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lfunc_lfunctions • Show schema
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{'Lhash': '2397344586761964824946996858947', 'a10': [11.0, -19.05255888325765], 'a2': [-1.0, -1.7320508075688772], 'a3': [0.0, 0.0], 'a4': [14.0, -24.24871130596428], 'a5': [5.5, 9.526279441628825], 'a6': [0.0, 0.0], 'a7': [129.5, -6.06217782649107], 'a8': [-120.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.104180648217781, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-129.5, 6.06217782649107]]]], 'bad_primes': [3, 7], 'central_character': '63.46', 'coefficient_field': 'CDF', 'conductor': 63, 'conductor_radical': 21, 'conjugate': '1192695415427993287682390016080', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 1.7320508075688772], [-16.0, 27.712812921102035]], [[1.0, 0], [0, 0]], [[1.0, 0], [-5.5, -9.526279441628825], [-1562.5, 2706.329386826371]], [[1.0, 0], [-129.5, 6.06217782649107]], [[1.0, 0], [-134.5, 232.960833618014], [-80525.5, 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0.5052830422350977, 'root_number': '-0.016596404692524703 + 0.9998622701908908*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.252641521118', 'prec': 47}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.89117142083973604670015071769', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.89150614055319611921541105177', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.64254554922747047630528466922', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.104180648217781, 'bad_primes': [3, 7], 'central_character': '7.4', 'conductor': 63, 'conductor_radical': 21, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/63/6/e/a/46/1'], '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': '2-63-7.4-c5-0-11', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-63-7.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.178707386378586, 'root_angle': 0.25264152111754884, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.89117142083973604670015071769', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2397344586761964824946996858947', 'Lhash_array': ['2397344586761964824946996858947'], 'label': '2-63-7.4-c5-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/63/6/e/a/46/1'}