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lfunc_lfunctions • Show schema
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{'Lhash': '1453467333554331319720339998733', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [4.295221619259397, -2.55950605419223], 'a6': [0, 0], 'a7': [2.420963376085834, -1.3977438568813816], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 44.1418028263681, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-4.295221619259397, 2.55950605419223]]]], 'bad_primes': [2, 3, 5], 'central_character': '1620.1349', 'coefficient_field': 'CDF', 'conductor': 1620, 'conductor_radical': 30, 'conjugate': '1484461807421154255434852861022', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-4.295221619259397, 2.55950605419223]], [[1.0, 0], [-2.420963376085834, 1.3977438568813816], [24.5, -42.4352447854375]], [[1.0, 0], [-15.715360457894612, 9.073267590777455], [60.5, -104.78907385791707]], [[1.0, 0], 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True, 'rational': False, 'root_analytic_conductor': 6.643929772835358, 'root_angle': 0.10671915766546136, 'root_number': '0.94432212553220694457763841852436255904375636654938661456 + 0.32902237496914216552776704695218364453391253239800415527*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.05335957883273068', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.14658355645684011104024560878', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.99620602658490960523931187767', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.30304529723378554087467008721', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 44.1418028263681, 'bad_primes': [2, 3, 5], 'central_character': '45.14', 'conductor': 1620, 'conductor_radical': 30, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1620/3/t/d/1349/4'], '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': '2-1620-45.14-c2-0-34', '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': '2-1620-45.14-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.643929772835358, 'root_angle': 0.05335957883273068, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.14658355645684011104024560878', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1453467333554331319720339998733', 'Lhash_array': ['1453467333554331319720339998733'], 'label': '2-1620-45.14-c2-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1620/3/t/d/1349/4'}