Properties

Label 9576.2.a.bh.1.2
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: \(\Q(\sqrt{7}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 7 \) 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 1.2
Root \(2.64575\) 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)
 
\(f(q)\) \(=\) \(q+1.64575 q^{5} +1.00000 q^{7} +O(q^{10})\) \(q+1.64575 q^{5} +1.00000 q^{7} -2.00000 q^{11} -4.00000 q^{13} +5.64575 q^{17} +1.00000 q^{19} +6.00000 q^{23} -2.29150 q^{25} -0.354249 q^{29} -9.29150 q^{31} +1.64575 q^{35} -5.29150 q^{37} -12.5830 q^{41} -2.00000 q^{43} -7.64575 q^{47} +1.00000 q^{49} -6.93725 q^{53} -3.29150 q^{55} +6.58301 q^{59} +13.2915 q^{61} -6.58301 q^{65} -6.58301 q^{67} -5.64575 q^{71} +1.29150 q^{73} -2.00000 q^{77} +0.708497 q^{79} -1.06275 q^{83} +9.29150 q^{85} -6.00000 q^{89} -4.00000 q^{91} +1.64575 q^{95} -4.58301 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{5} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{5} + 2 q^{7} - 4 q^{11} - 8 q^{13} + 6 q^{17} + 2 q^{19} + 12 q^{23} + 6 q^{25} - 6 q^{29} - 8 q^{31} - 2 q^{35} - 4 q^{41} - 4 q^{43} - 10 q^{47} + 2 q^{49} + 2 q^{53} + 4 q^{55} - 8 q^{59} + 16 q^{61} + 8 q^{65} + 8 q^{67} - 6 q^{71} - 8 q^{73} - 4 q^{77} + 12 q^{79} - 18 q^{83} + 8 q^{85} - 12 q^{89} - 8 q^{91} - 2 q^{95} + 12 q^{97}+O(q^{100}) \) 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
\(5\) 1.64575 0.736002 0.368001 0.929825i \(-0.380042\pi\)
0.368001 + 0.929825i \(0.380042\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 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
\(17\) 5.64575 1.36930 0.684648 0.728874i \(-0.259956\pi\)
0.684648 + 0.728874i \(0.259956\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 6.00000 1.25109 0.625543 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) 0 0
\(25\) −2.29150 −0.458301
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −0.354249 −0.0657823 −0.0328912 0.999459i \(-0.510471\pi\)
−0.0328912 + 0.999459i \(0.510471\pi\)
\(30\) 0 0
\(31\) −9.29150 −1.66880 −0.834402 0.551157i \(-0.814187\pi\)
−0.834402 + 0.551157i \(0.814187\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.64575 0.278183
\(36\) 0 0
\(37\) −5.29150 −0.869918 −0.434959 0.900450i \(-0.643237\pi\)
−0.434959 + 0.900450i \(0.643237\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −12.5830 −1.96514 −0.982568 0.185905i \(-0.940478\pi\)
−0.982568 + 0.185905i \(0.940478\pi\)
\(42\) 0 0
\(43\) −2.00000 −0.304997 −0.152499 0.988304i \(-0.548732\pi\)
−0.152499 + 0.988304i \(0.548732\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −7.64575 −1.11525 −0.557624 0.830094i \(-0.688287\pi\)
−0.557624 + 0.830094i \(0.688287\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −6.93725 −0.952905 −0.476453 0.879200i \(-0.658078\pi\)
−0.476453 + 0.879200i \(0.658078\pi\)
\(54\) 0 0
\(55\) −3.29150 −0.443826
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 6.58301 0.857034 0.428517 0.903534i \(-0.359036\pi\)
0.428517 + 0.903534i \(0.359036\pi\)
\(60\) 0 0
\(61\) 13.2915 1.70180 0.850901 0.525326i \(-0.176056\pi\)
0.850901 + 0.525326i \(0.176056\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −6.58301 −0.816521
\(66\) 0 0
\(67\) −6.58301 −0.804242 −0.402121 0.915587i \(-0.631727\pi\)
−0.402121 + 0.915587i \(0.631727\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −5.64575 −0.670027 −0.335014 0.942213i \(-0.608741\pi\)
−0.335014 + 0.942213i \(0.608741\pi\)
\(72\) 0 0
\(73\) 1.29150 0.151159 0.0755795 0.997140i \(-0.475919\pi\)
0.0755795 + 0.997140i \(0.475919\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.00000 −0.227921
\(78\) 0 0
\(79\) 0.708497 0.0797122 0.0398561 0.999205i \(-0.487310\pi\)
0.0398561 + 0.999205i \(0.487310\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −1.06275 −0.116652 −0.0583258 0.998298i \(-0.518576\pi\)
