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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3751.2546', 'a10': [0.6106478796354381, -0.7919022459222751], 'a2': [0.8973984286913584, 0.4412211012432213], 'a3': [0.30901699437494745, -0.9510565162951535], 'a4': [0.6106478796354381, 0.7919022459222751], 'a5': [0.19859046664574548, -0.9800825610923934], 'a6': [0.6969375686552934, -0.7171318047589635], 'a7': [-0.9983691039261356, -0.057088810862767986], 'a8': [0.19859046664574548, 0.9800825610923934], 'a9': [-0.8090169943749475, -0.5877852522924731], 'algebraic': True, 'analytic_conductor': 17.41957076659139, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [31, [1]]], 'bad_primes': [11, 31], 'central_character': '3751.2546', 'coeff_info': ['x^55 - 1', '0.993481735348550 + 0.113991409890541*I', '\\\\zeta_{55}'], 'conductor': 3751, 'conductor_radical': 341, 'conjugate': 'dirichlet_L_3751.1186', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^4', 'a^44', 'a^8', 'a^43', 'a^48', 'a^28', 'a^12', 'a^33', 'a^47', 0, 'a^52', 'a^30', 'a^32', 'a^32', 'a^16', 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'2.00777215615', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.89428853893', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 17.41957076659139, 'bad_primes': [11, 31], 'central_character': '3751.2546', 'conductor': 3751, 'conductor_radical': 341, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3751/2546'], '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': '1-3751-3751.2546-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': '1-3751-3751.2546-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.41957076659139, 'root_angle': 0.2216801808009467, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.16694113342', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3751.2546', 'Lhash_array': ['dirichlet_L_3751.2546'], 'factors': ['1-3751-3751.2546-r0-0-0'], 'label': '1-3751-3751.2546-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3751/2546'}
Lfunction data - 1-3751-3751.2546-r0-0-0