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lfunc_lfunctions • Show schema
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{'Lhash': '1895180621463865441471554706115', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6647545968271592, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [37, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 3, 37], 'central_character': '1332.253', 'coefficient_field': 'CDF', 'conductor': 1332, 'conductor_radical': 222, 'conjugate': '1202748503237378658245772751028', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [0, 1.0], [-1.0, 0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [-1.0, 1.0], [0, -1.0]], [[1.0, 0], [-1.0, 1.0], [0, -1.0]], [[1.0, 0], [-1.0, 1.0], [0, -1.0]], [[1.0, 0], [-1.0, -1.0], [0, 1.0]], [[1.0, 0], [0, 0], 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'root_number': '0.76301998247272570656116322085132 + 0.64637489613019575835840272602141*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.11185788582218664', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.49503390060530460768852581895', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.94629219843390123621995246818', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.74602960213799912227260790124', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6647545968271592, 'bad_primes': [2, 3, 37], 'central_character': '37.31', 'conductor': 1332, 'conductor_radical': 222, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1332/1/o/a/253/1'], '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': '2-1332-37.31-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1332-37.31-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8153248412915917, 'root_angle': 0.11185788582218664, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.49503390060530460768852581895', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1895180621463865441471554706115', 'Lhash_array': ['1895180621463865441471554706115'], 'factors': ['2-1332-37.31-c0-0-0'], 'label': '2-1332-37.31-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1332/1/o/a/253/1'}