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lfunc_lfunctions • Show schema
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{'Lhash': '2964471245209488853705051210320', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -4, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.1325108752343365, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]]], 'bad_primes': [2, 3], 'central_character': '768.1', 'coefficient_field': '1.1.1.1', 'conductor': 768, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 0, 5], [1, 4, 7], [1, 4, 11], [1, 4, 13], [1, 2, 17], [1, -4, 19], [1, 8, 23], [1, -8, 29], [1, 4, 31], [1, -4, 37], [1, -6, 41], [1, 4, 43], [1, 8, 47], [1, -8, 53], [1, -12, 59], [1, 12, 61], [1, 12, 67], [1, -8, 71], [1, 6, 73], [1, 4, 79], [1, -4, 83], [1, 6, 89], [1, 2, 97], [1, -8, 101], [1, -4, 103], [1, 4, 107], [1, 4, 109], [1, 14, 113]], 'euler_factors_factorization': [[1], [[[1, -1], 1]], [[[1, 0, 5], 1]], [[[1, 4, 7], 1]], [[[1, 4, 11], 1]], [[[1, 4, 13], 1]], [[[1, 2, 17], 1]], 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0.7687783883431952, -0.1950741935808, -0.807755388565293, -0.8859639197125314, -0.48050012945924536, 0.15777674976661868, 0.6893944187932028, 0.8310995270150525], 'positive_zeros': ['2.33855546999761743371608352814129', '3.10975929333988114178652450581031', '4.25300875683489800803673652067501', '5.47500942227311527725009815403503', '6.43663656032022884828664728498390', '7.42165581773296115004203753690823', '8.069916096323518080594124819658559', '9.230110611951262626128540633521391', '9.957439752177824708522207192035288'], 'prelabel': '2-768-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.4763906951921655, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 556228461161168918, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.33855546999761743371608352814', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.10975929333988114178652450581', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.25300875683489800803673652068', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.1325108752343365, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 768, 'conductor_radical': 6, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, -4, 0, 1, 0, -4, 0, -4, 0, 0, 0, -2, 0, 4, 0, -4, 0, -8, 0, -5, 0, 1, 0, 8, 0, -4, 0, -4, 0, 0, 0, 4, 0, -4, 0, 6, 0, -4, 0, 0, 0, -8, 0, 9, 0, -2, 0, 8, 0, 0, 0, 4, 0, 12, 0, -12, 0, -4, 0, 0, 0, -12, 0, -8, 0, 8, 0, -6, 0, -5, 0, 16, 0, -4, 0, 1, 0, 4, 0, 0, 0, 8, 0, -6, 0, 16, 0, -4, 0, 0, 0, -2, 0, -4, 0], 'euler11': [1, 4, 11], 'euler13': [1, 4, 13], 'euler17': [1, 2, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 8, 23], 'euler29': [1, -8, 29], 'euler3': [1, -1, 0], 'euler31': [1, 4, 31], 'euler37': [1, -4, 37], 'euler41': [1, -6, 41], 'euler43': [1, 4, 43], 'euler47': [1, 8, 47], 'euler5': [1, 0, 5], 'euler53': [1, -8, 53], 'euler59': [1, -12, 59], 'euler61': [1, 12, 61], 'euler67': [1, 12, 67], 'euler7': [1, 4, 7], 'euler71': [1, -8, 71], 'euler73': [1, 6, 73], 'euler79': [1, 4, 79], 'euler83': [1, -4, 83], 'euler89': [1, 6, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 0, 5], [1, 4, 7], [1, 4, 11], [1, 4, 13], [1, 2, 17], [1, -4, 19], [1, 8, 23], [1, -8, 29], [1, 4, 31], [1, -4, 37], [1, -6, 41], [1, 4, 43], [1, 8, 47], [1, -8, 53], [1, -12, 59], [1, 12, 61], [1, 12, 67], [1, -8, 71], [1, 6, 73], [1, 4, 79], [1, -4, 83], [1, 6, 89], [1, 2, 97]], 'index': 15, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/768/f', 'ModularForm/GL2/Q/holomorphic/768/2/a/f/1/1', 'ModularForm/GL2/Q/holomorphic/768/2/a/f'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, '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': '2-768-1.1-c1-0-15', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-768-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.4763906951921655, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 556228461161168918, 'z1': {'__RealLiteral__': 0, 'data': '2.33855546999761743371608352814', 'prec': 103}}
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lfunc_instances • Show schema
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id: 14397448
{'Lhash': '2964471245209488853705051210320', 'Lhash_array': ['2964471245209488853705051210320'], 'label': '2-768-1.1-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/768/2/a/f'}
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id: 24550471
{'Lhash': '2964471245209488853705051210320', 'Lhash_array': ['2964471245209488853705051210320'], 'label': '2-768-1.1-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/768/2/a/f/1/1'}
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id: 95129
{'Lhash': '556228461161168918', 'Lhash_array': ['556228461161168918'], 'label': '2-768-1.1-c1-0-15', 'type': 'ECQ', 'url': 'EllipticCurve/Q/768/f'}