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lfunc_lfunctions • Show schema
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{'Lhash': '1932992596742195457747883318997', 'a10': [1.0495574951345756, 1.8178869070378096], 'a2': [1.165029369783991, 2.0178900607758217], 'a3': [0.5, 0.8660254037844386], 'a4': [-1.7145868649185665, 2.9697515640291927], 'a5': [0.900885009730849, 0.0], 'a6': [-1.165029369783991, 2.0178900607758217], 'a7': [-0.5, 0.8660254037844386], 'a8': [-3.330058739567982, 0.0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.5, -0.8660254037844386]]], [7, [[1.0, 0], [0.5, -0.8660254037844386]]], [13, [[1.0, 0], [-1.5495574951345756, 3.255590817236137]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.211', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '3782806499520362859262336640459', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.165029369783991, -2.0178900607758217], [-1.0, 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'9.038783891113047961656514243106151', '9.944420580938999487452460297518853', '10.72385497460370232787119132581299', '11.79161196913066876871785831432171'], 'prelabel': '2-273-13.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': -0.7773022859155839, 'root_number': '-0.7650833915332266 - 0.6439312106118289*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.388651142958', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.52486228965156254413938250320', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.65582446043950492361987166498', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.92633861587325962106111808087', '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': '13.3', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/k/b/211/3'], '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': '2-273-13.3-c1-0-3', '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': '2-273-13.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': -0.38865114295779196, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.52486228965156254413938250320', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1932992596742195457747883318997', 'Lhash_array': ['1932992596742195457747883318997'], 'label': '2-273-13.3-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/k/b/211/3'}