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lfunc_lfunctions • Show schema
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{'Lhash': '665436075055357218639544481132', 'a10': [2.3219353559925042, 0.0], 'a2': [-1.879448334487499, 0.0], 'a3': [-2.611653804481257, 0.0], 'a4': [1.532326042007834, 0.0], 'a5': [-1.235434522665751, 0.0], 'a6': [4.9084683930902395, 0.0], 'a7': [-3.716920327984758, 0.0], 'a8': [0.8789690414315532, 0.0], 'a9': [3.8207355944614245, 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], [1.879448334487499, 0], [2.0, 0]], [[1.0, 0], [2.611653804481257, 0], [3.0, 0]], [[1.0, 0], [1.235434522665751, 0], [5.0, 0]], [[1.0, 0], [3.716920327984758, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [4.167603474652977, 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'2.92294531089646135990141379901925', '4.10672403959210829912240242453172', '4.67572784867519056245080839088405', '5.63137671548414809348188078619423', '6.31792258715173947724129036541967', '6.79792674847671930728001672354331', '7.59862284381547854866630986923218'], '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': '0.52493650453488624892835294245', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.87303305943635310292702496507', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.92294531089646135990141379902', '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': 114, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8041/2/a/g/1/15'], '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-c1-0-114', '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': '0.52493650453488624892835294245', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '665436075055357218639544481132', 'Lhash_array': ['665436075055357218639544481132'], 'label': '2-8041-1.1-c1-0-114', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8041/2/a/g/1/15'}