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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_121.56', 'a10': [0.41541501300188644, -0.9096319953545183], 'a2': [0.8412535328311812, 0.5406408174555976], 'a3': [1.0, 0.0], 'a4': [0.41541501300188644, 0.9096319953545183], 'a5': [-0.14231483827328514, -0.9898214418809327], 'a6': [0.8412535328311812, 0.5406408174555976], 'a7': [-0.6548607339452851, -0.7557495743542583], 'a8': [-0.14231483827328514, 0.9898214418809327], 'a9': [1.0, 0.0], 'algebraic': True, 'analytic_conductor': 0.5619216376319803, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]]], 'bad_primes': [11], 'central_character': '121.56', 'coeff_info': ['x^11 - 1', '0.841253532831181 + 0.540640817455598*I', '\\\\zeta_{11}'], 'conductor': 121, 'conductor_radical': 11, 'conjugate': 'dirichlet_L_121.67', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 'a^0', 'a^2', 'a^8', 'a^1', 'a^7', 'a^3', 'a^0', 'a^9', 0, 'a^2', 'a^2', 'a^8', 'a^8', 'a^4', 'a^5', 'a^1', 'a^6', 'a^10', 'a^7', 0, 'a^4', 'a^3', 'a^5', 'a^3', 'a^0', 'a^9', 'a^6', 'a^9', 'a^9', 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'197.79508803359567878083298856893', '198.77245683096454591784751542006', '199.73498433473435637003681729204'], 'prelabel': '1-11e2-121.56-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5619216376319803, 'root_angle': 0.1487603305785124, 'root_number': '0.892767845097863664257402717719+0.450517008290826806720771541350*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0743801652893', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(11)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.85114653250602678960828516134+0.364154146821133394359429489993*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.08362393539', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.85319760656', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.36976080202', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5619216376319803, 'bad_primes': [11], 'central_character': '121.56', 'conductor': 121, 'conductor_radical': 11, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/121/56'], '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': '1-11e2-121.56-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': '1-11e2-121.56-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5619216376319803, 'root_angle': 0.0743801652892562, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.08362393539', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_121.56', 'Lhash_array': ['dirichlet_L_121.56'], 'label': '1-11e2-121.56-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/121/56'}