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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_79.61', 'a10': [0.8854560256532099, 0.46472317204376856], 'a2': [-0.3546048870425356, 0.9350162426854148], 'a3': [-0.8854560256532099, -0.46472317204376856], 'a4': [-0.7485107481711011, -0.6631226582407952], 'a5': [0.12053668025532305, -0.992708874098054], 'a6': [0.7485107481711011, -0.6631226582407952], 'a7': [-0.8854560256532099, -0.46472317204376856], 'a8': [0.8854560256532099, -0.46472317204376856], 'a9': [0.5680647467311558, 0.8229838658936564], 'algebraic': True, 'analytic_conductor': 8.489729058775376, 'analytic_normalization': 0, 'bad_lfactors': [[79, [1]]], 'bad_primes': [79], 'central_character': '79.61', 'coeff_info': ['x^26 - 1', '0.970941817426052 + 0.239315664287558*I', '\\\\zeta_{26}'], 'conductor': 79, 'conductor_radical': 79, 'conjugate': 'dirichlet_L_79.57', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^8', 'a^15', 'a^16', 'a^20', 'a^23', 'a^15', 'a^24', 'a^4', 'a^2', 'a^6', 'a^5', 'a^16', 'a^23', 'a^9', 'a^6', 'a^3', 'a^12', 'a^12', 'a^10', 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'data': '0.364903242379', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(26)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.498024996790826594919186926409+0.108481158822250216146136732295*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.24679241836', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.47884028553', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.5798704548', 'prec': 40}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.489729058775376, 'bad_primes': [79], 'central_character': '79.61', 'conductor': 79, 'conductor_radical': 79, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/79/61'], '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': '1-79-79.61-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': '1-79-79.61-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.489729058775376, 'root_angle': 0.3649032423787545, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.24679241836', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_79.61', 'Lhash_array': ['dirichlet_L_79.61'], 'factors': ['1-79-79.61-r1-0-0'], 'label': '1-79-79.61-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/79/61'}