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lfunc_lfunctions • Show schema
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{'Lhash': '1221314683948427156015034619019', 'a10': [0.0, 0.0], 'a2': [-1.2143197433775352, 0.0], 'a3': [-1.0, 0.0], 'a4': [-0.525427560843517, 0.0], 'a5': [0.0, 0.0], 'a6': [1.2143197433775352, 0.0], 'a7': [4.903211925911553, 0.0], 'a8': [3.066676547602054, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.587658166755635, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '825.1', 'coefficient_field': 'CDF', 'conductor': 825, 'conductor_radical': 165, 'conjugate': '1221314683948427156015034619019', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.2143197433775352, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-4.903211925911553, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-4.147643195775481, 0], [13.0, 0]], [[1.0, 0], [5.331851412666624, 0], [17.0, 0]], 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'5.81889204724798485412087037557505', '6.96569658306558056074072397097006', '7.978377094133140898193965544622628', '8.511226800400000433009649511040874', '9.168836514074333158517830630843236', '10.45481668105131590752179542421931'], 'prelabel': '2-825-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.566643365712431, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.963447407139270182895892958408', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.08486401237106693669829180021', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.28930424590553349006082575792', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.587658166755635, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/2/a/n/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': '2-825-1.1-c1-0-7', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-825-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.566643365712431, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.963447407139270182895892958408', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1221314683948427156015034619019', 'Lhash_array': ['1221314683948427156015034619019'], 'label': '2-825-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/2/a/n/1/1'}