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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_75.23', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.9510565162951535, 0.30901699437494745], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.8090169943749475, 0.5877852522924731], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [2.9010907910729803e-30, -1.0], 'a8': [0.5877852522924731, 0.8090169943749475], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.34829853572230185, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '75.23', 'coeff_info': ['x^20 - 1', '0.951056516295154 + 0.309016994374947*I', '\\\\zeta_{20}'], 'conductor': 75, 'conductor_radical': 15, 'conjugate': 'dirichlet_L_75.62', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 0, 'a^2', 0, 0, 'a^15', 'a^3', 0, 0, 'a^6', 0, 'a^9', 'a^16', 0, 'a^4', 'a^13', 0, 'a^18', 0, 0, 'a^7', 'a^11', 0, 0, 'a^10', 0, 'a^17', 'a^12', 0, 'a^8', 'a^5', 0, 'a^14', 0, 0, 'a^19', 'a^19', 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'193.54442875120810263335573471204', '194.34644794213615152864407860420', '195.178328445431694852871040912579', '195.79551594836180377513397303727', '196.5991820739080107633344912791', '197.53706477015149000867690541522', '198.12547732671143017896680169743', '198.795890517053416755418298403148'], 'prelabel': '1-75-75.23-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.34829853572230185, 'root_angle': 0.14, 'root_number': '0.904827052466019527713668647933+0.425779291565072648862502445744*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.07', 'prec': 14}, 'spectral_label': 'r0-0', 'st_group': 'mu(20)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.56832535774417281962324979497+0.263772024258228651538706900157*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.34678333582', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.07164998332', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.11948836466', 'prec': 44}}
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lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.34829853572230185, 'bad_primes': [3, 5], 'central_character': '75.23', 'conductor': 75, 'conductor_radical': 15, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/75/23'], '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': '1-75-75.23-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': '1-75-75.23-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.34829853572230185, 'root_angle': 0.07, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.34678333582', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_75.23', 'Lhash_array': ['dirichlet_L_75.23'], 'label': '1-75-75.23-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/75/23'}