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lfunc_lfunctions • Show schema
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{'Lhash': '1719394405521719385256989613534', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0.5190334516386744, 0], 'a6': [0, 0], 'a7': [10.411719604342396, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 47.084589681459306, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1728.161', 'coefficient_field': 'CDF', 'conductor': 1728, 'conductor_radical': 6, 'conjugate': '469938207065404833037290851228', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.5190334516386744, 0], [25.0, 0]], [[1.0, 0], [-10.411719604342396, 0], [49.0, 0]], [[1.0, 0], [14.134635039815931, 0], [121.0, 0]], [[1.0, 0], [0, -5.390517634288619], [-169.0, 0]], [[1.0, 0], [0, 24.93261965794799], [-289.0, 0]], [[1.0, 0], [0, -13.336650421683876], [-361.0, 0]], [[1.0, 0], [0, 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'4.53331958880345318234268708071207', '5.33215458786281793451718036827284', '5.89441159931784388969617039624758', '7.21025284074308085522348160078990', '8.043748946304962456879250132190576', '8.192413045243281098029266572269727', '9.396905787225505400882839768729689'], 'prelabel': '2-12e3-24.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.861821163616792, 'root_angle': 0.2916666666666667, 'root_number': '-0.2588190451025207623488988376240483283490689013199305138 + 0.9659258262890682867497431997288973676339048390084045504*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2916666666666667', 'prec': 60}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.35636302717180701318905344389', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.22798262820290052660190342489', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.45878467101760420825636247855', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 47.084589681459306, 'bad_primes': [2, 3], 'central_character': '24.5', 'conductor': 1728, 'conductor_radical': 6, 'degree': 2, 'index': 53, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1728/3/h/j/161/8'], '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': '2-12e3-24.5-c2-0-53', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-12e3-24.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.861821163616792, 'root_angle': 0.2916666666666667, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.35636302717180701318905344389', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1719394405521719385256989613534', 'Lhash_array': ['1719394405521719385256989613534'], 'factors': ['2-12e3-24.5-c2-0-53'], 'label': '2-12e3-24.5-c2-0-53', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1728/3/h/j/161/8'}