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lfunc_lfunctions • Show schema
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{'Lhash': '661808956508839646338123598365', 'a10': [-1.6941865528926365, 0.0], 'a2': [0.7027841855191586, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.5060943885841729, 0.0], 'a5': [-2.410678253440083, 0.0], 'a6': [0.0, 0.0], 'a7': [0.3806081702550913, 0.0], 'a8': [-2.4640276892344204, 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], [-0.7027841855191586, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.410678253440083, 0], [5.0, 0]], [[1.0, 0], [-0.3806081702550913, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.873438772233348, 0], [13.0, 0]], [[1.0, 0], [-1.8524038314273497, 0], [17.0, 0]], 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'3.79316875034273049117567609648371', '4.24602776328073767912737091199389', '5.11569197480808407984153001787218', '5.82654815437674548105567404525400', '6.56930125735301914984570591350121', '7.45770392840612334214438951470915', '8.206086535154702371778552268694171'], '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': '0.52207521251493647622584291866', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.83121768819141626945028923268', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.22167679657598500593694251708', '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': 40, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6039/2/a/o/1/15'], '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-c1-0-40', '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': '0.52207521251493647622584291866', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '661808956508839646338123598365', 'Lhash_array': ['661808956508839646338123598365'], 'label': '2-6039-1.1-c1-0-40', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6039/2/a/o/1/15'}