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lfunc_lfunctions • Show schema
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{'Lhash': '1888398977080686625593816900677', 'a10': [-9.31541064587597, 0.0], 'a2': [-2.747316648766746, 0.0], 'a3': [2.1095992706751083, 0.0], 'a4': [5.547748768590944, 0.0], 'a5': [3.3907306061926286, 0.0], 'a6': [-5.79573719855191, 0.0], 'a7': [-0.07055010783883699, 0.0], 'a8': [-9.746789257591622, 0.0], 'a9': [1.4504090828329494, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.06397754167328, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[71, [[1.0, 0], [1.0, 0]]], [113, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [71, 113], 'central_character': '8023.1', 'coefficient_field': 'CDF', 'conductor': 8023, 'conductor_radical': 8023, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.747316648766746, 0], [2.0, 0]], [[1.0, 0], [-2.1095992706751083, 0], [3.0, 0]], [[1.0, 0], [-3.3907306061926286, 0], [5.0, 0]], [[1.0, 0], [0.07055010783883699, 0], [7.0, 0]], [[1.0, 0], [4.8603925657907405, 0], [11.0, 0]], [[1.0, 0], 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'3.11692937083432987676904503633618', '4.78350252288195893508422247805624', '5.85676000356556139519660142124225', '6.33054453299376766040801964050535', '7.06064199218653745973677926216244', '7.84962772009304103525926127246092'], 'prelabel': '2-8023-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.003997597555442, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.48968412647830317674959854595', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.02513223967374940954284552019', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.75904726414063340841950864336', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.06397754167328, 'bad_primes': [71, 113], 'central_character': '1.1', 'conductor': 8023, 'conductor_radical': 8023, 'degree': 2, 'index': 552, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8023/2/a/c/1/4'], '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': '2-8023-1.1-c1-0-552', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-8023-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.003997597555442, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.48968412647830317674959854595', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1888398977080686625593816900677', 'Lhash_array': ['1888398977080686625593816900677'], 'label': '2-8023-1.1-c1-0-552', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8023/2/a/c/1/4'}