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lfunc_lfunctions • Show schema
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{'Lhash': '787110624804316858895152113320', 'a10': [480010696.1983791, -319021262.1078907], 'a2': [200.3939895582315, 301.51989809784595], 'a3': [0, 0], 'a4': [-50756.49789787081, 120845.55062203754], 'a5': [0, -1591970.2123360736], 'a6': [0, 0], 'a7': [-16605540.178564789, 0], 'a8': [-46608635.21889316, 8912627.935541788], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 131.91990288808307, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '8.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-200.3939895582315, -301.51989809784595]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '72.37', 'coefficient_field': 'CDF', 'conductor': 72, 'conductor_radical': 6, 'conjugate': '541811398909396865549815662296', 'degree': 2, 'euler_factors': [[[1.0, 0], [-200.3939895582315, -301.51989809784595]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1591970.2123360736], [-762939453125.0, 0]], [[1.0, 0], [16605540.178564789, 0], [232630513987207.0, 0]], [[1.0, 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'7.82771892399664348654752851623405', '9.658288870871428167138765330238636', '10.35013327963404641223506770912770', '11.13174009945801384442928497049806'], 'prelabel': '2-72-8.5-c17-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.485638984753225, 'root_angle': -0.060142028972695806, 'root_number': '0.9822035439351052179529870518654278927961492619729200460 - 0.1878195897166209705357475688939020250879796571134628911*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.030071014486347906', 'prec': 70}, 'spectral_label': 'c17-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.62092079999220958546154276527', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.42322749921667785081192131928', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.10933921773178314656718339560', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 131.91990288808307, 'bad_primes': [2, 3], 'central_character': '8.5', 'conductor': 72, 'conductor_radical': 6, 'degree': 2, 'index': 39, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/72/18/d/b/37/12'], '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': '2-72-8.5-c17-0-39', 'motivic_weight': 17, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [17], 'order_of_vanishing': 0, 'prelabel': '2-72-8.5-c17-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.485638984753225, 'root_angle': -0.030071014486347903, 'self_dual': False, 'spectral_label': 'c17-0', 'z1': {'__RealLiteral__': 0, 'data': '0.62092079999220958546154276527', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '787110624804316858895152113320', 'Lhash_array': ['787110624804316858895152113320'], 'label': '2-72-8.5-c17-0-39', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/72/18/d/b/37/12'}