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lfunc_lfunctions • Show schema
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{'Lhash': '1493174771646930641425975530937,2533773013865001349768342026954', 'a10': -4, 'a2': -2, 'a3': 0, 'a4': 2, 'a5': 2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.065852091759074, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2, 2]], [3, [1]], [5, [1, -2, 5]]], 'bad_primes': [2, 3, 5], 'central_character': '180.1', 'coefficient_field': '1.1.1.1', 'conductor': 32400, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1, 2, 2], [1], [1, -2, 5], [1, 0, 0, 0, 49], [1, 0, -22, 0, 121], [1, -10, 50, -130, 169], [1, 6, 18, 102, 289], [1, 0, 38, 0, 361], [1, 0, 0, 0, 529], [1, 0, 42, 0, 841], [1, 0, -62, 0, 961], [1, -10, 50, -370, 1369], [1, -20, 182, -820, 1681], [1, 0, 0, 0, 1849], [1, 0, 0, 0, 2209], [1, 18, 162, 954, 2809], [1, 0, 118, 0, 3481], [1, 24, 266, 1464, 3721], [1, 0, 0, 0, 4489], [1, 0, -142, 0, 5041], [1, 10, 50, 730, 5329], [1, 0, 158, 0, 6241], [1, 0, 0, 0, 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-0.30957726242369027, 0.9776156479957457], 'positive_zeros': ['1.17790720201457529834445921806082', '1.99879447334211626090229653412308', '3.02669365898786424020353217411765', '4.16612828926509674736220026342974', '4.59652424833388629351632525704142', '6.03101414069381520735005196939062', '6.05281541199805411485597576183780', '6.50151887304805599112061858184941', '7.64530230168879810686107964961861', '7.74049675756344181815633037747825', '8.650779552603517603914584405882262', '8.897159471699952949424650508927952', '9.317463580516028159955219232479230', '9.733438715358766573245468454021013', '10.50438066563289087637408952686903', '10.87792335298834723839209377983571', '11.23982122252934138297467481386406', '11.41149446976614744378539998100015', '12.53586617313810056259335698501881', '13.28805447705671232113784380850955'], 'prelabel': '4-180e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.198877490147783, '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': 973726394020237485, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.17790720201457529834445921806', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.99879447334211626090229653412', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.02669365898786424020353217412', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.065852091759074, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 32400, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, -2, 0, 2, 2, 0, 0, 0, 0, -4, 0, 0, 10, 0, 0, -4, -6, 0, 0, 4, 0, 0, 0, 0, -1, -20, 0, 0, 0, 0, 0, 8, 0, 12, 0, 0, 10, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 20, -18, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, -8, 20, 0, 0, -12, 0, 0, 0, 0, -10, -20, 0, 0, 0, 0, 0, -8, 0, -40, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, -2], 'euler11': [1, 0, -22, 0, 121], 'euler13': [1, -10, 50, -130, 169], 'euler17': [1, 6, 18, 102, 289], 'euler19': [1, 0, 38, 0, 361], 'euler2': [1, 2, 2, 0, 0], 'euler23': [1, 0, 0, 0, 529], 'euler29': [1, 0, 42, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, -62, 0, 961], 'euler37': [1, -10, 50, -370, 1369], 'euler41': [1, -20, 182, -820, 1681], 'euler43': [1, 0, 0, 0, 1849], 'euler47': [1, 0, 0, 0, 2209], 'euler5': [1, -2, 5, 0, 0], 'euler53': [1, 18, 162, 954, 2809], 'euler59': [1, 0, 118, 0, 3481], 'euler61': [1, 24, 266, 1464, 3721], 'euler67': [1, 0, 0, 0, 4489], 'euler7': [1, 0, 0, 0, 49], 'euler71': [1, 0, -142, 0, 5041], 'euler73': [1, 10, 50, 730, 5329], 'euler79': [1, 0, 158, 0, 6241], 'euler83': [1, 0, 0, 0, 6889], 'euler89': [1, 0, -78, 0, 7921], 'euler97': [1, 10, 50, 970, 9409], 'euler_factors': [[1, 2, 2, 0, 0], [1, 0, 0, 0, 0], [1, -2, 5, 0, 0], [1, 0, 0, 0, 49], [1, 0, -22, 0, 121], [1, -10, 50, -130, 169], [1, 6, 18, 102, 289], [1, 0, 38, 0, 361], [1, 0, 0, 0, 529], [1, 0, 42, 0, 841], [1, 0, -62, 0, 961], [1, -10, 50, -370, 1369], [1, -20, 182, -820, 1681], [1, 0, 0, 0, 1849], [1, 0, 0, 0, 2209], [1, 18, 162, 954, 2809], [1, 0, 118, 0, 3481], [1, 24, 266, 1464, 3721], [1, 0, 0, 0, 4489], [1, 0, -142, 0, 5041], [1, 10, 50, 730, 5329], [1, 0, 158, 0, 6241], [1, 0, 0, 0, 6889], [1, 0, -78, 0, 7921], [1, 10, 50, 970, 9409]], 'index': 2, 'instance_types': ['ECNF', 'ECNF', 'CMF'], 'instance_urls': ['EllipticCurve/2.0.4.1/2025.1/CMc', 'EllipticCurve/2.0.4.1/2025.3/CMc', 'ModularForm/GL2/Q/holomorphic/180/2/k/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': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-180e2-1.1-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': '4-180e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.198877490147783, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 973726394020237485, 'z1': {'__RealLiteral__': 0, 'data': '1.17790720201457529834445921806', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10010624
{'Lhash': '1493174771646930641425975530937,2533773013865001349768342026954', 'Lhash_array': ['1493174771646930641425975530937', '2533773013865001349768342026954'], 'label': '4-180e2-1.1-c1e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/180/2/k/a'}
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id: 9656965
{'Lhash': '_1493174771646930641425975530937', 'Lhash_array': ['_1493174771646930641425975530937'], 'label': '4-180e2-1.1-c1e2-0-2', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/2025.3/CMc'}
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id: 9656414
{'Lhash': '_1493174771646930641425975530937', 'Lhash_array': ['_1493174771646930641425975530937'], 'label': '4-180e2-1.1-c1e2-0-2', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/2025.1/CMc'}