Properties

Label 9576.2.a.bf.1.1
Level $9576$
Weight $2$
Character 9576.1
Self dual yes
Analytic conductor $76.465$
Analytic rank $1$
Dimension $2$
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] = [9576,2,Mod(1,9576)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9576, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("9576.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9576 = 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9576.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: \(76.4647449756\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{12})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.73205\) of defining polynomial
Character \(\chi\) \(=\) 9576.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.73205 q^{5} -1.00000 q^{7} +O(q^{10})\) \(q-2.73205 q^{5} -1.00000 q^{7} -3.46410 q^{11} +4.00000 q^{13} -6.73205 q^{17} +1.00000 q^{19} +7.46410 q^{23} +2.46410 q^{25} -0.732051 q^{29} +3.46410 q^{31} +2.73205 q^{35} -0.535898 q^{37} -4.53590 q^{41} +4.92820 q^{43} +11.6603 q^{47} +1.00000 q^{49} +2.19615 q^{53} +9.46410 q^{55} -8.00000 q^{59} +11.4641 q^{61} -10.9282 q^{65} -4.00000 q^{67} -4.19615 q^{71} +7.46410 q^{73} +3.46410 q^{77} +1.46410 q^{79} -10.1962 q^{83} +18.3923 q^{85} -10.3923 q^{89} -4.00000 q^{91} -2.73205 q^{95} +6.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{5} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{5} - 2 q^{7} + 8 q^{13} - 10 q^{17} + 2 q^{19} + 8 q^{23} - 2 q^{25} + 2 q^{29} + 2 q^{35} - 8 q^{37} - 16 q^{41} - 4 q^{43} + 6 q^{47} + 2 q^{49} - 6 q^{53} + 12 q^{55} - 16 q^{59} + 16 q^{61} - 8 q^{65} - 8 q^{67} + 2 q^{71} + 8 q^{73} - 4 q^{79} - 10 q^{83} + 16 q^{85} - 8 q^{91} - 2 q^{95} + 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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
\(5\) −2.73205 −1.22181 −0.610905 0.791704i \(-0.709194\pi\)
−0.610905 + 0.791704i \(0.709194\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −3.46410 −1.04447 −0.522233 0.852803i \(-0.674901\pi\)
−0.522233 + 0.852803i \(0.674901\pi\)
\(12\) 0 0
\(13\) 4.00000 1.10940 0.554700 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −6.73205 −1.63276 −0.816381 0.577514i \(-0.804023\pi\)
−0.816381 + 0.577514i \(0.804023\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 7.46410 1.55637 0.778186 0.628033i \(-0.216140\pi\)
0.778186 + 0.628033i \(0.216140\pi\)
\(24\) 0 0
\(25\) 2.46410 0.492820
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −0.732051 −0.135938 −0.0679692 0.997687i \(-0.521652\pi\)
−0.0679692 + 0.997687i \(0.521652\pi\)
\(30\) 0 0
\(31\) 3.46410 0.622171 0.311086 0.950382i \(-0.399307\pi\)
0.311086 + 0.950382i \(0.399307\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.73205 0.461801
\(36\) 0 0
\(37\) −0.535898 −0.0881012 −0.0440506 0.999029i \(-0.514026\pi\)
−0.0440506 + 0.999029i \(0.514026\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −4.53590 −0.708388 −0.354194 0.935172i \(-0.615245\pi\)
−0.354194 + 0.935172i \(0.615245\pi\)
\(42\) 0 0
\(43\) 4.92820 0.751544 0.375772 0.926712i \(-0.377378\pi\)
0.375772 + 0.926712i \(0.377378\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 11.6603 1.70082 0.850411 0.526118i \(-0.176353\pi\)
0.850411 + 0.526118i \(0.176353\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 2.19615 0.301665 0.150832 0.988559i \(-0.451805\pi\)
0.150832 + 0.988559i \(0.451805\pi\)
\(54\) 0 0
\(55\) 9.46410 1.27614
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −8.00000 −1.04151 −0.520756 0.853706i \(-0.674350\pi\)
−0.520756 + 0.853706i \(0.674350\pi\)
\(60\) 0 0
\(61\) 11.4641 1.46783 0.733914 0.679243i \(-0.237692\pi\)
0.733914 + 0.679243i \(0.237692\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −10.9282 −1.35548
\(66\) 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
\(71\) −4.19615 −0.497992 −0.248996 0.968505i \(-0.580101\pi\)
−0.248996 + 0.968505i \(0.580101\pi\)
