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lfunc_lfunctions • Show schema
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{'Lhash': '1385032777139622784394994339371,3892506953457842976670865849010', 'a10': 0, 'a2': 2, 'a3': 0, 'a4': -1, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': -8, 'a9': 2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.114144506592745, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[13, [1, 2, 1]], [17, [1, -2, 17]]], 'bad_primes': [13, 17], 'central_character': '221.1', 'coefficient_field': '1.1.1.1', 'conductor': 48841, 'conductor_radical': 221, 'degree': 4, 'euler_factors': [[1, -2, 5, -4, 4], [1, 0, -2, 0, 9], [1, 0, -6, 0, 25], [1, 0, -14, 0, 49], [1, 0, -22, 0, 121], [1, 2, 1], [1, -2, 17], [1, -16, 102, -304, 361], [1, 0, -42, 0, 529], [1, 0, 6, 0, 841], [1, 0, -46, 0, 961], [1, 0, 26, 0, 1369], [1, 0, -78, 0, 1681], [1, 8, 102, 344, 1849], [1, 8, 110, 376, 2209], [1, -4, 110, -212, 2809], [1, 16, 182, 944, 3481], [1, 0, -106, 0, 3721], [1, 8, 150, 536, 4489], [1, 0, -142, 0, 5041], [1, 0, -46, 0, 5329], [1, 0, -154, 0, 6241], [1, 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'positive_zeros': ['1.09259821033513473568650343882568', '3.07064655888383687928589829176469', '3.13422340304376000753554160721030', '3.96147137343355908357418248453718', '4.76761372781537448004791781835820', '5.02601559772614000376654132131273', '5.51571643314335833471285867487362', '6.05153822256967727854534173394747', '6.90444905786425497934493499627055', '7.47911440404715108785774339056338', '7.88375998289842250682232661969579', '8.900403962196435046218316034674670', '8.991221120621212505531843607925410', '9.818846342213870054422795426746302', '9.828747935372716029753200366877086', '10.48620505760998326838569995995459', '11.59058139052802506104336248400892', '11.72120186931329960919213248392693', '12.17515416663513620558996049734143', '12.59566083378210742826865264821638'], 'prelabel': '4-221e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.3284178125387724, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 992793196002328157, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.09259821033513473568650343883', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.07064655888383687928589829176', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.13422340304376000753554160721', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.114144506592745, 'bad_primes': [13, 17], 'central_character': '1.1', 'conductor': 48841, 'conductor_radical': 221, 'degree': 4, 'dirichlet_coefficients': [1, 2, 0, -1, 0, 0, 0, -8, 2, 0, 0, 0, -2, 0, 0, -7, 2, 4, 16, 0, 0, 0, 0, 0, 6, -4, 0, 0, 0, 0, 0, 14, 0, 4, 0, -2, 0, 32, 0, 0, 0, 0, -8, 0, 0, 0, -8, 0, 14, 12, 0, 2, 4, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 35, 0, 0, -8, -2, 0, 0, 0, -16, 0, 0, 0, -16, 0, 0, 0, 0, -5, 0, -24, 0, 0, -16, 0, 0, 28, 0, 0, 0, 0, -16, 0, 0, 0, 28, 0, -6], 'euler11': [1, 0, -22, 0, 121], 'euler13': [1, 2, 1, 0, 0], 'euler17': [1, -2, 17, 0, 0], 'euler19': [1, -16, 102, -304, 361], 'euler2': [1, -2, 5, -4, 4], 'euler23': [1, 0, -42, 0, 529], 'euler29': [1, 0, 6, 0, 841], 'euler3': [1, 0, -2, 0, 9], 'euler31': [1, 0, -46, 0, 961], 'euler37': [1, 0, 26, 0, 1369], 'euler41': [1, 0, -78, 0, 1681], 'euler43': [1, 8, 102, 344, 1849], 'euler47': [1, 8, 110, 376, 2209], 'euler5': [1, 0, -6, 0, 25], 'euler53': [1, -4, 110, -212, 2809], 'euler59': [1, 16, 182, 944, 3481], 'euler61': [1, 0, -106, 0, 3721], 'euler67': [1, 8, 150, 536, 4489], 'euler7': [1, 0, -14, 0, 49], 'euler71': [1, 0, -142, 0, 5041], 'euler73': [1, 0, -46, 0, 5329], 'euler79': [1, 0, -154, 0, 6241], 'euler83': [1, 24, 310, 1992, 6889], 'euler89': [1, -28, 374, -2492, 7921], 'euler97': [1, 0, 2, 0, 9409], 'euler_factors': [[1, -2, 5, -4, 4], [1, 0, -2, 0, 9], [1, 0, -6, 0, 25], [1, 0, -14, 0, 49], [1, 0, -22, 0, 121], [1, 2, 1, 0, 0], [1, -2, 17, 0, 0], [1, -16, 102, -304, 361], [1, 0, -42, 0, 529], [1, 0, 6, 0, 841], [1, 0, -46, 0, 961], [1, 0, 26, 0, 1369], [1, 0, -78, 0, 1681], [1, 8, 102, 344, 1849], [1, 8, 110, 376, 2209], [1, -4, 110, -212, 2809], [1, 16, 182, 944, 3481], [1, 0, -106, 0, 3721], [1, 8, 150, 536, 4489], [1, 0, -142, 0, 5041], [1, 0, -46, 0, 5329], [1, 0, -154, 0, 6241], [1, 24, 310, 1992, 6889], [1, -28, 374, -2492, 7921], [1, 0, 2, 0, 9409]], 'index': 2, 'instance_types': ['ECNF', 'HMF', 'CMF'], 'instance_urls': ['EllipticCurve/2.2.17.1/169.1/a', 'ModularForm/GL2/TotallyReal/2.2.17.1/holomorphic/2.2.17.1-169.1-a', 'ModularForm/GL2/Q/holomorphic/221/2/d/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, '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': '4-221e2-1.1-c1e2-0-2', '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': '4-221e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.3284178125387724, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 992793196002328157, 'z1': {'__RealLiteral__': 0, 'data': '1.09259821033513473568650343883', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10057463
{'Lhash': '1385032777139622784394994339371,3892506953457842976670865849010', 'Lhash_array': ['1385032777139622784394994339371', '3892506953457842976670865849010'], 'label': '4-221e2-1.1-c1e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/221/2/d/a'}
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id: 9490103
{'Lhash': '_1385032777139622784394994339371', 'Lhash_array': ['_1385032777139622784394994339371'], 'label': '4-221e2-1.1-c1e2-0-2', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.17.1/holomorphic/2.2.17.1-169.1-a'}
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id: 9489814
{'Lhash': '_1385032777139622784394994339371', 'Lhash_array': ['_1385032777139622784394994339371'], 'label': '4-221e2-1.1-c1e2-0-2', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.17.1/169.1/a'}