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lfunc_lfunctions • Show schema
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{'Lhash': '1250896218404519208172678322630', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [4.209049769721573, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 33.058066436810094, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [23, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '4140.1', 'coefficient_field': 'CDF', 'conductor': 4140, 'conductor_radical': 690, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-4.209049769721573, 0], [7.0, 0]], [[1.0, 0], [2.753525097135825, 0], [11.0, 0]], [[1.0, 0], [0.753525097135825, 0], [13.0, 0]], [[1.0, 0], [-4.9625748668573975, 0], [17.0, 0]], [[1.0, 0], [-4.753525097135825, 0], [19.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], 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'5.42435831907342898944353143969444', '5.91259818132581918029414095652250', '7.40011767727810981457358770619760', '7.52791916103398432197664279855576', '8.313237247913776491781628023069502'], 'prelabel': '2-4140-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.749614459840772, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.986783123188129510261269133541', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.91798839493946426912604372779', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.80429404863676946273072101567', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 33.058066436810094, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 4140, 'conductor_radical': 690, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4140/2/a/s/1/3'], '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': '2-4140-1.1-c1-0-15', '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': '2-4140-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.749614459840772, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.986783123188129510261269133541', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1250896218404519208172678322630', 'Lhash_array': ['1250896218404519208172678322630'], 'label': '2-4140-1.1-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4140/2/a/s/1/3'}