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lfunc_lfunctions • Show schema
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{'Lhash': '50702059454674712478563975210', 'a10': [2.2028787402869012, 0], 'a2': [0, 1.0], 'a3': [0, 3.127030709438664], 'a4': [-1.0, 0], 'a5': [0, -2.2028787402869012], 'a6': [-3.127030709438664, 0], 'a7': [0, 0], 'a8': [0, -1.0], 'a9': [-6.778321057772471, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.607873337894029, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.0]]], [7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [1.4905297522114507, -2.962823156682233]]]], 'bad_primes': [2, 7, 11], 'central_character': '1078.1077', 'coefficient_field': 'CDF', 'conductor': 1078, 'conductor_radical': 154, 'conjugate': '3177409609945003406688487863091', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0]], [[1.0, 0], [0, -3.127030709438664], [-3.0, 0]], [[1.0, 0], [0, 2.2028787402869012], [-5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.4905297522114507, -2.962823156682233]], [[1.0, 0], [1.4593720833611863, 0], [13.0, 0]], 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['0.03999687251798425386462523067346', '1.56976949074715005063296826490545', '2.62900331074328782307552181694039', '3.19483576317159034464258206248917', '4.91506777228892041352407360853499', '6.07480603015160603525659126232232', '6.82320221125774771537372902817685', '7.34990602001853676278400265354173', '8.487142622316923217392837826218324', '8.895434505381250264075462926617812'], 'prelabel': '2-1078-77.76-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': 0.3755518646579594, 'root_number': '0.3810810967102964411030409164336716256023584359943987403 + 0.9245416149260549596618852759975401021161344511545598531*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.18777593232897974', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.03999687251798425386462523067', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.56976949074715005063296826491', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.62900331074328782307552181694', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.607873337894029, 'bad_primes': [2, 7, 11], 'central_character': '77.76', 'conductor': 1078, 'conductor_radical': 154, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1078/2/c/b/1077/16'], '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': '2-1078-77.76-c1-0-0', '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': '2-1078-77.76-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': 0.1877759323289797, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.03999687251798425386462523067', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '50702059454674712478563975210', 'Lhash_array': ['50702059454674712478563975210'], 'label': '2-1078-77.76-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1078/2/c/b/1077/16'}