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lfunc_lfunctions • Show schema
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{'Lhash': '960112909057753291818107628143', 'a10': [0.0, 0.0], 'a2': [1.82842712474619, 0.0], 'a3': [0.0, 0.0], 'a4': [-4.656854249492381, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [7.0, 0.0], 'a8': [-23.14213562373095, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 92.9280082590415, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-7.0, 0]]]], 'bad_primes': [3, 5, 7], 'central_character': '1575.1', 'coefficient_field': 'CDF', 'conductor': 1575, 'conductor_radical': 105, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.82842712474619, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-7.0, 0]], [[1.0, 0], [-64.5685424949238, 0], [1331.0, 0]], [[1.0, 0], [-32.34314575050762, 0], [2197.0, 0]], [[1.0, 0], [56.34314575050762, 0], [4913.0, 0]], [[1.0, 0], [2.7451660040609585, 0], [6859.0, 0]], [[1.0, 0], [-88.16652224137046, 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'3.41717496467596497901784353302606', '3.99789702734946826772808536766618', '4.77491454911165300070185180076727', '5.76120235415806023984537743350029', '6.43627307088392360868036088375839', '7.34273971571518094750399983006923', '8.484545641305012890080494909305830', '9.148862085010711906584867969919939'], 'prelabel': '2-1575-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.639917440468125, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.75739553855367824648032229375', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.91194494073805489290818219797', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.41717496467596497901784353303', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 92.9280082590415, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 1575, 'conductor_radical': 105, 'degree': 2, 'index': 50, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1575/4/a/q/1/2'], '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': '2-1575-1.1-c3-0-50', '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': '2-1575-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.639917440468125, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.75739553855367824648032229375', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '960112909057753291818107628143', 'Lhash_array': ['960112909057753291818107628143'], 'label': '2-1575-1.1-c3-0-50', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1575/4/a/q/1/2'}