−0.0583258 + 0.998298i \(0.518576\pi\)
\(84\) 0 0
\(85\) 9.29150 1.00780
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 0 0
\(91\) −4.00000 −0.419314
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1.64575 0.168851
\(96\) 0 0
\(97\) −4.58301 −0.465334 −0.232667 0.972556i \(-0.574745\pi\)
−0.232667 + 0.972556i \(0.574745\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −9.64575 −0.959788 −0.479894 0.877326i \(-0.659325\pi\)
−0.479894 + 0.877326i \(0.659325\pi\)
\(102\) 0 0
\(103\) 18.5830 1.83104 0.915519 0.402275i \(-0.131780\pi\)
0.915519 + 0.402275i \(0.131780\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.64575 0.159101 0.0795504 0.996831i \(-0.474652\pi\)
0.0795504 + 0.996831i \(0.474652\pi\)
\(108\) 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
\(113\) 1.06275 0.0999747 0.0499874 0.998750i \(-0.484082\pi\)
0.0499874 + 0.998750i \(0.484082\pi\)
\(114\) 0 0
\(115\) 9.87451 0.920803
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 5.64575 0.517545
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) −4.00000 −0.354943 −0.177471 0.984126i \(-0.556792\pi\)
−0.177471 + 0.984126i \(0.556792\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1.06275 0.0928526 0.0464263 0.998922i \(-0.485217\pi\)
0.0464263 + 0.998922i \(0.485217\pi\)
\(132\) 0 0
\(133\) 1.00000 0.0867110
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1.41699 −0.121062 −0.0605310 0.998166i \(-0.519279\pi\)
−0.0605310 + 0.998166i \(0.519279\pi\)
\(138\) 0 0
\(139\) −11.2915 −0.957733 −0.478866 0.877888i \(-0.658952\pi\)
−0.478866 + 0.877888i \(0.658952\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 8.00000 0.668994
\(144\) 0 0
\(145\) −0.583005 −0.0484160
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −4.70850 −0.385735 −0.192868 0.981225i \(-0.561779\pi\)
−0.192868 + 0.981225i \(0.561779\pi\)
\(150\) 0 0
\(151\) 8.70850 0.708687 0.354344 0.935115i \(-0.384704\pi\)
0.354344 + 0.935115i \(0.384704\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −15.2915 −1.22824
\(156\) 0 0
\(157\) −19.8745 −1.58616 −0.793079 0.609119i \(-0.791523\pi\)
−0.793079 + 0.609119i \(0.791523\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 6.00000 0.472866
\(162\) 0 0
\(163\) 8.58301 0.672273 0.336136 0.941813i \(-0.390880\pi\)
0.336136 + 0.941813i \(0.390880\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −4.70850 −0.364354 −0.182177 0.983266i \(-0.558314\pi\)
−0.182177 + 0.983266i \(0.558314\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 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
\(175\) −2.29150 −0.173221
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 11.5203 0.861065 0.430532 0.902575i \(-0.358326\pi\)
0.430532 + 0.902575i \(0.358326\pi\)
\(180\) 0 0
\(181\) −4.58301 −0.340652 −0.170326 0.985388i \(-0.554482\pi\)
−0.170326 + 0.985388i \(0.554482\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −8.70850 −0.640261
\(186\) 0 0
\(187\) −11.2915 −0.825716
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −6.00000 −0.434145 −0.217072 0.976156i \(-0.569651\pi\)
−0.217072 + 0.976156i \(0.569651\pi\)
\(192\) 0 0
\(193\) −14.7085 −1.05874 −0.529370 0.848391i \(-0.677572\pi\)
−0.529370 + 0.848391i \(0.677572\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 26.5830 1.89396 0.946980 0.321291i \(-0.104117\pi\)
0.946980 + 0.321291i \(0.104117\pi\)
\(198\) 0 0
\(199\) 22.5830 1.60087 0.800433 0.599422i \(-0.204603\pi\)
0.800433 + 0.599422i \(0.204603\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −0.354249 −0.0248634
\(204\) 0 0
\(205\) −20.7085 −1.44634
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2.00000 −0.138343
\(210\) 0 0
\(211\) −22.5830 −1.55468 −0.777339 0.629082i \(-0.783431\pi\)
−0.777339 + 0.629082i \(0.783431\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −3.29150 −0.224479
