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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': -4, 'A5': 0, 'A6': 0, 'A7': -2, 'A8': 0, 'A9': -5, 'Lhash': '676255727350632485,1904127031442102192', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [-2.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [-1.6666666666666667, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 63.88845252452729, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [1, 2, 7]], [11, [1, 2, 1]], [13, [1, 0, -1]]], 'bad_primes': [7, 11, 13], 'central_character': '1002001.1', 'coefficient_field': '1.1.1.1', 'conductor': 1002001, 'conductor_radical': 1001, 'degree': 4, 'euler_factors': [[1, 0, 4, 0, 4], [1, 0, 5, 0, 9], [1, 0, 9, 0, 25], [1, 2, 7], [1, 2, 1], [1, 0, -1], [1, 0, 18, 0, 289], [1, 0, 34, 0, 361], [1, -14, 95, -322, 529], [1, 4, 62, 116, 841], [1, 0, 53, 0, 961], [1, 22, 195, 814, 1369], [1, 0, -18, 0, 1681], [1, 8, 102, 344, 1849], [1, 0, 78, 0, 2209], [1, 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-4.041777651383444, -4.224614148674895, -3.9935876151342815], 'positive_zeros': ['1.28655472231449922500586089552966', '2.34448923217473262650057367431523', '3.29304594675951575785139026233224', '3.35775542055244311804083250513582', '3.70099161938712630953878841303852', '4.75768041533452306802121891709637', '4.95237769114385482752321677071558', '5.31104352782074944000454805478391', '5.82135849339387357739621546932222', '6.05777360202583450452013331209238', '6.96627157214221326686940120924599', '7.21661224338768342466420756205922', '7.85612481771897939782236601586171'], 'prelabel': '4-1001e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.827193881277011, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 274539749579040726, 'z1': {'__RealLiteral__': 0, 'data': '1.28655472231449922500586089552966', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.34448923217473262650057367431523', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.29304594675951575785139026233224', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 63.88845252452729, 'bad_primes': [7, 11, 13], 'central_character': '1.1', 'conductor': 1002001, 'conductor_radical': 1001, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -4, 0, 0, -2, 0, -5, 0, -2, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 14, 0, -9, 0, 0, 8, -4, 0, 0, 0, 0, 0, 0, 20, -22, 0, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, -3, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, -32, 0, 0, -2, 0, 0, 0, -18, 0, 0, 0, 0, 0, 4, 0, 16, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 10, 36], 'euler11': [1, 2, 1, 0, 0], 'euler13': [1, 0, -1, 0, 0], 'euler17': [1, 0, 18, 0, 289], 'euler19': [1, 0, 34, 0, 361], 'euler2': [1, 0, 4, 0, 4], 'euler23': [1, -14, 95, -322, 529], 'euler29': [1, 4, 62, 116, 841], 'euler3': [1, 0, 5, 0, 9], 'euler31': [1, 0, 53, 0, 961], 'euler37': [1, 22, 195, 814, 1369], 'euler41': [1, 0, -18, 0, 1681], 'euler43': [1, 8, 102, 344, 1849], 'euler47': [1, 0, 78, 0, 2209], 'euler5': [1, 0, 9, 0, 25], 'euler53': [1, -4, 110, -212, 2809], 'euler59': [1, 0, 117, 0, 3481], 'euler61': [1, 0, 118, 0, 3721], 'euler67': [1, 2, 135, 134, 4489], 'euler7': [1, 2, 7, 0, 0], 'euler71': [1, 18, 223, 1278, 5041], 'euler73': [1, 0, -110, 0, 5329], 'euler79': [1, -16, 222, -1264, 6241], 'euler83': [1, 0, 166, 0, 6889], 'euler89': [1, 0, 129, 0, 7921], 'euler97': [1, 0, 25, 0, 9409], 'euler_factors': [[1, 0, 4, 0, 4], [1, 0, 5, 0, 9], [1, 0, 9, 0, 25], [1, 2, 7, 0, 0], [1, 2, 1, 0, 0], [1, 0, -1, 0, 0], [1, 0, 18, 0, 289], [1, 0, 34, 0, 361], [1, -14, 95, -322, 529], [1, 4, 62, 116, 841], [1, 0, 53, 0, 961], [1, 22, 195, 814, 1369], [1, 0, -18, 0, 1681], [1, 8, 102, 344, 1849], [1, 0, 78, 0, 2209], [1, -4, 110, -212, 2809], [1, 0, 117, 0, 3481], [1, 0, 118, 0, 3721], [1, 2, 135, 134, 4489], [1, 18, 223, 1278, 5041], [1, 0, -110, 0, 5329], [1, -16, 222, -1264, 6241], [1, 0, 166, 0, 6889], [1, 0, 129, 0, 7921], [1, 0, 25, 0, 9409]], 'index': 6, 'instance_types': ['BMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/20449.2/a', 'EllipticCurve/2.0.7.1/20449.2/a'], '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': '4-1001e2-1.1-c1e2-0-6', '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': 2, 'prelabel': '4-1001e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.827193881277011, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 274539749579040726, 'z1': {'__RealLiteral__': 0, 'data': '1.28655472231449922500586089552966', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9608127
{'Lhash': '676255727350632485,1904127031442102192', 'Lhash_array': ['676255727350632485', '1904127031442102192'], 'label': '4-1001e2-1.1-c1e2-0-6', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/20449.2/a'}
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id: 9607556
{'Lhash': '676255727350632485,1904127031442102192', 'Lhash_array': ['676255727350632485', '1904127031442102192'], 'label': '4-1001e2-1.1-c1e2-0-6', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/20449.2/a'}