\(72\) 0 0
\(73\) 7.46410 0.873607 0.436804 0.899557i \(-0.356111\pi\)
0.436804 + 0.899557i \(0.356111\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3.46410 0.394771
\(78\) 0 0
\(79\) 1.46410 0.164724 0.0823622 0.996602i \(-0.473754\pi\)
0.0823622 + 0.996602i \(0.473754\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −10.1962 −1.11917 −0.559587 0.828772i \(-0.689040\pi\)
−0.559587 + 0.828772i \(0.689040\pi\)
\(84\) 0 0
\(85\) 18.3923 1.99493
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −10.3923 −1.10158 −0.550791 0.834643i \(-0.685674\pi\)
−0.550791 + 0.834643i \(0.685674\pi\)
\(90\) 0 0
\(91\) −4.00000 −0.419314
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −2.73205 −0.280302
\(96\) 0 0
\(97\) 6.00000 0.609208 0.304604 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 16.5885 1.65061 0.825307 0.564685i \(-0.191002\pi\)
0.825307 + 0.564685i \(0.191002\pi\)
\(102\) 0 0
\(103\) −6.92820 −0.682656 −0.341328 0.939944i \(-0.610877\pi\)
−0.341328 + 0.939944i \(0.610877\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 8.19615 0.792352 0.396176 0.918175i \(-0.370337\pi\)
0.396176 + 0.918175i \(0.370337\pi\)
\(108\) 0 0
\(109\) −11.8564 −1.13564 −0.567819 0.823154i \(-0.692213\pi\)
−0.567819 + 0.823154i \(0.692213\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −0.732051 −0.0688655 −0.0344328 0.999407i \(-0.510962\pi\)
−0.0344328 + 0.999407i \(0.510962\pi\)
\(114\) 0 0
\(115\) −20.3923 −1.90159
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 6.73205 0.617126
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 6.92820 0.619677
\(126\) 0 0
\(127\) −10.9282 −0.969721 −0.484861 0.874591i \(-0.661130\pi\)
−0.484861 + 0.874591i \(0.661130\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2.19615 0.191879 0.0959394 0.995387i \(-0.469415\pi\)
0.0959394 + 0.995387i \(0.469415\pi\)
\(132\) 0 0
\(133\) −1.00000 −0.0867110
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2.92820 −0.250173 −0.125087 0.992146i \(-0.539921\pi\)
−0.125087 + 0.992146i \(0.539921\pi\)
\(138\) 0 0
\(139\) 9.46410 0.802735 0.401367 0.915917i \(-0.368535\pi\)
0.401367 + 0.915917i \(0.368535\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −13.8564 −1.15873
\(144\) 0 0
\(145\) 2.00000 0.166091
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2.53590 0.207749 0.103874 0.994590i \(-0.466876\pi\)
0.103874 + 0.994590i \(0.466876\pi\)
\(150\) 0 0
\(151\) −14.5359 −1.18291 −0.591457 0.806336i \(-0.701447\pi\)
−0.591457 + 0.806336i \(0.701447\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −9.46410 −0.760175
\(156\) 0 0
\(157\) −6.39230 −0.510161 −0.255081 0.966920i \(-0.582102\pi\)
−0.255081 + 0.966920i \(0.582102\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −7.46410 −0.588254
\(162\) 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
\(167\) −16.3923 −1.26847 −0.634237 0.773138i \(-0.718686\pi\)
−0.634237 + 0.773138i \(0.718686\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −10.3923 −0.790112 −0.395056 0.918657i \(-0.629275\pi\)
−0.395056 + 0.918657i \(0.629275\pi\)
\(174\) 0 0
\(175\) −2.46410 −0.186269
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 19.5167 1.45874 0.729372 0.684117i \(-0.239812\pi\)
0.729372 + 0.684117i \(0.239812\pi\)
\(180\) 0 0
\(181\) 3.85641 0.286644 0.143322 0.989676i \(-0.454221\pi\)
0.143322 + 0.989676i \(0.454221\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.46410 0.107643
\(186\) 0 0
\(187\) 23.3205 1.70536
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2.39230 −0.173101 −0.0865506 0.996247i \(-0.527584\pi\)
−0.0865506 + 0.996247i \(0.527584\pi\)
\(192\) 0 0
\(193\) −17.3205 −1.24676 −0.623379 0.781920i \(-0.714240\pi\)
−0.623379 + 0.781920i \(0.714240\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 6.92820 0.493614 0.246807 0.969065i \(-0.420619\pi\)
0.246807 + 0.969065i \(0.420619\pi\)
\(198\) 0 0
