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lfunc_lfunctions • Show schema
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{'Lhash': '631121090628046888078508630344', 'a10': [0.0, 0.0], 'a2': [-1.9245199376465199, 0.0], 'a3': [-9.0, 0.0], 'a4': [-28.296223009601036, 0.0], 'a5': [0.0, 0.0], 'a6': [17.32067943881868, 0.0], 'a7': [59.11196972969573, 0.0], 'a8': [116.04128334675804, 0.0], 'a9': [81.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 132.31665134570906, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [9.0, 0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [121.0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '825.1', 'coefficient_field': 'CDF', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.9245199376465199, 0], [32.0, 0]], [[1.0, 0], [9.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-59.11196972969573, 0], [16807.0, 0]], [[1.0, 0], [121.0, 0]], [[1.0, 0], [599.6211239754357, 0], [371293.0, 0]], [[1.0, 0], [-2271.970947359925, 0], [1419857.0, 0]], [[1.0, 0], [2998.771826564815, 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-2.5650601704006526], 'positive_zeros': ['0.49786675485691329818516983670634', '1.52989506334743613380374036919844', '3.01005132576675512610223140723507', '4.40434583464631671920141281097971', '4.92107154516101017267205881966928', '5.84836692280294202190180363814164', '6.98865691925276867572811247763934', '7.971735546643385654251368216849854', '8.505931282417219050210173533472173', '9.632249531729967868029725102197387'], 'prelabel': '2-825-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.502897519569105, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.49786675485691329818516983671', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.52989506334743613380374036920', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.01005132576675512610223140724', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 132.31665134570906, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/6/a/s/1/4'], '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': '2-825-1.1-c5-0-25', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-825-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.502897519569105, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.49786675485691329818516983671', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '631121090628046888078508630344', 'Lhash_array': ['631121090628046888078508630344'], 'label': '2-825-1.1-c5-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/6/a/s/1/4'}