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{'Lhash': 'dirichlet_L_1728.1301', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.3007057995042731, 0.9537169507482269], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.9063077870366499, -0.42261826174069944], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 185.69939004511204, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '1728.1301', 'coeff_info': ['x^144 - 1', '0.999048221581858 + 0.0436193873653360*I', '\\\\zeta_{144}'], 'conductor': 1728, 'conductor_radical': 6, 'conjugate': 'dirichlet_L_1728.1469', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^173', 0, 'a^82', 0, 0, 0, 'a^97', 0, 'a^59', 0, 0, 0, 'a^132', 0, 'a^147', 0, 0, 0, 'a^62', 0, 'a^202', 0, 0, 0, 'a^175', 0, 'a^152', 0, 0, 0, 'a^255', 0, 'a^141', 0, 0, 0, 'a^158', 0, 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'199.018043603267738230062792246706', '199.56277428558335702507668250239'], 'prelabel': '1-12e3-1728.1301-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 185.69939004511204, 'root_angle': -0.9363425925925927, 'root_number': '-0.980069429944895152080949554391-0.198655260407290130680655316965*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.468171296296', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(144)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.867668593042562936400408024575+0.116689469211458334453734407334*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.10529789877', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.4709249669', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.12251628524', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 185.69939004511204, 'bad_primes': [2, 3], 'central_character': '1728.1301', 'conductor': 1728, 'conductor_radical': 6, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1728/1301'], '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': '1-12e3-1728.1301-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': '1-12e3-1728.1301-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 185.69939004511204, 'root_angle': -0.46817129629629634, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.10529789877', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1728.1301', 'Lhash_array': ['dirichlet_L_1728.1301'], 'label': '1-12e3-1728.1301-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1728/1301'}