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lfunc_lfunctions • Show schema
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{'Lhash': '2404311713080209264582941641506', 'a10': [1.9496858291468608, -3.3769549148794167], 'a2': [0.8660254037844386, -0.5], 'a3': [0.6628271480711836, 0.3826834323650898], 'a4': [0.5, -0.8660254037844386], 'a5': [3.3769549148794167, -1.9496858291468608], 'a6': [0.7653668647301796, 0], 'a7': [0, 0], 'a8': [0, -1.0], 'a9': [-1.2071067811865475, -2.0907702751760278], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.607873337894029, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, 0.5]]], [7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-2.7588056345200664, -1.8409213646813747]]]], 'bad_primes': [2, 7, 11], 'central_character': '1078.1011', 'coefficient_field': 'CDF', 'conductor': 1078, 'conductor_radical': 154, 'conjugate': '1708170496637372736333149793226', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, 0.5]], [[1.0, 0], [-0.6628271480711836, -0.3826834323650898], [1.5, 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'6.41912273890181938818108881080697', '7.29378924056488696354681728614292', '8.370315843632515554124495758118361', '9.112618540621463815429884042837052', '10.00376338742648718182692994700405'], 'prelabel': '2-1078-77.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': 0.3234700527603254, 'root_number': '0.52659070375511231693127061816072257889632283249736824758 + 0.85011895092316083410679544797168388686387838710839399264*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1617350263801627', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.89666751441393549052870676234', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.63378606639801375284434788726', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.69068389082145050034966236866', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.607873337894029, 'bad_primes': [2, 7, 11], 'central_character': '77.10', 'conductor': 1078, 'conductor_radical': 154, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1078/2/i/d/1011/12'], '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': '2-1078-77.10-c1-0-34', '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': '2-1078-77.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': 0.1617350263801627, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.89666751441393549052870676234', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2404311713080209264582941641506', 'Lhash_array': ['2404311713080209264582941641506'], 'label': '2-1078-77.10-c1-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1078/2/i/d/1011/12'}