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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1021.866', 'a10': [0.18374951781657034, 0.9829730996839018], 'a2': [-0.961825643172819, 0.2736629900720829], 'a3': [-0.9324722294043558, -0.3612416661871529], 'a4': [0.8502171357296141, -0.5264321628773558], 'a5': [0.092268359463302, -0.9957341762950345], 'a6': [0.9957341762950345, 0.092268359463302], 'a7': [-0.7980172272802395, -0.6026346363792564], 'a8': [-0.6736956436465572, 0.7390089172206591], 'a9': [0.7390089172206591, 0.6736956436465572], 'algebraic': True, 'analytic_conductor': 109.72168821531214, 'analytic_normalization': 0, 'bad_lfactors': [[1021, [1]]], 'bad_primes': [1021], 'central_character': '1021.866', 'coeff_info': ['x^68 - 1', '0.995734176295034 + 0.0922683594633020*I', '\\\\zeta_{68}'], 'conductor': 1021, 'conductor_radical': 1021, 'conjugate': 'dirichlet_L_1021.303', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^31', 'a^38', 'a^62', 'a^52', 'a^1', 'a^41', 'a^25', 'a^8', 'a^15', 'a^36', 'a^32', 'a^3', 'a^4', 'a^22', 'a^56', 'a^18', 'a^39', 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'gamma_factors': [[1], []], 'index': 0, 'label': '1-1021-1021.866-r1-0-0', 'leading_term': '0.262741166085394982010801821662-0.410911732009970402912391438891*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/1021/866', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.4877308395614805, -0.052853401293491, -0.4717731019227527, -0.3266037479647111, 0.400247308024389, 1.0782494987103453, 0.7038294390670726, -1.290587539570594, -4.2549016075454285, -6.369547286598847, -5.802628413647876, -2.2490484159737094, 2.471022193709956, 5.521087408706885, 5.179258563918728, 2.2197072162039526, -0.7690775021307725, -1.6292854575177436, -0.41211321635862697, 0.9837754780317102, 0.9127724532488521, -0.3485408593453724, -1.0929913891565124, -0.24721596744557833, 1.3265504669642747, 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-0.6378303948047745, 'root_number': '-0.419602133480796422065708458825-0.907708130170906810245572324984*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.318915197402', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(68)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.448169911052950966316023926211-0.110385192971903547475041498090*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.283783254299', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.0985347203', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.01582547785', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 109.72168821531214, 'bad_primes': [1021], 'central_character': '1021.866', 'conductor': 1021, 'conductor_radical': 1021, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1021/866'], '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': '1-1021-1021.866-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': '1-1021-1021.866-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 109.72168821531214, 'root_angle': -0.3189151974023873, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.283783254299', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1021.866', 'Lhash_array': ['dirichlet_L_1021.866'], 'label': '1-1021-1021.866-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1021/866'}