Properties

Label 9576.2.a.be.1.2
Level $9576$
Weight $2$
Character 9576.1
Self dual yes
Analytic conductor $76.465$
Analytic rank $0$
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: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.618034\) 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)
 
\(f(q)\) \(=\) \(q+1.23607 q^{5} -1.00000 q^{7} +O(q^{10})\) \(q+1.23607 q^{5} -1.00000 q^{7} -4.47214 q^{11} -4.47214 q^{13} -1.23607 q^{17} +1.00000 q^{19} -0.472136 q^{23} -3.47214 q^{25} +7.23607 q^{29} +6.47214 q^{31} -1.23607 q^{35} -4.47214 q^{37} -2.00000 q^{41} +8.00000 q^{43} -3.23607 q^{47} +1.00000 q^{49} -3.23607 q^{53} -5.52786 q^{55} -4.00000 q^{59} -3.52786 q^{61} -5.52786 q^{65} -1.52786 q^{67} +5.23607 q^{71} +4.47214 q^{73} +4.47214 q^{77} -12.0000 q^{79} -5.70820 q^{83} -1.52786 q^{85} +10.9443 q^{89} +4.47214 q^{91} +1.23607 q^{95} +3.52786 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{5} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{5} - 2 q^{7} + 2 q^{17} + 2 q^{19} + 8 q^{23} + 2 q^{25} + 10 q^{29} + 4 q^{31} + 2 q^{35} - 4 q^{41} + 16 q^{43} - 2 q^{47} + 2 q^{49} - 2 q^{53} - 20 q^{55} - 8 q^{59} - 16 q^{61} - 20 q^{65} - 12 q^{67} + 6 q^{71} - 24 q^{79} + 2 q^{83} - 12 q^{85} + 4 q^{89} - 2 q^{95} + 16 q^{97}+O(q^{100}) \) 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
\(5\) 1.23607 0.552786 0.276393 0.961045i \(-0.410861\pi\)
0.276393 + 0.961045i \(0.410861\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −4.47214 −1.34840 −0.674200 0.738549i \(-0.735511\pi\)
−0.674200 + 0.738549i \(0.735511\pi\)
\(12\) 0 0
\(13\) −4.47214 −1.24035 −0.620174 0.784465i \(-0.712938\pi\)
−0.620174 + 0.784465i \(0.712938\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.23607 −0.299791 −0.149895 0.988702i \(-0.547894\pi\)
−0.149895 + 0.988702i \(0.547894\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.472136 −0.0984472 −0.0492236 0.998788i \(-0.515675\pi\)
−0.0492236 + 0.998788i \(0.515675\pi\)
\(24\) 0 0
\(25\) −3.47214 −0.694427
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 7.23607 1.34370 0.671852 0.740685i \(-0.265499\pi\)
0.671852 + 0.740685i \(0.265499\pi\)
\(30\) 0 0
\(31\) 6.47214 1.16243 0.581215 0.813750i \(-0.302578\pi\)
0.581215 + 0.813750i \(0.302578\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.23607 −0.208934
\(36\) 0 0
\(37\) −4.47214 −0.735215 −0.367607 0.929981i \(-0.619823\pi\)
−0.367607 + 0.929981i \(0.619823\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −3.23607 −0.472029 −0.236015 0.971750i \(-0.575841\pi\)
−0.236015 + 0.971750i \(0.575841\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −3.23607 −0.444508 −0.222254 0.974989i \(-0.571341\pi\)
−0.222254 + 0.974989i \(0.571341\pi\)
\(54\) 0 0
\(55\) −5.52786 −0.745377
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −4.00000 −0.520756 −0.260378 0.965507i \(-0.583847\pi\)
−0.260378 + 0.965507i \(0.583847\pi\)
\(60\) 0 0
\(61\) −3.52786 −0.451697 −0.225848 0.974162i \(-0.572515\pi\)
−0.225848 + 0.974162i \(0.572515\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −5.52786 −0.685647
\(66\) 0 0
\(67\) −1.52786 −0.186658 −0.0933292 0.995635i \(-0.529751\pi\)
−0.0933292 + 0.995635i \(0.529751\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 5.23607 0.621407 0.310703 0.950507i \(-0.399435\pi\)
0.310703 + 0.950507i \(0.399435\pi\)
\(72\) 0 0
\(73\) 4.47214 0.523424 0.261712 0.965146i \(-0.415713\pi\)
0.261712 + 0.965146i \(0.415713\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 4.47214 0.509647
\(78\) 0 0
\(79\) −12.0000 −1.35011 −0.675053 0.737769i \(-0.735879\pi\)
−0.675053 + 0.737769i \(0.735879\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −5.70820 −0.626557 −0.313278 0.949661i \(-0.601427\pi\)
−0.313278 + 0.949661i \(0.601427\pi\)
\(84\) 0 0
\(85\) −1.52786 −0.165720