\(199\) 24.7846 1.75693 0.878467 0.477803i \(-0.158567\pi\)
0.878467 + 0.477803i \(0.158567\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0.732051 0.0513799
\(204\) 0 0
\(205\) 12.3923 0.865516
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −3.46410 −0.239617
\(210\) 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
\(215\) −13.4641 −0.918244
\(216\) 0 0
\(217\) −3.46410 −0.235159
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −26.9282 −1.81139
\(222\) 0 0
\(223\) −21.3205 −1.42773 −0.713863 0.700285i \(-0.753056\pi\)
−0.713863 + 0.700285i \(0.753056\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −6.53590 −0.433803 −0.216901 0.976194i \(-0.569595\pi\)
−0.216901 + 0.976194i \(0.569595\pi\)
\(228\) 0 0
\(229\) −12.9282 −0.854320 −0.427160 0.904176i \(-0.640486\pi\)
−0.427160 + 0.904176i \(0.640486\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −21.4641 −1.40616 −0.703080 0.711111i \(-0.748192\pi\)
−0.703080 + 0.711111i \(0.748192\pi\)
\(234\) 0 0
\(235\) −31.8564 −2.07808
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 7.85641 0.508189 0.254094 0.967179i \(-0.418223\pi\)
0.254094 + 0.967179i \(0.418223\pi\)
\(240\) 0 0
\(241\) 28.9282 1.86343 0.931715 0.363191i \(-0.118313\pi\)
0.931715 + 0.363191i \(0.118313\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −2.73205 −0.174544
\(246\) 0 0
\(247\) 4.00000 0.254514
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −7.26795 −0.458749 −0.229374 0.973338i \(-0.573668\pi\)
−0.229374 + 0.973338i \(0.573668\pi\)
\(252\) 0 0
\(253\) −25.8564 −1.62558
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 27.8564 1.73763 0.868817 0.495133i \(-0.164881\pi\)
0.868817 + 0.495133i \(0.164881\pi\)
\(258\) 0 0
\(259\) 0.535898 0.0332991
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −3.07180 −0.189415 −0.0947076 0.995505i \(-0.530192\pi\)
−0.0947076 + 0.995505i \(0.530192\pi\)
\(264\) 0 0
\(265\) −6.00000 −0.368577
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0.928203 0.0565935 0.0282968 0.999600i \(-0.490992\pi\)
0.0282968 + 0.999600i \(0.490992\pi\)
\(270\) 0 0
\(271\) −11.3205 −0.687672 −0.343836 0.939030i \(-0.611726\pi\)
−0.343836 + 0.939030i \(0.611726\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −8.53590 −0.514734
\(276\) 0 0
\(277\) −26.2487 −1.57713 −0.788566 0.614950i \(-0.789176\pi\)
−0.788566 + 0.614950i \(0.789176\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −15.2679 −0.910809 −0.455405 0.890285i \(-0.650505\pi\)
−0.455405 + 0.890285i \(0.650505\pi\)
\(282\) 0 0
\(283\) −5.85641 −0.348127 −0.174064 0.984734i \(-0.555690\pi\)
−0.174064 + 0.984734i \(0.555690\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 4.53590 0.267746
\(288\) 0 0
\(289\) 28.3205 1.66591
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −27.4641 −1.60447 −0.802235 0.597008i \(-0.796356\pi\)
−0.802235 + 0.597008i \(0.796356\pi\)
\(294\) 0 0
\(295\) 21.8564 1.27253
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 29.8564 1.72664
\(300\) 0 0
\(301\) −4.92820 −0.284057
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −31.3205 −1.79341
\(306\) 0 0
\(307\) 13.3205 0.760242 0.380121 0.924937i \(-0.375882\pi\)
0.380121 + 0.924937i \(0.375882\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −28.7321 −1.62925 −0.814623 0.579991i \(-0.803056\pi\)
−0.814623 + 0.579991i \(0.803056\pi\)
\(312\) 0 0
\(313\) −13.3205 −0.752920 −0.376460 0.926433i \(-0.622859\pi\)
−0.376460 + 0.926433i \(0.622859\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 11.2679 0.632871 0.316436 0.948614i \(-0.397514\pi\)
0.316436 + 0.948614i \(0.397514\pi\)
\(318\) 0 0
\(319\) 2.53590 0.141983
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −6.73205 −0.374581
\(324\) 0 0
\(325\) 9.85641 0.546735
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −11.6603 −0.642851
\(330\) 0 0
\(331\) 4.39230 0.241423 0.120711 0.992688i \(-0.461482\pi\)