\(216\) 0 0
\(217\) −9.29150 −0.630748
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −22.5830 −1.51910
\(222\) 0 0
\(223\) 5.29150 0.354345 0.177173 0.984180i \(-0.443305\pi\)
0.177173 + 0.984180i \(0.443305\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −23.2915 −1.54591 −0.772956 0.634460i \(-0.781223\pi\)
−0.772956 + 0.634460i \(0.781223\pi\)
\(228\) 0 0
\(229\) 12.5830 0.831508 0.415754 0.909477i \(-0.363518\pi\)
0.415754 + 0.909477i \(0.363518\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 4.70850 0.308464 0.154232 0.988035i \(-0.450710\pi\)
0.154232 + 0.988035i \(0.450710\pi\)
\(234\) 0 0
\(235\) −12.5830 −0.820825
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −13.2915 −0.859756 −0.429878 0.902887i \(-0.641443\pi\)
−0.429878 + 0.902887i \(0.641443\pi\)
\(240\) 0 0
\(241\) −10.0000 −0.644157 −0.322078 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1.64575 0.105143
\(246\) 0 0
\(247\) −4.00000 −0.254514
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −7.64575 −0.482596 −0.241298 0.970451i \(-0.577573\pi\)
−0.241298 + 0.970451i \(0.577573\pi\)
\(252\) 0 0
\(253\) −12.0000 −0.754434
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2.70850 −0.168951 −0.0844757 0.996426i \(-0.526922\pi\)
−0.0844757 + 0.996426i \(0.526922\pi\)
\(258\) 0 0
\(259\) −5.29150 −0.328798
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −13.2915 −0.819589 −0.409795 0.912178i \(-0.634400\pi\)
−0.409795 + 0.912178i \(0.634400\pi\)
\(264\) 0 0
\(265\) −11.4170 −0.701340
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −30.4575 −1.85703 −0.928514 0.371298i \(-0.878913\pi\)
−0.928514 + 0.371298i \(0.878913\pi\)
\(270\) 0 0
\(271\) 15.2915 0.928893 0.464446 0.885601i \(-0.346253\pi\)
0.464446 + 0.885601i \(0.346253\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 4.58301 0.276366
\(276\) 0 0
\(277\) 1.87451 0.112628 0.0563141 0.998413i \(-0.482065\pi\)
0.0563141 + 0.998413i \(0.482065\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 22.9373 1.36832 0.684161 0.729331i \(-0.260169\pi\)
0.684161 + 0.729331i \(0.260169\pi\)
\(282\) 0 0
\(283\) 8.00000 0.475551 0.237775 0.971320i \(-0.423582\pi\)
0.237775 + 0.971320i \(0.423582\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −12.5830 −0.742751
\(288\) 0 0
\(289\) 14.8745 0.874971
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −24.5830 −1.43615 −0.718077 0.695963i \(-0.754978\pi\)
−0.718077 + 0.695963i \(0.754978\pi\)
\(294\) 0 0
\(295\) 10.8340 0.630779
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −24.0000 −1.38796
\(300\) 0 0
\(301\) −2.00000 −0.115278
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 21.8745 1.25253
\(306\) 0 0
\(307\) 7.87451 0.449422 0.224711 0.974425i \(-0.427856\pi\)
0.224711 + 0.974425i \(0.427856\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 19.6458 1.11401 0.557004 0.830510i \(-0.311951\pi\)
0.557004 + 0.830510i \(0.311951\pi\)
\(312\) 0 0
\(313\) 6.70850 0.379187 0.189593 0.981863i \(-0.439283\pi\)
0.189593 + 0.981863i \(0.439283\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −10.9373 −0.614297 −0.307149 0.951662i \(-0.599375\pi\)
−0.307149 + 0.951662i \(0.599375\pi\)
\(318\) 0 0
\(319\) 0.708497 0.0396682
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 5.64575 0.314138
\(324\) 0 0
\(325\) 9.16601 0.508439
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −7.64575 −0.421524
\(330\) 0 0
\(331\) 28.4575 1.56417 0.782083 0.623174i \(-0.214157\pi\)
0.782083 + 0.623174i \(0.214157\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −10.8340 −0.591924
\(336\) 0 0
\(337\) −8.58301 −0.467546 −0.233773 0.972291i \(-0.575107\pi\)
−0.233773 + 0.972291i \(0.575107\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 18.5830 1.00633
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −11.8745 −0.637457 −0.318728 0.947846i \(-0.603256\pi\)