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 10.9443 1.16009 0.580045 0.814584i \(-0.303035\pi\)
0.580045 + 0.814584i \(0.303035\pi\)
\(90\) 0 0
\(91\) 4.47214 0.468807
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1.23607 0.126818
\(96\) 0 0
\(97\) 3.52786 0.358200 0.179100 0.983831i \(-0.442681\pi\)
0.179100 + 0.983831i \(0.442681\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 18.1803 1.80901 0.904506 0.426461i \(-0.140240\pi\)
0.904506 + 0.426461i \(0.140240\pi\)
\(102\) 0 0
\(103\) −8.94427 −0.881305 −0.440653 0.897678i \(-0.645253\pi\)
−0.440653 + 0.897678i \(0.645253\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −7.70820 −0.745180 −0.372590 0.927996i \(-0.621530\pi\)
−0.372590 + 0.927996i \(0.621530\pi\)
\(108\) 0 0
\(109\) 14.9443 1.43140 0.715701 0.698407i \(-0.246107\pi\)
0.715701 + 0.698407i \(0.246107\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 15.2361 1.43329 0.716644 0.697439i \(-0.245677\pi\)
0.716644 + 0.697439i \(0.245677\pi\)
\(114\) 0 0
\(115\) −0.583592 −0.0544202
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1.23607 0.113310
\(120\) 0 0
\(121\) 9.00000 0.818182
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −10.4721 −0.936656
\(126\) 0 0
\(127\) −10.4721 −0.929252 −0.464626 0.885507i \(-0.653811\pi\)
−0.464626 + 0.885507i \(0.653811\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 8.76393 0.765708 0.382854 0.923809i \(-0.374941\pi\)
0.382854 + 0.923809i \(0.374941\pi\)
\(132\) 0 0
\(133\) −1.00000 −0.0867110
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −0.944272 −0.0806746 −0.0403373 0.999186i \(-0.512843\pi\)
−0.0403373 + 0.999186i \(0.512843\pi\)
\(138\) 0 0
\(139\) −1.52786 −0.129592 −0.0647959 0.997899i \(-0.520640\pi\)
−0.0647959 + 0.997899i \(0.520640\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 20.0000 1.67248
\(144\) 0 0
\(145\) 8.94427 0.742781
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 10.4721 0.857911 0.428955 0.903326i \(-0.358882\pi\)
0.428955 + 0.903326i \(0.358882\pi\)
\(150\) 0 0
\(151\) 20.0000 1.62758 0.813788 0.581161i \(-0.197401\pi\)
0.813788 + 0.581161i \(0.197401\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 8.00000 0.642575
\(156\) 0 0
\(157\) 22.3607 1.78458 0.892288 0.451466i \(-0.149099\pi\)
0.892288 + 0.451466i \(0.149099\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0.472136 0.0372095
\(162\) 0 0
\(163\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −2.47214 −0.191300 −0.0956498 0.995415i \(-0.530493\pi\)
−0.0956498 + 0.995415i \(0.530493\pi\)
\(168\) 0 0
\(169\) 7.00000 0.538462
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 6.94427 0.527963 0.263982 0.964528i \(-0.414964\pi\)
0.263982 + 0.964528i \(0.414964\pi\)
\(174\) 0 0
\(175\) 3.47214 0.262469
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 7.70820 0.576138 0.288069 0.957610i \(-0.406987\pi\)
0.288069 + 0.957610i \(0.406987\pi\)
\(180\) 0 0
\(181\) 4.47214 0.332411 0.166206 0.986091i \(-0.446848\pi\)
0.166206 + 0.986091i \(0.446848\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −5.52786 −0.406417
\(186\) 0 0
\(187\) 5.52786 0.404237
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 24.4721 1.77074 0.885371 0.464886i \(-0.153905\pi\)
0.885371 + 0.464886i \(0.153905\pi\)
\(192\) 0 0
\(193\) −0.472136 −0.0339851 −0.0169925 0.999856i \(-0.505409\pi\)
−0.0169925 + 0.999856i \(0.505409\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4.00000 0.284988 0.142494 0.989796i \(-0.454488\pi\)
0.142494 + 0.989796i \(0.454488\pi\)
\(198\) 0 0
\(199\) 4.94427 0.350490 0.175245 0.984525i \(-0.443928\pi\)
0.175245 + 0.984525i \(0.443928\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −7.23607 −0.507872
\(204\) 0 0
\(205\) −2.47214 −0.172661
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −4.47214 −0.309344
\(210\) 0 0
\(211\) −6.47214 −0.445560 −0.222780 0.974869i \(-0.571513\pi\)
