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lfunc_lfunctions • Show schema
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{'Lhash': '405223505355832843188410884051', 'a10': [0, 0], 'a2': [0, 1.4142135623730951], 'a3': [2.2228476486906374, -2.014683183706685], 'a4': [-2.0, 0], 'a5': [0, 0], 'a6': [2.849192282283, 3.143581291867444], 'a7': [-2.6457513110645907, 0], 'a8': [0, -2.8284271247461903], 'a9': [0.8821033385789893, -8.956667555517946], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.61042775783118, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.4142135623730951]]], [3, [[1.0, 0], [-2.2228476486906374, 2.014683183706685]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2.6457513110645907, 0]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1050.701', 'coefficient_field': 'CDF', 'conductor': 1050, 'conductor_radical': 210, 'conjugate': '1825209645478180616726205382846', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.4142135623730951]], [[1.0, 0], [-2.2228476486906374, 2.014683183706685]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.31966498125183382222029477193', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.23089384020955371477626641105', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.86655447722820634649907807331', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 28.61042775783118, 'bad_primes': [2, 3, 5, 7], 'central_character': '3.2', 'conductor': 1050, 'conductor_radical': 210, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1050/3/e/e/701/8'], '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': '2-1050-3.2-c2-0-10', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-1050-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.348871634076778, 'root_angle': -0.36718795244897967, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.31966498125183382222029477193', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '405223505355832843188410884051', 'Lhash_array': ['405223505355832843188410884051'], 'label': '2-1050-3.2-c2-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1050/3/e/e/701/8'}