.581374\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 10.0000 0.419222 0.209611 − 0.977785i \(-0.432780\pi\)
0.209611 + 0.977785i \(0.432780\pi\)
\(570\) 0 0
\(571\) 12.0000 0.502184 0.251092 − 0.967963i \(-0.419210\pi\)
0.251092 + 0.967963i \(0.419210\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 20.0000 0.834058
\(576\) 0 0
\(577\) −32.0000 −1.33218 −0.666089 − 0.745873i \(-0.732033\pi\)
−0.666089 + 0.745873i \(0.732033\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 36.0000 1.48588 0.742940 − 0.669359i \(-0.233431\pi\)
0.742940 + 0.669359i \(0.233431\pi\)
\(588\) 0 0
\(589\) −32.0000 −1.31854
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −20.0000 −0.821302 −0.410651 − 0.911793i \(-0.634698\pi\)
−0.410651 + 0.911793i \(0.634698\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 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
\(601\) −16.0000 −0.652654 −0.326327 − 0.945257i \(-0.605811\pi\)
−0.326327 + 0.945257i \(0.605811\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 32.0000 1.29458
\(612\) 0 0
\(613\) 26.0000 1.05013 0.525065 − 0.851062i \(-0.324041\pi\)
0.525065 + 0.851062i \(0.324041\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −22.0000 −0.885687 −0.442843 − 0.896599i \(-0.646030\pi\)
−0.442843 + 0.896599i \(0.646030\pi\)
\(618\) 0 0
\(619\) −44.0000 −1.76851 −0.884255 − 0.467005i \(-0.845333\pi\)
−0.884255 + 0.467005i \(0.845333\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −24.0000 −0.956943
\(630\) 0 0
\(631\) 24.0000 0.955425 0.477712 − 0.878516i \(-0.341466\pi\)
0.477712 + 0.878516i \(0.341466\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −30.0000 −1.18493 −0.592464 − 0.805597i \(-0.701845\pi\)
−0.592464 + 0.805597i \(0.701845\pi\)
\(642\) 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
\(647\) −8.00000 −0.314512 −0.157256 − 0.987558i \(-0.550265\pi\)
−0.157256 + 0.987558i \(0.550265\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −2.00000 −0.0782660 −0.0391330 − 0.999234i \(-0.512460\pi\)
−0.0391330 + 0.999234i \(0.512460\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −40.0000 −1.55818 −0.779089 − 0.626913i \(-0.784318\pi\)
−0.779089 + 0.626913i \(0.784318\pi\)
\(660\) 0 0
\(661\) −4.00000 −0.155582 −0.0777910 − 0.996970i \(-0.524787\pi\)
−0.0777910 + 0.996970i \(0.524787\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 8.00000 0.309761
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 14.0000 0.539660 0.269830 − 0.962908i \(-0.413032\pi\)
0.269830 + 0.962908i \(0.413032\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −32.0000 −1.22986 −0.614930 − 0.788582i \(-0.710816\pi\)
−0.614930 + 0.788582i \(0.710816\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 48.0000 1.83667 0.918334 − 0.395805i \(-0.129534\pi\)
0.918334 + 0.395805i \(0.129534\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 24.0000 0.914327
\(690\) 0 0
\(691\) 20.0000 0.760836 0.380418 − 0.924815i \(-0.375780\pi\)
0.380418 + 0.924815i \(0.375780\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 48.0000 1.81813
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 46.0000 1.73740 0.868698 − 0.495342i \(-0.164957\pi\)
0.868698 + 0.495342i \(0.164957\pi\)
\(702\) 0 0
\(703\) −24.0000 −0.905177
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 26.0000 0.976450 0.488225 − 0.872718i \(-0.337644\pi\)
0.488225 + 0.872718i \(0.337644\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 32.0000 1.19841
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 40.0000 1.49175 0.745874 − 0.666087i \(-0.232032\pi\)
0.745874 + 0.666087i \(0.232032\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 10.0000 0.371391
