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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1441.311', 'a10': [-0.8619696668800493, 0.5069598538135904], 'a2': [-0.16835704134703855, 0.9857260809316509], 'a3': [-0.07243480016176236, -0.9973731496914912], 'a4': [-0.943311813257743, -0.33190785312852844], 'a5': [0.6448422127361706, 0.7643157205458483], 'a6': [0.9953316347176486, 0.09651392091451512], 'a7': [-0.7485107481711011, 0.6631226582407952], 'a8': [0.4859834132426061, -0.873968032626518], 'a9': [-0.9895063994510511, 0.14448904956922132], 'algebraic': True, 'analytic_conductor': 6.691975866344493, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [131, [1]]], 'bad_primes': [11, 131], 'central_character': '1441.311', 'coeff_info': ['x^65 - 1', '0.995331634717649 + 0.0965139209145151*I', '\\\\zeta_{65}'], 'conductor': 1441, 'conductor_radical': 1441, 'conjugate': 'dirichlet_L_1441.1302', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^18', 'a^48', 'a^36', 'a^9', 'a^1', 'a^25', 'a^54', 'a^31', 'a^27', 0, 'a^19', 'a^25', 'a^43', 'a^57', 'a^7', 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'197.65669544905188462370404913176', '198.04914640187798918491430717276', '199.0281791298969638256031703491', '199.57725345969131709492368635442'], 'prelabel': '1-1441-1441.311-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.691975866344493, 'root_angle': 0.9531779790741028, 'root_number': '-0.989200917888684197218825042036+0.146565835201061316729350950172*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.476588989537', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(65)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.674551523020824583707524163473+0.329487552036182676511359814433*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.27679122289', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.4901934329', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.17175299175', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.691975866344493, 'bad_primes': [11, 131], 'central_character': '1441.311', 'conductor': 1441, 'conductor_radical': 1441, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1441/311'], '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': '1-1441-1441.311-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': '1-1441-1441.311-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.691975866344493, 'root_angle': 0.4765889895370514, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.27679122289', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1441.311', 'Lhash_array': ['dirichlet_L_1441.311'], 'label': '1-1441-1441.311-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1441/311'}