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lfunc_lfunctions • Show schema
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{'Lhash': '1235827832422660170663649128979', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [2.1213203435596424, -2.1213203435596424], 'a4': [0.0, 0.0], 'a5': [11.791063975681036, 11.791063975681036], 'a6': [0.0, 0.0], 'a7': [0.0, 12.575351738582292], 'a8': [0.0, 0.0], 'a9': [0.0, -9.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.328366721102203, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-2.1213203435596424, 2.1213203435596424]]]], 'bad_primes': [2, 3], 'central_character': '192.49', 'coefficient_field': 'CDF', 'conductor': 192, 'conductor_radical': 6, 'conjugate': '2492033786120283070653459018085', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.1213203435596424, 2.1213203435596424]], [[1.0, 0], [-11.791063975681036, -11.791063975681036], [0, 125.0]], [[1.0, 0], [0, -12.575351738582292], [-343.0, 0]], [[1.0, 0], [-17.004190467192206, -17.004190467192206], [0, 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['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.974896262582260585158975970089', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.70999735016914728561708016160', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.41955137338626121544336522831', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.328366721102203, 'bad_primes': [2, 3], 'central_character': '16.5', 'conductor': 192, 'conductor_radical': 6, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/192/4/j/a/49/12'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, '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': '2-192-16.5-c3-0-3', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-192-16.5-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.365763913452963, 'root_angle': -0.1576218683425039, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.974896262582260585158975970089', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1235827832422660170663649128979', 'Lhash_array': ['1235827832422660170663649128979'], 'factors': ['2-192-16.5-c3-0-3'], 'label': '2-192-16.5-c3-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/192/4/j/a/49/12'}