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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_275.92', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.5877852522924731, -0.8090169943749475], 'a3': [0.5877852522924731, 0.8090169943749475], 'a4': [-0.30901699437494745, -0.9510565162951535], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, 0.0], 'a7': [-0.5877852522924731, -0.8090169943749475], 'a8': [-0.9510565162951535, -0.30901699437494745], 'a9': [-0.30901699437494745, 0.9510565162951535], 'algebraic': True, 'analytic_conductor': 29.55285431852188, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]]], 'bad_primes': [5, 11], 'central_character': '275.92', 'coeff_info': ['x^20 - 1', '0.951056516295154 + 0.309016994374947*I', '\\\\zeta_{20}'], 'conductor': 275, 'conductor_radical': 55, 'conjugate': 'dirichlet_L_275.3', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^17', 'a^3', 'a^14', 0, 'a^0', 'a^13', 'a^11', 'a^6', 0, 0, 'a^17', 'a^11', 'a^10', 0, 'a^8', 'a^5', 'a^3', 'a^6', 0, 'a^16', 0, 'a^3', 'a^14', 0, 'a^8', 'a^9', 'a^7', 'a^14', 0, 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'1-275-275.92-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 29.55285431852188, 'root_angle': 0.3137837371021717, 'root_number': '-0.390122876595606595487652032262+0.920762803960264843436948303419*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.313783737102', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(20)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.11959205819733978477911363035-0.206081431623979647947155053825*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.73053524487', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.09551897496', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.84106325335', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 29.55285431852188, 'bad_primes': [5, 11], 'central_character': '275.92', 'conductor': 275, 'conductor_radical': 55, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/275/92'], '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': '1-275-275.92-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': '1-275-275.92-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 29.55285431852188, 'root_angle': 0.3137837371021717, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.73053524487', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_275.92', 'Lhash_array': ['dirichlet_L_275.92'], 'factors': ['1-275-275.92-r1-0-0'], 'label': '1-275-275.92-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/275/92'}
Lfunction data - 1-275-275.92-r1-0-0