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lfunc_lfunctions • Show schema
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{'Lhash': '2401019507098608161192979421875', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-2.671402261898268, 1.365141001920614], 'a4': [0, 0], 'a5': [-4.4521506046703765, -7.7113510502375915], 'a6': [0, 0], 'a7': [-2.281428315781934, -3.9515497567606017], 'a8': [0, 0], 'a9': [5.272780089750364, -7.293681520681592], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.63765008224431, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [2.671402261898268, -1.365141001920614]]], [19, [[1.0, 0], [-17.671980309763242, 6.978618196415409]]]], 'bad_primes': [2, 3, 19], 'central_character': '684.445', 'coefficient_field': 'CDF', 'conductor': 684, 'conductor_radical': 114, 'conjugate': '266306352446874399570526206636', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.671402261898268, -1.365141001920614]], [[1.0, 0], [4.4521506046703765, 7.7113510502375915], [-12.5, 21.650635094610966]], [[1.0, 0], 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'3.21037758366307137387316743928254', '4.25676955373845290047479411997128', '5.64514328741389626328092029170022', '6.45235604552743118215288267839722', '7.19825411673563956478669942438891', '7.76662681843118298263794447365873', '9.130510745278583730654794805725984', '10.21516721603882373576049167848103', '10.88752725891221979277548646664880'], 'prelabel': '2-684-171.103-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.317134475811972, 'root_angle': -0.8405203620971948, 'root_number': '-0.87709306314887521737101118263578182540610317368797191531 - 0.4803204748666489963212495452125619500162143676070155341*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4202601810485974', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.89407042182311561437172164595', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.21037758366307137387316743928', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.25676955373845290047479411997', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.63765008224431, 'bad_primes': [2, 3, 19], 'central_character': '171.103', 'conductor': 684, 'conductor_radical': 114, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/684/3/s/a/445/6'], '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': '2-684-171.103-c2-0-34', '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': '2-684-171.103-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.317134475811972, 'root_angle': -0.4202601810485974, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.89407042182311561437172164595', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2401019507098608161192979421875', 'Lhash_array': ['2401019507098608161192979421875'], 'label': '2-684-171.103-c2-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/684/3/s/a/445/6'}