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lfunc_lfunctions • Show schema
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{'Lhash': '774662319452723557840705373790', 'a10': [-8.900682880132855, 0.0], 'a2': [0.0, 2.548139112243958], 'a3': [-1.0, 0.0], 'a4': [-4.493012935347427, 0.0], 'a5': [0.0, 3.4930129353474273], 'a6': [0.0, -2.548139112243958], 'a7': [0.0, 1.0], 'a8': [0.0, -6.352543767888898], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [0, -1.0]]], [13, [[1.0, 0], [3.2562655434009815, 1.5481391122439583]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.64', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '4072878812466805451908054317327', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -2.548139112243958], [-2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, -3.4930129353474273], [-5.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 0.7081264311570232], [-11.0, 0]], [[1.0, 0], 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'1.92744139719366819874944200990097', '3.84971803648037961104394204621543', '4.69181573237370921403565320531611', '5.61203138308652424944243048644555', '7.70087234672170235415865169373486', '8.780765930652761598321662860504024', '9.896426141759503732059870521470132', '10.12355057560218663891081180891448', '11.61165441808029078694967834136850'], 'prelabel': '2-273-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.6412666665268626, 'root_number': '-0.42937653467283776 + 0.9031255679429884*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.320633333263', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.61110081856408412835972233806', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.92744139719366819874944200990', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.84971803648037961104394204622', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'bad_primes': [3, 7, 13], 'central_character': '13.12', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/c/c/64/7'], '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': '2-273-13.12-c1-0-1', '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': '2-273-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.3206333332634313, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.61110081856408412835972233806', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '774662319452723557840705373790', 'Lhash_array': ['774662319452723557840705373790'], 'label': '2-273-13.12-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/c/c/64/7'}