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lfunc_lfunctions • Show schema
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{'Lhash': '3191686346315567628726021156638', 'a10': [-42.0, -72.74613391789285], 'a2': [2.0, -3.4641016151377544], 'a3': [14.90175425099138, 25.81059548462257], 'a4': [-8.0, -13.856406460551018], 'a5': [10.5, -18.186533479473212], 'a6': [119.21403400793103, -6.925056353035662e-60], 'a7': [-10.410525505948279, -129.22314405202343], 'a8': [-64.0, 0.0], 'a9': [-322.6245595138793, 558.8021288475679], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.2453734773817295, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-2.0, 3.4641016151377544]]], [7, [[1.0, 0], [10.410525505948279, 129.22314405202343]]]], 'bad_primes': [2, 7], 'central_character': '14.9', 'coefficient_field': 'CDF', 'conductor': 14, 'conductor_radical': 14, 'conjugate': '4222563222370827803752763577877', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.0, 3.4641016151377544]], [[1.0, 0], [-14.90175425099138, -25.81059548462257], [-121.5, 210.4441731196186]], 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'7.61079083741375787374510149103737', '8.963875289832457624649367349786202', '12.14620085077557419061462290640894', '13.10071771384482645734271213575401', '14.33343898144087727219906519046061', '15.36412048777110957358309552440616', '17.66920126648807823487630291292075', '18.42802034860173992316376362552103'], 'prelabel': '2-14-7.2-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4984570322107102, 'root_angle': -0.022880747538142527, 'root_number': '0.9896837459691957 - 0.143269267340838*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0228807475381', 'prec': 54}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.51779658033604245689268018810', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.22842519636896385324830299461', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.61079083741375787374510149104', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.2453734773817295, 'bad_primes': [2, 7], 'central_character': '7.2', 'conductor': 14, 'conductor_radical': 14, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/14/6/c/b/9/2'], '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': '2-14-7.2-c5-0-1', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-14-7.2-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4984570322107102, 'root_angle': -0.022880747538142527, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '2.51779658033604245689268018810', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3191686346315567628726021156638', 'Lhash_array': ['3191686346315567628726021156638'], 'factors': ['2-14-7.2-c5-0-1'], 'label': '2-14-7.2-c5-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/14/6/c/b/9/2'}