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lfunc_lfunctions • Show schema
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{'Lhash': '1002729926307465749683055353117', 'a10': [-359853008914409600000000000000000000000000, 0], 'a2': [-2199023255552.0, 0], 'a3': [2324063824724569600, 0], 'a4': [4835703278458517000000000, 0], 'a5': [163642202512350940000000000000, 0], 'a6': [-5110670397956456000000000000000, 0], 'a7': [-8777019720709744000000000000000000, 0], 'a8': [-10633823966279327000000000000000000000, 0], 'a9': [-3985437121525947000000000000000000000000, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 87.25442565326811, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '41.5', 'prec': 14}, 'bad_lfactors': [[2, [[1.0, 0], [2199023255552.0, 0]]]], 'bad_primes': [2], 'central_character': '2.1', 'coefficient_field': 'CDF', 'conductor': 2, 'conductor_radical': 2, 'degree': 2, 'euler_factors': [[[1.0, 0], [2199023255552.0, 0]], [[1.0, 0], [-2324063824724569600, 0], [3990838394187340000000000000000000000000, 0]], [[1.0, 0], [-163642202512350940000000000000, 0], 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True, 'rational': False, 'root_analytic_conductor': 9.341007742918753, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c83-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.791014437359105890905061053263', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.01471965848111635953369991381', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.02793283270186350080828190482', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 87.25442565326811, 'bad_primes': [2], 'central_character': '1.1', 'conductor': 2, 'conductor_radical': 2, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2/84/a/a/1/3'], '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': '2-2-1.1-c83-0-2', 'motivic_weight': 83, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [83], 'order_of_vanishing': 0, 'prelabel': '2-2-1.1-c83-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.341007742918753, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c83-0', 'z1': {'__RealLiteral__': 0, 'data': '0.791014437359105890905061053263', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1002729926307465749683055353117', 'Lhash_array': ['1002729926307465749683055353117'], 'factors': ['2-2-1.1-c83-0-2'], 'label': '2-2-1.1-c83-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2/84/a/a/1/3'}