0.120711 + 0.992688i \(0.461482\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 10.9282 0.597072
\(336\) 0 0
\(337\) 3.07180 0.167331 0.0836657 0.996494i \(-0.473337\pi\)
0.0836657 + 0.996494i \(0.473337\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −12.0000 −0.649836
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −35.8564 −1.92487 −0.962436 0.271507i \(-0.912478\pi\)
−0.962436 + 0.271507i \(0.912478\pi\)
\(348\) 0 0
\(349\) 23.8564 1.27700 0.638502 0.769620i \(-0.279554\pi\)
0.638502 + 0.769620i \(0.279554\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 7.80385 0.415357 0.207678 0.978197i \(-0.433409\pi\)
0.207678 + 0.978197i \(0.433409\pi\)
\(354\) 0 0
\(355\) 11.4641 0.608451
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −4.53590 −0.239396 −0.119698 0.992810i \(-0.538193\pi\)
−0.119698 + 0.992810i \(0.538193\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −20.3923 −1.06738
\(366\) 0 0
\(367\) −25.8564 −1.34969 −0.674847 0.737958i \(-0.735790\pi\)
−0.674847 + 0.737958i \(0.735790\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −2.19615 −0.114019
\(372\) 0 0
\(373\) 25.7128 1.33136 0.665679 0.746238i \(-0.268142\pi\)
0.665679 + 0.746238i \(0.268142\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2.92820 −0.150810
\(378\) 0 0
\(379\) −30.2487 −1.55377 −0.776886 0.629641i \(-0.783202\pi\)
−0.776886 + 0.629641i \(0.783202\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −21.4641 −1.09676 −0.548382 0.836228i \(-0.684756\pi\)
−0.548382 + 0.836228i \(0.684756\pi\)
\(384\) 0 0
\(385\) −9.46410 −0.482335
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −2.53590 −0.128575 −0.0642876 0.997931i \(-0.520477\pi\)
−0.0642876 + 0.997931i \(0.520477\pi\)
\(390\) 0 0
\(391\) −50.2487 −2.54119
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −4.00000 −0.201262
\(396\) 0 0
\(397\) 6.00000 0.301131 0.150566 0.988600i \(-0.451890\pi\)
0.150566 + 0.988600i \(0.451890\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 16.0526 0.801627 0.400813 0.916160i \(-0.368728\pi\)
0.400813 + 0.916160i \(0.368728\pi\)
\(402\) 0 0
\(403\) 13.8564 0.690237
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.85641 0.0920187
\(408\) 0 0
\(409\) 35.7128 1.76588 0.882942 0.469481i \(-0.155559\pi\)
0.882942 + 0.469481i \(0.155559\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 8.00000 0.393654
\(414\) 0 0
\(415\) 27.8564 1.36742
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 10.1962 0.498115 0.249057 0.968489i \(-0.419879\pi\)
0.249057 + 0.968489i \(0.419879\pi\)
\(420\) 0 0
\(421\) −25.3205 −1.23405 −0.617023 0.786945i \(-0.711661\pi\)
−0.617023 + 0.786945i \(0.711661\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −16.5885 −0.804658
\(426\) 0 0
\(427\) −11.4641 −0.554787
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 22.0526 1.06223 0.531117 0.847298i \(-0.321772\pi\)
0.531117 + 0.847298i \(0.321772\pi\)
\(432\) 0 0
\(433\) −4.92820 −0.236834 −0.118417 0.992964i \(-0.537782\pi\)
−0.118417 + 0.992964i \(0.537782\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 7.46410 0.357056
\(438\) 0 0
\(439\) 11.4641 0.547152 0.273576 0.961850i \(-0.411794\pi\)
0.273576 + 0.961850i \(0.411794\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 19.8564 0.943406 0.471703 0.881757i \(-0.343639\pi\)
0.471703 + 0.881757i \(0.343639\pi\)
\(444\) 0 0
\(445\) 28.3923 1.34592
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −34.5885 −1.63233 −0.816165 0.577819i \(-0.803904\pi\)
−0.816165 + 0.577819i \(0.803904\pi\)
\(450\) 0 0
\(451\) 15.7128 0.739887
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 10.9282 0.512322
\(456\) 0 0
\(457\) −8.39230 −0.392575 −0.196288 0.980546i \(-0.562889\pi\)
−0.196288 + 0.980546i \(0.562889\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 3.51666 0.163787 0.0818936 0.996641i \(-0.473903\pi\)
0.0818936 + 0.996641i \(0.473903\pi\)
\(462\) 0 0
\(463\) 13.8564 0.643962 0.321981 0.946746i \(-0.395651\pi\)
