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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': '1311032360338836725888751994302', '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': 57.58677475339073, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 2, 3]], [7, [1, 0, 1]]], 'bad_primes': [2, 3, 7], 'central_character': '903168.1', 'coefficient_field': '1.1.1.1', 'conductor': 903168, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1], [1, 2, 3], [1, 0, 2, 0, 25], [1, 0, 1], [1, -8, 38, -88, 121], [1, 0, -6, 0, 169], [1, 4, 34, 68, 289], [1, 10, 54, 190, 361], [1, 0, -22, 0, 529], [1, 0, -26, 0, 841], [1, 0, 14, 0, 961], [1, 0, -10, 0, 1369], [1, -12, 82, -492, 1681], [1, 12, 86, 516, 1849], [1, 0, 10, 0, 2209], [1, 0, 38, 0, 2809], [1, 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-2.651889123149008, -3.365992680664727, -3.8797703637959633, -4.113982687478438], 'positive_zeros': ['1.03422217455093447514352401669621', '1.82490893418859332873477226891424', '2.37074517208793522328749795218772', '3.31521081303494035975598512057229', '3.97866110572214522332153756235536', '4.31934901513247275960207087579987', '4.58077044621379342973063667196292', '5.30294344081322495998967730744556', '5.93748531640264652548242255626297', '6.26685641768808272430261263019411', '6.45660456938174818200867480597657', '6.92350012506979572055111258126723', '7.23825847434985008786092467133462', '8.056046829545666874703724421529349'], 'prelabel': '4-903168-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.7547404677686584, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 2259606209801649167, 'z1': {'__RealLiteral__': 0, 'data': '1.03422217455093447514352401669621', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.82490893418859332873477226891424', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.37074517208793522328749795218772', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 57.58677475339073, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 903168, 'conductor_radical': 42, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 0, 0, 0, 0, 0, 1, 0, 8, 0, 0, 0, 0, 0, -4, 0, -10, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 12, 0, -12, 0, 0, 0, 0, 0, -1, 0, 8, 0, 0, 0, 0, 0, 20, 0, 14, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -12, 0, 4, 0, 0, 0, 0, 0, -11, 0, -10, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 16, 0, 8, 0], 'euler11': [1, -8, 38, -88, 121], 'euler13': [1, 0, -6, 0, 169], 'euler17': [1, 4, 34, 68, 289], 'euler19': [1, 10, 54, 190, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -22, 0, 529], 'euler29': [1, 0, -26, 0, 841], 'euler3': [1, 2, 3, 0, 0], 'euler31': [1, 0, 14, 0, 961], 'euler37': [1, 0, -10, 0, 1369], 'euler41': [1, -12, 82, -492, 1681], 'euler43': [1, 12, 86, 516, 1849], 'euler47': [1, 0, 10, 0, 2209], 'euler5': [1, 0, 2, 0, 25], 'euler53': [1, 0, 38, 0, 2809], 'euler59': [1, -14, 158, -826, 3481], 'euler61': [1, 0, -70, 0, 3721], 'euler67': [1, 4, 38, 268, 4489], 'euler7': [1, 0, 1, 0, 0], 'euler71': [1, 0, 110, 0, 5041], 'euler73': [1, 12, 118, 876, 5329], 'euler79': [1, 0, -30, 0, 6241], 'euler83': [1, 10, 182, 830, 6889], 'euler89': [1, -8, 190, -712, 7921], 'euler97': [1, -16, 242, -1552, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 2, 3, 0, 0], [1, 0, 2, 0, 25], [1, 0, 1, 0, 0], [1, -8, 38, -88, 121], [1, 0, -6, 0, 169], [1, 4, 34, 68, 289], [1, 10, 54, 190, 361], [1, 0, -22, 0, 529], [1, 0, -26, 0, 841], [1, 0, 14, 0, 961], [1, 0, -10, 0, 1369], [1, -12, 82, -492, 1681], [1, 12, 86, 516, 1849], [1, 0, 10, 0, 2209], [1, 0, 38, 0, 2809], [1, -14, 158, -826, 3481], [1, 0, -70, 0, 3721], [1, 4, 38, 268, 4489], [1, 0, 110, 0, 5041], [1, 12, 118, 876, 5329], [1, 0, -30, 0, 6241], [1, 10, 182, 830, 6889], [1, -8, 190, -712, 7921], [1, -16, 242, -1552, 9409]], 'index': 22, 'instance_types': ['ECNF', 'BMF', 'ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.8.1/14112.1/b', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/14112.3/b', 'EllipticCurve/2.0.8.1/14112.3/b', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/14112.1/b'], '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': '4-903168-1.1-c1e2-0-22', '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': '4-903168-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.7547404677686584, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2259606209801649167, 'z1': {'__RealLiteral__': 0, 'data': '1.03422217455093447514352401669621', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9820965
{'Lhash': '1311032360338836725888751994302', 'Lhash_array': ['1311032360338836725888751994302'], 'label': '4-903168-1.1-c1e2-0-22', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/14112.1/b'}
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id: 9820540
{'Lhash': '1311032360338836725888751994302', 'Lhash_array': ['1311032360338836725888751994302'], 'label': '4-903168-1.1-c1e2-0-22', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/14112.3/b'}
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id: 9820383
{'Lhash': '1311032360338836725888751994302', 'Lhash_array': ['1311032360338836725888751994302'], 'label': '4-903168-1.1-c1e2-0-22', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/14112.3/b'}
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id: 9820360
{'Lhash': '1311032360338836725888751994302', 'Lhash_array': ['1311032360338836725888751994302'], 'label': '4-903168-1.1-c1e2-0-22', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/14112.1/b'}