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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 2, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '76457298939458310,972972732953355218', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [1.1547005383792515, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.401922408716853, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -2, 3]]], 'bad_primes': [2, 3], 'central_character': '147456.1', 'coefficient_field': '1.1.1.1', 'conductor': 147456, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1, -2, 3], [1, 0, 6, 0, 25], [1, 0, -2, 0, 49], [1, 4, 26, 44, 121], [1, -4, 30, -52, 169], [1, 0, 30, 0, 289], [1, 0, 34, 0, 361], [1, -8, 62, -184, 529], [1, 0, 22, 0, 841], [1, 0, 62, 0, 961], [1, -20, 174, -740, 1369], [1, 0, 46, 0, 1681], [1, 0, 50, 0, 1849], [1, 16, 158, 752, 2209], [1, 0, 70, 0, 2809], [1, -28, 314, 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-11.67708309385539, -11.194566208713479, -10.265635865485757, -8.990879268794712, -7.493451735651052], 'positive_zeros': ['1.02724387350145696940295704376494', '2.44235807183272353930685105041810', '2.46608091328452001690059553408192', '3.56276783709589056726776122484057', '3.73824894896581631226090928700139', '4.62995407509459210959268189868973', '5.34050418818343429420051907290944', '5.64130249043000575312616744005033', '6.52256885432452015704757780959986', '6.78571919296342801026858814861792', '7.63242500478736670765641851926187', '8.088659191412945349881968287052322', '8.173183686627627779120693205031062', '8.675368536957604275874860747441054', '9.385355573475711088007535446098546'], 'prelabel': '4-384e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.7510726534376488, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1049430031892813528, 'z1': {'__RealLiteral__': 0, 'data': '1.02724387350145696940295704376494', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.44235807183272353930685105041810', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.46608091328452001690059553408192', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.401922408716853, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 147456, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 2, 0, 0, 0, 0, 0, 1, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, -6, 0, -4, 0, 0, 0, 0, 0, -8, 0, 0, 0, 20, 0, 8, 0, 0, 0, 0, 0, 0, 0, -16, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, 4, 0, 0, 0, 0, 0, 0, 0, 16, 0, 24, 0, 28, 0, -12, 0, 0, 0, 0, 0, -11, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 0], 'euler11': [1, 4, 26, 44, 121], 'euler13': [1, -4, 30, -52, 169], 'euler17': [1, 0, 30, 0, 289], 'euler19': [1, 0, 34, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -8, 62, -184, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, -2, 3, 0, 0], 'euler31': [1, 0, 62, 0, 961], 'euler37': [1, -20, 174, -740, 1369], 'euler41': [1, 0, 46, 0, 1681], 'euler43': [1, 0, 50, 0, 1849], 'euler47': [1, 16, 158, 752, 2209], 'euler5': [1, 0, 6, 0, 25], 'euler53': [1, 0, 70, 0, 2809], 'euler59': [1, -28, 314, -1652, 3481], 'euler61': [1, -4, 126, -244, 3721], 'euler67': [1, 0, 34, 0, 4489], 'euler7': [1, 0, -2, 0, 49], 'euler71': [1, -24, 286, -1704, 5041], 'euler73': [1, -28, 342, -2044, 5329], 'euler79': [1, 0, 94, 0, 6241], 'euler83': [1, 12, 202, 996, 6889], 'euler89': [1, 0, 174, 0, 7921], 'euler97': [1, 4, 198, 388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -2, 3, 0, 0], [1, 0, 6, 0, 25], [1, 0, -2, 0, 49], [1, 4, 26, 44, 121], [1, -4, 30, -52, 169], [1, 0, 30, 0, 289], [1, 0, 34, 0, 361], [1, -8, 62, -184, 529], [1, 0, 22, 0, 841], [1, 0, 62, 0, 961], [1, -20, 174, -740, 1369], [1, 0, 46, 0, 1681], [1, 0, 50, 0, 1849], [1, 16, 158, 752, 2209], [1, 0, 70, 0, 2809], [1, -28, 314, -1652, 3481], [1, -4, 126, -244, 3721], [1, 0, 34, 0, 4489], [1, -24, 286, -1704, 5041], [1, -28, 342, -2044, 5329], [1, 0, 94, 0, 6241], [1, 12, 202, 996, 6889], [1, 0, 174, 0, 7921], [1, 4, 198, 388, 9409]], 'index': 15, 'instance_types': ['ECNF', 'HMF'], 'instance_urls': ['EllipticCurve/2.2.12.1/1024.1/e', 'ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-1024.1-e'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-384e2-1.1-c1e2-0-15', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-384e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.7510726534376488, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1049430031892813528, 'z1': {'__RealLiteral__': 0, 'data': '1.02724387350145696940295704376494', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9567694
{'Lhash': '76457298939458310,972972732953355218', 'Lhash_array': ['76457298939458310', '972972732953355218'], 'label': '4-384e2-1.1-c1e2-0-15', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-1024.1-e'}
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id: 9567692
{'Lhash': '76457298939458310,972972732953355218', 'Lhash_array': ['76457298939458310', '972972732953355218'], 'label': '4-384e2-1.1-c1e2-0-15', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.12.1/1024.1/e'}