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lfunc_lfunctions • Show schema
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{'Lhash': '184888252763776003642209691715', 'a10': [0.0, 0.0], 'a2': [2.772092547743646, -4.801405135975049], 'a3': [-0.32081921699137633, 5.186239006255789], 'a4': [-11.36899418651172, -19.691675561993495], 'a5': [0.0, 0.0], 'a6': [24.011894040435937, 15.917117536240976], 'a7': [-12.856329690662566, 22.267816223083834], 'a8': [-81.71013547518157, 0.0], 'a9': [-26.79415006001808, -3.3276902742342322], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.275429751291645, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.32081921699137633, -5.186239006255789]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '225.151', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '2765661037540947498099434257007', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.772092547743646, 4.801405135975049], [-4.0, -6.928203230275509]], [[1.0, 0], [0.32081921699137633, 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[-216.82800722779953, -375.5571250224605], [-721448.5, 1249585.457044355]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-15e2-9.7-c3-0-6', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/225/4/e/f/151/12', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.5138667853152562, 0.07694384373004716, -0.4005967004908588, -0.9143258374982028, -1.4586649447962308, -2.026472156988359, -2.608678878366441, -3.1940327669861985, -3.7689982357020426, -4.317856516021366, -4.823035129452501, -5.265681497536368, -5.626477590624351, -5.886672301867431, -6.029286343750884, -6.040422128171962, -5.910590089481677, -5.6359454900137465, -5.219318425866359, -4.67091703338159, -4.0085919433396064, -3.2575702920089467, -2.4496004734717602, -1.62149336280994, 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'7.16669498435109386229899806781019', '8.108939364929335372101366279444167', '9.054035756965855822261201223764738', '10.82663589725446866879656426651645', '12.29227379032109464539729980188530'], 'prelabel': '2-15e2-9.7-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': -0.40511345008933836, 'root_number': '0.2936996485831705 - 0.9558977541673179*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.202556725045', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.14585111443996357599321898183', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.13656598219883568616755231129', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.34245112604866919399221601710', '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': '9.7', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/4/e/f/151/12'], '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': '2-15e2-9.7-c3-0-6', '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': '2-15e2-9.7-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': -0.20255672504466918, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.14585111443996357599321898183', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '184888252763776003642209691715', 'Lhash_array': ['184888252763776003642209691715'], 'label': '2-15e2-9.7-c3-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/4/e/f/151/12'}