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lfunc_lfunctions • Show schema
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{'Lhash': '938637277137150806614554191252', 'a10': [-1.0, 0.0], 'a2': [0.7071067811865476, 0.7071067811865476], 'a3': [0.0, 1.0], 'a4': [0.0, 1.0], 'a5': [-0.7071067811865476, 0.7071067811865476], 'a6': [-0.7071067811865476, 0.7071067811865476], 'a7': [0.0, 0.0], 'a8': [-0.7071067811865476, 0.7071067811865476], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7785414197074838, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]]], [3, [[1.0, 0], [0, -1.0]]], [5, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [13, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1560.1403', 'coefficient_field': 'CDF', 'conductor': 1560, 'conductor_radical': 390, 'conjugate': '3531257841848502516671689824698', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, 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'5.06808002884782947531880488265460', '5.67056732946157086730293372167884', '6.89651324810535105516244453191327', '7.39349888205057143726986260399971', '8.466103488921207574889386950426428', '9.197607796521076055857795209307538'], 'prelabel': '2-1560-1560.1403-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8823499417507114, 'root_angle': 0.9262081911747834, 'root_number': '-0.97324898946773016378805774830813 + 0.22975292054736118352393736938184*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4631040955873917', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.74045425211659851367426791725', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.98583808909537944933566435786', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.03073712906181149412029151633', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7785414197074838, 'bad_primes': [2, 3, 5, 13], 'central_character': '1560.1403', 'conductor': 1560, 'conductor_radical': 390, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1560/1/cs/a/1403/2'], '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': '2-1560-1560.1403-c0-0-4', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1560-1560.1403-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8823499417507114, 'root_angle': 0.4631040955873917, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.74045425211659851367426791725', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '938637277137150806614554191252', 'Lhash_array': ['938637277137150806614554191252'], 'label': '2-1560-1560.1403-c0-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1560/1/cs/a/1403/2'}