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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_283.103', 'a10': [-0.2534346579436158, -0.9673525076997539], 'a2': [-0.296275580885634, 0.9551024972069124], 'a3': [-0.9701157849175226, 0.24264246094585157], 'a4': [-0.8244415603417603, -0.5659470943305952], 'a5': [-0.8488342952846072, 0.5286590008206464], 'a6': [0.05567319732494821, -0.9984490448188217], 'a7': [0.5567275569205216, 0.8306951470697944], 'a8': [0.784799385278661, -0.6197498889602449], 'a9': [0.8822492722922818, -0.4707825629096082], 'algebraic': True, 'analytic_conductor': 1.3142464747921523, 'analytic_normalization': 0, 'bad_lfactors': [[283, [1]]], 'bad_primes': [283], 'central_character': '283.103', 'coeff_info': ['x^141 - 1', '0.999007296282201 + 0.0445468514591922*I', '\\\\zeta_{141}'], 'conductor': 283, 'conductor_radical': 283, 'conjugate': 'dirichlet_L_283.11', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^42', 'a^65', 'a^84', 'a^58', 'a^107', 'a^22', 'a^126', 'a^130', 'a^100', 'a^10', 'a^8', 'a^13', 'a^64', 'a^123', 'a^27', 'a^124', 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'3.77048506231', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.70005922283', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3142464747921523, 'bad_primes': [283], 'central_character': '283.103', 'conductor': 283, 'conductor_radical': 283, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/283/103'], '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': '1-283-283.103-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': '1-283-283.103-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3142464747921523, 'root_angle': 0.44690211216340125, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.39336709556', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_283.103', 'Lhash_array': ['dirichlet_L_283.103'], 'label': '1-283-283.103-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/283/103'}