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lfunc_lfunctions • Show schema
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{'Lhash': '1278768789045606521772129576085', 'a10': [0.0, 0.0], 'a2': [-0.36602540378443865, 1.3660254037844386], 'a3': [0.0, 1.7320508075688772], 'a4': [-1.7320508075688772, -1.0], 'a5': [0.0, 0.0], 'a6': [-2.366025403784439, -0.6339745962155614], 'a7': [2.0, -1.7320508075688772], 'a8': [2.0, -2.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.589528141489629, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.36602540378443865, -1.3660254037844386]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.0, 1.7320508075688772]]]], 'bad_primes': [2, 5, 7], 'central_character': '700.699', 'coefficient_field': 'CDF', 'conductor': 700, 'conductor_radical': 70, 'conjugate': '1823212321026399203848018558501', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.36602540378443865, -1.3660254037844386]], [[1.0, 0], [0, -1.7320508075688772], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.0, 1.7320508075688772]], 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'3.22403684253494160205145639730490', '4.40573596692281607346223255677128', '5.69016982181752223593134501351055', '6.59950314775382354753394256828128', '7.894144110209467326063670541775709', '8.579758605855998703974627700667754', '8.958842322549404919030797848891240', '10.50360860692252732553995161502903'], 'prelabel': '2-700-140.139-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.364218293958836, 'root_angle': -0.7081024768122717, 'root_number': '-0.6081858837725431 - 0.7937946401808282*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.354051238406', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.00877070449489424581020370471', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.97529746044495163547024368569', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.22403684253494160205145639730', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.589528141489629, 'bad_primes': [2, 5, 7], 'central_character': '140.139', 'conductor': 700, 'conductor_radical': 70, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/700/2/c/e/699/2'], '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': '2-700-140.139-c1-0-20', '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': '2-700-140.139-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.364218293958836, 'root_angle': -0.35405123840613584, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.00877070449489424581020370471', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1278768789045606521772129576085', 'Lhash_array': ['1278768789045606521772129576085'], 'label': '2-700-140.139-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/700/2/c/e/699/2'}