−0.222780 + 0.974869i \(0.571513\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 9.88854 0.674393
\(216\) 0 0
\(217\) −6.47214 −0.439357
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 5.52786 0.371844
\(222\) 0 0
\(223\) −23.4164 −1.56808 −0.784039 0.620711i \(-0.786844\pi\)
−0.784039 + 0.620711i \(0.786844\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −15.4164 −1.02322 −0.511611 0.859217i \(-0.670951\pi\)
−0.511611 + 0.859217i \(0.670951\pi\)
\(228\) 0 0
\(229\) 22.9443 1.51620 0.758100 0.652138i \(-0.226128\pi\)
0.758100 + 0.652138i \(0.226128\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −2.47214 −0.161955 −0.0809775 0.996716i \(-0.525804\pi\)
−0.0809775 + 0.996716i \(0.525804\pi\)
\(234\) 0 0
\(235\) −4.00000 −0.260931
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −5.05573 −0.327028 −0.163514 0.986541i \(-0.552283\pi\)
−0.163514 + 0.986541i \(0.552283\pi\)
\(240\) 0 0
\(241\) 0.472136 0.0304130 0.0152065 0.999884i \(-0.495159\pi\)
0.0152065 + 0.999884i \(0.495159\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1.23607 0.0789695
\(246\) 0 0
\(247\) −4.47214 −0.284555
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −0.180340 −0.0113830 −0.00569148 0.999984i \(-0.501812\pi\)
−0.00569148 + 0.999984i \(0.501812\pi\)
\(252\) 0 0
\(253\) 2.11146 0.132746
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 12.4721 0.777990 0.388995 0.921240i \(-0.372822\pi\)
0.388995 + 0.921240i \(0.372822\pi\)
\(258\) 0 0
\(259\) 4.47214 0.277885
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 2.94427 0.181552 0.0907758 0.995871i \(-0.471065\pi\)
0.0907758 + 0.995871i \(0.471065\pi\)
\(264\) 0 0
\(265\) −4.00000 −0.245718
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 15.5279 0.946751 0.473375 0.880861i \(-0.343035\pi\)
0.473375 + 0.880861i \(0.343035\pi\)
\(270\) 0 0
\(271\) −5.52786 −0.335794 −0.167897 0.985805i \(-0.553698\pi\)
−0.167897 + 0.985805i \(0.553698\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 15.5279 0.936365
\(276\) 0 0
\(277\) −4.47214 −0.268705 −0.134352 0.990934i \(-0.542895\pi\)
−0.134352 + 0.990934i \(0.542895\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 8.18034 0.487998 0.243999 0.969775i \(-0.421541\pi\)
0.243999 + 0.969775i \(0.421541\pi\)
\(282\) 0 0
\(283\) −7.05573 −0.419419 −0.209710 0.977764i \(-0.567252\pi\)
−0.209710 + 0.977764i \(0.567252\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2.00000 0.118056
\(288\) 0 0
\(289\) −15.4721 −0.910126
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 26.0000 1.51894 0.759468 0.650545i \(-0.225459\pi\)
0.759468 + 0.650545i \(0.225459\pi\)
\(294\) 0 0
\(295\) −4.94427 −0.287867
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2.11146 0.122109
\(300\) 0 0
\(301\) −8.00000 −0.461112
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −4.36068 −0.249692
\(306\) 0 0
\(307\) 17.5279 1.00037 0.500184 0.865919i \(-0.333266\pi\)
0.500184 + 0.865919i \(0.333266\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −16.1803 −0.917503 −0.458751 0.888565i \(-0.651703\pi\)
−0.458751 + 0.888565i \(0.651703\pi\)
\(312\) 0 0
\(313\) 3.52786 0.199407 0.0997033 0.995017i \(-0.468211\pi\)
0.0997033 + 0.995017i \(0.468211\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 13.1246 0.737152 0.368576 0.929598i \(-0.379845\pi\)
0.368576 + 0.929598i \(0.379845\pi\)
\(318\) 0 0
\(319\) −32.3607 −1.81185
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1.23607 −0.0687767
\(324\) 0 0
\(325\) 15.5279 0.861331
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 3.23607 0.178410
\(330\) 0 0
\(331\) −9.88854 −0.543524 −0.271762 0.962365i \(-0.587606\pi\)
−0.271762 + 0.962365i \(0.587606\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −1.88854 −0.103182
\(336\) 0 0
\(337\) 2.94427 0.160385 0.0801924 0.996779i \(-0.474447\pi\)
0.0801924 + 0.996779i \(0.474447\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −28.9443 −1.56742