−0.318728 + 0.947846i \(0.603256\pi\)
\(348\) 0 0
\(349\) 10.0000 0.535288 0.267644 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 14.3542 0.764000 0.382000 0.924162i \(-0.375236\pi\)
0.382000 + 0.924162i \(0.375236\pi\)
\(354\) 0 0
\(355\) −9.29150 −0.493142
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 11.4170 0.602566 0.301283 0.953535i \(-0.402585\pi\)
0.301283 + 0.953535i \(0.402585\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 2.12549 0.111253
\(366\) 0 0
\(367\) 25.1660 1.31366 0.656828 0.754041i \(-0.271898\pi\)
0.656828 + 0.754041i \(0.271898\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −6.93725 −0.360164
\(372\) 0 0
\(373\) −26.0000 −1.34623 −0.673114 0.739538i \(-0.735044\pi\)
−0.673114 + 0.739538i \(0.735044\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.41699 0.0729789
\(378\) 0 0
\(379\) −3.29150 −0.169073 −0.0845366 0.996420i \(-0.526941\pi\)
−0.0845366 + 0.996420i \(0.526941\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 33.8745 1.73091 0.865453 0.500990i \(-0.167031\pi\)
0.865453 + 0.500990i \(0.167031\pi\)
\(384\) 0 0
\(385\) −3.29150 −0.167751
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −9.87451 −0.500657 −0.250329 0.968161i \(-0.580539\pi\)
−0.250329 + 0.968161i \(0.580539\pi\)
\(390\) 0 0
\(391\) 33.8745 1.71311
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1.16601 0.0586684
\(396\) 0 0
\(397\) −18.0000 −0.903394 −0.451697 0.892171i \(-0.649181\pi\)
−0.451697 + 0.892171i \(0.649181\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −8.35425 −0.417191 −0.208596 0.978002i \(-0.566889\pi\)
−0.208596 + 0.978002i \(0.566889\pi\)
\(402\) 0 0
\(403\) 37.1660 1.85137
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 10.5830 0.524580
\(408\) 0 0
\(409\) 29.1660 1.44217 0.721083 0.692848i \(-0.243645\pi\)
0.721083 + 0.692848i \(0.243645\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 6.58301 0.323929
\(414\) 0 0
\(415\) −1.74902 −0.0858558
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −22.9373 −1.12056 −0.560279 0.828304i \(-0.689306\pi\)
−0.560279 + 0.828304i \(0.689306\pi\)
\(420\) 0 0
\(421\) −11.8745 −0.578728 −0.289364 0.957219i \(-0.593444\pi\)
−0.289364 + 0.957219i \(0.593444\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −12.9373 −0.627549
\(426\) 0 0
\(427\) 13.2915 0.643221
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −28.9373 −1.39386 −0.696929 0.717140i \(-0.745451\pi\)
−0.696929 + 0.717140i \(0.745451\pi\)
\(432\) 0 0
\(433\) −14.0000 −0.672797 −0.336399 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 6.00000 0.287019
\(438\) 0 0
\(439\) −4.12549 −0.196899 −0.0984495 0.995142i \(-0.531388\pi\)
−0.0984495 + 0.995142i \(0.531388\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −10.7085 −0.508776 −0.254388 0.967102i \(-0.581874\pi\)
−0.254388 + 0.967102i \(0.581874\pi\)
\(444\) 0 0
\(445\) −9.87451 −0.468097
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −4.35425 −0.205490 −0.102745 0.994708i \(-0.532763\pi\)
−0.102745 + 0.994708i \(0.532763\pi\)
\(450\) 0 0
\(451\) 25.1660 1.18502
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −6.58301 −0.308616
\(456\) 0 0
\(457\) −2.12549 −0.0994263 −0.0497132 0.998764i \(-0.515831\pi\)
−0.0497132 + 0.998764i \(0.515831\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 4.93725 0.229951 0.114975 0.993368i \(-0.463321\pi\)
0.114975 + 0.993368i \(0.463321\pi\)
\(462\) 0 0
\(463\) 13.1660 0.611876 0.305938 0.952051i \(-0.401030\pi\)
0.305938 + 0.952051i \(0.401030\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 18.2288 0.843526 0.421763 0.906706i \(-0.361411\pi\)
0.421763 + 0.906706i \(0.361411\pi\)
\(468\) 0 0
\(469\) −6.58301 −0.303975
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 4.00000 0.183920
\(474\) 0 0
