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lfunc_lfunctions • Show schema
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{'Lhash': '1068274770662538429960493737587', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [1.9133242114244196, -1.1572339702830725], 'a6': [0, 0], 'a7': [-0.8143131398684654, 3.0390580112600545], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.935765127447429, '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], [-1.9133242114244196, 1.1572339702830725]]]], 'bad_primes': [2, 3, 5], 'central_character': '1620.377', 'coefficient_field': 'CDF', 'conductor': 1620, 'conductor_radical': 30, 'conjugate': '1753181943471267358577695790380', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.9133242114244196, 1.1572339702830725]], [[1.0, 0], [0.8143131398684654, -3.0390580112600545], [-6.06217782649107, -3.5]], [[1.0, 0], [-4.917884355638806, 2.8393418565715143], [5.5, -9.526279441628825]], [[1.0, 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'9.442059536423654834882896571768486'], 'prelabel': '2-1620-45.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.596632470443349, 'root_angle': -0.23824577643446596, 'root_number': '0.73273011567505109723542375200184696913167468474538170137 - 0.6805193440181008097306943864421979211600663724291819074*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.11912288821723298', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.842720202609618851195842107020', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.19628296028529705161086035252', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.22229534000171449075294863685', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.935765127447429, 'bad_primes': [2, 3, 5], 'central_character': '45.32', 'conductor': 1620, 'conductor_radical': 30, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1620/2/x/d/377/3'], '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': '2-1620-45.32-c1-0-10', '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': '2-1620-45.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.596632470443349, 'root_angle': -0.11912288821723298, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.842720202609618851195842107020', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1068274770662538429960493737587', 'Lhash_array': ['1068274770662538429960493737587'], 'label': '2-1620-45.32-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1620/2/x/d/377/3'}