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lfunc_lfunctions • Show schema
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{'Lhash': '195681030505771844368187650361', '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': '894996797231406691848294757937', '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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'2.02760830744348645074468119265730', '2.82422346458096772464314264420644', '3.58927663806281652252839198671972', '4.73790557457294990129462561288364', '5.32143544516393940414266226173508', '5.98056543857813524977605405312074', '7.11738237606814922921942523508760', '7.75224204941441804568791888057427', '8.358388856442276777409127836577198'], 'prelabel': '2-3744-104.77-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.467722607884145, 'root_angle': -0.36458376200909925, 'root_number': '0.41270580312126659234878883759160597411560821556909358094 - 0.9108643807230746786462855842981382384264028797268554980*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.18229188100454963', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.15436511485936360270871583126', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.02760830744348645074468119266', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.82422346458096772464314264421', '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': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3744/2/m/h/1585/1'], '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': '2-3744-104.77-c1-0-7', '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': -0.18229188100454963, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.15436511485936360270871583126', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '195681030505771844368187650361', 'Lhash_array': ['195681030505771844368187650361'], 'label': '2-3744-104.77-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3744/2/m/h/1585/1'}