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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_51.8', 'a10': [0.7071067811865476, -0.7071067811865476], 'a2': [-7.040766286173228e-31, 1.0], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-1.0, -1.4081532572346456e-30], 'a5': [-0.7071067811865476, -0.7071067811865476], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.7071067811865476, -0.7071067811865476], 'a8': [2.9010907910729803e-30, -1.0], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 5.480711164525876, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [17, [1]]], 'bad_primes': [3, 17], 'central_character': '51.8', 'coeff_info': ['x^8 - 1', '0.707106781186548 + 0.707106781186547*I', '\\\\zeta_{8}'], 'conductor': 51, 'conductor_radical': 51, 'conjugate': 'dirichlet_L_51.32', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 0, 'a^4', 'a^5', 0, 'a^7', 'a^6', 0, 'a^7', 'a^7', 0, 'a^4', 'a^1', 0, 'a^0', 0, 0, 'a^6', 'a^1', 0, 'a^1', 'a^7', 0, 'a^2', 'a^6', 0, 'a^3', 'a^5', 0, 'a^5', 'a^2', 0, 0, 'a^4', 0, 'a^5', 'a^0', 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'199.64582611133184053799576586515'], 'prelabel': '1-51-51.8-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.480711164525876, 'root_angle': -0.11291074295044418, 'root_number': '0.758727356476261289179969185973-0.651408319362398323341418504665*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.11291074295', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(8)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.877284957394767772733895240214+0.0667661832228226351281885840159*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.625967519688', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '4.02630910765', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.12563508344', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 5.480711164525876, 'bad_primes': [3, 17], 'central_character': '51.8', 'conductor': 51, 'conductor_radical': 51, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/51/8'], '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': '1-51-51.8-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': '1-51-51.8-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.480711164525876, 'root_angle': -0.11291074295044418, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.625967519688', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_51.8', 'Lhash_array': ['dirichlet_L_51.8'], 'factors': ['1-51-51.8-r1-0-0'], 'label': '1-51-51.8-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/51/8'}
Lfunction data - 1-51-51.8-r1-0-0