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lfunc_lfunctions • Show schema
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{'Lhash': '906816142547819757579999577854', 'a10': [0.0, 0.0], 'a2': [-1.7015621187164243, 0.0], 'a3': [0.0, 0.0], 'a4': [-5.104686356149273, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-22.209372712298546, 0.0], 'a8': [22.298437881283576, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.275429751291645, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '225.1', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '906816142547819757579999577854', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.7015621187164243, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [22.209372712298546, 0], [343.0, 0]], [[1.0, 0], [-1.790627287701454, 0], [1331.0, 0]], [[1.0, 0], [58.209372712298546, 0], [2197.0, 0]], [[1.0, 0], [-18.984378812835757, 0], [4913.0, 0]], [[1.0, 0], 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'4.29877697518416051588241199469222', '5.55077672619013929452988806514093', '6.94352074344351613310366883575156', '7.87282757374301840820356457018993', '9.074810765468157147871308543604048', '9.809125067411754901408620420159313', '10.36240979570695940946407032854904', '11.94903704569756358426326497766548'], 'prelabel': '2-15e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.71535180307929917258243212967', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.85016827522063193080890320155', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.29877697518416051588241199469', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.275429751291645, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/4/a/o/1/1'], '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': '2-15e2-1.1-c3-0-0', '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': '2-15e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.71535180307929917258243212967', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '906816142547819757579999577854', 'Lhash_array': ['906816142547819757579999577854'], 'label': '2-15e2-1.1-c3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/4/a/o/1/1'}