0.321981 + 0.946746i \(0.395651\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 3.26795 0.151223 0.0756113 0.997137i \(-0.475909\pi\)
0.0756113 + 0.997137i \(0.475909\pi\)
\(468\) 0 0
\(469\) 4.00000 0.184703
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −17.0718 −0.784962
\(474\) 0 0
\(475\) 2.46410 0.113061
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −32.7321 −1.49557 −0.747783 0.663943i \(-0.768882\pi\)
−0.747783 + 0.663943i \(0.768882\pi\)
\(480\) 0 0
\(481\) −2.14359 −0.0977395
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −16.3923 −0.744336
\(486\) 0 0
\(487\) −33.8564 −1.53418 −0.767090 0.641539i \(-0.778296\pi\)
−0.767090 + 0.641539i \(0.778296\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −19.8564 −0.896107 −0.448054 0.894007i \(-0.647883\pi\)
−0.448054 + 0.894007i \(0.647883\pi\)
\(492\) 0 0
\(493\) 4.92820 0.221955
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 4.19615 0.188223
\(498\) 0 0
\(499\) 4.00000 0.179065 0.0895323 0.995984i \(-0.471463\pi\)
0.0895323 + 0.995984i \(0.471463\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −11.6603 −0.519905 −0.259953 0.965621i \(-0.583707\pi\)
−0.259953 + 0.965621i \(0.583707\pi\)
\(504\) 0 0
\(505\) −45.3205 −2.01674
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −26.7846 −1.18721 −0.593603 0.804758i \(-0.702295\pi\)
−0.593603 + 0.804758i \(0.702295\pi\)
\(510\) 0 0
\(511\) −7.46410 −0.330192
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 18.9282 0.834076
\(516\) 0 0
\(517\) −40.3923 −1.77645
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −37.7128 −1.65223 −0.826114 0.563503i \(-0.809453\pi\)
−0.826114 + 0.563503i \(0.809453\pi\)
\(522\) 0 0
\(523\) −7.46410 −0.326382 −0.163191 0.986594i \(-0.552179\pi\)
−0.163191 + 0.986594i \(0.552179\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −23.3205 −1.01586
\(528\) 0 0
\(529\) 32.7128 1.42230
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −18.1436 −0.785886
\(534\) 0 0
\(535\) −22.3923 −0.968104
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −3.46410 −0.149209
\(540\) 0 0
\(541\) 4.14359 0.178147 0.0890735 0.996025i \(-0.471609\pi\)
0.0890735 + 0.996025i \(0.471609\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 32.3923 1.38753
\(546\) 0 0
\(547\) −36.1051 −1.54374 −0.771872 0.635778i \(-0.780679\pi\)
−0.771872 + 0.635778i \(0.780679\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −0.732051 −0.0311864
\(552\) 0 0
\(553\) −1.46410 −0.0622599
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 6.53590 0.276935 0.138467 0.990367i \(-0.455782\pi\)
0.138467 + 0.990367i \(0.455782\pi\)
\(558\) 0 0
\(559\) 19.7128 0.833763
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −21.4641 −0.904604 −0.452302 0.891865i \(-0.649397\pi\)
−0.452302 + 0.891865i \(0.649397\pi\)
\(564\) 0 0
\(565\) 2.00000 0.0841406
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −16.0526 −0.672958 −0.336479 0.941691i \(-0.609236\pi\)
−0.336479 + 0.941691i \(0.609236\pi\)
\(570\) 0 0
\(571\) −30.9282 −1.29431 −0.647153 0.762361i \(-0.724040\pi\)
−0.647153 + 0.762361i \(0.724040\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 18.3923 0.767012
\(576\) 0 0
\(577\) 10.6795 0.444593 0.222297 0.974979i \(-0.428645\pi\)
0.222297 + 0.974979i \(0.428645\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 10.1962 0.423008
\(582\) 0 0
\(583\) −7.60770 −0.315079
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −16.0526 −0.662560 −0.331280 0.943532i \(-0.607480\pi\)
−0.331280 + 0.943532i \(0.607480\pi\)
\(588\) 0 0
\(589\) 3.46410 0.142736
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 20.9808 0.861577 0.430788 0.902453i \(-0.358236\pi\)
0.430788 + 0.902453i \(0.358236\pi\)
\(594\) 0 0
\(595\) −18.3923 −0.754011
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −18.0526 −0.737608 −0.368804 0.929507i \(-0.620233\pi\)
