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lfunc_lfunctions • Show schema
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{'Lhash': '808723166250740971147940672964', 'a10': [0.0, 0.0], 'a2': [2.5615528128088303, 0.0], 'a3': [-3.0, 0.0], 'a4': [-1.4384471871911697, 0.0], 'a5': [0.0, 0.0], 'a6': [-7.68465843842649, 0.0], 'a7': [-6.246211251235321, 0.0], 'a8': [-24.177080940897135, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.67657575473603, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [3.0, 0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [11.0, 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], [-2.5615528128088303, 0], [8.0, 0]], [[1.0, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [6.246211251235321, 0], [343.0, 0]], [[1.0, 0], [11.0, 0]], [[1.0, 0], [-49.12310562561766, 0], [2197.0, 0]], [[1.0, 0], [82.70832376358854, 0], [4913.0, 0]], [[1.0, 0], [130.35416188179425, 0], [6859.0, 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'3.66192660395499297026734709011188', '4.47846261270584869041862970750343', '5.28967833031309285134040649406368', '6.32318897000562416886075608312718', '6.71788831850485457084068465705737', '8.277786429051531621205711879598221', '8.954080081240248141494269535549444', '9.876528510536384947953267090958136'], 'prelabel': '2-825-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.976860021151064, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.63797008900176234647170914173', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.42307071631622425828895461978', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.66192660395499297026734709011', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 48.67657575473603, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/4/a/m/1/2'], '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-c3-0-14', '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': '2-825-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.976860021151064, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.63797008900176234647170914173', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '808723166250740971147940672964', 'Lhash_array': ['808723166250740971147940672964'], 'label': '2-825-1.1-c3-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/4/a/m/1/2'}