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lfunc_lfunctions • Show schema
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{'Lhash': '1231700555069711323309982952129', 'a10': [-0.3919998475303698, 0], 'a2': [0, 0.9838197466143516], 'a3': [-1.571709016713467, 0], 'a4': [1.032098706171673, 0], 'a5': [0, 0.398446818006419], 'a6': [0, -1.5462783665745348], 'a7': [0, -1.0], 'a8': [0, 2.9830385808155184], 'a9': [-0.5297307667815866, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.446302559117473, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 1.0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [7, 13], 'central_character': '1183.337', 'coefficient_field': 'CDF', 'conductor': 1183, 'conductor_radical': 91, 'conjugate': '1173088760006643888695000199662', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -0.9838197466143516], [-2.0, 0]], [[1.0, 0], [1.571709016713467, 0], [3.0, 0]], [[1.0, 0], [0, -0.398446818006419], [-5.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 4.242059675195182], [-11.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'positive_zeros': ['0.971640414833515175997645849941596', '2.24814371900872787862372524869562', '3.24706696582998438317687771043291', '4.56341095170484072998254880993623', '5.37331408022243021956384664190288', '6.32950167391484361651545434520738', '7.00398449171251019210494940679640', '7.969570092436168440184363798515039', '9.079098103754906849206359920578754', '10.09381115150737767392685280736283'], 'prelabel': '2-1183-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0734837821464867, 'root_angle': -0.24313786824084244, 'root_number': '0.7221851175239742895525008756977393835712075807514874811 - 0.6916998308709374287080491938581327632030041385121643854*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1215689341204212', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.971640414833515175997645849942', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.24814371900872787862372524870', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.24706696582998438317687771043', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.446302559117473, 'bad_primes': [7, 13], 'central_character': '13.12', 'conductor': 1183, 'conductor_radical': 91, 'degree': 2, 'index': 33, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1183/2/c/j/337/16'], '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': '2-1183-13.12-c1-0-33', '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': '2-1183-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0734837821464867, 'root_angle': -0.12156893412042122, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.971640414833515175997645849942', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1231700555069711323309982952129', 'Lhash_array': ['1231700555069711323309982952129'], 'label': '2-1183-13.12-c1-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1183/2/c/j/337/16'}