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lfunc_lfunctions • Show schema
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{'Lhash': '2500067106626052551661413465662', 'a10': [-46.233687939614086, 0.0], 'a2': [-2.3722813232690143, 0.0], 'a3': [3.0, 0.0], 'a4': [-2.3722813232690143, 0.0], 'a5': [19.489125293076057, 0.0], 'a6': [-7.116843969807043, 0.0], 'a7': [6.744562646538029, 0.0], 'a8': [24.6059692628831, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.9470630301894412, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-3.0, 0]]], [11, [[1.0, 0], [-11.0, 0]]]], 'bad_primes': [3, 11], 'central_character': '33.1', 'coefficient_field': 'CDF', 'conductor': 33, 'conductor_radical': 33, 'conjugate': '2500067106626052551661413465662', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.3722813232690143, 0], [8.0, 0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [-19.489125293076057, 0], [125.0, 0]], [[1.0, 0], [-6.744562646538029, 0], [343.0, 0]], [[1.0, 0], [-11.0, 0]], [[1.0, 0], [60.978250586152114, 0], [2197.0, 0]], [[1.0, 0], 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.9470630301894412, 'bad_primes': [3, 11], 'central_character': '1.1', 'conductor': 33, 'conductor_radical': 33, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/33/4/a/d/1/1'], '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': '2-33-1.1-c3-0-1', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-33-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.395372004230213, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.97220520084630365736708225749', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2500067106626052551661413465662', 'Lhash_array': ['2500067106626052551661413465662'], 'label': '2-33-1.1-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/33/4/a/d/1/1'}