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lfunc_lfunctions • Show schema
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{'Lhash': '107054555295084745639381297662', 'a10': [0.29677156062714666, -0.09578352077391276], 'a2': [-0.09861432048588012, 0.09861432048588012], 'a3': [0, 0], 'a4': [0, 1.9805504315902163], 'a5': [-1.9903553533954867, -1.019061120448586], 'a6': [0, 0], 'a7': [0.9085711745221556, 0.9085711745221556], 'a8': [-0.392539275971046, -0.392539275971046], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.264516609202524, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.9903553533954867, 1.019061120448586]]], [23, [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]]]], 'bad_primes': [3, 5, 23], 'central_character': '1035.737', 'coefficient_field': 'CDF', 'conductor': 1035, 'conductor_radical': 345, 'conjugate': '2465701602331846565243287305803', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.09861432048588012, -0.09861432048588012], [0, -2.0]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'-0.96884021726307024864370637707425076084613560084065702988 + 0.2476865628443473664377615386545538110026089839673506619*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.46016484162691457', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.084451153398113415040093539834', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.73679112214212240391959033781', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.96881585278643219518219927737', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.264516609202524, 'bad_primes': [3, 5, 23], 'central_character': '15.2', 'conductor': 1035, 'conductor_radical': 345, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1035/2/j/b/737/11'], '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': '2-1035-15.2-c1-0-1', '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': '2-1035-15.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.874807229920386, 'root_angle': 0.4601648416269145, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.084451153398113415040093539834', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '107054555295084745639381297662', 'Lhash_array': ['107054555295084745639381297662'], 'label': '2-1035-15.2-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1035/2/j/b/737/11'}