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lfunc_lfunctions • Show schema
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{'Lhash': '95080481807045740135088458822', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-2.6899940478558295, 0], 'a6': [0, 0], 'a7': [0, 4.151634374255492], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.89599051676739, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-3.53159113644255, -0.7265425280053609]]]], 'bad_primes': [2, 3, 13], 'central_character': '3744.1585', 'coefficient_field': 'CDF', 'conductor': 3744, 'conductor_radical': 78, 'conjugate': '2049462245546554845679749210316', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.6899940478558295, 0], [5.0, 0]], [[1.0, 0], [0, -4.151634374255492], [-7.0, 0]], [[1.0, 0], [4.352501798965643, 0], [11.0, 0]], [[1.0, 0], [-3.53159113644255, -0.7265425280053609]], [[1.0, 0], [5.871297638086454, 0], [17.0, 0]], [[1.0, 0], 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'2.52509188019800680677701282082705', '3.60789519853199344109995103363128', '4.05471347782454822569411054504964', '4.84622531472751442601475059679562', '5.78630272683835508259394967336960', '6.87936630574805624582300260576282', '7.43495403919853057234364166428405', '7.87465601407067729129408992116940'], 'prelabel': '2-3744-104.77-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.467722607884145, 'root_angle': 0.7645837620090993, 'root_number': '-0.7387503979061972427325665582150306539226499335593193984 + 0.6739791165855476597422958399304907898822988009730289941*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.38229188100454964', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.07500527494715604688295289499', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.964018436896238674879896646475', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '2.52509188019800680677701282083', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.89599051676739, 'bad_primes': [2, 3, 13], 'central_character': '104.77', 'conductor': 3744, 'conductor_radical': 78, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3744/2/m/h/1585/4'], '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': '2-3744-104.77-c1-0-3', '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': '2-3744-104.77-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.467722607884145, 'root_angle': 0.38229188100454964, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.07500527494715604688295289499', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '95080481807045740135088458822', 'Lhash_array': ['95080481807045740135088458822'], 'label': '2-3744-104.77-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3744/2/m/h/1585/4'}