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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_709.136', 'a10': [-0.7226196156272872, -0.6912458977170655], 'a2': [0.6313872057279536, 0.7754677275316149], 'a3': [-0.2716539772434387, 0.9623949899328349], 'a4': [-0.20270039288609357, 0.9792408032367848], 'a5': [-0.9922916653833246, 0.12392437536977255], 'a6': [-0.9178251014476466, 0.3969849910923802], 'a7': [-0.560173490430346, 0.8283753138638807], 'a8': [-0.8873520750565715, 0.46109250144932584], 'a9': [-0.8524082332956425, -0.5228768533888275], 'algebraic': True, 'analytic_conductor': 3.292582157694827, 'analytic_normalization': 0, 'bad_lfactors': [[709, [1]]], 'bad_primes': [709], 'central_character': '709.136', 'coeff_info': ['x^177 - 1', '0.999370004274994 + 0.0354907671852732*I', '\\\\zeta_{177}'], 'conductor': 709, 'conductor_radical': 709, 'conjugate': 'dirichlet_L_709.391', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^25', 'a^52', 'a^50', 'a^85', 'a^77', 'a^61', 'a^75', 'a^104', 'a^110', 'a^112', 'a^102', 'a^57', 'a^86', 'a^137', 'a^100', 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{'__RealLiteral__': 0, 'data': '3.33141538898', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.43447762955', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.292582157694827, 'bad_primes': [709], 'central_character': '709.136', 'conductor': 709, 'conductor_radical': 709, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/709/136'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-709-709.136-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-709-709.136-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.292582157694827, 'root_angle': -0.11723172872351562, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.85520840836', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_709.136', 'Lhash_array': ['dirichlet_L_709.136'], 'label': '1-709-709.136-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/709/136'}