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lfunc_lfunctions • Show schema
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{'Lhash': '1607952045713574523882390894195', 'a10': [3.8724702114036735, 0.0], 'a2': [1.0, 0.0], 'a3': [-0.8730436642827083, 0.0], 'a4': [1.0, 0.0], 'a5': [3.8724702114036735, 0.0], 'a6': [-0.8730436642827083, 0.0], 'a7': [2.6733537726558816, 0.0], 'a8': [1.0, 0.0], 'a9': [-2.2377947602558215, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.017990645468853, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [17, [[1.0, 0], [-1.0, 0]]], [59, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 17, 59], 'central_character': '2006.1', 'coefficient_field': 'CDF', 'conductor': 2006, 'conductor_radical': 2006, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.8730436642827083, 0], [3.0, 0]], [[1.0, 0], [-3.8724702114036735, 0], [5.0, 0]], [[1.0, 0], [-2.6733537726558816, 0], [7.0, 0]], [[1.0, 0], [2.908242728288898, 0], [11.0, 0]], [[1.0, 0], [-1.1187147785634832, 0], [13.0, 0]], [[1.0, 0], 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[[1.0, 0], [2.6962385077407016, 0], [109.0, 0]], [[1.0, 0], [-6.6093269848862795, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 37, 'label': '2-2006-1.1-c1-0-37', 'leading_term': '3.4071365855520830773591803112171', '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/2006/2/a/w/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [3.407136585552083, 3.4019024774710713, 3.386014355493472, 3.358928952009701, 3.3197867447070903, 3.267476967755336, 3.2007215114490104, 3.118171889250499, 3.0185132454097356, 2.900569740505011, 2.7634063720239137, 2.6064231449522763, 2.4294383348984296, 2.232758286284035, 2.0172317305352463, 1.784287012759902, 1.5359509255702983, 1.2748481189576728, 1.0041803342024358, 0.7276850350076217, 0.44957340382161254, 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'4.68676872298449392660904660199388', '5.25530636777461471356470084007043', '5.76237177769614248386505017863988', '6.43782664703125777001213000202113', '7.44354690748366747465389615612678', '8.410799903635217272128079018599124', '9.172394360045327636710875485607369'], 'prelabel': '2-2006-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.002248198883829, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.26845050633358815433344640171', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.30440868235115838504251656538', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.08661854251317501826449044305', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 16.017990645468853, 'bad_primes': [2, 17, 59], 'central_character': '1.1', 'conductor': 2006, 'conductor_radical': 2006, 'degree': 2, 'index': 37, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2006/2/a/w/1/4'], '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': '2-2006-1.1-c1-0-37', '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': '2-2006-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.002248198883829, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.26845050633358815433344640171', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1607952045713574523882390894195', 'Lhash_array': ['1607952045713574523882390894195'], 'label': '2-2006-1.1-c1-0-37', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2006/2/a/w/1/4'}