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lfunc_lfunctions • Show schema
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{'Lhash': '620059548784370722101654945361', 'a10': [3261.5901002590963, -3489.7651971147448], 'a2': [-3.2956613045347702, -10.823059482687517], 'a3': [44.45414835094301, -14.51994126683546], 'a4': [-106.27723313158435, 71.33827666754271], 'a5': [211.10031268990645, 365.636467072595], 'a6': [-303.65600456234034, -433.2770832772441], 'a7': [-1251.6436034170008, -722.6367713622786], 'a8': [1122.352176550017, 915.1380178931698], 'a9': [1765.3426112152972, -1290.9432462457657], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.491721834856776, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [3.2956613045347702, 10.823059482687517]]], [3, [[1.0, 0], [-44.45414835094301, 14.51994126683546]]]], 'bad_primes': [2, 3], 'central_character': '72.11', 'coefficient_field': 'CDF', 'conductor': 72, 'conductor_radical': 6, 'conjugate': '2171329018740157302333544757499', 'degree': 2, 'euler_factors': [[[1.0, 0], [3.2956613045347702, 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-0.0859035786121885, 0.1361188932543817, 0.3312654365143013], 'positive_zeros': ['0.48914073694497081803223057968692', '2.61160604297619810521349537252077', '4.65775293601286647139807426477830', '5.72817002502299904139193970611058', '7.26668309329937248236064398250635', '8.723620051666384156410989623378390', '9.384539353165096526759571681802671', '9.904489071202723667013507828568874', '12.60070268842313947735282730505358', '13.14107364132903518167378315887948'], 'prelabel': '2-72-72.11-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.74254381475351, 'root_angle': -0.2610220195502835, 'root_number': '0.682203031490217 - 0.7311627888682233*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.13051100977514174', 'prec': 67}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.48914073694497081803223057968692', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.61160604297619810521349537252077', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '4.65775293601286647139807426477830', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.491721834856776, 'bad_primes': [2, 3], 'central_character': '72.11', 'conductor': 72, 'conductor_radical': 6, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/72/8/l/b/11/35'], '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': '2-72-72.11-c7-0-19', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-72-72.11-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.74254381475351, 'root_angle': -0.13051100977514174, 'self_dual': False, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '0.48914073694497081803223057968692', 'prec': 113}}
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lfunc_instances • Show schema
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{'Lhash': '620059548784370722101654945361', 'Lhash_array': ['620059548784370722101654945361'], 'label': '2-72-72.11-c7-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/72/8/l/b/11/35'}