\(475\) −2.29150 −0.105141
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 6.22876 0.284599 0.142300 0.989824i \(-0.454550\pi\)
0.142300 + 0.989824i \(0.454550\pi\)
\(480\) 0 0
\(481\) 21.1660 0.965087
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −7.54249 −0.342487
\(486\) 0 0
\(487\) −27.7490 −1.25743 −0.628714 0.777637i \(-0.716418\pi\)
−0.628714 + 0.777637i \(0.716418\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 1.29150 0.0582847 0.0291423 0.999575i \(-0.490722\pi\)
0.0291423 + 0.999575i \(0.490722\pi\)
\(492\) 0 0
\(493\) −2.00000 −0.0900755
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −5.64575 −0.253247
\(498\) 0 0
\(499\) 12.0000 0.537194 0.268597 0.963253i \(-0.413440\pi\)
0.268597 + 0.963253i \(0.413440\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −13.5203 −0.602839 −0.301419 0.953492i \(-0.597460\pi\)
−0.301419 + 0.953492i \(0.597460\pi\)
\(504\) 0 0
\(505\) −15.8745 −0.706406
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −10.7085 −0.474646 −0.237323 0.971431i \(-0.576270\pi\)
−0.237323 + 0.971431i \(0.576270\pi\)
\(510\) 0 0
\(511\) 1.29150 0.0571327
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 30.5830 1.34765
\(516\) 0 0
\(517\) 15.2915 0.672520
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −15.8745 −0.695475 −0.347737 0.937592i \(-0.613050\pi\)
−0.347737 + 0.937592i \(0.613050\pi\)
\(522\) 0 0
\(523\) −7.87451 −0.344328 −0.172164 0.985068i \(-0.555076\pi\)
−0.172164 + 0.985068i \(0.555076\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −52.4575 −2.28509
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 50.3320 2.18012
\(534\) 0 0
\(535\) 2.70850 0.117099
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −2.00000 −0.0861461
\(540\) 0 0
\(541\) −27.1660 −1.16796 −0.583979 0.811769i \(-0.698505\pi\)
−0.583979 + 0.811769i \(0.698505\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 16.4575 0.704962
\(546\) 0 0
\(547\) 4.70850 0.201321 0.100660 0.994921i \(-0.467904\pi\)
0.100660 + 0.994921i \(0.467904\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −0.354249 −0.0150915
\(552\) 0 0
\(553\) 0.708497 0.0301284
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −21.8745 −0.926853 −0.463426 0.886135i \(-0.653380\pi\)
−0.463426 + 0.886135i \(0.653380\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −9.87451 −0.416161 −0.208080 0.978112i \(-0.566722\pi\)
−0.208080 + 0.978112i \(0.566722\pi\)
\(564\) 0 0
\(565\) 1.74902 0.0735816
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −23.6458 −0.991281 −0.495641 0.868528i \(-0.665067\pi\)
−0.495641 + 0.868528i \(0.665067\pi\)
\(570\) 0 0
\(571\) −23.7490 −0.993865 −0.496933 0.867789i \(-0.665540\pi\)
−0.496933 + 0.867789i \(0.665540\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −13.7490 −0.573374
\(576\) 0 0
\(577\) 33.0405 1.37549 0.687747 0.725950i \(-0.258600\pi\)
0.687747 + 0.725950i \(0.258600\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1.06275 −0.0440901
\(582\) 0 0
\(583\) 13.8745 0.574623
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.06275 −0.0438642 −0.0219321 0.999759i \(-0.506982\pi\)
−0.0219321 + 0.999759i \(0.506982\pi\)
\(588\) 0 0
\(589\) −9.29150 −0.382850
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −26.3542 −1.08224 −0.541120 0.840946i \(-0.681999\pi\)
−0.541120 + 0.840946i \(0.681999\pi\)
\(594\) 0 0
\(595\) 9.29150 0.380914
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −0.479741 −0.0196017 −0.00980084 0.999952i \(-0.503120\pi\)
−0.00980084 + 0.999952i \(0.503120\pi\)
\(600\) 0 0
\(601\) 40.3320 1.64518 0.822589 0.568637i \(-0.192529\pi\)
0.822589 + 0.568637i \(0.192529\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −11.5203 −0.468365
\(606\) 0 0
\(607\) 22.5830 0.916616 0.458308 0.888793i \(-0.348456\pi\)
