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lfunc_lfunctions • Show schema
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{'Lhash': '2316159043376406329644733160620', 'a10': [3.0154063313312127, -0.5051805715216254], 'a2': [-0.5778563439579557, 1.2392169286781878], 'a3': [-1.6180247335802957, 0.6180582185542177], 'a4': [0.08383457730293296, 0.09991015868438737], 'a5': [-1.2668644103987765, -1.8425673842942516], 'a6': [0.16907764963918512, -2.3622325033996248], 'a7': [-0.6361511935505305, 2.3741485756261627], 'a8': [-2.81372298254181, 0.753934800896968], 'a9': [2.236008076955174, -2.0000669688266006], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.275736457606492, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.6180247335802957, -0.6180582185542177]]], [5, [[1.0, 0], [1.2668644103987765, 1.8425673842942516]]], [19, [[1.0, 0], [2.957948373144594, 3.2016466734808904]]]], 'bad_primes': [3, 5, 19], 'central_character': '285.62', 'coefficient_field': 'CDF', 'conductor': 285, 'conductor_radical': 285, 'conjugate': 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'0.03666864901959105 + 0.9993274789472558*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.244162694623', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.82712731959374464464859422679', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.41955778966388833770048479379', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.83073408591576881251414667331', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.275736457606492, 'bad_primes': [3, 5, 19], 'central_character': '285.62', 'conductor': 285, 'conductor_radical': 285, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/285/2/bi/a/62/11'], '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': '2-285-285.62-c1-0-19', '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': '2-285-285.62-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5085544264647834, 'root_angle': 0.24416269462309909, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.82712731959374464464859422679', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2316159043376406329644733160620', 'Lhash_array': ['2316159043376406329644733160620'], 'label': '2-285-285.62-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/285/2/bi/a/62/11'}