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lfunc_lfunctions • Show schema
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{'Lhash': '4463195604100378182409895449883', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.5, -0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.5, 0.8660254037844386], 'a8': [0.0, 0.0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.041921461061172206, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.5, 0.8660254037844386]]], [7, [[1.0, 0], [0.5, -0.8660254037844386]]]], 'bad_primes': [2, 3, 7], 'central_character': '84.65', 'coefficient_field': 'CDF', 'conductor': 84, 'conductor_radical': 42, 'conjugate': '3251491262760798411050136400988', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0.5, 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'4.89098280278214127535463544376791', '6.33268371238830377081639818437894', '7.74268924650426005669373898018713', '9.514310179830675798001626081591795', '10.10977840826758241325303230439487', '11.28616606617349332842095808165103', '12.33651690769049716182029767607925', '13.63570593099300485737171669080124', '14.74600246740631530719188745074261'], 'prelabel': '2-84-21.2-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.20474731026602574, 'root_angle': 0.14649371361272057, 'root_number': '0.89595321966310477774725020770463 + 0.44414843034206066891807967048929*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.07324685680636027', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.52084052442906496218604031148', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.89098280278214127535463544377', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.33268371238830377081639818438', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.041921461061172206, 'bad_primes': [2, 3, 7], 'central_character': '21.2', 'conductor': 84, 'conductor_radical': 42, 'degree': 2, 'index': 0, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/84/1/p/a/65/1', 'ArtinRepresentation/2.84.6t5.b.b'], 'is_instance_Artin': True, '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': '2-84-21.2-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-84-21.2-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.20474731026602574, 'root_angle': 0.07324685680636028, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.52084052442906496218604031148', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24596371
{'Lhash': '4463195604100378182409895449883', 'Lhash_array': ['4463195604100378182409895449883'], 'label': '2-84-21.2-c0-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/2.84.6t5.b.b'}
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id: 19807717
{'Lhash': '4463195604100378182409895449883', 'Lhash_array': ['4463195604100378182409895449883'], 'label': '2-84-21.2-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/84/1/p/a/65/1'}