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 30.0000 1.61048 0.805242 0.592946i \(-0.202035\pi\)
0.805242 + 0.592946i \(0.202035\pi\)
\(348\) 0 0
\(349\) −24.8328 −1.32927 −0.664635 0.747168i \(-0.731413\pi\)
−0.664635 + 0.747168i \(0.731413\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 27.7082 1.47476 0.737379 0.675479i \(-0.236063\pi\)
0.737379 + 0.675479i \(0.236063\pi\)
\(354\) 0 0
\(355\) 6.47214 0.343505
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −2.58359 −0.136357 −0.0681784 0.997673i \(-0.521719\pi\)
−0.0681784 + 0.997673i \(0.521719\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 5.52786 0.289342
\(366\) 0 0
\(367\) 4.94427 0.258089 0.129044 0.991639i \(-0.458809\pi\)
0.129044 + 0.991639i \(0.458809\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 3.23607 0.168008
\(372\) 0 0
\(373\) −14.9443 −0.773785 −0.386893 0.922125i \(-0.626452\pi\)
−0.386893 + 0.922125i \(0.626452\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −32.3607 −1.66666
\(378\) 0 0
\(379\) −20.9443 −1.07583 −0.537917 0.842997i \(-0.680789\pi\)
−0.537917 + 0.842997i \(0.680789\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −1.52786 −0.0780702 −0.0390351 0.999238i \(-0.512428\pi\)
−0.0390351 + 0.999238i \(0.512428\pi\)
\(384\) 0 0
\(385\) 5.52786 0.281726
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −4.58359 −0.232397 −0.116199 0.993226i \(-0.537071\pi\)
−0.116199 + 0.993226i \(0.537071\pi\)
\(390\) 0 0
\(391\) 0.583592 0.0295135
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −14.8328 −0.746320
\(396\) 0 0
\(397\) 23.8885 1.19893 0.599466 0.800400i \(-0.295380\pi\)
0.599466 + 0.800400i \(0.295380\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 7.81966 0.390495 0.195248 0.980754i \(-0.437449\pi\)
0.195248 + 0.980754i \(0.437449\pi\)
\(402\) 0 0
\(403\) −28.9443 −1.44182
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 20.0000 0.991363
\(408\) 0 0
\(409\) 22.3607 1.10566 0.552832 0.833293i \(-0.313547\pi\)
0.552832 + 0.833293i \(0.313547\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 4.00000 0.196827
\(414\) 0 0
\(415\) −7.05573 −0.346352
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 21.1246 1.03200 0.516002 0.856587i \(-0.327420\pi\)
0.516002 + 0.856587i \(0.327420\pi\)
\(420\) 0 0
\(421\) −39.3050 −1.91561 −0.957803 0.287425i \(-0.907201\pi\)
−0.957803 + 0.287425i \(0.907201\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 4.29180 0.208183
\(426\) 0 0
\(427\) 3.52786 0.170725
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 36.0689 1.73738 0.868688 0.495359i \(-0.164963\pi\)
0.868688 + 0.495359i \(0.164963\pi\)
\(432\) 0 0
\(433\) −0.472136 −0.0226894 −0.0113447 0.999936i \(-0.503611\pi\)
−0.0113447 + 0.999936i \(0.503611\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −0.472136 −0.0225853
\(438\) 0 0
\(439\) −39.4164 −1.88124 −0.940621 0.339458i \(-0.889756\pi\)
−0.940621 + 0.339458i \(0.889756\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 15.8885 0.754887 0.377444 0.926033i \(-0.376803\pi\)
0.377444 + 0.926033i \(0.376803\pi\)
\(444\) 0 0
\(445\) 13.5279 0.641282
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −15.2361 −0.719035 −0.359517 0.933138i \(-0.617059\pi\)
−0.359517 + 0.933138i \(0.617059\pi\)
\(450\) 0 0
\(451\) 8.94427 0.421169
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 5.52786 0.259150
\(456\) 0 0
\(457\) 21.4164 1.00182 0.500909 0.865500i \(-0.332999\pi\)
0.500909 + 0.865500i \(0.332999\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 5.23607 0.243868 0.121934 0.992538i \(-0.461090\pi\)
0.121934 + 0.992538i \(0.461090\pi\)
\(462\) 0 0
\(463\) −25.8885 −1.20314 −0.601571 0.798819i \(-0.705458\pi\)
−0.601571 + 0.798819i \(0.705458\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −24.1803 −1.11893 −0.559466 0.828853i \(-0.688994\pi\)