−0.368804 + 0.929507i \(0.620233\pi\)
\(600\) 0 0
\(601\) −28.6410 −1.16829 −0.584146 0.811649i \(-0.698570\pi\)
−0.584146 + 0.811649i \(0.698570\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −2.73205 −0.111074
\(606\) 0 0
\(607\) 16.7846 0.681266 0.340633 0.940196i \(-0.389359\pi\)
0.340633 + 0.940196i \(0.389359\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 46.6410 1.88689
\(612\) 0 0
\(613\) 28.3923 1.14675 0.573377 0.819292i \(-0.305633\pi\)
0.573377 + 0.819292i \(0.305633\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 19.7128 0.793608 0.396804 0.917903i \(-0.370119\pi\)
0.396804 + 0.917903i \(0.370119\pi\)
\(618\) 0 0
\(619\) −6.53590 −0.262700 −0.131350 0.991336i \(-0.541931\pi\)
−0.131350 + 0.991336i \(0.541931\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 10.3923 0.416359
\(624\) 0 0
\(625\) −31.2487 −1.24995
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 3.60770 0.143848
\(630\) 0 0
\(631\) −7.07180 −0.281524 −0.140762 0.990043i \(-0.544955\pi\)
−0.140762 + 0.990043i \(0.544955\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 29.8564 1.18482
\(636\) 0 0
\(637\) 4.00000 0.158486
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −17.1244 −0.676371 −0.338186 0.941079i \(-0.609813\pi\)
−0.338186 + 0.941079i \(0.609813\pi\)
\(642\) 0 0
\(643\) −41.5692 −1.63933 −0.819665 0.572843i \(-0.805840\pi\)
−0.819665 + 0.572843i \(0.805840\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −5.12436 −0.201459 −0.100730 0.994914i \(-0.532118\pi\)
−0.100730 + 0.994914i \(0.532118\pi\)
\(648\) 0 0
\(649\) 27.7128 1.08782
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 26.9282 1.05378 0.526891 0.849933i \(-0.323358\pi\)
0.526891 + 0.849933i \(0.323358\pi\)
\(654\) 0 0
\(655\) −6.00000 −0.234439
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 13.2679 0.516846 0.258423 0.966032i \(-0.416797\pi\)
0.258423 + 0.966032i \(0.416797\pi\)
\(660\) 0 0
\(661\) −42.6410 −1.65854 −0.829272 0.558846i \(-0.811244\pi\)
−0.829272 + 0.558846i \(0.811244\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 2.73205 0.105944
\(666\) 0 0
\(667\) −5.46410 −0.211571
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −39.7128 −1.53310
\(672\) 0 0
\(673\) 16.2487 0.626342 0.313171 0.949697i \(-0.398609\pi\)
0.313171 + 0.949697i \(0.398609\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 8.92820 0.343139 0.171569 0.985172i \(-0.445116\pi\)
0.171569 + 0.985172i \(0.445116\pi\)
\(678\) 0 0
\(679\) −6.00000 −0.230259
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 18.7321 0.716762 0.358381 0.933575i \(-0.383329\pi\)
0.358381 + 0.933575i \(0.383329\pi\)
\(684\) 0 0
\(685\) 8.00000 0.305664
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 8.78461 0.334667
\(690\) 0 0
\(691\) −39.3205 −1.49582 −0.747911 0.663799i \(-0.768943\pi\)
−0.747911 + 0.663799i \(0.768943\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −25.8564 −0.980789
\(696\) 0 0
\(697\) 30.5359 1.15663
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −12.0000 −0.453234 −0.226617 0.973984i \(-0.572767\pi\)
−0.226617 + 0.973984i \(0.572767\pi\)
\(702\) 0 0
\(703\) −0.535898 −0.0202118
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −16.5885 −0.623873
\(708\) 0 0
\(709\) −34.2487 −1.28624 −0.643119 0.765767i \(-0.722360\pi\)
−0.643119 + 0.765767i \(0.722360\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 25.8564 0.968330
\(714\) 0 0
\(715\) 37.8564 1.41575
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 38.5885 1.43911 0.719553 0.694437i \(-0.244347\pi\)
0.719553 + 0.694437i \(0.244347\pi\)
\(720\) 0 0
\(721\) 6.92820 0.258020
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1.80385 −0.0669932
\(726\) 0 0
\(727\) 12.3923 0.459605 0.229803 0.973237i \(-0.426192\pi\)
0.229803 + 0.973237i \(0.426192\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −33.1769 −1.22709
\(732\) 0 0
