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lfunc_lfunctions • Show schema
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{'Lhash': '2142238696395814665869901418163', 'a10': [-4.769322476215943, -4.769322476215943], 'a2': [-1.5390597014918863, -1.5390597014918863], 'a3': [-1.7307233012946315, -0.06780010586873879], 'a4': [0.0, 2.737409529512589], 'a5': [3.0988547563117947, 0.0], 'a6': [2.5593380767561085, 2.768034898155027], 'a7': [1.2533967617757868, -1.2533967617757868], 'a8': [1.1349172903689173, -1.1349172903689173], 'a9': [2.9908062912883757, 0.23468644611453823], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.4612623569894316, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.7307233012946315, 0.06780010586873879]]], [61, [[1.0, 0], [5.454567689478976, -5.5899634453985465]]]], 'bad_primes': [3, 61], 'central_character': '183.50', 'coefficient_field': 'CDF', 'conductor': 183, 'conductor_radical': 183, 'conjugate': '1300407901040225103720718996632', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.5390597014918863, 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0.9307765485669265*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.309566138833', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.68992835723828263744370990370', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.90186482422356482840783455385', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.86807235736085727758038242463', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.4612623569894316, 'bad_primes': [3, 61], 'central_character': '183.50', 'conductor': 183, 'conductor_radical': 183, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/183/2/g/c/50/2'], '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': '2-183-183.50-c1-0-5', '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': '2-183-183.50-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.208826851533929, 'root_angle': 0.30956613883264283, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.68992835723828263744370990370', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2142238696395814665869901418163', 'Lhash_array': ['2142238696395814665869901418163'], 'label': '2-183-183.50-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/183/2/g/c/50/2'}