−0.559466 + 0.828853i \(0.688994\pi\)
\(468\) 0 0
\(469\) 1.52786 0.0705502
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −35.7771 −1.64503
\(474\) 0 0
\(475\) −3.47214 −0.159313
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 21.1246 0.965208 0.482604 0.875839i \(-0.339691\pi\)
0.482604 + 0.875839i \(0.339691\pi\)
\(480\) 0 0
\(481\) 20.0000 0.911922
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 4.36068 0.198008
\(486\) 0 0
\(487\) 23.4164 1.06110 0.530549 0.847654i \(-0.321986\pi\)
0.530549 + 0.847654i \(0.321986\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 30.0000 1.35388 0.676941 0.736038i \(-0.263305\pi\)
0.676941 + 0.736038i \(0.263305\pi\)
\(492\) 0 0
\(493\) −8.94427 −0.402830
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −5.23607 −0.234870
\(498\) 0 0
\(499\) 37.8885 1.69612 0.848062 0.529897i \(-0.177769\pi\)
0.848062 + 0.529897i \(0.177769\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −28.1803 −1.25650 −0.628250 0.778012i \(-0.716228\pi\)
−0.628250 + 0.778012i \(0.716228\pi\)
\(504\) 0 0
\(505\) 22.4721 0.999997
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 31.5279 1.39745 0.698724 0.715391i \(-0.253752\pi\)
0.698724 + 0.715391i \(0.253752\pi\)
\(510\) 0 0
\(511\) −4.47214 −0.197836
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −11.0557 −0.487174
\(516\) 0 0
\(517\) 14.4721 0.636484
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.41641 −0.0620540 −0.0310270 0.999519i \(-0.509878\pi\)
−0.0310270 + 0.999519i \(0.509878\pi\)
\(522\) 0 0
\(523\) −21.5279 −0.941348 −0.470674 0.882307i \(-0.655989\pi\)
−0.470674 + 0.882307i \(0.655989\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −8.00000 −0.348485
\(528\) 0 0
\(529\) −22.7771 −0.990308
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 8.94427 0.387419
\(534\) 0 0
\(535\) −9.52786 −0.411925
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −4.47214 −0.192629
\(540\) 0 0
\(541\) −35.8885 −1.54297 −0.771485 0.636248i \(-0.780485\pi\)
−0.771485 + 0.636248i \(0.780485\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 18.4721 0.791259
\(546\) 0 0
\(547\) −14.8328 −0.634205 −0.317103 0.948391i \(-0.602710\pi\)
−0.317103 + 0.948391i \(0.602710\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 7.23607 0.308267
\(552\) 0 0
\(553\) 12.0000 0.510292
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0.583592 0.0247276 0.0123638 0.999924i \(-0.496064\pi\)
0.0123638 + 0.999924i \(0.496064\pi\)
\(558\) 0 0
\(559\) −35.7771 −1.51321
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 23.4164 0.986884 0.493442 0.869779i \(-0.335739\pi\)
0.493442 + 0.869779i \(0.335739\pi\)
\(564\) 0 0
\(565\) 18.8328 0.792303
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −25.7082 −1.07774 −0.538872 0.842388i \(-0.681149\pi\)
−0.538872 + 0.842388i \(0.681149\pi\)
\(570\) 0 0
\(571\) 5.88854 0.246428 0.123214 0.992380i \(-0.460680\pi\)
0.123214 + 0.992380i \(0.460680\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.63932 0.0683644
\(576\) 0 0
\(577\) −25.4164 −1.05810 −0.529049 0.848591i \(-0.677451\pi\)
−0.529049 + 0.848591i \(0.677451\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 5.70820 0.236816
\(582\) 0 0
\(583\) 14.4721 0.599375
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −22.2918 −0.920081 −0.460040 0.887898i \(-0.652165\pi\)
−0.460040 + 0.887898i \(0.652165\pi\)
\(588\) 0 0
\(589\) 6.47214 0.266680
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −39.7082 −1.63062 −0.815310 0.579024i \(-0.803434\pi\)
−0.815310 + 0.579024i \(0.803434\pi\)
\(594\) 0 0
\(595\) 1.52786 0.0626363
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 21.5967 0.882419 0.441210 0.897404i \(-0.354550\pi\)
0.441210 + 0.897404i \(0.354550\pi\)
\(600\) 0 0
\(601\) 18.5836 0.758041 0.379020 0.925388i \(-0.376261\pi\)
