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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_3381.647', 'a10': [0.27520155655898504, 0.9613865524686268], 'a2': [0.9999075218579183, 0.01359954896150994], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.999630104536087, 0.027196582600977664], 'a5': [0.28825052992157085, 0.9575550281837246], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.9991677993445829, 0.04078858606158557], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 15.701297990361368, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [23, [1]]], 'bad_primes': [3, 7, 23], 'central_character': '3381.647', 'coeff_info': ['x^462 - 1', '0.999907521857918 + 0.0135995489615099*I', '\\\\zeta_{462}'], 'conductor': 3381, 'conductor_radical': 483, 'conjugate': 'dirichlet_L_3381.1181', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 0, 'a^2', 'a^94', 0, 0, 'a^3', 0, 'a^95', 'a^197', 0, 'a^183', 0, 0, 'a^4', 'a^152', 0, 'a^343', 'a^96', 0, 'a^198', 0, 0, 'a^188', 'a^184', 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'1-3381-3381.647-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.701297990361368, 'root_angle': 0.7721527160573942, 'root_number': '-0.754566305144377103309616297135+0.656223811775192123161431232822*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(462)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.60608264329672094448989901602+0.636634589545086071800197582168*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.59634714383', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.39006580577', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.85879126295', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.701297990361368, 'bad_primes': [3, 7, 23], 'central_character': '3381.647', 'conductor': 3381, 'conductor_radical': 483, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3381/647'], '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': '1-3381-3381.647-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': '1-3381-3381.647-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.701297990361368, 'root_angle': 0.3860763580286971, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.59634714383', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_3381.647', 'Lhash_array': ['dirichlet_L_3381.647'], 'label': '1-3381-3381.647-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3381/647'}