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lfunc_lfunctions • Show schema
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{'Lhash': '2324404226942534047854885079509', 'a10': [-6.0631865023484055, 3.5005823592777574], 'a2': [-1.5903556340296539, -0.9181922534142587], 'a3': [-0.5400459297781633, 1.645706654823404], 'a4': [0.6861540284599084, 1.1884536391106229], 'a5': [1.9062360558265392, -3.301697699911269], 'a6': [2.369940188908628, -2.1213928612482857], 'a7': [-2.4673867962175566, 0.9549881663409558], 'a8': [0.0, 1.152683759333536], 'a9': [-2.416700787460078, -1.7775143610924322], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.5400459297781633, -1.645706654823404]]], [7, [[1.0, 0], [2.4673867962175566, -0.9549881663409558]]], [13, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.131', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '694322223367214980056979781878', 'degree': 2, 'euler_factors': 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'7.10827588872524832921313152680768', '8.204467342183940851876997153487884', '9.392459394235300124421825363485320', '10.26111263464220517395147858405936', '10.85207359054637682570861467292456', '12.30955291909565117862417654724129'], 'prelabel': '2-273-21.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.6903949637085713, 'root_number': '-0.5631091989441608 + 0.826382496223429*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.345197481854', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.83363162256543356668734065118', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.50340835034046346685326190139', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.08619376711195019570617660497', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'bad_primes': [3, 7, 13], 'central_character': '21.5', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/bh/a/131/8'], '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': '2-273-21.5-c1-0-16', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-273-21.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.34519748185428567, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.83363162256543356668734065118', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2324404226942534047854885079509', 'Lhash_array': ['2324404226942534047854885079509'], 'label': '2-273-21.5-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/bh/a/131/8'}