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lfunc_lfunctions • Show schema
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{'Lhash': '1884609904753451060402586566293', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0.20710678118654752, 0.3587194676071504], 'a4': [0, 0], 'a5': [1.7071067811865475, -2.956795678960466], 'a6': [0, 0], 'a7': [2.6213203435596424, 0.3587194676071504], 'a8': [0, 0], 'a9': [1.4142135623730951, -2.449489742783178], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.837569529021748, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.6213203435596424, -0.3587194676071504]]], [11, [[1.0, 0], [-0.5, -0.8660254037844386]]]], 'bad_primes': [2, 7, 11], 'central_character': '1232.177', 'coefficient_field': 'CDF', 'conductor': 1232, 'conductor_radical': 154, 'conjugate': '1561586019275934057153153115914', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.20710678118654752, -0.3587194676071504], [-1.5, 2.598076211353316]], [[1.0, 0], [-1.7071067811865475, 2.956795678960466], [-2.5, 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'7.935134415795430969629338323096004', '9.067677356937518852724875729092980', '9.887158846617842178881359337986047'], 'prelabel': '2-1232-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.13649000142225, 'root_angle': 0.18978452306496227, 'root_number': '0.82746088188798633832672431794945460845963684638391124795 + 0.56152336455855149265339362891639412714020691254723053175*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.09489226153248115', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.48669507545229224292878013407', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.47584334545804387681865554557', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.43582504747756555725779251957', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.837569529021748, 'bad_primes': [2, 7, 11], 'central_character': '7.2', 'conductor': 1232, 'conductor_radical': 154, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1232/2/q/f/177/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, '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': '2-1232-7.2-c1-0-27', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1232-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.13649000142225, 'root_angle': 0.09489226153248113, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.48669507545229224292878013407', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1884609904753451060402586566293', 'Lhash_array': ['1884609904753451060402586566293'], 'label': '2-1232-7.2-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1232/2/q/f/177/2'}