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lfunc_lfunctions • Show schema
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{'Lhash': '804140092876077398505273444050', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-3.20506107842232, 4.089936855696229], 'a4': [0, 0], 'a5': [-7.665465553118919, 0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [-6.45516696716471, -26.216994858793896], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 34.6931230833755, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [3.20506107842232, -4.089936855696229]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '588.293', 'coefficient_field': 'CDF', 'conductor': 588, 'conductor_radical': 42, 'conjugate': '748674730956344793220953529855', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [3.20506107842232, -4.089936855696229]], [[1.0, 0], [7.665465553118919, 0], [125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.3147083131568675], [-1331.0, 0]], [[1.0, 0], [0, -23.975367529156575], [-2197.0, 0]], [[1.0, 0], 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0.3279241839498855], 'positive_zeros': ['0.63435468159073092316541261023534', '2.03585572416187970954216501860990', '3.46706730386036268458665580368381', '4.73156028805143406900923059499368', '5.71693974829907138094564479720746', '6.66664220378027383755721728612424', '7.56835399719024151020546232952820', '8.176468773771974667705589087757358', '9.287376892926673024990135681159279', '10.49650597926661348502779006490945'], 'prelabel': '2-588-21.20-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.890086848542685, 'root_angle': -0.15426364797301342, 'root_number': '0.88484573493208268963777534626116596448378674834720357912 - 0.4658841329907066708458521948972579825052873944495234666*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.07713182398650671', 'prec': 67}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.63435468159073092316541261024', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 34.6931230833755, 'bad_primes': [2, 3, 7], 'central_character': '21.20', 'conductor': 588, 'conductor_radical': 42, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/588/4/f/d/293/6'], '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': '2-588-21.20-c3-0-14', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-588-21.20-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.890086848542685, 'root_angle': -0.07713182398650671, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.63435468159073092316541261024', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '804140092876077398505273444050', 'Lhash_array': ['804140092876077398505273444050'], 'label': '2-588-21.20-c3-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/588/4/f/d/293/6'}