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lfunc_lfunctions • Show schema
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{'Lhash': '1700838264939912606649165966018', 'a10': [-7.64274377733136, 4.412540177189598], 'a2': [-0.36602540378443865, 1.3660254037844386], 'a3': [-0.8660254037844386, -1.5], 'a4': [-1.7320508075688772, -1.0], 'a5': [4.412540177189598, 4.412540177189598], 'a6': [2.366025403784439, -0.6339745962155614], 'a7': [2.1151018000708808, 7.893667381044917], 'a8': [2.0, -2.0], 'a9': [-1.5, 2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.125346062010316, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.36602540378443865, -1.3660254037844386]]], [3, [[1.0, 0], [0.8660254037844386, 1.5]]], [13, [[1.0, 0], [12.921309358305395, 1.4282032302755092]]]], 'bad_primes': [2, 3, 13], 'central_character': '78.37', 'coefficient_field': 'CDF', 'conductor': 78, 'conductor_radical': 78, 'conjugate': '2875460132561814764036768352841', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.36602540378443865, 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'6.87258450767649471244018423051648', '8.842022789598711718916878496088432', '9.493986630827335430761874838347658', '10.68289343287142191293046141659472', '11.62723073396572357982864676244859', '12.90138915821490620126516335882817', '13.80009031915004076243281517699928'], 'prelabel': '2-78-13.11-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4578566671694155, 'root_angle': -0.393916981983864, 'root_number': '0.3271344992912275 - 0.9449777877672458*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.196958490992', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.34172481331503456514989208179', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.93440274553145140442271240797', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.11250641520283181732055064418', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.125346062010316, 'bad_primes': [2, 3, 13], 'central_character': '13.11', 'conductor': 78, 'conductor_radical': 78, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/78/3/l/c/37/2'], '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': '2-78-13.11-c2-0-1', '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': '2-78-13.11-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4578566671694155, 'root_angle': -0.196958490991932, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.34172481331503456514989208179', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1700838264939912606649165966018', 'Lhash_array': ['1700838264939912606649165966018'], 'label': '2-78-13.11-c2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/78/3/l/c/37/2'}