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lfunc_lfunctions • Show schema
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{'Lhash': '2245107034687734732862152196308', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-0.3423708244910499, 0.5930036630477453], 'a6': [0, 0], 'a7': [1.8027756377319946, -1.9364916731037085], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.09784104749013, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.8027756377319946, 1.9364916731037085]]]], 'bad_primes': [2, 3, 7], 'central_character': '2016.289', 'coefficient_field': 'CDF', 'conductor': 2016, 'conductor_radical': 42, 'conjugate': '222358884309366664339384999219', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.3423708244910499, -0.5930036630477453], [-2.5, -4.330127018922194]], [[1.0, 0], [-1.8027756377319946, 1.9364916731037085]], [[1.0, 0], [1.7655644370746375, 3.058047309050016], [-5.5, 9.526279441628825]], [[1.0, 0], 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'root_analytic_conductor': 4.0122114908726, 'root_angle': 0.8851158142845197, 'root_number': '-0.93557257765835474822685871524877405944527683935673898198 + 0.3531344672128476526813908036832355078174002542023239382*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4425579071422599', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.77107716770182797284447918480', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.46555518251041896985139407049', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.81873097474905170882839269418', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 16.09784104749013, 'bad_primes': [2, 3, 7], 'central_character': '7.2', 'conductor': 2016, 'conductor_radical': 42, 'degree': 2, 'index': 37, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2016/2/s/x/289/2'], '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': '2-2016-7.2-c1-0-37', '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': '2-2016-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.0122114908726, 'root_angle': 0.44255790714225984, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.77107716770182797284447918480', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2245107034687734732862152196308', 'Lhash_array': ['2245107034687734732862152196308'], 'label': '2-2016-7.2-c1-0-37', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2016/2/s/x/289/2'}