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lfunc_lfunctions • Show schema
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{'Lhash': '2455264293566860323683850539538', 'a10': [-2.2359665682776417, -0.021295669623332566], 'a2': [-0.5, -0.8660254037844386], 'a3': [0.533793382171979, -0.9245572586658987], 'a4': [-0.5, 0.8660254037844386], 'a5': [1.1364258750232274, -1.925756015329484], 'a6': [-1.067586764343958, 3.325136716092755e-61], 'a7': [1.2210675077887796, -2.3471246540016786], 'a8': [1.0, 0.0], 'a9': [0.9301292502987991, 1.6110311191234694], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.148480955638592, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [5, [[1.0, 0], [-1.1364258750232274, 1.925756015329484]]], [7, [[1.0, 0], [-1.2210675077887796, 2.3471246540016786]]], [11, [[1.0, 0], [2.752058327859928, 1.8509929659663265]]]], 'bad_primes': [2, 5, 7, 11], 'central_character': '770.549', 'coefficient_field': 'CDF', 'conductor': 770, 'conductor_radical': 770, 'conjugate': 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'6.38897866717942728314021617431329', '7.15255270155505600269844910313261', '8.151224544874206408099872647361552', '9.081134819412966340142921607238616', '9.668192357021525458003350305879482', '10.39910230225174433450243128064861'], 'prelabel': '2-770-385.164-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4796130657097675, 'root_angle': 0.8038491053873347, 'root_number': '-0.8160653610050683 + 0.5779596236482853*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.401924552694', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.93686201317998150723399940381', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.08221955202945798521214040390', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.48376149664715241132803571520', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.148480955638592, 'bad_primes': [2, 5, 7, 11], 'central_character': '385.164', 'conductor': 770, 'conductor_radical': 770, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/770/2/o/a/549/15'], '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': '2-770-385.164-c1-0-38', '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': '2-770-385.164-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4796130657097675, 'root_angle': 0.40192455269366734, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.93686201317998150723399940381', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2455264293566860323683850539538', 'Lhash_array': ['2455264293566860323683850539538'], 'label': '2-770-385.164-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/770/2/o/a/549/15'}