\(726\) 0 0
\(727\) −24.0000 −0.890111 −0.445055 − 0.895503i \(-0.646816\pi\)
−0.445055 + 0.895503i \(0.646816\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 16.0000 0.591781
\(732\) 0 0
\(733\) 4.00000 0.147743 0.0738717 − 0.997268i \(-0.476464\pi\)
0.0738717 + 0.997268i \(0.476464\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 20.0000 0.735712 0.367856 − 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 4.00000 0.146746 0.0733729 − 0.997305i \(-0.476624\pi\)
0.0733729 + 0.997305i \(0.476624\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 32.0000 1.16770 0.583848 − 0.811863i \(-0.301546\pi\)
0.583848 + 0.811863i \(0.301546\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −22.0000 −0.799604 −0.399802 − 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 12.0000 0.435000 0.217500 − 0.976060i \(-0.430210\pi\)
0.217500 + 0.976060i \(0.430210\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −48.0000 −1.73318
\(768\) 0 0
\(769\) 8.00000 0.288487 0.144244 − 0.989542i \(-0.453925\pi\)
0.144244 + 0.989542i \(0.453925\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 24.0000 0.863220 0.431610 − 0.902060i \(-0.357946\pi\)
0.431610 + 0.902060i \(0.357946\pi\)
\(774\) 0 0
\(775\) 40.0000 1.43684
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 48.0000 1.71978
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 52.0000 1.85360 0.926800 − 0.375555i \(-0.122548\pi\)
0.926800 + 0.375555i \(0.122548\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 16.0000 0.568177
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 16.0000 0.566749 0.283375 − 0.959009i \(-0.408546\pi\)
0.283375 + 0.959009i \(0.408546\pi\)
\(798\) 0 0
\(799\) −32.0000 −1.13208
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 38.0000 1.33601 0.668004 − 0.744157i \(-0.267149\pi\)
0.668004 + 0.744157i \(0.267149\pi\)
\(810\) 0 0
\(811\) 20.0000 0.702295 0.351147 − 0.936320i \(-0.385792\pi\)
0.351147 + 0.936320i \(0.385792\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 16.0000 0.559769
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 26.0000 0.907406 0.453703 − 0.891153i \(-0.350103\pi\)
0.453703 + 0.891153i \(0.350103\pi\)
\(822\) 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
\(827\) 8.00000 0.278187 0.139094 − 0.990279i \(-0.455581\pi\)
0.139094 + 0.990279i \(0.455581\pi\)
\(828\) 0 0
\(829\) 20.0000 0.694629 0.347314 − 0.937749i \(-0.387094\pi\)
0.347314 + 0.937749i \(0.387094\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −24.0000 −0.828572 −0.414286 − 0.910147i \(-0.635969\pi\)
−0.414286 + 0.910147i \(0.635969\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 24.0000 0.822709
\(852\) 0 0
\(853\) 4.00000 0.136957 0.0684787 − 0.997653i \(-0.478185\pi\)
0.0684787 + 0.997653i \(0.478185\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −36.0000 −1.22974 −0.614868 − 0.788630i \(-0.710791\pi\)
−0.614868 + 0.788630i \(0.710791\pi\)
\(858\) 0 0
\(859\) −36.0000 −1.22830 −0.614152 − 0.789188i \(-0.710502\pi\)
−0.614152 + 0.789188i \(0.710502\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −20.0000 −0.680808 −0.340404 − 0.940279i \(-0.610564\pi\)
−0.340404 + 0.940279i \(0.610564\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 16.0000 0.542139
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 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
\(881\) 12.0000 0.404290 0.202145 − 0.979356i \(-0.435209\pi\)
0.202145 + 0.979356i \(0.435209\pi\)
\(882\) 0 0
\(883\) −44.0000 −1.48072 −0.740359 − 0.672212i \(-0.765344\pi\)
−0.740359 + 0.672212i \(0.765344\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −56.0000 −1.88030 −0.940148 − 0.340766i \(-0.889313\pi\)
