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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': -6, 'A8': 1, 'A9': 0, 'Lhash': '776455036717969712952551445392', 'a10': [0.0, 0], 'a2': [0.7071067811865476, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-2.2677868380553634, 0], 'a8': [0.3535533905932738, 0], 'a9': [0.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.83090420500103, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [19, [1, 0, 19]]], 'bad_primes': [2, 3, 19], 'central_character': '467856.1', 'coefficient_field': '1.1.1.1', 'conductor': 467856, 'conductor_radical': 114, 'degree': 4, 'euler_factors': [[1, -1], [1], [1, 0, -2, 0, 25], [1, 6, 19, 42, 49], [1, 0, -6, 0, 121], [1, 0, -3, 0, 169], [1, 0, -25, 0, 289], [1, 0, 19], [1, 0, -1, 0, 529], [1, 4, 37, 116, 841], [1, 0, 30, 0, 961], [1, 0, 54, 0, 1369], [1, -8, 82, -328, 1681], [1, 12, 122, 516, 1849], [1, 0, 2, 0, 2209], [1, -20, 205, -1060, 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0.9215849541998895, 0.7224209885109829, 0.37549344320578437, -0.056356782043638726, -0.48955979435307756], 'positive_zeros': ['0.61251502312875154700840843574045', '1.91217842788625439513224721260843', '2.65093922967544299455930389543641', '3.22115591001299469894859390508590', '3.53039413426168323522471706795825', '4.10615666775996438894538229566117', '4.70810817426002516539312362729801', '5.38267257036589829821591587006865', '5.80584807659940157336037178502854', '6.31425452124810997436354918497183', '6.55362099532961595941847068962316', '7.11486476424775968783668661249280', '7.39951749410871353220847562436596', '8.033016170548982971841517444486273', '8.634785421396690321233299085650049'], 'prelabel': '4-684e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.337042468218235, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 2072573685637676086, 'z1': {'__RealLiteral__': 0, 'data': '0.61251502312875154700840843574045', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.91217842788625439513224721260843', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.65093922967544299455930389543641', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.83090420500103, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 467856, 'conductor_radical': 114, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, 1, 0, 0, -6, 1, 0, 0, 0, 0, 0, -6, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -6, -4, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, -12, 0, 0, 0, 0, 0, 17, 2, 0, 0, 20, 0, 0, -6, 0, -4, -16, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -8, 0, 22, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17, 0, 2], 'euler11': [1, 0, -6, 0, 121], 'euler13': [1, 0, -3, 0, 169], 'euler17': [1, 0, -25, 0, 289], 'euler19': [1, 0, 19, 0, 0], 'euler2': [1, -1, 0, 0, 0], 'euler23': [1, 0, -1, 0, 529], 'euler29': [1, 4, 37, 116, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, 30, 0, 961], 'euler37': [1, 0, 54, 0, 1369], 'euler41': [1, -8, 82, -328, 1681], 'euler43': [1, 12, 122, 516, 1849], 'euler47': [1, 0, 2, 0, 2209], 'euler5': [1, 0, -2, 0, 25], 'euler53': [1, -20, 205, -1060, 2809], 'euler59': [1, 16, 173, 944, 3481], 'euler61': [1, 0, 122, 0, 3721], 'euler67': [1, 0, -75, 0, 4489], 'euler7': [1, 6, 19, 42, 49], 'euler71': [1, 8, 94, 568, 5041], 'euler73': [1, -22, 251, -1606, 5329], 'euler79': [1, 0, -126, 0, 6241], 'euler83': [1, 0, 90, 0, 6889], 'euler89': [1, 0, -18, 0, 7921], 'euler97': [1, 0, -130, 0, 9409], 'euler_factors': [[1, -1, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, -2, 0, 25], [1, 6, 19, 42, 49], [1, 0, -6, 0, 121], [1, 0, -3, 0, 169], [1, 0, -25, 0, 289], [1, 0, 19, 0, 0], [1, 0, -1, 0, 529], [1, 4, 37, 116, 841], [1, 0, 30, 0, 961], [1, 0, 54, 0, 1369], [1, -8, 82, -328, 1681], [1, 12, 122, 516, 1849], [1, 0, 2, 0, 2209], [1, -20, 205, -1060, 2809], [1, 16, 173, 944, 3481], [1, 0, 122, 0, 3721], [1, 0, -75, 0, 4489], [1, 8, 94, 568, 5041], [1, -22, 251, -1606, 5329], [1, 0, -126, 0, 6241], [1, 0, 90, 0, 6889], [1, 0, -18, 0, 7921], [1, 0, -130, 0, 9409]], 'index': 7, 'instance_types': ['ECNF', 'HMF', 'HMF', 'ECNF'], 'instance_urls': ['EllipticCurve/2.2.57.1/144.3/n', 'ModularForm/GL2/TotallyReal/2.2.57.1/holomorphic/2.2.57.1-144.3-n', 'ModularForm/GL2/TotallyReal/2.2.57.1/holomorphic/2.2.57.1-144.2-n', 'EllipticCurve/2.2.57.1/144.2/n'], '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': '4-684e2-1.1-c1e2-0-7', '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': '4-684e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.337042468218235, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2072573685637676086, 'z1': {'__RealLiteral__': 0, 'data': '0.61251502312875154700840843574045', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9487441
{'Lhash': '776455036717969712952551445392', 'Lhash_array': ['776455036717969712952551445392'], 'label': '4-684e2-1.1-c1e2-0-7', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.57.1/144.2/n'}
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id: 9487393
{'Lhash': '776455036717969712952551445392', 'Lhash_array': ['776455036717969712952551445392'], 'label': '4-684e2-1.1-c1e2-0-7', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.57.1/holomorphic/2.2.57.1-144.2-n'}
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id: 9486869
{'Lhash': '776455036717969712952551445392', 'Lhash_array': ['776455036717969712952551445392'], 'label': '4-684e2-1.1-c1e2-0-7', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.57.1/holomorphic/2.2.57.1-144.3-n'}
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id: 9486866
{'Lhash': '776455036717969712952551445392', 'Lhash_array': ['776455036717969712952551445392'], 'label': '4-684e2-1.1-c1e2-0-7', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.57.1/144.3/n'}