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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': '419730519136265012,1404448508184033733', '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': 21.22777793843102, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -2, 3]], [17, [1, 0, -1]]], 'bad_primes': [2, 3, 17], 'central_character': '332928.1', 'coefficient_field': '1.1.1.1', 'conductor': 332928, 'conductor_radical': 102, 'degree': 4, 'euler_factors': [[1], [1, -2, 3], [1, 0, 10, 0, 25], [1, 0, 14, 0, 49], [1, -4, 26, -44, 121], [1, 12, 62, 156, 169], [1, 0, -1], [1, 0, 22, 0, 361], [1, -8, 62, -184, 529], [1, 0, 58, 0, 841], [1, 0, -2, 0, 961], [1, 8, 90, 296, 1369], [1, 0, 46, 0, 1681], [1, 0, 22, 0, 1849], [1, 16, 158, 752, 2209], [1, 0, 6, 0, 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0.13457405718356552, -0.4301101145912609, -1.0603614106502872, -1.6461655496643055, -2.079557612441981], 'positive_zeros': ['1.62565942265304447284805954300898', '2.33145296998291404024563148828655', '2.65731672220088998433790242397648', '3.65040990576825303475268770323902', '3.69893087635466446387661413771574', '4.70132376102771618663878285353441', '5.22026991260055872535309051671159', '5.27740412064621881845926355385516', '6.48858014013781204324172880722247', '6.84063454436614469172097574332528', '7.04028809245781208083955490002383', '7.915799644978553160956414624198664', '7.918822763878182275157603554743897', '8.422820303858929928484512856269087'], 'prelabel': '4-332928-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.1464764795303726, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1824179027320298745, 'z1': {'__RealLiteral__': 0, 'data': '1.62565942265304447284805954300898', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.33145296998291404024563148828655', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.65731672220088998433790242397648', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.22777793843102, 'bad_primes': [2, 3, 17], 'central_character': '1.1', 'conductor': 332928, 'conductor_radical': 102, 'degree': 4, 'dirichlet_coefficients': [1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 4, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, -10, 0, -4, 0, 0, 0, 0, 0, 8, 0, 0, 0, -8, 0, -24, 0, 0, 0, 0, 0, 0, 0, -16, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 16, 0, 24, 0, 4, 0, -20, 0, 0, 0, 0, 0, -11, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -36, 0, 4, 0], 'euler11': [1, -4, 26, -44, 121], 'euler13': [1, 12, 62, 156, 169], 'euler17': [1, 0, -1, 0, 0], 'euler19': [1, 0, 22, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -8, 62, -184, 529], 'euler29': [1, 0, 58, 0, 841], 'euler3': [1, -2, 3, 0, 0], 'euler31': [1, 0, -2, 0, 961], 'euler37': [1, 8, 90, 296, 1369], 'euler41': [1, 0, 46, 0, 1681], 'euler43': [1, 0, 22, 0, 1849], 'euler47': [1, 16, 158, 752, 2209], 'euler5': [1, 0, 10, 0, 25], 'euler53': [1, 0, 6, 0, 2809], 'euler59': [1, 0, 118, 0, 3481], 'euler61': [1, -24, 266, -1464, 3721], 'euler67': [1, 0, 70, 0, 4489], 'euler7': [1, 0, 14, 0, 49], 'euler71': [1, -24, 286, -1704, 5041], 'euler73': [1, -4, 150, -292, 5329], 'euler79': [1, 0, 142, 0, 6241], 'euler83': [1, -32, 422, -2656, 6889], 'euler89': [1, 0, 78, 0, 7921], 'euler97': [1, 36, 518, 3492, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -2, 3, 0, 0], [1, 0, 10, 0, 25], [1, 0, 14, 0, 49], [1, -4, 26, -44, 121], [1, 12, 62, 156, 169], [1, 0, -1, 0, 0], [1, 0, 22, 0, 361], [1, -8, 62, -184, 529], [1, 0, 58, 0, 841], [1, 0, -2, 0, 961], [1, 8, 90, 296, 1369], [1, 0, 46, 0, 1681], [1, 0, 22, 0, 1849], [1, 16, 158, 752, 2209], [1, 0, 6, 0, 2809], [1, 0, 118, 0, 3481], [1, -24, 266, -1464, 3721], [1, 0, 70, 0, 4489], [1, -24, 286, -1704, 5041], [1, -4, 150, -292, 5329], [1, 0, 142, 0, 6241], [1, -32, 422, -2656, 6889], [1, 0, 78, 0, 7921], [1, 36, 518, 3492, 9409]], 'index': 30, 'instance_types': ['ECNF', 'HMF'], 'instance_urls': ['EllipticCurve/2.2.12.1/2312.1/b', 'ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-2312.1-b'], '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': '4-332928-1.1-c1e2-0-30', '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': '4-332928-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.1464764795303726, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1824179027320298745, 'z1': {'__RealLiteral__': 0, 'data': '1.62565942265304447284805954300898', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9573282
{'Lhash': '419730519136265012,1404448508184033733', 'Lhash_array': ['419730519136265012', '1404448508184033733'], 'label': '4-332928-1.1-c1e2-0-30', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-2312.1-b'}
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id: 9573653
{'Lhash': '419730519136265012,1404448508184033733', 'Lhash_array': ['419730519136265012', '1404448508184033733'], 'label': '4-332928-1.1-c1e2-0-30', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.12.1/2312.1/b'}