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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1441.142', 'a10': [-0.024163745236132288, -0.9997080140801929], 'a2': [0.9068743608505454, -0.4214011077725291], 'a3': [0.9953316347176486, 0.09651392091451512], 'a4': [0.6448422127361706, -0.7643157205458483], 'a5': [0.39936458356569554, -0.9167921953165824], 'a6': [0.943311813257743, -0.33190785312852844], 'a7': [0.6071625078187112, -0.7945776797137543], 'a8': [0.2627073781985869, -0.9648755533435515], 'a9': [0.9813701261394134, 0.19212671735370837], 'algebraic': True, 'analytic_conductor': 154.85695662905465, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [131, [1]]], 'bad_primes': [11, 131], 'central_character': '1441.142', 'coeff_info': ['x^130 - 1', '0.998832226832327 + 0.0483133795255071*I', '\\\\zeta_{130}'], 'conductor': 1441, 'conductor_radical': 1441, 'conjugate': 'dirichlet_L_1441.274', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^121', 'a^2', 'a^112', 'a^106', 'a^123', 'a^111', 'a^103', 'a^4', 'a^97', 0, 'a^114', 'a^33', 'a^102', 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'195.116301934979976276012743599677', '195.36196358403516735325180921371', '196.07629746425839717048146570642', '196.46614448201557806108230033479', '197.149426368729109712196056382245', '197.566409159268948865759064136629', '198.14879198826426453207033643226', '198.836848797355071763350491856908', '199.604328559830363459662163057405'], 'prelabel': '1-1441-1441.142-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 154.85695662905465, 'root_angle': -0.6828136137375952, 'root_number': '-0.543268972581777852962068212754-0.839558707554117089355818493830*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.341406806869', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(130)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.52660992530321729704822955733-1.67828830961843555386470630819*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.807560842071', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.68477009563', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.29812517194', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 154.85695662905465, 'bad_primes': [11, 131], 'central_character': '1441.142', 'conductor': 1441, 'conductor_radical': 1441, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1441/142'], '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': '1-1441-1441.142-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': '1-1441-1441.142-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 154.85695662905465, 'root_angle': -0.3414068068687976, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.807560842071', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1441.142', 'Lhash_array': ['dirichlet_L_1441.142'], 'label': '1-1441-1441.142-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1441/142'}