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lfunc_lfunctions • Show schema
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{'Lhash': '2217935576882790100417547246142', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0.5, 0.8660254037844386], 'a6': [0, 0], 'a7': [1.3660254037844386, -2.366025403784439], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.935765127447429, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.5, -0.8660254037844386]]]], 'bad_primes': [2, 3, 5], 'central_character': '1620.541', 'coefficient_field': 'CDF', 'conductor': 1620, 'conductor_radical': 30, 'conjugate': '387639615603099855303787379532', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [-1.3660254037844386, 2.366025403784439], [-3.5, -6.06217782649107]], [[1.0, 0], [0.8660254037844386, -1.5], [-5.5, -9.526279441628825]], [[1.0, 0], [2.732050807568877, 4.732050807568878], [-6.5, 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0.7222222222222222, 'root_number': '-0.6427876096865393263226434099072634329075598842056817904 + 0.7660444431189780352023926505554166739358324570803952459*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.36111111111111116', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.74964266690164482367419634496', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.44486083734049427229520071585', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.88363869172167148416973020818', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.935765127447429, 'bad_primes': [2, 3, 5], 'central_character': '9.7', 'conductor': 1620, 'conductor_radical': 30, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1620/2/i/n/541/2'], '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': '2-1620-9.7-c1-0-15', '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': '2-1620-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.596632470443349, 'root_angle': 0.3611111111111111, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.74964266690164482367419634496', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2217935576882790100417547246142', 'Lhash_array': ['2217935576882790100417547246142'], 'label': '2-1620-9.7-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1620/2/i/n/541/2'}