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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_539.212', 'a10': [0.36534102436639504, 0.9308737486442042], 'a2': [0.4203572283095655, 0.9073586945678649], 'a3': [0.7123760969513449, -0.7017979028839914], 'a4': [-0.6465996012157996, 0.7628295718622665], 'a5': [0.9982101297677352, 0.05980415394503417], 'a6': [0.9362348706397372, 0.3513748240813427], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.9639628606958532, -0.2660368455666751], 'a9': [0.01495940701526362, -0.9998881018102734], 'algebraic': True, 'analytic_conductor': 2.503105476724276, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '539.212', 'coeff_info': ['x^105 - 1', '0.998210129767735 + 0.0598041539450342*I', '\\\\zeta_{105}'], 'conductor': 539, 'conductor_radical': 77, 'conjugate': 'dirichlet_L_539.389', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^19', 'a^92', 'a^38', 'a^1', 'a^6', 0, 'a^57', 'a^79', 'a^20', 0, 'a^25', 'a^54', 0, 'a^93', 'a^76', 'a^11', 'a^98', 'a^7', 'a^39', 0, 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2.503105476724276, 'root_angle': 0.24685429450313956, 'root_number': '0.714060138815502122765740922181+0.700084365026662939181229655307*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.123427147252', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(105)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.67069235931735861794600911968+0.516770732149270976504266323355*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.34168266607', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.6939956222', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.51346965699', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.503105476724276, 'bad_primes': [7, 11], 'central_character': '539.212', 'conductor': 539, 'conductor_radical': 77, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/539/212'], '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': '1-539-539.212-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': '1-539-539.212-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.503105476724276, 'root_angle': 0.12342714725156978, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.34168266607', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_539.212', 'Lhash_array': ['dirichlet_L_539.212'], 'label': '1-539-539.212-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/539/212'}