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lfunc_lfunctions • Show schema
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{'Lhash': '1539695010485910891548360691192', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.341725404492242, 1.6980058150444048], 'a4': [0.0, 0.0], 'a5': [0.5260043502600147, 0.0], 'a6': [0.0, 0.0], 'a7': [2.4396253008731286, -1.023830255139834], 'a8': [0.0, 0.0], 'a9': [-2.7664474958492273, -1.1605034479524565], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.024460261872533, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.341725404492242, -1.6980058150444048]]], [7, [[1.0, 0], [-2.4396253008731286, 1.023830255139834]]]], 'bad_primes': [2, 3, 7], 'central_character': '504.457', 'coefficient_field': 'CDF', 'conductor': 504, 'conductor_radical': 42, 'conjugate': '1937599180116793555048203036771', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.341725404492242, -1.6980058150444048]], [[1.0, 0], [-0.5260043502600147, 0], [5.0, 0]], [[1.0, 0], [-2.4396253008731286, 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'7.88788368929033202230037570823119', '8.960397646362298184144992677354849', '9.759662846625592551033798324744615', '11.16662096704495971067276262512868'], 'prelabel': '2-504-63.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0061057454363, 'root_angle': -0.2979980154871407, 'root_number': '0.592861840866531 - 0.8053041895112356*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.148999007744', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.21460519973619092970711817697', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.36968825754051751187730441321', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.98802084907591521889385300040', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.024460261872533, 'bad_primes': [2, 3, 7], 'central_character': '63.16', 'conductor': 504, 'conductor_radical': 42, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/504/2/t/c/457/6'], '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': '2-504-63.16-c1-0-10', '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': '2-504-63.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0061057454363, 'root_angle': -0.14899900774357036, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.21460519973619092970711817697', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1539695010485910891548360691192', 'Lhash_array': ['1539695010485910891548360691192'], 'label': '2-504-63.16-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/504/2/t/c/457/6'}