0.458308 + 0.888793i \(0.348456\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 30.5830 1.23726
\(612\) 0 0
\(613\) −20.7085 −0.836408 −0.418204 0.908353i \(-0.637340\pi\)
−0.418204 + 0.908353i \(0.637340\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −37.1660 −1.49625 −0.748124 0.663559i \(-0.769045\pi\)
−0.748124 + 0.663559i \(0.769045\pi\)
\(618\) 0 0
\(619\) −6.12549 −0.246204 −0.123102 0.992394i \(-0.539284\pi\)
−0.123102 + 0.992394i \(0.539284\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −6.00000 −0.240385
\(624\) 0 0
\(625\) −8.29150 −0.331660
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −29.8745 −1.19117
\(630\) 0 0
\(631\) 34.0000 1.35352 0.676759 0.736204i \(-0.263384\pi\)
0.676759 + 0.736204i \(0.263384\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −6.58301 −0.261239
\(636\) 0 0
\(637\) −4.00000 −0.158486
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −11.6458 −0.459980 −0.229990 0.973193i \(-0.573869\pi\)
−0.229990 + 0.973193i \(0.573869\pi\)
\(642\) 0 0
\(643\) −21.1660 −0.834706 −0.417353 0.908744i \(-0.637042\pi\)
−0.417353 + 0.908744i \(0.637042\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −22.2288 −0.873903 −0.436951 0.899485i \(-0.643942\pi\)
−0.436951 + 0.899485i \(0.643942\pi\)
\(648\) 0 0
\(649\) −13.1660 −0.516811
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 5.16601 0.202162 0.101081 0.994878i \(-0.467770\pi\)
0.101081 + 0.994878i \(0.467770\pi\)
\(654\) 0 0
\(655\) 1.74902 0.0683397
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −20.9373 −0.815600 −0.407800 0.913071i \(-0.633704\pi\)
−0.407800 + 0.913071i \(0.633704\pi\)
\(660\) 0 0
\(661\) −13.4170 −0.521861 −0.260930 0.965358i \(-0.584029\pi\)
−0.260930 + 0.965358i \(0.584029\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.64575 0.0638195
\(666\) 0 0
\(667\) −2.12549 −0.0822994
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −26.5830 −1.02623
\(672\) 0 0
\(673\) 30.4575 1.17405 0.587025 0.809568i \(-0.300299\pi\)
0.587025 + 0.809568i \(0.300299\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −22.4575 −0.863112 −0.431556 0.902086i \(-0.642035\pi\)
−0.431556 + 0.902086i \(0.642035\pi\)
\(678\) 0 0
\(679\) −4.58301 −0.175880
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 34.1033 1.30493 0.652463 0.757821i \(-0.273736\pi\)
0.652463 + 0.757821i \(0.273736\pi\)
\(684\) 0 0
\(685\) −2.33202 −0.0891019
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 27.7490 1.05715
\(690\) 0 0
\(691\) −36.7085 −1.39646 −0.698229 0.715875i \(-0.746028\pi\)
−0.698229 + 0.715875i \(0.746028\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −18.5830 −0.704894
\(696\) 0 0
\(697\) −71.0405 −2.69085
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 25.1660 0.950507 0.475254 0.879849i \(-0.342356\pi\)
0.475254 + 0.879849i \(0.342356\pi\)
\(702\) 0 0
\(703\) −5.29150 −0.199573
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −9.64575 −0.362766
\(708\) 0 0
\(709\) 31.0405 1.16575 0.582876 0.812561i \(-0.301928\pi\)
0.582876 + 0.812561i \(0.301928\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −55.7490 −2.08782
\(714\) 0 0
\(715\) 13.1660 0.492381
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −25.0627 −0.934683 −0.467341 0.884077i \(-0.654788\pi\)
−0.467341 + 0.884077i \(0.654788\pi\)
\(720\) 0 0
\(721\) 18.5830 0.692067
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0.811762 0.0301481
\(726\) 0 0
\(727\) −41.8745 −1.55304 −0.776520 0.630093i \(-0.783017\pi\)
−0.776520 + 0.630093i \(0.783017\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −11.2915 −0.417631
\(732\) 0 0
\(733\) 11.8745 0.438595 0.219297 0.975658i \(-0.429623\pi\)
0.219297 + 0.975658i \(0.429623\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 13.1660 0.484976
\(738\) 0 0
\(739\) 26.0000 0.956425 0.478213 0.878244i \(-0.341285\pi\)
