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lfunc_lfunctions • Show schema
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{'Lhash': '2786754804446586792504632356112', 'a10': [-0.5891079338223374, -1.9054422795904826e-61], 'a2': [1.1803698940356526, -0.8575889267940829], 'a3': [-0.30901699437494745, -0.9510565162951535], 'a4': [0.03978033063601579, -0.12243126870185418], 'a5': [-0.32665705080718505, -0.23733023948422782], 'a6': [-1.1803698940356526, -0.8575889267940829], 'a7': [1.4859315249711427, -4.573226991773405], 'a8': [0.843682164774491, 2.5965867091348307], 'a9': [-0.8090169943749475, 0.5877852522924731], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.42558224671293, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.30901699437494745, 0.9510565162951535]]], [11, [[1.0, 0], [-0.8516909145409864, 3.2054052140233904]]], [13, [[1.0, 0], [0.8090169943749475, -0.5877852522924731]]]], 'bad_primes': [3, 11, 13], 'central_character': '429.157', 'coefficient_field': 'CDF', 'conductor': 429, 'conductor_radical': 429, 'conjugate': 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[25.648410533120636, 78.93769085249775]], [[1.0, 0], [-3.7044723708234972, 0], [89.0, 0]], [[1.0, 0], [-14.585043889011363, 10.596654658191456], [29.974648454369902, -92.2524820806299]], [[1.0, 0], [-7.895180381426634, 5.736184313380036], [31.210716431869688, -96.05670814581052]], [[1.0, 0], [-3.03236716113955, 9.332666490510052], [-83.32875042061958, -60.54188098612473]], [[1.0, 0], [-3.492926147632861, -10.750121301138634], [-86.56481839811937, 62.893021995294625]], [[1.0, 0], [15.668768071693714, 0], [109.0, 0]], [[1.0, 0], [-0.3724507045359066, -1.1462854017594843], [-91.41892036436906, 66.41973350904946]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 20, 'label': '2-429-11.3-c1-0-20', '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/429/2/n/c/157/6', 'plot_delta': {'__RealLiteral__': 0, 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'0.295116909743', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.19836191766473819186680022767', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.83366996854770768019010079335', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.94061007913765744289470023046', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.42558224671293, 'bad_primes': [3, 11, 13], 'central_character': '11.3', 'conductor': 429, 'conductor_radical': 429, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/429/2/n/c/157/6'], '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': '2-429-11.3-c1-0-20', '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': '2-429-11.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8508328521811281, 'root_angle': 0.2951169097434047, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.19836191766473819186680022767', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2786754804446586792504632356112', 'Lhash_array': ['2786754804446586792504632356112'], 'label': '2-429-11.3-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/429/2/n/c/157/6'}