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lfunc_lfunctions • Show schema
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{'Lhash': '1847064614337331546394253464608', 'a10': [0.5675704452131273, -0.3276869493278748], 'a2': [-1.0, 0.0], 'a3': [-0.4365929261145125, 1.6761224945888555], 'a4': [1.0, 0.0], 'a5': [-0.5675704452131273, 0.3276869493278748], 'a6': [0.4365929261145125, -1.6761224945888555], 'a7': [-2.3728944074009584, 1.1702017481294646], 'a8': [-1.0, 0.0], 'a9': [-2.6187732337335357, -1.463566448877809], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.359831950361911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [3, [[1.0, 0], [0.4365929261145125, -1.6761224945888555]]], [7, [[1.0, 0], [2.3728944074009584, -1.1702017481294646]]], [13, [[1.0, 0], [-3.5053511259595327, 0.844105137843762]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.17', 'coefficient_field': 'CDF', 'conductor': 546, 'conductor_radical': 546, 'conjugate': '271955663713265583218570054938', 'degree': 2, 'euler_factors': [[[1.0, 0], 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0], [-2.2550629883132682, 1.301961223342227], [56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 16, 'label': '2-546-273.17-c1-0-16', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/546/2/bi/e/17/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.28526532313096653, 0.42400495682353545, 0.545815041558087, 0.6503242922662873, 0.7342419408361175, 0.7917105710158964, 0.8151128648160043, 0.7961795934352738, 0.7272768110933474, 0.6027795057047818, 0.4204426367777021, 0.18266215875112188, -0.1025073981491356, -0.420731978681806, -0.7513301095842322, -1.067894685656318, -1.3396951082286384, -1.5338786957534734, -1.618396840335433, -1.5654743425979776, -1.35533161747664, -0.9797739378025979, -0.4451960379067767, 0.2254698269850994, 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'8.249044467384189824723745227588043', '9.153428401415813254825205907486205', '10.20680368149140731664792651760831', '10.91043476600451017125458265630922'], 'prelabel': '2-546-273.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.4822952908630233, 'root_number': '0.05559230954484956 + 0.9984535518087306*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.241147645432', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.45707706366784642410043206249', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.83533389763802231420388216586', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.31944504079909517875701564252', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.359831950361911, 'bad_primes': [2, 3, 7, 13], 'central_character': '273.17', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/bi/e/17/8'], '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': '2-546-273.17-c1-0-16', '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': '2-546-273.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.24114764543151165, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.45707706366784642410043206249', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1847064614337331546394253464608', 'Lhash_array': ['1847064614337331546394253464608'], 'label': '2-546-273.17-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/bi/e/17/8'}