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lfunc_lfunctions • Show schema
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{'Lhash': '1732610209907514782599944362720', 'a10': [1.6309863136978342, 1.0897902135516373], 'a2': [0.9238795325112867, -0.3826834323650898], 'a3': [0.0, 0.0], 'a4': [0.7071067811865476, -0.7071067811865476], 'a5': [1.0897902135516373, 1.6309863136978342], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.3826834323650898, -0.9238795325112867], 'a9': [0.9238795325112867, 0.3826834323650898], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9238795325112867, 0.3826834323650898]]], [7, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [0.3826834323650898, 0.9238795325112867]]]], 'bad_primes': [2, 7, 17], 'central_character': '3332.2547', 'coefficient_field': 'CDF', 'conductor': 3332, 'conductor_radical': 238, 'conjugate': '2422728759653019357257089636012', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.9238795325112867, 0.3826834323650898]], [[1.0, 0], [0, 0], 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'6.23851949515265335598200283215943', '7.24281537781091256121382202001287', '7.936445552035025418717927714435143', '8.769684432833278011057139629083645'], 'prelabel': '2-3332-476.167-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': -0.07137058215724044, 'root_number': '0.97496843457065373237104635820461 - 0.22234331919544803822966687045697*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.03568529107862022', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.36678845858280938826912420401', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.17660335775675869784094409658', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.43566043374277552351188392069', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'bad_primes': [2, 7, 17], 'central_character': '476.167', 'conductor': 3332, 'conductor_radical': 238, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3332/1/bn/b/2547/1'], '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': '2-3332-476.167-c0-0-2', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3332-476.167-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': -0.03568529107862022, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.36678845858280938826912420401', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1732610209907514782599944362720', 'Lhash_array': ['1732610209907514782599944362720'], 'label': '2-3332-476.167-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3332/1/bn/b/2547/1'}