0.379020 + 0.925388i \(0.376261\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 11.1246 0.452280
\(606\) 0 0
\(607\) −16.0000 −0.649420 −0.324710 0.945814i \(-0.605267\pi\)
−0.324710 + 0.945814i \(0.605267\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 14.4721 0.585480
\(612\) 0 0
\(613\) 10.3607 0.418464 0.209232 0.977866i \(-0.432904\pi\)
0.209232 + 0.977866i \(0.432904\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 48.9443 1.97042 0.985211 0.171345i \(-0.0548113\pi\)
0.985211 + 0.171345i \(0.0548113\pi\)
\(618\) 0 0
\(619\) 4.58359 0.184230 0.0921151 0.995748i \(-0.470637\pi\)
0.0921151 + 0.995748i \(0.470637\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −10.9443 −0.438473
\(624\) 0 0
\(625\) 4.41641 0.176656
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 5.52786 0.220410
\(630\) 0 0
\(631\) −16.9443 −0.674541 −0.337270 0.941408i \(-0.609504\pi\)
−0.337270 + 0.941408i \(0.609504\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −12.9443 −0.513678
\(636\) 0 0
\(637\) −4.47214 −0.177192
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 33.7082 1.33139 0.665697 0.746222i \(-0.268134\pi\)
0.665697 + 0.746222i \(0.268134\pi\)
\(642\) 0 0
\(643\) 15.0557 0.593740 0.296870 0.954918i \(-0.404057\pi\)
0.296870 + 0.954918i \(0.404057\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 6.65248 0.261536 0.130768 0.991413i \(-0.458256\pi\)
0.130768 + 0.991413i \(0.458256\pi\)
\(648\) 0 0
\(649\) 17.8885 0.702187
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 6.11146 0.239160 0.119580 0.992825i \(-0.461845\pi\)
0.119580 + 0.992825i \(0.461845\pi\)
\(654\) 0 0
\(655\) 10.8328 0.423273
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 43.7082 1.70263 0.851315 0.524655i \(-0.175806\pi\)
0.851315 + 0.524655i \(0.175806\pi\)
\(660\) 0 0
\(661\) 25.4164 0.988584 0.494292 0.869296i \(-0.335427\pi\)
0.494292 + 0.869296i \(0.335427\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1.23607 −0.0479327
\(666\) 0 0
\(667\) −3.41641 −0.132284
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 15.7771 0.609068
\(672\) 0 0
\(673\) −36.2492 −1.39730 −0.698652 0.715461i \(-0.746217\pi\)
−0.698652 + 0.715461i \(0.746217\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −9.41641 −0.361902 −0.180951 0.983492i \(-0.557918\pi\)
−0.180951 + 0.983492i \(0.557918\pi\)
\(678\) 0 0
\(679\) −3.52786 −0.135387
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 18.7639 0.717982 0.358991 0.933341i \(-0.383121\pi\)
0.358991 + 0.933341i \(0.383121\pi\)
\(684\) 0 0
\(685\) −1.16718 −0.0445958
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 14.4721 0.551344
\(690\) 0 0
\(691\) 22.4721 0.854880 0.427440 0.904044i \(-0.359415\pi\)
0.427440 + 0.904044i \(0.359415\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.88854 −0.0716366
\(696\) 0 0
\(697\) 2.47214 0.0936388
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −14.8328 −0.560228 −0.280114 0.959967i \(-0.590372\pi\)
−0.280114 + 0.959967i \(0.590372\pi\)
\(702\) 0 0
\(703\) −4.47214 −0.168670
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −18.1803 −0.683742
\(708\) 0 0
\(709\) −36.2492 −1.36137 −0.680684 0.732577i \(-0.738317\pi\)
−0.680684 + 0.732577i \(0.738317\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −3.05573 −0.114438
\(714\) 0 0
\(715\) 24.7214 0.924526
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 41.1246 1.53369 0.766845 0.641833i \(-0.221826\pi\)
0.766845 + 0.641833i \(0.221826\pi\)
\(720\) 0 0
\(721\) 8.94427 0.333102
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −25.1246 −0.933105
\(726\) 0 0
\(727\) 4.36068 0.161729 0.0808643 0.996725i \(-0.474232\pi\)
0.0808643 + 0.996725i \(0.474232\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −9.88854 −0.365741
\(732\) 0 0
\(733\) 11.5279 0.425791 0.212896 0.977075i \(-0.431711\pi\)
0.212896 + 0.977075i \(0.431711\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 6.83282 0.251690
