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lfunc_lfunctions • Show schema
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{'Lhash': '2258200830026913440761274193621', 'a10': [0.7783446563551086, 0.0], 'a2': [1.8748113347734632, 0.0], 'a3': [-1.0, 0.0], 'a4': [1.5149175409950548, 0.0], 'a5': [0.41515892395069043, 0.0], 'a6': [-1.8748113347734632, 0.0], 'a7': [5.013689565098303, 0.0], 'a8': [-0.909438092442255, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 49.27568308733215, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [11, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 11, 17], 'central_character': '6171.1', 'coefficient_field': 'CDF', 'conductor': 6171, 'conductor_radical': 561, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.8748113347734632, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-0.41515892395069043, 0], [5.0, 0]], [[1.0, 0], [-5.013689565098303, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.355754608028533, 0], [13.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], 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[[1.0, 0], [-12.060525780622257, 0], [109.0, 0]], [[1.0, 0], [12.678418892179149, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 278, 'label': '2-6171-1.1-c1-0-278', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/6171/2/a/bo/1/11', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [1.1401973890940502e-59, 0.32644946817417225, 0.6520186884625914, 0.9757663852345758, 1.2966330315580623, 1.6133909617587103, 1.924604843581365, 2.2286048529294766, 2.5234741201369113, 2.807051227156747, 3.076947794736679, 3.330580551767571, 3.5652167473643894, 3.7780313523211717, 3.966174189200903, 4.126844911145378, 4.2573735986858035, 4.355304644092331, 4.41848153155766, 4.445130091627618, 4.433937807633653, 4.384126782255329, 4.2955180381772875, 4.168584933840731, 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'5.29294826846734550665306275593010', '5.89815066331632752055956318438225', '6.86959600353326936030486120868229', '7.60065497737819605483033824830258'], 'prelabel': '2-6171-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.019664029519657, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.78140635094587115366211477532', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.18441954194491518993483637018', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.57933056448517990692148224812', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 49.27568308733215, 'bad_primes': [3, 11, 17], 'central_character': '1.1', 'conductor': 6171, 'conductor_radical': 561, 'degree': 2, 'index': 278, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6171/2/a/bo/1/11'], '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': '2-6171-1.1-c1-0-278', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-6171-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.019664029519657, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.78140635094587115366211477532', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2258200830026913440761274193621', 'Lhash_array': ['2258200830026913440761274193621'], 'label': '2-6171-1.1-c1-0-278', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6171/2/a/bo/1/11'}