0.478213 + 0.878244i \(0.341285\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 33.6458 1.23434 0.617171 0.786829i \(-0.288278\pi\)
0.617171 + 0.786829i \(0.288278\pi\)
\(744\) 0 0
\(745\) −7.74902 −0.283902
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1.64575 0.0601344
\(750\) 0 0
\(751\) 44.4575 1.62228 0.811139 0.584854i \(-0.198848\pi\)
0.811139 + 0.584854i \(0.198848\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 14.3320 0.521596
\(756\) 0 0
\(757\) −52.3320 −1.90204 −0.951020 0.309130i \(-0.899962\pi\)
−0.951020 + 0.309130i \(0.899962\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −28.9373 −1.04897 −0.524487 0.851418i \(-0.675743\pi\)
−0.524487 + 0.851418i \(0.675743\pi\)
\(762\) 0 0
\(763\) 10.0000 0.362024
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −26.3320 −0.950794
\(768\) 0 0
\(769\) −22.4575 −0.809839 −0.404919 0.914352i \(-0.632700\pi\)
−0.404919 + 0.914352i \(0.632700\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −12.5830 −0.452579 −0.226290 0.974060i \(-0.572660\pi\)
−0.226290 + 0.974060i \(0.572660\pi\)
\(774\) 0 0
\(775\) 21.2915 0.764813
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −12.5830 −0.450833
\(780\) 0 0
\(781\) 11.2915 0.404042
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −32.7085 −1.16742
\(786\) 0 0
\(787\) −18.4575 −0.657939 −0.328970 0.944340i \(-0.606701\pi\)
−0.328970 + 0.944340i \(0.606701\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 1.06275 0.0377869
\(792\) 0 0
\(793\) −53.1660 −1.88798
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 47.1660 1.67071 0.835353 0.549714i \(-0.185263\pi\)
0.835353 + 0.549714i \(0.185263\pi\)
\(798\) 0 0
\(799\) −43.1660 −1.52710
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −2.58301 −0.0911523
\(804\) 0 0
\(805\) 9.87451 0.348031
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −23.7490 −0.834971 −0.417485 0.908684i \(-0.637089\pi\)
−0.417485 + 0.908684i \(0.637089\pi\)
\(810\) 0 0
\(811\) −34.3320 −1.20556 −0.602780 0.797907i \(-0.705940\pi\)
−0.602780 + 0.797907i \(0.705940\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 14.1255 0.494794
\(816\) 0 0
\(817\) −2.00000 −0.0699711
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 7.29150 0.254475 0.127238 0.991872i \(-0.459389\pi\)
0.127238 + 0.991872i \(0.459389\pi\)
\(822\) 0 0
\(823\) 16.5830 0.578047 0.289024 0.957322i \(-0.406669\pi\)
0.289024 + 0.957322i \(0.406669\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 11.7712 0.409326 0.204663 0.978832i \(-0.434390\pi\)
0.204663 + 0.978832i \(0.434390\pi\)
\(828\) 0 0
\(829\) 35.1660 1.22137 0.610683 0.791875i \(-0.290895\pi\)
0.610683 + 0.791875i \(0.290895\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 5.64575 0.195614
\(834\) 0 0
\(835\) −7.74902 −0.268166
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 30.5830 1.05584 0.527921 0.849293i \(-0.322972\pi\)
0.527921 + 0.849293i \(0.322972\pi\)
\(840\) 0 0
\(841\) −28.8745 −0.995673
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 4.93725 0.169847
\(846\) 0 0
\(847\) −7.00000 −0.240523
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −31.7490 −1.08834
\(852\) 0 0
\(853\) −52.5830 −1.80041 −0.900204 0.435469i \(-0.856583\pi\)
−0.900204 + 0.435469i \(0.856583\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 13.7490 0.469657 0.234829 0.972037i \(-0.424547\pi\)
0.234829 + 0.972037i \(0.424547\pi\)
\(858\) 0 0
\(859\) −38.5830 −1.31644 −0.658218 0.752828i \(-0.728689\pi\)
−0.658218 + 0.752828i \(0.728689\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −16.2288 −0.552433 −0.276217 0.961095i \(-0.589081\pi\)
−0.276217 + 0.961095i \(0.589081\pi\)
\(864\) 0 0
\(865\) −23.0405 −0.783401
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −1.41699 −0.0480683
\(870\) 0 0
\(871\) 26.3320 0.892226
