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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_177.98', 'a10': [-0.9766205557100867, 0.21497044021102407], 'a2': [0.6473862847818277, 0.7621620551276365], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.16178199655276473, 0.9868265225415261], 'a5': [-0.46840844069979015, 0.8835120444460229], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.9941379571543596, 0.10811901842394177], 'a8': [-0.8568571761675893, 0.5155538571770217], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.8219845443046324, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [59, [1]]], 'bad_primes': [3, 59], 'central_character': '177.98', 'coeff_info': ['x^58 - 1', '0.994137957154360 + 0.108119018423942*I', '\\\\zeta_{58}'], 'conductor': 177, 'conductor_radical': 177, 'conjugate': 'dirichlet_L_177.56', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^8', 0, 'a^16', 'a^19', 0, 'a^28', 'a^24', 0, 'a^27', 'a^26', 0, 'a^41', 'a^36', 0, 'a^32', 'a^1', 0, 'a^14', 'a^35', 0, 'a^34', 'a^4', 0, 'a^38', 'a^49', 0, 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'0.723509836046866305986002863344+0.736146085655739637779545870670*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.90095280743', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.48391634057', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.15344429548', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8219845443046324, 'bad_primes': [3, 59], 'central_character': '177.98', 'conductor': 177, 'conductor_radical': 177, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/177/98'], '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': '1-177-177.98-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': '1-177-177.98-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8219845443046324, 'root_angle': 0.4780050661466806, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.90095280743', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_177.98', 'Lhash_array': ['dirichlet_L_177.98'], 'label': '1-177-177.98-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/177/98'}