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lfunc_lfunctions • Show schema
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{'Lhash': '988506897659712060396409474470', 'a10': [-0.3706151667436809, -2.205140448628965], 'a2': [-0.7071067811865476, 0.7071067811865476], 'a3': [0.079203527724496, -1.7302389433820968], 'a4': [0.0, -1.0], 'a5': [-1.297205267079247, 1.8213342623093267], 'a6': [1.1674583383906396, 1.2794690414864154], 'a7': [2.175555829080792, 2.175555829080792], 'a8': [0.7071067811865476, 0.7071067811865476], 'a9': [-2.98745360239199, -0.2740820562443331], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.426087387979079, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [3, [[1.0, 0], [-0.079203527724496, 1.7302389433820968]]], [5, [[1.0, 0], [1.297205267079247, -1.8213342623093267]]], [31, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '930.497', 'coefficient_field': 'CDF', 'conductor': 930, 'conductor_radical': 930, 'conjugate': 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2.7250848405103056, 'root_angle': -0.10732498527729652, 'root_number': '0.7811174833858057 - 0.6243840782315205*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.107324985277', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.77979444610505453211744600178', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.39290110882422335655173186010', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.82925060932294136478849801970', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.426087387979079, 'bad_primes': [2, 3, 5, 31], 'central_character': '15.2', 'conductor': 930, 'conductor_radical': 930, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/930/2/j/h/497/6'], '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': '2-930-15.2-c1-0-16', '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': '2-930-15.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7250848405103056, 'root_angle': -0.10732498527729652, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.77979444610505453211744600178', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '988506897659712060396409474470', 'Lhash_array': ['988506897659712060396409474470'], 'factors': ['2-930-15.2-c1-0-16'], 'label': '2-930-15.2-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/930/2/j/h/497/6'}