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lfunc_lfunctions • Show schema
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{'Lhash': '2757496098583453835851013672236', 'a10': [6.758702196952065, -2.0784476449781777], 'a2': [-0.36602540378443865, 1.3660254037844386], 'a3': [1.2629799649550757, -2.7211912112385774], 'a4': [-1.7320508075688772, -1.0], 'a5': [-2.6565344920871414, -4.235897129576132], 'a6': [3.2549335714625056, 2.721287828467679], 'a7': [3.4703943124946064, 6.0791745587542625], 'a8': [2.0, -2.0], 'a9': [-5.809763216244152, -6.8736199612123166], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.722085551566235, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.36602540378443865, -1.3660254037844386]]], [3, [[1.0, 0], [-1.2629799649550757, 2.7211912112385774]]], [5, [[1.0, 0], [2.6565344920871414, 4.235897129576132]]], [7, [[1.0, 0], [-3.4703943124946064, -6.0791745587542625]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '210.143', 'coefficient_field': 'CDF', 'conductor': 210, 'conductor_radical': 210, 'conjugate': 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['2.17528086847195180213887907848572', '3.87637139490439009853535463038719', '4.19120941809219167491487190229431', '6.13728396793408851224702048483966', '7.84787867755413253485083627122512', '8.308323532034878303725326163747565', '9.844711263056963839572231240891746', '10.53568953391507497056442971862199', '11.03325145830579262415518263324920', '12.12506705446738113852867193977979'], 'prelabel': '2-210-105.38-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.392088115343211, 'root_angle': 0.5141008304417143, 'root_number': '-0.04428457794607702 + 0.999018956855243*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.257050415221', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.17528086847195180213887907849', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.87637139490439009853535463039', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.19120941809219167491487190229', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.722085551566235, 'bad_primes': [2, 3, 5, 7], 'central_character': '105.38', 'conductor': 210, 'conductor_radical': 210, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/210/3/w/b/143/11'], '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': '2-210-105.38-c2-0-24', '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': '2-210-105.38-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.392088115343211, 'root_angle': 0.25705041522085714, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.17528086847195180213887907849', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2757496098583453835851013672236', 'Lhash_array': ['2757496098583453835851013672236'], 'label': '2-210-105.38-c2-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/210/3/w/b/143/11'}