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lfunc_lfunctions • Show schema
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{'Lhash': '686585349350867329012787578709', 'a10': [0.07513875066782114, 0.13014413377391612], 'a2': [0.09210992028436366, -0.05317968727121233], 'a3': [-0.5, -0.8660254037844386], 'a4': [-0.9943438417234721, 1.7222540540582798], 'a5': [0.0, 1.412922010703434], 'a6': [-0.09210992028436366, -0.05317968727121233], 'a7': [-0.8660254037844386, -0.5], 'a8': [0.0, 0.4242343272564897], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.5, 0.8660254037844386]]], [7, [[1.0, 0], [0.8660254037844386, 0.5]]], [13, [[1.0, 0], [2.158313249068302, -2.888197347636797]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.127', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '3003276722888834499063567182966', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.09210992028436366, 0.05317968727121233], 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'9.567607483041878899122077677603374', '10.60757303112628751593354901516259', '11.44529016761128860832504209155654'], 'prelabel': '2-273-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': -0.6249720088820917, 'root_number': '-0.3826021879771705 - 0.9239131808536352*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.312486004441', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.54162034020040983132923793345', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.95372017102436677146215278842', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.83344314546502243424178501133', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'bad_primes': [3, 7, 13], 'central_character': '13.10', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/bd/a/127/5'], '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': '2-273-13.10-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': '2-273-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': -0.31248600444104585, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.54162034020040983132923793345', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '686585349350867329012787578709', 'Lhash_array': ['686585349350867329012787578709'], 'label': '2-273-13.10-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/bd/a/127/5'}