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lfunc_lfunctions • Show schema
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{'Lhash': '1378672967195456465111057408676', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0.2069539376226517, 0], 'a6': [0, 0], 'a7': [0, 3.0395694357925356], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.394448407831774, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '5184.2591', 'coefficient_field': 'CDF', 'conductor': 5184, 'conductor_radical': 6, 'conjugate': '542275492125738459588922746232', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.2069539376226517, 0], [5.0, 0]], [[1.0, 0], [0, -3.0395694357925356], [-7.0, 0]], [[1.0, 0], [0, 5.023192347700234], [-11.0, 0]], [[1.0, 0], [0, 4.039569435792536], [-13.0, 0]], [[1.0, 0], [0, -4.816238410077582], [-17.0, 0]], [[1.0, 0], [1.0395694357925354, 0], [19.0, 0]], [[1.0, 0], [-5.437100222945537, 0], 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'5.23129759458219933185133820715127', '6.62515879075996061842506133178559', '6.83024059440550196867557193003606', '7.51429700573703427952442628807087', '8.226555627726181775361021350146224'], 'prelabel': '2-72e2-24.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.433851755195466, 'root_angle': 0.4166666666666667, 'root_number': '0.2588190451025207623488988376240483283490689013199305138 + 0.9659258262890682867497431997288973676339048390084045504*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.20833333333333334', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.08758120490554610050782233685', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.01769411257238888089809725724', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.02178837486166528212812209830', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 41.394448407831774, 'bad_primes': [2, 3], 'central_character': '24.11', 'conductor': 5184, 'conductor_radical': 6, 'degree': 2, 'index': 69, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5184/2/f/e/2591/10'], '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': '2-72e2-24.11-c1-0-69', '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': '2-72e2-24.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.433851755195466, 'root_angle': 0.20833333333333334, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.08758120490554610050782233685', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1378672967195456465111057408676', 'Lhash_array': ['1378672967195456465111057408676'], 'label': '2-72e2-24.11-c1-0-69', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5184/2/f/e/2591/10'}