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lfunc_lfunctions • Show schema
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{'Lhash': '863010056768794807790216593966', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 2.0], 'a6': [0, 0], 'a7': [0, 9.797958971132712], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 31.389726454306206, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1152.703', 'coefficient_field': 'CDF', 'conductor': 1152, 'conductor_radical': 6, 'conjugate': '1719916365861793090905779297947', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -2.0], [-25.0, 0]], [[1.0, 0], [0, -9.797958971132712], [-49.0, 0]], [[1.0, 0], [-19.595917942265423, 0], [121.0, 0]], [[1.0, 0], [0, 0], [-169.0, 0]], [[1.0, 0], [0, 0], [289.0, 0]], [[1.0, 0], [0, 0], [361.0, 0]], [[1.0, 0], [0, 0], [-529.0, 0]], [[1.0, 0], [0, -50.0], [-841.0, 0]], [[1.0, 0], [0, 48.98979485566356], 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'primitive': True, 'rational': False, 'root_analytic_conductor': 5.602653519030621, 'root_angle': -0.5, 'root_number': '0.e-56 - 1.00000000000000000000000000000000000000000000000000000000*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.68079489459746825856764101310', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.61123040821872616575888505994', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.35846041890088462009654509504', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 31.389726454306206, 'bad_primes': [2, 3], 'central_character': '8.3', 'conductor': 1152, 'conductor_radical': 6, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1152/3/b/f/703/4'], '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': '2-1152-8.3-c2-0-14', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-1152-8.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.602653519030621, 'root_angle': -0.25, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.68079489459746825856764101310', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '863010056768794807790216593966', 'Lhash_array': ['863010056768794807790216593966'], 'label': '2-1152-8.3-c2-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1152/3/b/f/703/4'}