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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_71.8', 'a10': [-0.044864830350514924, -0.9989930665413147], 'a2': [-0.9639628606958532, -0.2660368455666751], 'a3': [-0.3930250316539236, -0.9195277725514507], 'a4': [0.8584487936018661, 0.5128992774059061], 'a5': [0.30901699437494745, 0.9510565162951535], 'a6': [0.1342332658176555, 0.9909497617679347], 'a7': [-0.044864830350514924, 0.9989930665413147], 'a8': [-0.6910626489868646, -0.7227948638273916], 'a9': [-0.6910626489868646, 0.7227948638273916], 'algebraic': True, 'analytic_conductor': 0.32972261381711243, 'analytic_normalization': 0, 'bad_lfactors': [[71, [1]]], 'bad_primes': [71], 'central_character': '71.8', 'coeff_info': ['x^35 - 1', '0.983929588598630 + 0.178556894798637*I', '\\\\zeta_{35}'], 'conductor': 71, 'conductor_radical': 71, 'conjugate': 'dirichlet_L_71.9', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^19', 'a^24', 'a^3', 'a^7', 'a^8', 'a^9', 'a^22', 'a^13', 'a^26', 'a^34', 'a^27', 'a^1', 'a^28', 'a^31', 'a^6', 'a^21', 'a^32', 'a^4', 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'unitary', 'types': ['DIR'], 'values': [[1, '0.673646325417687924674605346728-0.0483424653029913552226596234460*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.68748306588', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.00557751154', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '6.06222233222', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.32972261381711243, 'bad_primes': [71], 'central_character': '71.8', 'conductor': 71, 'conductor_radical': 71, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/71/8'], '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': '1-71-71.8-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': '1-71-71.8-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.32972261381711243, 'root_angle': 0.0047368210259390595, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.68748306588', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_71.8', 'Lhash_array': ['dirichlet_L_71.8'], 'label': '1-71-71.8-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/71/8'}