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lfunc_lfunctions • Show schema
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{'Lhash': '1019321924536653180779235923418', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.3208844994474864, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.41178332170387, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '4560.1', 'coefficient_field': 'CDF', 'conductor': 4560, 'conductor_radical': 570, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.3208844994474864, 0], [7.0, 0]], [[1.0, 0], [3.7073893592230958, 0], [11.0, 0]], [[1.0, 0], [-3.3208844994474864, 0], [13.0, 0]], [[1.0, 0], [-1.6134951402243907, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-7.670042857565555, 0], [23.0, 0]], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 19, 'label': '2-4560-1.1-c1-0-19', 'leading_term': '1.838590180667632616633964701963', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/4560/2/a/br/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.8385901806676326, 1.8311007798511818, 1.8085929623351413, 1.7709554453188565, 1.7180274260782795, 1.6496337565634165, 1.5656307332064383, 1.4659594773420312, 1.3507035383492587, 1.2201472653722714, 1.0748316202216364, 0.9156043842543371, 0.7436620858498239, 0.5605813933011992, 0.36833814706910084, 0.16931262791224072, -0.033719931227030576, -0.23761417788517172, -0.4388950019091879, -0.6338132000658088, -0.8184157937022364, -0.9886299129938227, -1.1403587145248766, -1.269587349796884, -1.3724965622491048, 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'5.98139400138620937695997937571878', '6.88086063007551704425284640357355', '7.59110956580293799470602896135683', '8.237461006035578476351754527824201'], 'prelabel': '2-4560-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.034217705859134, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.804103216101608112698240117450', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.81425456961360794284694198743', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.87160566060930521026877425123', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 36.41178332170387, 'bad_primes': [2, 3, 5, 19], 'central_character': '1.1', 'conductor': 4560, 'conductor_radical': 570, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4560/2/a/br/1/3'], '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': '2-4560-1.1-c1-0-19', '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': '2-4560-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.034217705859134, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.804103216101608112698240117450', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1019321924536653180779235923418', 'Lhash_array': ['1019321924536653180779235923418'], 'label': '2-4560-1.1-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4560/2/a/br/1/3'}