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lfunc_lfunctions • Show schema
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{'Lhash': '430995816836213247911142077570', 'a10': [4.7919185933482735, 0.0], 'a2': [-2.4169522662103087, 0.0], 'a3': [1.0, 0.0], 'a4': [3.8416582571391467, 0.0], 'a5': [-1.9826285609114755, 0.0], 'a6': [-2.4169522662103087, 0.0], 'a7': [-1.0, 0.0], 'a8': [-4.451200098177388, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.338907677352424, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7, 13], 'central_character': '3549.1', 'coefficient_field': 'CDF', 'conductor': 3549, 'conductor_radical': 273, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.4169522662103087, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.9826285609114755, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [5.561840092219688, 0], [11.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.662084047719078, 0], [17.0, 0]], [[1.0, 0], [2.77488945140476, 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[-17.56938809042358, 0], [109.0, 0]], [[1.0, 0], [-14.291357259327867, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-3549-1.1-c1-0-2', 'leading_term': '0.24537356425584633845721909557922', '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/3549/2/a/bh/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.24537356425584633, 0.23990364800468192, 0.22348719803439943, 0.1961084482615523, 0.15775527123387464, 0.10843935219726546, 0.04822244244919352, -0.022753064473514144, -0.10423120733842632, -0.19580923041437934, -0.29690605697223726, -0.40673432851197444, -0.5242776801295469, -0.6482746945317609, -0.777210734156738, -0.9093186020871469, -1.0425887306343986, -1.174789339946518, -1.3034967441380279, -1.4261357057197983, 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'2.57543990869740904906702035716559', '3.67164738693881587563700878491214', '4.62724415864580241854557887015495', '5.83544459521431687077728656670245', '6.87969499210271111521913253119895', '7.36512543410732956349220521030020', '8.074644063095379925599153704823961', '8.474793313593424769440906494325008'], 'prelabel': '2-3549-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.3234300669166705, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.33999575021588458312404706749', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.99926795703766382000004245444', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.57543990869740904906702035717', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 28.338907677352424, 'bad_primes': [3, 7, 13], 'central_character': '1.1', 'conductor': 3549, 'conductor_radical': 273, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3549/2/a/bh/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': '2-3549-1.1-c1-0-2', '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': '2-3549-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.3234300669166705, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.33999575021588458312404706749', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '430995816836213247911142077570', 'Lhash_array': ['430995816836213247911142077570'], 'label': '2-3549-1.1-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3549/2/a/bh/1/3'}