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lfunc_lfunctions • Show schema
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{'Lhash': '1189053811521644427388566258038', 'a10': [0, 0], 'a2': [1.224744871391589, -0.7071067811865476], 'a3': [-0.8660254037844386, 1.5], 'a4': [1.0, -1.7320508075688772], 'a5': [0, 0], 'a6': [0, 2.449489742783178], 'a7': [-5.761401956295186, 3.9757071695483304], 'a8': [0, -2.8284271247461903], 'a9': [-1.5, -2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.61042775783118, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.224744871391589, 0.7071067811865476]]], [3, [[1.0, 0], [0.8660254037844386, -1.5]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [5.761401956295186, -3.9757071695483304]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1050.199', 'coefficient_field': 'CDF', 'conductor': 1050, 'conductor_radical': 210, 'conjugate': '1000868973745431259341339663337', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.224744871391589, 0.7071067811865476]], [[1.0, 0], [0.8660254037844386, -1.5]], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 19, 'label': '2-1050-35.24-c2-0-19', 'leading_term': '2.242419454369325024542154260816480398757629945756047661', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1050/3/q/b/199/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.242419454369325, 2.2641880804114187, 2.263652240721222, 2.2406231708181723, 2.194957799550136, 2.126575267016825, 2.0354801155537254, 1.9217911126135128, 1.7857743789658858, 1.6278792738384162, 1.4487753347218848, 1.24938848311874, 1.0309346846250709, 0.7949492865262755, 0.5433103420583505, 0.2782543615638608, 0.0023831019044964134, -0.2813397871641774, -0.5696032002116607, -0.8587747655713619, -1.1449391546329897, -1.4239485511724586, -1.6914849705701416, -1.943133750470731, 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'6.47175860020781512434452377806960', '6.93165902215166465753951594330069', '7.989222987535708054706218153345974', '8.703363378235741666492768758107186', '9.910242644235566914367976111481860'], 'prelabel': '2-1050-35.24-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.348871634076778, 'root_angle': 0.11980400447608511, 'root_number': '0.9300029779311933905230419428224728545856185642080253102 + 0.367551984131649355234118568750693076522470573402408141*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.059902002238042554', 'prec': 67}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.937998066113458779694047016295', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.49921578844200502860215506583', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.63045250231413156788072006773', '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': '35.24', 'conductor': 1050, 'conductor_radical': 210, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1050/3/q/b/199/5'], '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': '2-1050-35.24-c2-0-19', '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': '2-1050-35.24-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.348871634076778, 'root_angle': 0.059902002238042554, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.937998066113458779694047016295', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1189053811521644427388566258038', 'Lhash_array': ['1189053811521644427388566258038'], 'label': '2-1050-35.24-c2-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1050/3/q/b/199/5'}