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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -3, 'A8': 0, 'A9': 0, 'Lhash': '1682911664492427065', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-1.1338934190276817, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 373.6998814595924, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]], [13, [1, 1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '46800.1', 'coefficient_field': '1.1.1.1', 'conductor': 46800, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1], [1], [1], [1, 3, 7], [1, 1, 11], [1, 1], [1, 5, 17], [1, -8, 19], [1, 0, 23], [1, 1, 29], [1, 3, 31], [1, -8, 37], [1, -2, 41], [1, -8, 43], [1, -11, 47], [1, 11, 53], [1, -5, 59], [1, -1, 61], [1, -3, 67], [1, -16, 71], [1, -4, 73], [1, 12, 79], [1, -3, 83], [1, 0, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 21, 'label': '2-46800-1.1-c1-0-21', 'leading_term': '1.41978730912', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'EllipticCurve/Q/46800/x', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.419787309117506, 0.9312998601668272, -0.3003818177386976, -1.522456619513928, -1.668147534736356, -0.1517108362962858, 2.318947078305432, 3.966555813905135, 3.446336583239041, 1.323643638107064, -0.2585846330919135, 0.1955422720289192, 1.75127412655654, 2.059740551942975, 0.3429400084745155, -1.346881604390659, -0.6326977891512497, 1.818596735643403, 2.748401038802364, 0.5410198798420793, -2.340582283073304, -2.481708241866355, -0.2296871020974288, 0.7917064865193106, -1.020929933526839, -2.884356796588429, -1.950191392885404, 0.193774439722125, 0.04609263769356996, -2.035968274760805, -2.264886935681365, 0.1690973039659016, 1.173714469065468, -1.848527620339955, -5.342883723060595, -4.713975505015897, -1.294765059311594, 0.2280699777720228, -0.4916193108688889, 0.2252306103547459, 2.620679396360396, 2.548150885220675, -0.8486752096531281, -2.785105091581337, -0.8738246563504295, 0.5151012001253915, -2.0498716647421, -4.714738564190874, -3.018373203622666, 0.2044039060583902, 0.02933753784940479, -1.878128034399364, -1.085030423598336, 0.9327240317384036, 0.04112059778130108, -1.8575967728368, -0.238573090079836, 2.585806946137895, 0.9597960989288716, -3.221458306806377, -3.179409077573519, 0.7534776605044305, 2.205677690703985, 0.4323555913287338, 0.1149209956301498, 0.9406160545558627, -1.275883248095048, -4.501015941376032, -3.224534808672848, 0.3620766735584963, -0.1714415581087217, -3.166326603291468, -2.271953525298273, 0.9541759691454655, 0.555443483403842, -1.599571484309497, -0.008824332008174132, 2.792528048088649, 1.453818546415193, -1.20960209608574, -0.5488012118995305, 0.2170028981744041, -1.944623045388383, -1.748130782119589, 3.584902207583091, 6.676177053148827, 3.120898141671216, -0.4139274492869588, 0.5760651046664158, 1.278447297508009, -0.3213451332609743, 0.2942888304392325, 2.226221920111603, -0.1902841505324358, -4.250205469300855, -3.006504638452815, 0.5095869163656297, -0.3345353488980492, -2.009300568376966, 0.7077965385084357, 2.799659752375138, -0.1197557700392919, -2.218143370157791, -0.2149444139707171, 0.03338681026733553, -2.711962877129555, -2.459855275742268, 0.05072163461831242, -0.4737961579232308, -0.412933922552341, 5.089094757414899, 8.973405032836286, 4.694810538950666, -0.7023079574777127, -0.6674728537665017, 0.1614855662328103, -0.732085976251351, 0.7685565567348884, 2.501155196124645, -0.7360360452213408, -3.703717984248853], 'positive_zeros': ['0.4457739248832207', '1.266725974943807', '2.431099096553462', '2.711216604885336', '3.539043005343747', '4.070078705353342', '4.791426614117790', '5.526346694520244', '5.892748024528998', '6.719015947131495', '7.006927107238403', '7.733809486944402', '8.130671854860632', '9.145853598386566', '9.355122299998301', '9.720785123676934', '10.44336531584675', '11.08992229009291', '11.33883984915471', '12.22594087512269', '12.50380794633016', '13.11443484895200', '13.50444216868461', '14.01784929934627', '14.55557084724605', '15.20139161564931', '15.83521991608143', '15.96635535090362', '16.40414261956959', '17.21435232385612', '17.48474688845691', '18.16162477021367', '18.55432074295335', '19.00065675127193', '19.61314588973012'], 'prelabel': '2-46800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 19.331318668409363, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1682911664492427065, 'z1': {'__RealLiteral__': 0, 'data': '0.4457739248832207', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.266725974943807', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.431099096553462', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 373.6998814595924, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 46800, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -3, 0, 0, 0, -1, 0, -1, 0, 0, 0, -5, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -3, 0, 0, 0, 0, 0, 8, 0, 0, 0, 2, 0, 8, 0, 0, 0, 11, 0, 2, 0, 0, 0, -11, 0, 0, 0, 0, 0, 5, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 16, 0, 4, 0, 0, 0, 3, 0, -12, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2, 0, 0, 0], 'euler11': [1, 1, 11], 'euler13': [1, 1, 0], 'euler17': [1, 5, 17], 'euler19': [1, -8, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, 1, 29], 'euler3': [1, 0, 0], 'euler31': [1, 3, 31], 'euler37': [1, -8, 37], 'euler41': [1, -2, 41], 'euler43': [1, -8, 43], 'euler47': [1, -11, 47], 'euler5': [1, 0, 0], 'euler53': [1, 11, 53], 'euler59': [1, -5, 59], 'euler61': [1, -1, 61], 'euler67': [1, -3, 67], 'euler7': [1, 3, 7], 'euler71': [1, -16, 71], 'euler73': [1, -4, 73], 'euler79': [1, 12, 79], 'euler83': [1, -3, 83], 'euler89': [1, 0, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 3, 7], [1, 1, 11], [1, 1, 0], [1, 5, 17], [1, -8, 19], [1, 0, 23], [1, 1, 29], [1, 3, 31], [1, -8, 37], [1, -2, 41], [1, -8, 43], [1, -11, 47], [1, 11, 53], [1, -5, 59], [1, -1, 61], [1, -3, 67], [1, -16, 71], [1, -4, 73], [1, 12, 79], [1, -3, 83], [1, 0, 89], [1, -2, 97]], 'index': 21, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/46800/x'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-46800-1.1-c1-0-21', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-46800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 19.331318668409363, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1682911664492427065, 'z1': {'__RealLiteral__': 0, 'data': '0.4457739248832207', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1682911664492427065', 'Lhash_array': ['1682911664492427065'], 'label': '2-46800-1.1-c1-0-21', 'type': 'ECQ', 'url': 'EllipticCurve/Q/46800/x'}