\(738\) 0 0
\(739\) 17.8885 0.658041 0.329020 0.944323i \(-0.393282\pi\)
0.329020 + 0.944323i \(0.393282\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −4.65248 −0.170683 −0.0853414 0.996352i \(-0.527198\pi\)
−0.0853414 + 0.996352i \(0.527198\pi\)
\(744\) 0 0
\(745\) 12.9443 0.474241
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 7.70820 0.281652
\(750\) 0 0
\(751\) 18.8328 0.687219 0.343610 0.939113i \(-0.388350\pi\)
0.343610 + 0.939113i \(0.388350\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 24.7214 0.899702
\(756\) 0 0
\(757\) 19.8885 0.722861 0.361431 0.932399i \(-0.382288\pi\)
0.361431 + 0.932399i \(0.382288\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −38.7639 −1.40519 −0.702596 0.711589i \(-0.747976\pi\)
−0.702596 + 0.711589i \(0.747976\pi\)
\(762\) 0 0
\(763\) −14.9443 −0.541019
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 17.8885 0.645918
\(768\) 0 0
\(769\) −14.3607 −0.517859 −0.258930 0.965896i \(-0.583370\pi\)
−0.258930 + 0.965896i \(0.583370\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −31.8885 −1.14695 −0.573476 0.819223i \(-0.694405\pi\)
−0.573476 + 0.819223i \(0.694405\pi\)
\(774\) 0 0
\(775\) −22.4721 −0.807223
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −2.00000 −0.0716574
\(780\) 0 0
\(781\) −23.4164 −0.837905
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 27.6393 0.986490
\(786\) 0 0
\(787\) −16.5836 −0.591141 −0.295571 0.955321i \(-0.595510\pi\)
−0.295571 + 0.955321i \(0.595510\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −15.2361 −0.541732
\(792\) 0 0
\(793\) 15.7771 0.560261
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −25.0557 −0.887519 −0.443760 0.896146i \(-0.646356\pi\)
−0.443760 + 0.896146i \(0.646356\pi\)
\(798\) 0 0
\(799\) 4.00000 0.141510
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −20.0000 −0.705785
\(804\) 0 0
\(805\) 0.583592 0.0205689
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 24.0000 0.843795 0.421898 0.906644i \(-0.361364\pi\)
0.421898 + 0.906644i \(0.361364\pi\)
\(810\) 0 0
\(811\) 6.83282 0.239933 0.119966 0.992778i \(-0.461721\pi\)
0.119966 + 0.992778i \(0.461721\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 8.00000 0.279885
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 28.3607 0.989795 0.494897 0.868951i \(-0.335206\pi\)
0.494897 + 0.868951i \(0.335206\pi\)
\(822\) 0 0
\(823\) −42.8328 −1.49306 −0.746529 0.665353i \(-0.768281\pi\)
−0.746529 + 0.665353i \(0.768281\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −26.7639 −0.930673 −0.465337 0.885134i \(-0.654067\pi\)
−0.465337 + 0.885134i \(0.654067\pi\)
\(828\) 0 0
\(829\) −16.4721 −0.572101 −0.286050 0.958215i \(-0.592343\pi\)
−0.286050 + 0.958215i \(0.592343\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −1.23607 −0.0428272
\(834\) 0 0
\(835\) −3.05573 −0.105748
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −4.00000 −0.138095 −0.0690477 0.997613i \(-0.521996\pi\)
−0.0690477 + 0.997613i \(0.521996\pi\)
\(840\) 0 0
\(841\) 23.3607 0.805541
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 8.65248 0.297654
\(846\) 0 0
\(847\) −9.00000 −0.309244
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 2.11146 0.0723798
\(852\) 0 0
\(853\) 33.7771 1.15651 0.578253 0.815858i \(-0.303735\pi\)
0.578253 + 0.815858i \(0.303735\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 28.8328 0.984910 0.492455 0.870338i \(-0.336100\pi\)
0.492455 + 0.870338i \(0.336100\pi\)
\(858\) 0 0
\(859\) 0.944272 0.0322181 0.0161091 0.999870i \(-0.494872\pi\)
0.0161091 + 0.999870i \(0.494872\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −34.1803 −1.16351 −0.581756 0.813363i \(-0.697634\pi\)
−0.581756 + 0.813363i \(0.697634\pi\)
\(864\) 0 0
\(865\) 8.58359 0.291851
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 53.6656 1.82048
