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lfunc_lfunctions • Show schema
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{'Lhash': '2528087729866932641408205414034', 'a10': [0.641763945362931, -2.1419941732955774], 'a2': [-0.35836794954530027, -0.9335804264972017], 'a3': [-1.2031531405245508, -1.8526933671972394], 'a4': [-0.7431448254773942, 0.6691306063588582], 'a5': [1.7697362046679908, 1.3667603176443688], 'a6': [-1.2984667399577636, 1.7871861452110107], 'a7': [-2.1027462851430916, -1.6057577838257329], 'a8': [0.8910065241883679, 0.4539904997395468], 'a9': [-0.7646853040751544, 1.7175113134169244], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.148480955638592, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.35836794954530027, 0.9335804264972017]]], [5, [[1.0, 0], [-1.7697362046679908, -1.3667603176443688]]], [7, [[1.0, 0], [2.1027462851430916, 1.6057577838257329]]], [11, [[1.0, 0], [-1.5608583548962045, 2.9263836378627315]]]], 'bad_primes': [2, 5, 7, 11], 'central_character': '770.157', 'coefficient_field': 'CDF', 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-0.7527634157628433, 'root_number': '-0.7132188236821142 - 0.7009414451617919*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.376381707881', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.99430957506096124649244652416', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.83972777200680828663069077910', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.85591298655948373273419815528', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.148480955638592, 'bad_primes': [2, 5, 7, 11], 'central_character': '385.157', 'conductor': 770, 'conductor_radical': 770, 'degree': 2, 'index': 44, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/770/2/bv/a/157/5'], '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': '2-770-385.157-c1-0-44', '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': '2-770-385.157-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4796130657097675, 'root_angle': -0.37638170788142167, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.99430957506096124649244652416', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2528087729866932641408205414034', 'Lhash_array': ['2528087729866932641408205414034'], 'label': '2-770-385.157-c1-0-44', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/770/2/bv/a/157/5'}