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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_967.145', 'a10': [-0.06824241336467098, -0.9976687691905392], 'a2': [0.9958568425315313, 0.09093486230884695], 'a3': [-0.06824241336467098, -0.9976687691905392], 'a4': [0.9834617016337421, 0.18111620970985576], 'a5': [-0.1586825464562513, -0.9873296559154696], 'a6': [0.022763197856105682, -0.9997408848413492], 'a7': [-0.9496396989003193, -0.31334396798488223], 'a8': [0.9629172873477992, 0.2697967711570243], 'a9': [-0.9906859460363308, 0.1361666490962466], 'algebraic': True, 'analytic_conductor': 4.490729120579545, 'analytic_normalization': 0, 'bad_lfactors': [[967, [1]]], 'bad_primes': [967], 'central_character': '967.145', 'coeff_info': ['x^69 - 1', '0.995856842531531 + 0.0909348623088469*I', '\\\\zeta_{69}'], 'conductor': 967, 'conductor_radical': 967, 'conjugate': 'dirichlet_L_967.947', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 'a^51', 'a^2', 'a^50', 'a^52', 'a^38', 'a^3', 'a^33', 'a^51', 'a^33', 'a^53', 'a^59', 'a^39', 'a^32', 'a^4', 'a^60', 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False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.482302622472', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(69)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.15367079273494742460493016545-0.806349880290648107283606119975*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.435332462303', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.70735007372', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.78668973495', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.490729120579545, 'bad_primes': [967], 'central_character': '967.145', 'conductor': 967, 'conductor_radical': 967, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/967/145'], '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': '1-967-967.145-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': '1-967-967.145-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.490729120579545, 'root_angle': -0.4823026224716811, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.435332462303', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_967.145', 'Lhash_array': ['dirichlet_L_967.145'], 'label': '1-967-967.145-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/967/145'}