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lfunc_lfunctions • Show schema
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{'Lhash': '945765139620403338148235722165', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-0.2820640087175659, 0.48854919408537484], 'a4': [0, 0], 'a5': [-0.5, 0.8660254037844386], 'a6': [0, 0], 'a7': [1.5641280174351317, 0], 'a8': [0, 0], 'a9': [1.340879789972354, 2.322471923074402], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.137261107234623, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.5, -0.8660254037844386]]], [19, [[1.0, 0], [-2.782064008717566, -3.355610205521247]]]], 'bad_primes': [2, 5, 19], 'central_character': '1520.961', 'coefficient_field': 'CDF', 'conductor': 1520, 'conductor_radical': 190, 'conjugate': '1782474111091469446165950220828', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.2820640087175659, -0.48854919408537484], [-1.5, -2.598076211353316]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [-1.5641280174351317, 0], [7.0, 0]], [[1.0, 0], 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'8.608336066292474407996404772306227', '9.458418052719167061713935417799088'], 'prelabel': '2-1520-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': -0.4547610351929863, 'root_number': '0.14164443270402751342613045695677036815285606221355932344 - 0.9899175999465582898002096330456479138883978597071236108*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.22738051759649314', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.74607714416742799479961913656', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.83762390044130515244781233912', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.26709701895622672715526805313', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.137261107234623, 'bad_primes': [2, 5, 19], 'central_character': '19.11', 'conductor': 1520, 'conductor_radical': 190, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1520/2/q/n/961/2'], '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': '2-1520-19.11-c1-0-11', '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': '2-1520-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': -0.22738051759649314, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.74607714416742799479961913656', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '945765139620403338148235722165', 'Lhash_array': ['945765139620403338148235722165'], 'label': '2-1520-19.11-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1520/2/q/n/961/2'}