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lfunc_lfunctions • Show schema
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{'Lhash': '2580223179958794024458748503819', 'a10': [-6.784030722351684, -1.994223447407157], 'a2': [-0.36602540378443865, 1.3660254037844386], 'a3': [-1.7349937001199554, -2.447406149486445], 'a4': [-1.7320508075688772, -1.0], 'a5': [-0.12051615277297228, 4.998547374680048], 'a6': [3.9782707432266027, -1.4742326456795252], 'a7': [4.070549086094672, -5.694789736038885], 'a8': [2.0, -2.0], 'a9': [-2.9795937210881323, 8.49246850198764], '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], [1.7349937001199554, 2.447406149486445]]], [5, [[1.0, 0], [0.12051615277297228, -4.998547374680048]]], [7, [[1.0, 0], [-4.070549086094672, 5.694789736038885]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '210.143', 'coefficient_field': 'CDF', 'conductor': 210, 'conductor_radical': 210, 'conjugate': 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'positive_zeros': ['2.03543719341453190021100496085272', '3.94233385772039233458106418502584', '5.05678122482433285221197954149717', '5.72429618979808741118104857931450', '7.925915379424504958504079858528838', '8.666604489342874412106698233862725', '9.844951033458439444427833234619928', '10.39972192148103925102171253109582', '11.60556479707541308444053699040362', '12.37317748878686038129153576367542'], 'prelabel': '2-210-105.38-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.392088115343211, 'root_angle': 0.7281095020987081, 'root_number': '-0.6568451876598224 + 0.7540254633950586*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.364054751049', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.03543719341453190021100496085', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.94233385772039233458106418503', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.05678122482433285221197954150', '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': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/210/3/w/b/143/5'], '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-c2-0-22', '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': 0.36405475104935403, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.03543719341453190021100496085', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2580223179958794024458748503819', 'Lhash_array': ['2580223179958794024458748503819'], 'label': '2-210-105.38-c2-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/210/3/w/b/143/5'}