\(870\) 0 0
\(871\) 6.83282 0.231521
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 10.4721 0.354023
\(876\) 0 0
\(877\) 39.8885 1.34694 0.673470 0.739214i \(-0.264803\pi\)
0.673470 + 0.739214i \(0.264803\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 11.7082 0.394459 0.197230 0.980357i \(-0.436806\pi\)
0.197230 + 0.980357i \(0.436806\pi\)
\(882\) 0 0
\(883\) 18.1115 0.609499 0.304750 0.952433i \(-0.401427\pi\)
0.304750 + 0.952433i \(0.401427\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −3.63932 −0.122196 −0.0610982 0.998132i \(-0.519460\pi\)
−0.0610982 + 0.998132i \(0.519460\pi\)
\(888\) 0 0
\(889\) 10.4721 0.351224
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −3.23607 −0.108291
\(894\) 0 0
\(895\) 9.52786 0.318481
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 46.8328 1.56196
\(900\) 0 0
\(901\) 4.00000 0.133259
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 5.52786 0.183752
\(906\) 0 0
\(907\) 12.5836 0.417831 0.208916 0.977934i \(-0.433007\pi\)
0.208916 + 0.977934i \(0.433007\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −35.1246 −1.16373 −0.581865 0.813285i \(-0.697677\pi\)
−0.581865 + 0.813285i \(0.697677\pi\)
\(912\) 0 0
\(913\) 25.5279 0.844849
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −8.76393 −0.289411
\(918\) 0 0
\(919\) 25.8885 0.853984 0.426992 0.904255i \(-0.359573\pi\)
0.426992 + 0.904255i \(0.359573\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −23.4164 −0.770760
\(924\) 0 0
\(925\) 15.5279 0.510553
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −33.0132 −1.08313 −0.541563 0.840660i \(-0.682167\pi\)
−0.541563 + 0.840660i \(0.682167\pi\)
\(930\) 0 0
\(931\) 1.00000 0.0327737
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 6.83282 0.223457
\(936\) 0 0
\(937\) −22.0000 −0.718709 −0.359354 0.933201i \(-0.617003\pi\)
−0.359354 + 0.933201i \(0.617003\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −15.3050 −0.498927 −0.249464 0.968384i \(-0.580254\pi\)
−0.249464 + 0.968384i \(0.580254\pi\)
\(942\) 0 0
\(943\) 0.944272 0.0307497
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −28.4721 −0.925220 −0.462610 0.886562i \(-0.653087\pi\)
−0.462610 + 0.886562i \(0.653087\pi\)
\(948\) 0 0
\(949\) −20.0000 −0.649227
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 52.5410 1.70197 0.850985 0.525190i \(-0.176006\pi\)
0.850985 + 0.525190i \(0.176006\pi\)
\(954\) 0 0
\(955\) 30.2492 0.978842
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0.944272 0.0304921
\(960\) 0 0
\(961\) 10.8885 0.351243
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −0.583592 −0.0187865
\(966\) 0 0
\(967\) 34.8328 1.12015 0.560074 0.828443i \(-0.310773\pi\)
0.560074 + 0.828443i \(0.310773\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −14.8328 −0.476008 −0.238004 0.971264i \(-0.576493\pi\)
−0.238004 + 0.971264i \(0.576493\pi\)
\(972\) 0 0
\(973\) 1.52786 0.0489811
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −5.12461 −0.163951 −0.0819754 0.996634i \(-0.526123\pi\)
−0.0819754 + 0.996634i \(0.526123\pi\)
\(978\) 0 0
\(979\) −48.9443 −1.56427
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 19.0557 0.607783 0.303892 0.952707i \(-0.401714\pi\)
0.303892 + 0.952707i \(0.401714\pi\)
\(984\) 0 0
\(985\) 4.94427 0.157538
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −3.77709 −0.120104
\(990\) 0 0
\(991\) −0.583592 −0.0185384 −0.00926921 0.999957i \(-0.502951\pi\)
−0.00926921 + 0.999957i \(0.502951\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 6.11146 0.193746
\(996\) 0 0
\(997\) −10.3607 −0.328126 −0.164063 0.986450i \(-0.552460\pi\)
−0.164063 + 0.986450i \(0.552460\pi\)
\(998\) 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.be.1.2 2
3.2 odd 2 9576.2.a.bq.1.1 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
9576.2.a.be.1.2 2 1.1 even 1 trivial
9576.2.a.bq.1.1 yes 2 3.2 odd 2