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lfunc_lfunctions • Show schema
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{'Lhash': '724585540210197708997671323327', 'a10': [-1395246.1041931119, -1.2945049741386135e-66], 'a2': [-104.53823725009431, -60.35517941695091], 'a3': [0, 0], 'a4': [-906.5046350953302, -1570.1120852817971], 'a5': [10010.06527058012, -5779.313878575156], 'a6': [0, 0], 'a7': [308433.19694750215, -534221.9678539716], 'a8': [0, 2196567.5187085527], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 33.56882140101463, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '7.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '27.8', 'coefficient_field': 'CDF', 'conductor': 27, 'conductor_radical': 3, 'conjugate': '1132735735606176796220334590138', 'degree': 2, 'euler_factors': [[[1.0, 0], [104.53823725009431, 60.35517941695091], [8192.0, 14188.960215604242]], [[1.0, 0], [0, 0]], [[1.0, 0], [-10010.06527058012, 5779.313878575156], [3051757812.5, -5285799583.645255]], [[1.0, 0], [-308433.19694750215, 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'primitive': True, 'rational': False, 'root_analytic_conductor': 5.793860664618595, 'root_angle': 0.031108896433389824, 'root_number': '0.98095785806999036942213653081090254383998975299560070925 + 0.1942207009840522387387313543968686167394427272253988449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.031108896433389824', 'prec': 67}, 'spectral_label': 'c14-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.57159720516027241336591808298', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.50996892214174093533900647263', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.47359732214265480119059316373', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 33.56882140101463, 'bad_primes': [3], 'central_character': '9.2', 'conductor': 27, 'conductor_radical': 3, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/27/15/d/a/8/5'], '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': '2-3e3-9.2-c14-0-5', 'motivic_weight': 14, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [14], 'order_of_vanishing': 0, 'prelabel': '2-3e3-9.2-c14-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.793860664618595, 'root_angle': 0.031108896433389824, 'self_dual': False, 'spectral_label': 'c14-0', 'z1': {'__RealLiteral__': 0, 'data': '0.57159720516027241336591808298', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '724585540210197708997671323327', 'Lhash_array': ['724585540210197708997671323327'], 'factors': ['2-3e3-9.2-c14-0-5'], 'label': '2-3e3-9.2-c14-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/27/15/d/a/8/5'}