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lfunc_lfunctions • Show schema
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{'Lhash': '1668752484780965820573384435733', 'a10': [-1.3308300260037729, -2.9141112722038773], 'a2': [-0.9594929736144974, 0.28173255684142967], 'a3': [-0.6548607339452851, -0.7557495743542583], 'a4': [0.8412535328311812, -0.5406408174555976], 'a5': [0.455922039387389, 3.1710074359578133], 'a6': [0.8412535328311812, 0.5406408174555976], 'a7': [0.6286629476107245, -1.3765798383362702], 'a8': [-0.6548607339452851, 0.7557495743542583], 'a9': [-0.14231483827328514, 0.9898214418809327], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.1019355478936699, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9594929736144974, -0.28173255684142967]]], [3, [[1.0, 0], [0.6548607339452851, 0.7557495743542583]]], [23, [[1.0, 0], [4.667523982149345, -1.1019164560259174]]]], 'bad_primes': [2, 3, 23], 'central_character': '138.55', 'coefficient_field': 'CDF', 'conductor': 138, 'conductor_radical': 138, 'conjugate': 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59.704216373986405]], [[1.0, 0], [-2.218524263973989, 15.430175183825394], [-79.63791681000329, -23.383802217838664]], [[1.0, 0], [-3.6792951759009034, -4.246132985189964], [-12.666020606322377, 88.094108327403]], [[1.0, 0], [-1.0313935236319969, -7.173499524678293], [-93.07081844060625, 27.32805801361868]], [[1.0, 0], [-0.1456986713566004, 1.0133565179295716], [-96.90879033506424, -28.4549882409844]], [[1.0, 0], [4.3649698858555, 1.2816707993653336], [86.64911388161165, 55.68600419792655]], [[1.0, 0], [-0.3948724530229233, 0.45570710355223426], [-15.22768769524151, -105.9108942812598]], [[1.0, 0], [4.943008090180925, 3.1766784093866387], [45.28023641720562, 99.1498874936425]], [[1.0, 0], [11.809091869897719, -3.4674622305450464], [95.06164920992347, -61.09241237248253]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-138-23.9-c1-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 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'root_number': '0.8037856211726127 - 0.594919049279948*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.10140794867', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.31641359573412542343833701690', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.83719798466757548392497230868', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.29925624134385364483494857606', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.1019355478936699, 'bad_primes': [2, 3, 23], 'central_character': '23.9', 'conductor': 138, 'conductor_radical': 138, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/138/2/e/a/55/1'], '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': '2-138-23.9-c1-0-0', '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': '2-138-23.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0497311788708907, 'root_angle': -0.10140794867042305, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.31641359573412542343833701690', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1668752484780965820573384435733', 'Lhash_array': ['1668752484780965820573384435733'], 'label': '2-138-23.9-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/138/2/e/a/55/1'}