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lfunc_lfunctions • Show schema
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{'Lhash': '1014766842333735248180236077077', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-10.427528091910006, 0], 'a4': [0, 0], 'a5': [17.9907395772898, 52.92762312311161], 'a6': [0, 0], 'a7': [0, 86.73907257134965], 'a8': [0, 0], 'a9': [-134.26665789242767, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 51.32282234015381, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-17.9907395772898, -52.92762312311161]]]], 'bad_primes': [2, 5], 'central_character': '320.289', 'coefficient_field': 'CDF', 'conductor': 320, 'conductor_radical': 10, 'conjugate': '537838972709615504356220979134', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [10.427528091910006, 0], [243.0, 0]], [[1.0, 0], [-17.9907395772898, -52.92762312311161]], [[1.0, 0], [0, -86.73907257134965], [-16807.0, 0]], [[1.0, 0], [0, 258.63332894621385], [-161051.0, 0]], [[1.0, 0], [465.1652043829222, 0], [371293.0, 0]], [[1.0, 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'0.800509889831658151805998370560', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.11130631221896629197328060309', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.96504698178832432732878747374', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 51.32282234015381, 'bad_primes': [2, 5], 'central_character': '40.29', 'conductor': 320, 'conductor_radical': 10, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/320/6/f/c/289/8'], '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': '2-320-40.29-c5-0-34', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-320-40.29-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.163994859026199, 'root_angle': 0.07285133688161624, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.800509889831658151805998370560', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1014766842333735248180236077077', 'Lhash_array': ['1014766842333735248180236077077'], 'label': '2-320-40.29-c5-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/320/6/f/c/289/8'}