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lfunc_lfunctions • Show schema
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{'Lhash': '292241411674094931047409939982', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 3.0971662328267526], 'a4': [0, 0], 'a5': [-0.5610740374668346, 0], 'a6': [0, 0], 'a7': [-1.402367486703952, -2.243516309777052], 'a8': [0, 0], 'a9': [-6.592438673762259, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.284731780340918, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.402367486703952, 2.243516309777052]]], [23, [[1.0, 0], [1.780040434162966, 4.453252300593906]]]], 'bad_primes': [2, 7, 23], 'central_character': '1288.321', 'coefficient_field': 'CDF', 'conductor': 1288, 'conductor_radical': 322, 'conjugate': '2788676256281472362819131233636', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -3.0971662328267526], [-3.0, 0]], [[1.0, 0], [0.5610740374668346, 0], [5.0, 0]], [[1.0, 0], [1.402367486703952, 2.243516309777052]], [[1.0, 0], [0, -5.177676101990353], [-11.0, 0]], 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-0.01206896021898064, -0.23070955930937978], 'positive_zeros': ['0.23053782455629289437213633275713', '1.44208092917685372589080796747903', '2.89495330919214222556572450632038', '3.28479219729912179557806266104684', '5.56091602934850016654488676098831', '5.72309761162678476724160113781808', '6.64627781755915846634667353719438', '7.64100498623814371578268274828531', '8.153984974547240963724293338876805', '8.775689015926683447897748281986332'], 'prelabel': '2-1288-161.160-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.2069817243540566, 'root_angle': 0.701133728704396, 'root_number': '-0.5906630049076850438694702726475439167170037184946243862 + 0.8069183444645585908037474152308523723162719523323852498*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.350566864352198', 'prec': 57}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.23053782455629289437213633276', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.44208092917685372589080796748', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.89495330919214222556572450632', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.284731780340918, 'bad_primes': [2, 7, 23], 'central_character': '161.160', 'conductor': 1288, 'conductor_radical': 322, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1288/2/f/b/321/8'], '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': '2-1288-161.160-c1-0-3', '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': '2-1288-161.160-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.2069817243540566, 'root_angle': 0.350566864352198, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.23053782455629289437213633276', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '292241411674094931047409939982', 'Lhash_array': ['292241411674094931047409939982'], 'label': '2-1288-161.160-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1288/2/f/b/321/8'}