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lfunc_lfunctions • Show schema
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{'Lhash': '1644567709462444059811700928460', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-22.72486991634567, 40.87273280911331], 'a4': [0, 0], 'a5': [3.0577178973208756, 5.2961227533724315], 'a6': [0, 0], 'a7': [-422.4747548554947, 731.7477403249231], 'a8': [0, 0], 'a9': [-1154.1605745703348, -1857.6550724253075], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.491721834856776, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [22.72486991634567, -40.87273280911331]]]], 'bad_primes': [2, 3], 'central_character': '72.25', 'coefficient_field': 'CDF', 'conductor': 72, 'conductor_radical': 6, 'conjugate': '103444009168869149982931617292', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [22.72486991634567, -40.87273280911331]], [[1.0, 0], [-3.0577178973208756, -5.2961227533724315], [-39062.5, 67658.23467065927]], [[1.0, 0], [422.4747548554947, -731.7477403249231], [-411771.5, 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'7.44187921661860174922653350427474', '8.741187245883292618200756862957568', '10.41566370286459617832913780414631', '11.24358273586820026590035888607202', '12.55313041218223479187194123575601', '13.37742936180959078745378572478447'], 'prelabel': '2-72-9.7-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.74254381475351, 'root_angle': 0.5452629298429148, 'root_number': '-0.14171896159566838 + 0.9899069329609959*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2726314649214574', 'prec': 60}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.29733517198378956312505836891218', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '3.18605081622563419291268666369213', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '5.12186846540493627939398710188585', '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': '9.7', 'conductor': 72, 'conductor_radical': 6, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/72/8/i/a/25/4'], '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': '2-72-9.7-c7-0-12', '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': '2-72-9.7-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.74254381475351, 'root_angle': 0.2726314649214574, 'self_dual': False, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '1.29733517198378956312505836891218', 'prec': 113}}
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lfunc_instances • Show schema
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{'Lhash': '1644567709462444059811700928460', 'Lhash_array': ['1644567709462444059811700928460'], 'label': '2-72-9.7-c7-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/72/8/i/a/25/4'}