−0.940148 + 0.340766i \(0.889313\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −32.0000 −1.07084
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 16.0000 0.533630
\(900\) 0 0
\(901\) −24.0000 −0.799556
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 44.0000 1.46100 0.730498 − 0.682915i \(-0.239288\pi\)
0.730498 + 0.682915i \(0.239288\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −36.0000 −1.19273 −0.596367 − 0.802712i \(-0.703390\pi\)
−0.596367 + 0.802712i \(0.703390\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −48.0000 −1.57994
\(924\) 0 0
\(925\) 30.0000 0.986394
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 28.0000 0.918650 0.459325 − 0.888268i \(-0.348091\pi\)
0.459325 + 0.888268i \(0.348091\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(942\) 0 0
\(943\) −48.0000 −1.56310
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 40.0000 1.29983 0.649913 − 0.760009i \(-0.274805\pi\)
0.649913 + 0.760009i \(0.274805\pi\)
\(948\) 0 0
\(949\) 32.0000 1.03876
\(950\) 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
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 33.0000 1.06452
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 16.0000 0.514525 0.257263 − 0.966342i \(-0.417179\pi\)
0.257263 + 0.966342i \(0.417179\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 28.0000 0.898563 0.449281 − 0.893390i \(-0.351680\pi\)
0.449281 + 0.893390i \(0.351680\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 34.0000 1.08776 0.543878 − 0.839164i \(-0.316955\pi\)
0.543878 + 0.839164i \(0.316955\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −56.0000 −1.78612 −0.893061 − 0.449935i \(-0.851447\pi\)
−0.893061 + 0.449935i \(0.851447\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −16.0000 −0.508770
\(990\) 0 0
\(991\) −8.00000 −0.254128 −0.127064 − 0.991894i \(-0.540555\pi\)
−0.127064 + 0.991894i \(0.540555\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 28.0000 0.886769 0.443384 − 0.896332i \(-0.353778\pi\)
0.443384 + 0.896332i \(0.353778\pi\)
\(998\) 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 3528.2.a.m.1.1 1
3.2 odd 2 1176.2.a.b.1.1 ✓ 1
4.3 odd 2 7056.2.a.ba.1.1 1
7.2 even 3 3528.2.s.m.361.1 2
7.3 odd 6 3528.2.s.n.3313.1 2
7.4 even 3 3528.2.s.m.3313.1 2
7.5 odd 6 3528.2.s.n.361.1 2
7.6 odd 2 3528.2.a.n.1.1 1
12.11 even 2 2352.2.a.r.1.1 1
21.2 odd 6 1176.2.q.h.361.1 2
21.5 even 6 1176.2.q.c.361.1 2
21.11 odd 6 1176.2.q.h.961.1 2
21.17 even 6 1176.2.q.c.961.1 2
21.20 even 2 1176.2.a.h.1.1 yes 1
24.5 odd 2 9408.2.a.cl.1.1 1
24.11 even 2 9408.2.a.v.1.1 1
28.27 even 2 7056.2.a.bc.1.1 1
84.11 even 6 2352.2.q.h.961.1 2
84.23 even 6 2352.2.q.h.1537.1 2
84.47 odd 6 2352.2.q.t.1537.1 2
84.59 odd 6 2352.2.q.t.961.1 2
84.83 odd 2 2352.2.a.h.1.1 1
168.83 odd 2 9408.2.a.ck.1.1 1
168.125 even 2 9408.2.a.u.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1176.2.a.b.1.1 ✓ 1 3.2 odd 2
1176.2.a.h.1.1 yes 1 21.20 even 2
1176.2.q.c.361.1 2 21.5 even 6
1176.2.q.c.961.1 2 21.17 even 6
1176.2.q.h.361.1 2 21.2 odd 6
1176.2.q.h.961.1 2 21.11 odd 6
2352.2.a.h.1.1 1 84.83 odd 2
2352.2.a.r.1.1 1 12.11 even 2
2352.2.q.h.961.1 2 84.11 even 6
2352.2.q.h.1537.1 2 84.23 even 6
2352.2.q.t.961.1 2 84.59 odd 6
2352.2.q.t.1537.1 2 84.47 odd 6
3528.2.a.m.1.1 1 1.1 even 1 trivial
3528.2.a.n.1.1 1 7.6 odd 2
3528.2.s.m.361.1 2 7.2 even 3
3528.2.s.m.3313.1 2 7.4 even 3
3528.2.s.n.361.1 2 7.5 odd 6
3528.2.s.n.3313.1 2 7.3 odd 6
7056.2.a.ba.1.1 1 4.3 odd 2
7056.2.a.bc.1.1 1 28.27 even 2
9408.2.a.u.1.1 1 168.125 even 2
9408.2.a.v.1.1 1 24.11 even 2
9408.2.a.ck.1.1 1 168.83 odd 2
9408.2.a.cl.1.1 1 24.5 odd 2