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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_2057.150', 'a10': [-0.17755319625430327, 0.9841112043361161], 'a2': [0.9828184036767557, 0.1845751483658454], 'a3': [0.5224985647159489, 0.8526401643540922], 'a4': [0.9318640292114523, 0.362807705350641], 'a5': [0.007139922638469387, 0.9999745104274992], 'a6': [0.3561450204591895, 0.934430695344563], 'a7': [-0.12108188703135471, 0.9926425220757603], 'a8': [0.8488878315900227, 0.528573031262842], 'a9': [-0.4539904997395468, 0.8910065241883679], 'algebraic': True, 'analytic_conductor': 9.552667839743666, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [17, [1]]], 'bad_primes': [11, 17], 'central_character': '2057.150', 'coeff_info': ['x^880 - 1', '0.999974510427499 + 0.00713992263846939*I', '\\\\zeta_{880}'], 'conductor': 2057, 'conductor_radical': 187, 'conjugate': 'dirichlet_L_2057.96', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^26', 'a^143', 'a^52', 'a^219', 'a^169', 'a^237', 'a^78', 'a^286', 'a^245', 0, 'a^195', 'a^756', 'a^263', 'a^362', 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[1, 'a^20'], [1, 'a^771'], [1, 'a^656']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-2057-2057.150-r0-0-0', 'leading_term': '0.788861064425409261959033771465+3.73572333925474896309414609803*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/2057/150', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [3.8181056358381498, 5.953886191689193, 8.415774321989712, 9.219442584371503, 7.2693708985050645, 3.4280492031886, -0.10204629118180314, -1.5506554314902687, -0.9942432207538061, -0.042485708891679574, -0.06237578232620651, -0.7964693201868475, -0.9064461656127687, 0.1834205047627782, 1.385622064222384, 1.2189706893273882, -0.229060834585396, -1.2207695338016877, -0.5366106166335002, 0.7678070746086958, 0.5232257791203571, -1.6170389528313485, -3.2810146677803456, 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{'__RealLiteral__': 0, 'data': '0.433756678764', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(880)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.64452264966085749932138768258+1.58070694843896429171306974315*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.8631758578', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.83749581037', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.08678614187', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.552667839743666, 'bad_primes': [11, 17], 'central_character': '2057.150', 'conductor': 2057, 'conductor_radical': 187, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2057/150'], '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': '1-2057-2057.150-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': '1-2057-2057.150-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.552667839743666, 'root_angle': 0.43375667876355056, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.8631758578', 'prec': 40}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_2057.150', 'Lhash_array': ['dirichlet_L_2057.150'], 'factors': ['1-2057-2057.150-r0-0-0'], 'label': '1-2057-2057.150-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2057/150'}