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lfunc_lfunctions • Show schema
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{'Lhash': '685839654945723948576808036701', 'a10': [7.717335386993123, 0.0], 'a2': [-2.5115206483207757, 0.0], 'a3': [-1.728469339268054, 0.0], 'a4': [4.307735966941609, 0.0], 'a5': [-3.072774015277557, 0.0], 'a6': [4.341086435561086, 0.0], 'a7': [-4.070057750349161, 0.0], 'a8': [-5.79592653184636, 0.0], 'a9': [-0.012393743210256882, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.20770826531158, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [-1.0, 0]]], [17, [[1.0, 0], [-1.0, 0]]], [43, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [11, 17, 43], 'central_character': '8041.1', 'coefficient_field': 'CDF', 'conductor': 8041, 'conductor_radical': 8041, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.5115206483207757, 0], [2.0, 0]], [[1.0, 0], [1.728469339268054, 0], [3.0, 0]], [[1.0, 0], [3.072774015277557, 0], [5.0, 0]], [[1.0, 0], [4.070057750349161, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], 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'4.67624903730089491705637612899287', '5.87714880800210085050917148191175', '6.35340609343460052697311988243942', '6.96575558764678127014773656059897', '7.47410527006347504181211230689481'], 'prelabel': '2-8041-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.012971250747851, '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': '0.54103209103695018031698565389', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.82060945846565938792581070256', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.09935538281183946417590927633', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.20770826531158, 'bad_primes': [11, 17, 43], 'central_character': '1.1', 'conductor': 8041, 'conductor_radical': 8041, 'degree': 2, 'index': 122, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8041/2/a/c/1/5'], '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': '2-8041-1.1-c1-0-122', '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': '2-8041-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.012971250747851, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.54103209103695018031698565389', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '685839654945723948576808036701', 'Lhash_array': ['685839654945723948576808036701'], 'label': '2-8041-1.1-c1-0-122', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8041/2/a/c/1/5'}