\(733\) 0.535898 0.0197939 0.00989693 0.999951i \(-0.496850\pi\)
0.00989693 + 0.999951i \(0.496850\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 13.8564 0.510407
\(738\) 0 0
\(739\) 40.9282 1.50557 0.752784 0.658267i \(-0.228710\pi\)
0.752784 + 0.658267i \(0.228710\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −52.3013 −1.91875 −0.959374 0.282138i \(-0.908956\pi\)
−0.959374 + 0.282138i \(0.908956\pi\)
\(744\) 0 0
\(745\) −6.92820 −0.253830
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −8.19615 −0.299481
\(750\) 0 0
\(751\) 4.39230 0.160277 0.0801387 0.996784i \(-0.474464\pi\)
0.0801387 + 0.996784i \(0.474464\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 39.7128 1.44530
\(756\) 0 0
\(757\) 49.7128 1.80684 0.903421 0.428754i \(-0.141047\pi\)
0.903421 + 0.428754i \(0.141047\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −10.7321 −0.389037 −0.194518 0.980899i \(-0.562314\pi\)
−0.194518 + 0.980899i \(0.562314\pi\)
\(762\) 0 0
\(763\) 11.8564 0.429231
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −32.0000 −1.15545
\(768\) 0 0
\(769\) 32.5359 1.17327 0.586637 0.809850i \(-0.300451\pi\)
0.586637 + 0.809850i \(0.300451\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 30.3923 1.09314 0.546568 0.837415i \(-0.315934\pi\)
0.546568 + 0.837415i \(0.315934\pi\)
\(774\) 0 0
\(775\) 8.53590 0.306619
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −4.53590 −0.162515
\(780\) 0 0
\(781\) 14.5359 0.520135
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 17.4641 0.623321
\(786\) 0 0
\(787\) 23.4641 0.836405 0.418202 0.908354i \(-0.362660\pi\)
0.418202 + 0.908354i \(0.362660\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0.732051 0.0260287
\(792\) 0 0
\(793\) 45.8564 1.62841
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 12.2487 0.433872 0.216936 0.976186i \(-0.430394\pi\)
0.216936 + 0.976186i \(0.430394\pi\)
\(798\) 0 0
\(799\) −78.4974 −2.77704
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −25.8564 −0.912453
\(804\) 0 0
\(805\) 20.3923 0.718734
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 25.0718 0.881477 0.440739 0.897635i \(-0.354717\pi\)
0.440739 + 0.897635i \(0.354717\pi\)
\(810\) 0 0
\(811\) 27.7128 0.973128 0.486564 0.873645i \(-0.338250\pi\)
0.486564 + 0.873645i \(0.338250\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 27.3205 0.956996
\(816\) 0 0
\(817\) 4.92820 0.172416
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −15.3205 −0.534689 −0.267345 0.963601i \(-0.586146\pi\)
−0.267345 + 0.963601i \(0.586146\pi\)
\(822\) 0 0
\(823\) −10.0000 −0.348578 −0.174289 0.984695i \(-0.555763\pi\)
−0.174289 + 0.984695i \(0.555763\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −0.483340 −0.0168074 −0.00840368 0.999965i \(-0.502675\pi\)
−0.00840368 + 0.999965i \(0.502675\pi\)
\(828\) 0 0
\(829\) 52.9282 1.83827 0.919136 0.393940i \(-0.128888\pi\)
0.919136 + 0.393940i \(0.128888\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −6.73205 −0.233252
\(834\) 0 0
\(835\) 44.7846 1.54984
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −8.78461 −0.303278 −0.151639 0.988436i \(-0.548455\pi\)
−0.151639 + 0.988436i \(0.548455\pi\)
\(840\) 0 0
\(841\) −28.4641 −0.981521
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −8.19615 −0.281956
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −4.00000 −0.137118
\(852\) 0 0
\(853\) −32.9282 −1.12744 −0.563720 0.825966i \(-0.690630\pi\)
−0.563720 + 0.825966i \(0.690630\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 6.39230 0.218357 0.109178 0.994022i \(-0.465178\pi\)
0.109178 + 0.994022i \(0.465178\pi\)
\(858\) 0 0
\(859\) 0.784610 0.0267705 0.0133853 0.999910i \(-0.495739\pi\)
0.0133853 + 0.999910i \(0.495739\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −22.0526 −0.750678 −0.375339 0.926888i \(-0.622474\pi\)
−0.375339 + 0.926888i \(0.622474\pi\)
\(864\) 0 0
\(865\) 28.3923 0.965367
