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lfunc_lfunctions • Show schema
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{'Lhash': '1757457729568463642058972872453', 'a10': [3.7015621187164243, 0.0], 'a2': [1.0, 0.0], 'a3': [1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [3.7015621187164243, 0.0], 'a6': [1.0, 0.0], 'a7': [0.0, 0.0], 'a8': [1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 30.518823652533378, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '3822.1', 'coefficient_field': 'CDF', 'conductor': 3822, 'conductor_radical': 546, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-3.7015621187164243, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-5.701562118716424, 0], [11.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [3.7015621187164243, 0], [17.0, 0]], [[1.0, 0], [5.701562118716424, 0], [19.0, 0]], [[1.0, 0], [1.7015621187164243, 0], 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'group': 'GL2', 'index': 58, 'label': '2-3822-1.1-c1-0-58', 'leading_term': '5.50033028002984899889779702152', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3822/2/a/bt/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [5.500330280029849, 5.493773681879103, 5.473957849949389, 5.440454894914918, 5.3925850579522105, 5.3294644751567, 5.250067689486794, 5.153301151180804, 5.038083591198133, 4.903429137158427, 4.748529295833168, 4.572830358033354, 4.37610330026214, 4.15850379023566, 3.9206204030408234, 3.663509599066217, 3.3887164017175766, 3.098280053180705, 2.7947242372634102, 2.481031757644545, 2.160603862925398, 1.8372047271861778, 1.5148919312466897, 1.1979341450389187, 0.8907175801101297, 0.5976431539812409, 0.32301667250907834, 0.07093467802507353, 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'6.75608033364335078939690047309539', '7.59584046041812661538650921091883', '8.792089130817399362758465445364331'], 'prelabel': '2-3822-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.5243844591531985, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.38638969543504239388096097368', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.12843806786283010744424863656', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.80037503134609174492594909662', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 30.518823652533378, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 3822, 'conductor_radical': 546, 'degree': 2, 'index': 58, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3822/2/a/bt/1/2'], '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': '2-3822-1.1-c1-0-58', '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': '2-3822-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.5243844591531985, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.38638969543504239388096097368', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1757457729568463642058972872453', 'Lhash_array': ['1757457729568463642058972872453'], 'label': '2-3822-1.1-c1-0-58', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3822/2/a/bt/1/2'}