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lfunc_lfunctions • Show schema
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{'Lhash': '585239168455831451968469787248', 'a10': [0, 0], 'a2': [-1.4142135623730951, 0], 'a3': [-1.438374941882731, 0], 'a4': [2.0, 0], 'a5': [0, 0], 'a6': [2.0341693505881704, 0], 'a7': [0, 10.186564078960892], 'a8': [-2.8284271247461903, 0], 'a9': [-6.9310775265638505, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 31.335230401434146, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.4142135623730951, 0]]], [5, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [-17.39985793635233, 15.041440881602961]]]], 'bad_primes': [2, 5, 23], 'central_character': '1150.551', 'coefficient_field': 'CDF', 'conductor': 1150, 'conductor_radical': 230, 'conjugate': '836341068000363580341258974874', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.4142135623730951, 0]], [[1.0, 0], [1.438374941882731, 0], [9.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -10.186564078960892], [-49.0, 0]], [[1.0, 0], [0, 13.023724231391114], [-121.0, 0]], [[1.0, 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0.4684688863557611, -0.11423926494976282, -0.6671680463500772, -1.14962114544712], 'positive_zeros': ['0.46167230019885941694539316298455', '1.82595263521715727628555735477066', '3.10799324280939369565542974702257', '4.45282590665044072242909921815793', '5.14089209357940565142487269204169', '6.53626902481560543000541953977834', '7.02667120384222301206390105826682', '7.81215193802985610959684826682980', '8.646255196618321754286567869918328', '9.866356913518640852382183339820387'], 'prelabel': '2-1150-23.22-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.597787991826249, 'root_angle': -0.2269001496897473, 'root_number': '0.7565155624501013048061985462058103587184482076387241201 - 0.6539756905044765291031865866931659981947101199059169825*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.11345007484487366', 'prec': 67}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.46167230019885941694539316298', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.82595263521715727628555735477', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.10799324280939369565542974702', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 31.335230401434146, 'bad_primes': [2, 5, 23], 'central_character': '23.22', 'conductor': 1150, 'conductor_radical': 230, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1150/3/d/b/551/4'], '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': '2-1150-23.22-c2-0-18', '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': '2-1150-23.22-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.597787991826249, 'root_angle': -0.11345007484487366, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.46167230019885941694539316298', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '585239168455831451968469787248', 'Lhash_array': ['585239168455831451968469787248'], 'label': '2-1150-23.22-c2-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1150/3/d/b/551/4'}