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −12.0000 −0.405674
\(876\) 0 0
\(877\) −8.58301 −0.289827 −0.144914 0.989444i \(-0.546290\pi\)
−0.144914 + 0.989444i \(0.546290\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 51.5203 1.73576 0.867881 0.496772i \(-0.165482\pi\)
0.867881 + 0.496772i \(0.165482\pi\)
\(882\) 0 0
\(883\) −1.16601 −0.0392394 −0.0196197 0.999808i \(-0.506246\pi\)
−0.0196197 + 0.999808i \(0.506246\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −37.8745 −1.27170 −0.635851 0.771812i \(-0.719351\pi\)
−0.635851 + 0.771812i \(0.719351\pi\)
\(888\) 0 0
\(889\) −4.00000 −0.134156
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −7.64575 −0.255855
\(894\) 0 0
\(895\) 18.9595 0.633746
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 3.29150 0.109778
\(900\) 0 0
\(901\) −39.1660 −1.30481
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −7.54249 −0.250721
\(906\) 0 0
\(907\) 17.1660 0.569988 0.284994 0.958529i \(-0.408008\pi\)
0.284994 + 0.958529i \(0.408008\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 3.06275 0.101473 0.0507367 0.998712i \(-0.483843\pi\)
0.0507367 + 0.998712i \(0.483843\pi\)
\(912\) 0 0
\(913\) 2.12549 0.0703435
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 1.06275 0.0350950
\(918\) 0 0
\(919\) 24.0000 0.791687 0.395843 0.918318i \(-0.370452\pi\)
0.395843 + 0.918318i \(0.370452\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 22.5830 0.743329
\(924\) 0 0
\(925\) 12.1255 0.398684
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −22.3542 −0.733419 −0.366710 0.930335i \(-0.619516\pi\)
−0.366710 + 0.930335i \(0.619516\pi\)
\(930\) 0 0
\(931\) 1.00000 0.0327737
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −18.5830 −0.607729
\(936\) 0 0
\(937\) −38.0000 −1.24141 −0.620703 0.784046i \(-0.713153\pi\)
−0.620703 + 0.784046i \(0.713153\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 5.29150 0.172498 0.0862490 0.996274i \(-0.472512\pi\)
0.0862490 + 0.996274i \(0.472512\pi\)
\(942\) 0 0
\(943\) −75.4980 −2.45855
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 6.00000 0.194974 0.0974869 0.995237i \(-0.468920\pi\)
0.0974869 + 0.995237i \(0.468920\pi\)
\(948\) 0 0
\(949\) −5.16601 −0.167696
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −17.5203 −0.567537 −0.283768 0.958893i \(-0.591585\pi\)
−0.283768 + 0.958893i \(0.591585\pi\)
\(954\) 0 0
\(955\) −9.87451 −0.319532
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −1.41699 −0.0457571
\(960\) 0 0
\(961\) 55.3320 1.78490
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −24.2065 −0.779236
\(966\) 0 0
\(967\) 43.1660 1.38813 0.694063 0.719915i \(-0.255819\pi\)
0.694063 + 0.719915i \(0.255819\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 26.5830 0.853089 0.426545 0.904467i \(-0.359731\pi\)
0.426545 + 0.904467i \(0.359731\pi\)
\(972\) 0 0
\(973\) −11.2915 −0.361989
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 59.3948 1.90021 0.950103 0.311935i \(-0.100977\pi\)
0.950103 + 0.311935i \(0.100977\pi\)
\(978\) 0 0
\(979\) 12.0000 0.383522
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 21.4170 0.683096 0.341548 0.939864i \(-0.389049\pi\)
0.341548 + 0.939864i \(0.389049\pi\)
\(984\) 0 0
\(985\) 43.7490 1.39396
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −12.0000 −0.381578
\(990\) 0 0
\(991\) 16.0000 0.508257 0.254128 0.967170i \(-0.418211\pi\)
0.254128 + 0.967170i \(0.418211\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 37.1660 1.17824
\(996\) 0 0
\(997\) 7.87451 0.249388 0.124694 0.992195i \(-0.460205\pi\)
0.124694 + 0.992195i \(0.460205\pi\)
\(998\) 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.bh.1.2 2
3.2 odd 2 9576.2.a.bu.1.1 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
9576.2.a.bh.1.2 2 1.1 even 1 trivial
9576.2.a.bu.1.1 yes 2 3.2 odd 2