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lfunc_lfunctions • Show schema
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{'Lhash': '969595622942641386867548042102', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, -1.4142135623730951], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 56.342443666215466, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '7056.4607', 'coefficient_field': 'CDF', 'conductor': 7056, 'conductor_radical': 42, 'conjugate': '600903460299281206193980833333', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.4142135623730951], [-5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [11.0, 0]], [[1.0, 0], [6.0, 0], [13.0, 0]], [[1.0, 0], [0, -7.0710678118654755], [-17.0, 0]], [[1.0, 0], [0, 0], [-19.0, 0]], [[1.0, 0], [0, 0], [23.0, 0]], [[1.0, 0], [0, 4.242640687119285], [-29.0, 0]], [[1.0, 0], [0, 0], 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'root_analytic_conductor': 7.506160381061377, 'root_angle': 0.3040867239846964, 'root_number': '0.5773502691896257645091487805019574556476017512701268760 + 0.8164965809277260327324280249019637973219824935522233762*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1520433619923482', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.76487608081286292668065186274', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.21362794244526274173414342729', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.77550747225285505653088259414', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 56.342443666215466, 'bad_primes': [2, 3, 7], 'central_character': '12.11', 'conductor': 7056, 'conductor_radical': 42, 'degree': 2, 'index': 41, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7056/2/h/a/4607/1'], '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': '2-84e2-12.11-c1-0-41', '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': '2-84e2-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.506160381061377, 'root_angle': 0.1520433619923482, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.76487608081286292668065186274', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '969595622942641386867548042102', 'Lhash_array': ['969595622942641386867548042102'], 'label': '2-84e2-12.11-c1-0-41', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7056/2/h/a/4607/1'}