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lfunc_lfunctions • Show schema
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{'Lhash': '1206770680243658903448454882751', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [5.132444468702838, 0], 'a6': [0, 0], 'a7': [0, -4.025159310547453], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 47.084589681459306, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1728.703', 'coefficient_field': 'CDF', 'conductor': 1728, 'conductor_radical': 6, 'conjugate': '1341628505005235890206163318773', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-5.132444468702838, 0], [25.0, 0]], [[1.0, 0], [0, 4.025159310547453], [-49.0, 0]], [[1.0, 0], [0, 4.303437580862017], [-121.0, 0]], [[1.0, 0], [-18.486200670659763, 0], [169.0, 0]], [[1.0, 0], [-23.575067935211006, 0], [289.0, 0]], [[1.0, 0], [0, -21.725930297517984], [-361.0, 0]], [[1.0, 0], [0, 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'2.08386496587734030294022076837637', '2.98253527947236713919839635130354', '4.15702007443495061760026190023362', '5.22643469173148103713410034251920', '5.95401640101779527348931775087480', '6.49189595374886431817795780481185', '7.60980972445605752962990370091510', '8.462454279312951190086764849722526', '9.236562121597200113105609066017007'], 'prelabel': '2-12e3-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.861821163616792, 'root_angle': 0.0, 'root_number': '1', 'self_dual': False, 'sign_arg': 0, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.951974211211188949844246594516', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.08386496587734030294022076838', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.98253527947236713919839635130', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 47.084589681459306, 'bad_primes': [2, 3], 'central_character': '4.3', 'conductor': 1728, 'conductor_radical': 6, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1728/3/g/m/703/5'], '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': '2-12e3-4.3-c2-0-38', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-12e3-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.861821163616792, 'root_angle': 0.0, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.951974211211188949844246594516', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1206770680243658903448454882751', 'Lhash_array': ['1206770680243658903448454882751'], 'label': '2-12e3-4.3-c2-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1728/3/g/m/703/5'}