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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1495026692938847180191107494051', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 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': 84.91111175372409, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, -1]], [17, [1, 0, -1]]], 'bad_primes': [2, 3, 17], 'central_character': '1331712.1', 'coefficient_field': '1.1.1.1', 'conductor': 1331712, 'conductor_radical': 102, 'degree': 4, 'euler_factors': [[1], [1, 0, -1], [1, 0, 7, 0, 25], [1, 0, 6, 0, 49], [1, -4, 17, -44, 121], [1, 0, -7, 0, 169], [1, 0, -1], [1, 6, 43, 114, 361], [1, 0, 7, 0, 529], [1, 0, -6, 0, 841], [1, 0, -10, 0, 961], [1, 0, -10, 0, 1369], [1, 8, 73, 328, 1681], [1, -10, 75, -430, 1849], [1, 0, -50, 0, 2209], [1, 0, 74, 0, 2809], [1, 8, 98, 472, 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1.953723257764764, 1.3450420023154088], 'positive_zeros': ['1.17936811032131464476739569596573', '1.86384252111108591100447362051889', '2.29797876162604127452448796692509', '3.18814896405265808525428870028419', '3.64511211944713533425618859934629', '4.16325627767695906900503147781854', '4.50039821916535027419511669789403', '4.96881480855263395402488533363121', '5.76409840260950063862800786131288', '6.01964370481355274429680532044152', '6.44035802983983911246380784719031', '6.83674245963916537171790690283577', '7.34778867136867385082748203484383', '7.70983329729751689519406930260609'], 'prelabel': '4-1331712-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.035576148666708, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 815898815365255495, 'z1': {'__RealLiteral__': 0, 'data': '1.17936811032131464476739569596573', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.86384252111108591100447362051889', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.29797876162604127452448796692509', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 84.91111175372409, 'bad_primes': [2, 3, 17], 'central_character': '1.1', 'conductor': 1331712, 'conductor_radical': 102, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 10, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 1, 0, -12, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0], 'euler11': [1, -4, 17, -44, 121], 'euler13': [1, 0, -7, 0, 169], 'euler17': [1, 0, -1, 0, 0], 'euler19': [1, 6, 43, 114, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 7, 0, 529], 'euler29': [1, 0, -6, 0, 841], 'euler3': [1, 0, -1, 0, 0], 'euler31': [1, 0, -10, 0, 961], 'euler37': [1, 0, -10, 0, 1369], 'euler41': [1, 8, 73, 328, 1681], 'euler43': [1, -10, 75, -430, 1849], 'euler47': [1, 0, -50, 0, 2209], 'euler5': [1, 0, 7, 0, 25], 'euler53': [1, 0, 74, 0, 2809], 'euler59': [1, 8, 98, 472, 3481], 'euler61': [1, 0, -22, 0, 3721], 'euler67': [1, 0, 118, 0, 4489], 'euler7': [1, 0, 6, 0, 49], 'euler71': [1, 0, -46, 0, 5041], 'euler73': [1, 4, 114, 292, 5329], 'euler79': [1, 0, 14, 0, 6241], 'euler83': [1, 12, 166, 996, 6889], 'euler89': [1, -4, 118, -356, 7921], 'euler97': [1, -4, 198, -388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -1, 0, 0], [1, 0, 7, 0, 25], [1, 0, 6, 0, 49], [1, -4, 17, -44, 121], [1, 0, -7, 0, 169], [1, 0, -1, 0, 0], [1, 6, 43, 114, 361], [1, 0, 7, 0, 529], [1, 0, -6, 0, 841], [1, 0, -10, 0, 961], [1, 0, -10, 0, 1369], [1, 8, 73, 328, 1681], [1, -10, 75, -430, 1849], [1, 0, -50, 0, 2209], [1, 0, 74, 0, 2809], [1, 8, 98, 472, 3481], [1, 0, -22, 0, 3721], [1, 0, 118, 0, 4489], [1, 0, -46, 0, 5041], [1, 4, 114, 292, 5329], [1, 0, 14, 0, 6241], [1, 12, 166, 996, 6889], [1, -4, 118, -356, 7921], [1, -4, 198, -388, 9409]], 'index': 19, 'instance_types': ['ECNF', 'BMF', 'ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.8.1/20808.5/d', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/20808.5/e', 'EllipticCurve/2.0.8.1/20808.5/e', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/20808.5/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': '4-1331712-1.1-c1e2-0-19', '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': '4-1331712-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.035576148666708, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 815898815365255495, 'z1': {'__RealLiteral__': 0, 'data': '1.17936811032131464476739569596573', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9831270
{'Lhash': '1495026692938847180191107494051', 'Lhash_array': ['1495026692938847180191107494051'], 'label': '4-1331712-1.1-c1e2-0-19', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/20808.5/d'}
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id: 9831015
{'Lhash': '1495026692938847180191107494051', 'Lhash_array': ['1495026692938847180191107494051'], 'label': '4-1331712-1.1-c1e2-0-19', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/20808.5/e'}
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id: 9830931
{'Lhash': '1495026692938847180191107494051', 'Lhash_array': ['1495026692938847180191107494051'], 'label': '4-1331712-1.1-c1e2-0-19', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/20808.5/e'}
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id: 9830454
{'Lhash': '1495026692938847180191107494051', 'Lhash_array': ['1495026692938847180191107494051'], 'label': '4-1331712-1.1-c1e2-0-19', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/20808.5/d'}