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lfunc_lfunctions • Show schema
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{'Lhash': '888729873432642703160137904863', 'a10': [0.0, 0.0], 'a2': [-6.874424007110001, 0.0], 'a3': [5.754214296306107, 0.0], 'a4': [15.257705429530318, 0.0], 'a5': [0.0, 0.0], 'a6': [-39.55690890058228, 0.0], 'a7': [159.97653454922371, 0.0], 'a8': [115.0936317293442, 0.0], 'a9': [-209.88901783218643, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 172.41260629895422, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [43, [[1.0, 0], [1849.0, 0]]]], 'bad_primes': [5, 43], 'central_character': '1075.1', 'coefficient_field': 'CDF', 'conductor': 1075, 'conductor_radical': 215, 'degree': 2, 'euler_factors': [[[1.0, 0], [6.874424007110001, 0], [32.0, 0]], [[1.0, 0], [-5.754214296306107, 0], [243.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-159.97653454922371, 0], [16807.0, 0]], [[1.0, 0], [66.6997836780352, 0], [161051.0, 0]], [[1.0, 0], [3.1500158199275656, 0], [371293.0, 0]], [[1.0, 0], [-1887.9590112430599, 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'positive_zeros': ['0.70108425245302977320723813301291', '1.47005034758242845904699169900843', '2.57944792069428019412413649041509', '3.73360337977605637871403077176348', '5.04755138781048143210386755000926', '5.62162292415828923722043155205449', '7.19948741218049886625758768807243', '7.79844596656850709069079965477654', '8.306446241657040054825745327865291', '9.092815827727739599994166205770231'], 'prelabel': '2-1075-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 13.130598093725746, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.70108425245302977320723813301', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.47005034758242845904699169901', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.57944792069428019412413649042', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 172.41260629895422, 'bad_primes': [5, 43], 'central_character': '1.1', 'conductor': 1075, 'conductor_radical': 215, 'degree': 2, 'index': 123, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1075/6/a/i/1/10'], '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': '2-1075-1.1-c5-0-123', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-1075-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 13.130598093725746, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.70108425245302977320723813301', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '888729873432642703160137904863', 'Lhash_array': ['888729873432642703160137904863'], 'label': '2-1075-1.1-c5-0-123', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1075/6/a/i/1/10'}