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lfunc_lfunctions • Show schema
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{'Lhash': '668380663319140321161312487830', 'a10': [6.958306168409122, 0.0], 'a2': [-1.6599150549920012, 0.0], 'a3': [0.7482998043890643, 0.0], 'a4': [0.755317989789098, 0.0], 'a5': [-4.1919652138118915, 0.0], 'a6': [-1.2421141109529774, 0.0], 'a7': [-4.843939874191655, 0.0], 'a8': [2.0660664074267836, 0.0], 'a9': [-2.440047402751288, 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], [1.6599150549920012, 0], [2.0, 0]], [[1.0, 0], [-0.7482998043890643, 0], [3.0, 0]], [[1.0, 0], [4.1919652138118915, 0], [5.0, 0]], [[1.0, 0], [4.843939874191655, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], 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'3.79308168396772767146636335237118', '4.43679077331383586643033438305606', '5.35651655704514572223077105437935', '6.54921930512005432410905447640984', '7.22707915031745877289578615611120', '7.45068487275710253355771916238166'], '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': '0.52725937509815735467575552514', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.41913450830850318632166436065', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.96181329938245598878087329234', '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': 116, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8041/2/a/h/1/20'], '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-c1-0-116', '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': '0.52725937509815735467575552514', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '668380663319140321161312487830', 'Lhash_array': ['668380663319140321161312487830'], 'label': '2-8041-1.1-c1-0-116', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8041/2/a/h/1/20'}