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −5.07180 −0.172049
\(870\) 0 0
\(871\) −16.0000 −0.542139
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −6.92820 −0.234216
\(876\) 0 0
\(877\) 54.7846 1.84994 0.924972 0.380034i \(-0.124088\pi\)
0.924972 + 0.380034i \(0.124088\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 27.5167 0.927060 0.463530 0.886081i \(-0.346583\pi\)
0.463530 + 0.886081i \(0.346583\pi\)
\(882\) 0 0
\(883\) 15.7128 0.528778 0.264389 0.964416i \(-0.414830\pi\)
0.264389 + 0.964416i \(0.414830\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −40.1051 −1.34660 −0.673299 0.739370i \(-0.735123\pi\)
−0.673299 + 0.739370i \(0.735123\pi\)
\(888\) 0 0
\(889\) 10.9282 0.366520
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 11.6603 0.390196
\(894\) 0 0
\(895\) −53.3205 −1.78231
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −2.53590 −0.0845769
\(900\) 0 0
\(901\) −14.7846 −0.492547
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −10.5359 −0.350225
\(906\) 0 0
\(907\) −30.6410 −1.01742 −0.508709 0.860938i \(-0.669877\pi\)
−0.508709 + 0.860938i \(0.669877\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −9.94744 −0.329573 −0.164787 0.986329i \(-0.552694\pi\)
−0.164787 + 0.986329i \(0.552694\pi\)
\(912\) 0 0
\(913\) 35.3205 1.16894
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −2.19615 −0.0725233
\(918\) 0 0
\(919\) −13.8564 −0.457081 −0.228540 0.973534i \(-0.573395\pi\)
−0.228540 + 0.973534i \(0.573395\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −16.7846 −0.552472
\(924\) 0 0
\(925\) −1.32051 −0.0434180
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 32.1962 1.05632 0.528161 0.849144i \(-0.322882\pi\)
0.528161 + 0.849144i \(0.322882\pi\)
\(930\) 0 0
\(931\) 1.00000 0.0327737
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −63.7128 −2.08363
\(936\) 0 0
\(937\) 12.1436 0.396714 0.198357 0.980130i \(-0.436439\pi\)
0.198357 + 0.980130i \(0.436439\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 28.6410 0.933670 0.466835 0.884344i \(-0.345394\pi\)
0.466835 + 0.884344i \(0.345394\pi\)
\(942\) 0 0
\(943\) −33.8564 −1.10252
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 33.0333 1.07344 0.536719 0.843761i \(-0.319663\pi\)
0.536719 + 0.843761i \(0.319663\pi\)
\(948\) 0 0
\(949\) 29.8564 0.969180
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −34.5885 −1.12043 −0.560215 0.828347i \(-0.689281\pi\)
−0.560215 + 0.828347i \(0.689281\pi\)
\(954\) 0 0
\(955\) 6.53590 0.211497
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 2.92820 0.0945566
\(960\) 0 0
\(961\) −19.0000 −0.612903
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 47.3205 1.52330
\(966\) 0 0
\(967\) 2.78461 0.0895470 0.0447735 0.998997i \(-0.485743\pi\)
0.0447735 + 0.998997i \(0.485743\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 54.9282 1.76273 0.881365 0.472436i \(-0.156625\pi\)
0.881365 + 0.472436i \(0.156625\pi\)
\(972\) 0 0
\(973\) −9.46410 −0.303405
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 21.1244 0.675828 0.337914 0.941177i \(-0.390279\pi\)
0.337914 + 0.941177i \(0.390279\pi\)
\(978\) 0 0
\(979\) 36.0000 1.15056
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −28.7846 −0.918086 −0.459043 0.888414i \(-0.651808\pi\)
−0.459043 + 0.888414i \(0.651808\pi\)
\(984\) 0 0
\(985\) −18.9282 −0.603103
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 36.7846 1.16968
\(990\) 0 0
\(991\) −11.2154 −0.356269 −0.178134 0.984006i \(-0.557006\pi\)
−0.178134 + 0.984006i \(0.557006\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −67.7128 −2.14664
\(996\) 0 0
\(997\) 30.1051 0.953439 0.476719 0.879056i \(-0.341826\pi\)
0.476719 + 0.879056i \(0.341826\pi\)
\(998\) 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 9576.2.a.bf.1.1 2
3.2 odd 2 9576.2.a.br.1.2 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
9576.2.a.bf.1.1 2 1.1 even 1 trivial
9576.2.a.br.1.2 yes 2 3.2 odd 2