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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_283.223', 'a10': [-0.420934762428335, 0.9070909137343407], 'a2': [-0.10009569162409834, -0.994977815088504], 'a3': [-0.9644691750543766, 0.264195401871286], 'a4': [-0.9799617050365869, 0.1991859851038361], 'a5': [-0.8604015792601394, -0.5096166425919174], 'a6': [0.35940777283751285, 0.9331806110416025], 'a7': [0.4805817551866838, 0.8769499282066715], 'a8': [0.296275580885634, 0.9551024972069124], 'a9': [0.8604015792601394, -0.5096166425919174], 'algebraic': True, 'analytic_conductor': 30.41257371687888, 'analytic_normalization': 0, 'bad_lfactors': [[283, [1]]], 'bad_primes': [283], 'central_character': '283.223', 'coeff_info': ['x^94 - 1', '0.997766878623153 + 0.0667926337451216*I', '\\\\zeta_{94}'], 'conductor': 283, 'conductor_radical': 283, 'conjugate': 'dirichlet_L_283.33', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^69', 'a^43', 'a^44', 'a^55', 'a^18', 'a^16', 'a^19', 'a^86', 'a^30', 'a^50', 'a^87', 'a^18', 'a^85', 'a^4', 'a^88', 'a^9', 'a^61', 'a^65', 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'gamma_factors': [[1], []], 'index': 0, 'label': '1-283-283.223-r1-0-0', 'leading_term': '0.0280297909744005149300051556481-0.147863786871935989292320737018*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/283/223', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-0.15049707189901704, 0.4775817169710206, 0.8930909552570991, 0.8655773823401042, 0.29578971408338983, -0.6726765838908133, -1.6346486181546633, -2.07480027935462, -1.647186252606705, -0.4268989550797557, 1.0502215349286403, 2.0435323010583084, 2.051568894507442, 1.1722457823086114, 0.10337683445591768, -0.2895630151510294, 0.39562506071806103, 1.7017023669331335, 2.495209531045916, 1.7009400675730597, -0.8661421215100031, -4.1811123992537444, -6.523397433020831, -6.563772529296873, -4.293980984792404, 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{'__RealLiteral__': 0, 'data': '2.90158935004', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 30.41257371687888, 'bad_primes': [283], 'central_character': '283.223', 'conductor': 283, 'conductor_radical': 283, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/283/223'], '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': '1-283-283.223-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-283-283.223-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 30.41257371687888, 'root_angle': 0.4403671833873054, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0724665076941', 'prec': 50}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_283.223', 'Lhash_array': ['dirichlet_L_283.223'], 'label': '1-283-283.223-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/283/223'}