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lfunc_lfunctions • Show schema
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{'Lhash': '306277551663536859276892716858', 'a10': [1.1752184489322965, -0.6785126878476759], 'a2': [-0.20401144537981153, -0.11778606290779882], 'a3': [0.0, 0.0], 'a4': [-1.97225288676936, -3.4160422052589197], 'a5': [-2.880275777528983, 4.9887839864901515], 'a6': [0.0, 0.0], 'a7': [1.9445057735387203, 0.0], 'a8': [0.0, 1.8715041136268051], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.6594125205610775, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-17.818137547952997, -6.596512284702242]]]], 'bad_primes': [3, 19], 'central_character': '171.46', 'coefficient_field': 'CDF', 'conductor': 171, 'conductor_radical': 57, 'conjugate': '2823500898065171259269501748679', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.20401144537981153, 0.11778606290779882], [2.0, 3.4641016151377544]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.880275777528983, -4.9887839864901515], [-12.5, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-171-19.8-c2-0-1', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/171/3/p/c/46/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.39735509922817985, 0.19608474713275556, -0.01443894794396849, -0.23510943193925535, -0.4663559470146075, -0.707736712780663, -0.9575948205493652, -1.2128013078632311, -1.4686025700622751, -1.7185846933703, -1.9547648224940097, -2.167817611450962, -2.3474414180185903, -2.482863032873062, -2.5634709792021715, -2.579556055792955, -2.5231246463860844, -2.3887366090460924, -2.1743068153095226, -1.881799337059993, -1.5177376380977354, -1.093454565219117, -0.625013796387563, -0.13275052768246193, 0.3595963101299236, 0.826155880499629, 1.2405588849057623, 1.5778490784812862, 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'9.032432339798642021888118125194921', '9.863455089780649066671900806674168', '11.55102204976583797254777941731801', '12.12334306928055431209374601631578'], 'prelabel': '2-171-19.8-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.158567237905986, 'root_angle': -0.7516310641431463, 'root_number': '-0.7107207956957798 - 0.7034742003553205*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.375815532072', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.24161038665417289696026948509', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.90844033227225179242095487131', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.51786428977261461144157534958', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.6594125205610775, 'bad_primes': [3, 19], 'central_character': '19.8', 'conductor': 171, 'conductor_radical': 57, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/171/3/p/c/46/2'], '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': '2-171-19.8-c2-0-1', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-171-19.8-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.158567237905986, 'root_angle': -0.37581553207157314, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.24161038665417289696026948509', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '306277551663536859276892716858', 'Lhash_array': ['306277551663536859276892716858'], 'label': '2-171-19.8-c2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/3/p/c/46/2'}