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lfunc_lfunctions • Show schema
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{'Lhash': '1470206024560781313078287786781', 'a10': [-6.91431792683857, 0.0], 'a2': [2.6340058737001675, 0.0], 'a3': [0.0, 0.0], 'a4': [4.937986942686983, 0.0], 'a5': [-2.6250199347982304, 0.0], 'a6': [0.0, 0.0], 'a7': [5.1885154106704015, 0.0], 'a8': [7.738674863891912, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.22165778065125, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-1.0, 0]]], [61, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 11, 61], 'central_character': '6039.1', 'coefficient_field': 'CDF', 'conductor': 6039, 'conductor_radical': 2013, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.6340058737001675, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.6250199347982304, 0], [5.0, 0]], [[1.0, 0], [-5.1885154106704015, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [3.472801957145104, 0], [13.0, 0]], [[1.0, 0], [1.948702987170978, 0], [17.0, 0]], [[1.0, 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'4.03050806744284436847454688038498', '4.55184548599567171019139140009562', '4.81533840861761459607708639583410', '5.63507063350523898300299784407325', '6.59636156464413398051104174794808', '7.27315260468101370481981372303718', '7.86323455114375661372439844207897'], 'prelabel': '2-6039-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.94418157745398, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.15978805539640306195740486671', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.24681508121850018364887130734', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.94385867771379151246537435115', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 48.22165778065125, 'bad_primes': [3, 11, 61], 'central_character': '1.1', 'conductor': 6039, 'conductor_radical': 2013, 'degree': 2, 'index': 159, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6039/2/a/j/1/14'], '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': '2-6039-1.1-c1-0-159', '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': '2-6039-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.94418157745398, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.15978805539640306195740486671', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1470206024560781313078287786781', 'Lhash_array': ['1470206024560781313078287786781'], 'label': '2-6039-1.1-c1-0-159', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6039/2/a/j/1/14'}