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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -2, 'Lhash': '1427367043717476171978360498361', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896257, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 43.39724012202222, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 1, 3]], [5, [1]], [11, [1, 0, 11]]], 'bad_primes': [3, 5, 11], 'central_character': '680625.1', 'coefficient_field': '1.1.1.1', 'conductor': 680625, 'conductor_radical': 165, 'degree': 4, 'euler_factors': [[1, 0, -1, 0, 4], [1, 1, 3], [1], [1, 0, -4, 0, 49], [1, 0, 11], [1, 0, -1, 0, 169], [1, 0, -16, 0, 289], [1, 0, 22, 0, 361], [1, 0, 10, 0, 529], [1, 0, -32, 0, 841], [1, -5, 12, -155, 961], [1, 6, 58, 222, 1369], [1, 0, -8, 0, 1681], [1, 0, 44, 0, 1849], [1, 0, 85, 0, 2209], [1, -15, 160, -795, 2809], [1, 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2.7201686669176706, 1.8112870457694956], 'positive_zeros': ['1.12599405818960778465998620700847', '2.03324398628771102650193833768137', '2.67590504465410219362787567140032', '3.07413865425757737195029516830555', '3.89226962219140458079806836180861', '4.39182612394845217583441195266418', '4.92209969516231962309625978337078', '5.48485015186966660312866520558862', '5.80112125357453558344195791989807', '6.35662915666782164579168470253056', '6.69679809007542057142536961356558', '7.18724875958368574351346895755643', '7.53258059126941734857294977471444', '8.138641774942249567494218686021568'], 'prelabel': '4-825e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.566643365712431, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1076888791224567282, 'z1': {'__RealLiteral__': 0, 'data': '1.12599405818960778465998620700847', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.03324398628771102650193833768137', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.67590504465410219362787567140032', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 43.39724012202222, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 680625, 'conductor_radical': 165, 'degree': 4, 'dirichlet_coefficients': [1, 0, -1, 1, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 5, 0, 0, 0, 0, -2, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 4, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7, 0, 0, -9, 0, 0, 0, -15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -15, 0, 0, 0, -5, 0, 0, 0, 6, 0, 0, 0], 'euler11': [1, 0, 11, 0, 0], 'euler13': [1, 0, -1, 0, 169], 'euler17': [1, 0, -16, 0, 289], 'euler19': [1, 0, 22, 0, 361], 'euler2': [1, 0, -1, 0, 4], 'euler23': [1, 0, 10, 0, 529], 'euler29': [1, 0, -32, 0, 841], 'euler3': [1, 1, 3, 0, 0], 'euler31': [1, -5, 12, -155, 961], 'euler37': [1, 6, 58, 222, 1369], 'euler41': [1, 0, -8, 0, 1681], 'euler43': [1, 0, 44, 0, 1849], 'euler47': [1, 0, 85, 0, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, -15, 160, -795, 2809], 'euler59': [1, 0, 118, 0, 3481], 'euler61': [1, 0, 43, 0, 3721], 'euler67': [1, 9, 148, 603, 4489], 'euler7': [1, 0, -4, 0, 49], 'euler71': [1, 15, 178, 1065, 5041], 'euler73': [1, 0, -91, 0, 5329], 'euler79': [1, 0, -68, 0, 6241], 'euler83': [1, 0, 101, 0, 6889], 'euler89': [1, 15, 232, 1335, 7921], 'euler97': [1, -6, 178, -582, 9409], 'euler_factors': [[1, 0, -1, 0, 4], [1, 1, 3, 0, 0], [1, 0, 0, 0, 0], [1, 0, -4, 0, 49], [1, 0, 11, 0, 0], [1, 0, -1, 0, 169], [1, 0, -16, 0, 289], [1, 0, 22, 0, 361], [1, 0, 10, 0, 529], [1, 0, -32, 0, 841], [1, -5, 12, -155, 961], [1, 6, 58, 222, 1369], [1, 0, -8, 0, 1681], [1, 0, 44, 0, 1849], [1, 0, 85, 0, 2209], [1, -15, 160, -795, 2809], [1, 0, 118, 0, 3481], [1, 0, 43, 0, 3721], [1, 9, 148, 603, 4489], [1, 15, 178, 1065, 5041], [1, 0, -91, 0, 5329], [1, 0, -68, 0, 6241], [1, 0, 101, 0, 6889], [1, 15, 232, 1335, 7921], [1, -6, 178, -582, 9409]], 'index': 13, 'instance_types': ['BMF', 'ECNF', 'BMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/5625.3/d', 'EllipticCurve/2.0.11.1/5625.13/d', 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/5625.13/d', 'EllipticCurve/2.0.11.1/5625.3/d'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-825e2-1.1-c1e2-0-13', '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': 1, 'prelabel': '4-825e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.566643365712431, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1076888791224567282, 'z1': {'__RealLiteral__': 0, 'data': '1.12599405818960778465998620700847', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9943459
{'Lhash': '1427367043717476171978360498361', 'Lhash_array': ['1427367043717476171978360498361'], 'label': '4-825e2-1.1-c1e2-0-13', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.11.1/5625.3/d'}
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id: 9943456
{'Lhash': '1427367043717476171978360498361', 'Lhash_array': ['1427367043717476171978360498361'], 'label': '4-825e2-1.1-c1e2-0-13', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/5625.13/d'}
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id: 9943453
{'Lhash': '1427367043717476171978360498361', 'Lhash_array': ['1427367043717476171978360498361'], 'label': '4-825e2-1.1-c1e2-0-13', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.11.1/5625.13/d'}
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id: 9943339
{'Lhash': '1427367043717476171978360498361', 'Lhash_array': ['1427367043717476171978360498361'], 'label': '4-825e2-1.1-c1e2-0-13', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/5625.3/d'}