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lfunc_lfunctions • Show schema
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{'Lhash': '4190474406446225983534184577923', 'a10': [-3.205308530366011e-59, -123.77391473257825], 'a2': [1.6625077511098136, -2.288245611270737], 'a3': [0.30928769102415693, -0.9518896349159942], 'a4': [-2.4721359549995796, -7.608452130361228], 'a5': [35.40313964707758, -25.721886578514564], 'a6': [-1.66396409586011, -2.290250097855018], 'a7': [-65.60727013341265, 21.317094282418665], 'a8': [-21.519952382846636, -6.9922563911811375], 'a9': [64.7199415431293, 47.02178994110433], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.274139187844576, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.6625077511098136, 2.288245611270737]]], [11, [[1.0, 0], [-65.63740005934856, -101.65004531946373]]]], 'bad_primes': [2, 11], 'central_character': '22.7', 'coefficient_field': 'CDF', 'conductor': 22, 'conductor_radical': 22, 'conjugate': '2528703904830375129841407077766', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'0.169813516139', 'prec': 47}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.30570143357465197730561399986', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.03748520886147936328687265830', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.90630606187539462479666828803', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.274139187844576, 'bad_primes': [2, 11], 'central_character': '11.7', 'conductor': 22, 'conductor_radical': 22, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/22/5/d/a/7/3'], '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': '2-22-11.7-c4-0-2', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-22-11.7-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5080249294506294, 'root_angle': 0.169813516138897, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '3.30570143357465197730561399986', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4190474406446225983534184577923', 'Lhash_array': ['4190474406446225983534184577923'], 'label': '2-22-11.7-c4-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/22/5/d/a/7/3'}