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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 4, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 6, 'Lhash': '1354001870116862942,2170957549448318893', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [2.309401076758503, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [2.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.892524287407611, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [19, [1, 2, 1]]], 'bad_primes': [2, 19], 'central_character': '92416.1', 'coefficient_field': '1.1.1.1', 'conductor': 92416, 'conductor_radical': 38, 'degree': 4, 'euler_factors': [[1], [1, -4, 10, -12, 9], [1, 0, 9, 0, 25], [1, 0, 5, 0, 49], [1, -10, 47, -110, 121], [1, 0, 10, 0, 169], [1, 6, 43, 102, 289], [1, 2, 1], [1, 0, -18, 0, 529], [1, 0, 54, 0, 841], [1, 0, 46, 0, 961], [1, 0, -26, 0, 1369], [1, -20, 182, -820, 1681], [1, -2, 87, -86, 1849], [1, 0, 93, 0, 2209], [1, 0, 90, 0, 2809], [1, -12, 154, -708, 3481], 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0.17087753928487728, 0.32234534991386743, 0.38287078290175564], 'positive_zeros': ['1.55214010532178794455093749689161', '2.22354879090908877160738042468544', '2.82511261070703297705797963036697', '3.73571330395388729025783799540842', '4.15537276955970084853193543261599', '4.17947794613570531538770424507798', '5.61135260065455155907566257543481', '6.39486340421971046323119110374081', '6.44323514092267885981017350010136', '7.46802549489449929304458830546739', '7.62429229152375892340957919668121', '8.381087888928782814621554216261113', '8.762972910391102183787591721206182', '9.084561409834522310688102275121865', '9.470845631762160929353564163989257'], 'prelabel': '4-304e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.5580283121454903, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1219116410351487884, 'z1': {'__RealLiteral__': 0, 'data': '1.55214010532178794455093749689161', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.22354879090908877160738042468544', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.82511261070703297705797963036697', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.892524287407611, 'bad_primes': [2, 19], 'central_character': '1.1', 'conductor': 92416, 'conductor_radical': 38, 'degree': 4, 'dirichlet_coefficients': [1, 0, 4, 0, 0, 0, 0, 0, 6, 0, 10, 0, 0, 0, 0, 0, -6, 0, -2, 0, 0, 0, 0, 0, -9, 0, -4, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 20, 0, 2, 0, 0, 0, 0, 0, -5, 0, -24, 0, 0, 0, 0, 0, -8, 0, 12, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 18, 0, -36, 0, 0, 0, 0, 0, -37, 0, -24, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, -16, 0, 60, 0], 'euler11': [1, -10, 47, -110, 121], 'euler13': [1, 0, 10, 0, 169], 'euler17': [1, 6, 43, 102, 289], 'euler19': [1, 2, 1, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -18, 0, 529], 'euler29': [1, 0, 54, 0, 841], 'euler3': [1, -4, 10, -12, 9], 'euler31': [1, 0, 46, 0, 961], 'euler37': [1, 0, -26, 0, 1369], 'euler41': [1, -20, 182, -820, 1681], 'euler43': [1, -2, 87, -86, 1849], 'euler47': [1, 0, 93, 0, 2209], 'euler5': [1, 0, 9, 0, 25], 'euler53': [1, 0, 90, 0, 2809], 'euler59': [1, -12, 154, -708, 3481], 'euler61': [1, 0, -47, 0, 3721], 'euler67': [1, 24, 278, 1608, 4489], 'euler7': [1, 0, 5, 0, 49], 'euler71': [1, 0, 138, 0, 5041], 'euler73': [1, -18, 227, -1314, 5329], 'euler79': [1, 0, 94, 0, 6241], 'euler83': [1, 24, 310, 1992, 6889], 'euler89': [1, -24, 322, -2136, 7921], 'euler97': [1, 16, 258, 1552, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -4, 10, -12, 9], [1, 0, 9, 0, 25], [1, 0, 5, 0, 49], [1, -10, 47, -110, 121], [1, 0, 10, 0, 169], [1, 6, 43, 102, 289], [1, 2, 1, 0, 0], [1, 0, -18, 0, 529], [1, 0, 54, 0, 841], [1, 0, 46, 0, 961], [1, 0, -26, 0, 1369], [1, -20, 182, -820, 1681], [1, -2, 87, -86, 1849], [1, 0, 93, 0, 2209], [1, 0, 90, 0, 2809], [1, -12, 154, -708, 3481], [1, 0, -47, 0, 3721], [1, 24, 278, 1608, 4489], [1, 0, 138, 0, 5041], [1, -18, 227, -1314, 5329], [1, 0, 94, 0, 6241], [1, 24, 310, 1992, 6889], [1, -24, 322, -2136, 7921], [1, 16, 258, 1552, 9409]], 'index': 11, 'instance_types': ['ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.8.1/1444.2/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/1444.2/a'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, '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': '4-304e2-1.1-c1e2-0-11', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-304e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.5580283121454903, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1219116410351487884, 'z1': {'__RealLiteral__': 0, 'data': '1.55214010532178794455093749689161', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9820791
{'Lhash': '1354001870116862942,2170957549448318893', 'Lhash_array': ['1354001870116862942', '2170957549448318893'], 'label': '4-304e2-1.1-c1e2-0-11', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/1444.2/a'}
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id: 9820513
{'Lhash': '1354001870116862942,2170957549448318893', 'Lhash_array': ['1354001870116862942', '2170957549448318893'], 'label': '4-304e2-1.1-c1e2-0-11', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/1444.2/a'}