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lfunc_lfunctions • Show schema
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{'Lhash': '2241335452284312815416213096095', 'a10': [0, 4.071461717525471], 'a2': [1.0, 0], 'a3': [-0.4233850732204458, -1.6795073919974624], 'a4': [1.0, 0], 'a5': [0, 4.071461717525471], 'a6': [-0.4233850732204458, -1.6795073919974624], 'a7': [0, -4.794756189767088], 'a8': [1.0, 0], 'a9': [-2.6414901595482356, 1.4221567202702512], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.959215106787664, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [0.4233850732204458, 1.6795073919974624]]], [11, [[1.0, 0], [2.781510029753558, 1.8064334901624137]]], [17, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 11, 17], 'central_character': '1122.1055', 'coefficient_field': 'CDF', 'conductor': 1122, 'conductor_radical': 1122, 'conjugate': '771772362098688587638365767283', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.4233850732204458, 1.6795073919974624]], [[1.0, 0], [0, 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103}, 'z2': {'__RealLiteral__': 0, 'data': '2.98443499636693358285559064883', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.42009501753338576640177611539', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.959215106787664, 'bad_primes': [2, 3, 11, 17], 'central_character': '33.32', 'conductor': 1122, 'conductor_radical': 1122, 'degree': 2, 'index': 47, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1122/2/b/c/1055/5'], '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': '2-1122-33.32-c1-0-47', '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': '2-1122-33.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9931947993386037, 'root_angle': 0.3023683766686079, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.76810191379294891971500099326', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2241335452284312815416213096095', 'Lhash_array': ['2241335452284312815416213096095'], 'label': '2-1122-33.32-c1-0-47', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1122/2/b/c/1055/5'}