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lfunc_lfunctions • Show schema
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{'Lhash': '170561049853163221758167318529', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-3.4122608274063984, -5.910209121744897], 'a6': [0, 0], 'a7': [14.93856473402778, -10.947113029802036], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 59.473925285786564, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-14.93856473402778, 10.947113029802036]]]], 'bad_primes': [2, 3, 7], 'central_character': '1008.17', 'coefficient_field': 'CDF', 'conductor': 1008, 'conductor_radical': 42, 'conjugate': '1314470992939077602313912569157', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.4122608274063984, 5.910209121744897], [-62.5, 108.25317547305482]], [[1.0, 0], [-14.93856473402778, 10.947113029802036]], [[1.0, 0], [50.53030172814528, 29.17368330497769], [665.5, 1152.6798124370878]], [[1.0, 0], 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'6.84723974220290179644924209093061', '7.82313484454120123615336461560620', '8.334000939950050925740056446347333', '9.382650576425237948786416864104050'], 'prelabel': '2-1008-21.17-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.711933952374499, 'root_angle': -0.5457342561178588, 'root_number': '-0.1431845759048354368652040946470895361914938322950142543 - 0.9896960024284994651583395399991550299297667688863393208*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2728671280589294', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.13454894418261246178983100699', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.11883087752529687761457754884', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.57429718181268971484786199900', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 59.473925285786564, 'bad_primes': [2, 3, 7], 'central_character': '21.17', 'conductor': 1008, 'conductor_radical': 42, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1008/4/bt/b/17/4'], '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': '2-1008-21.17-c3-0-4', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-1008-21.17-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.711933952374499, 'root_angle': -0.2728671280589294, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.13454894418261246178983100699', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '170561049853163221758167318529', 'Lhash_array': ['170561049853163221758167318529'], 'label': '2-1008-21.17-c3-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1008/4/bt/b/17/4'}