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lfunc_lfunctions • Show schema
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{'Lhash': '3873642543082248284211853638817,5931621833330563178449509137765', 'a10': 0, 'a2': -1, 'a3': 0, 'a4': -1, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 3, 'a9': -6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.04998851975120723, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1, 2]], [7, [1, 0, 7]]], 'bad_primes': [2, 7], 'central_character': '28.1', 'coefficient_field': '1.1.1.1', 'conductor': 784, 'conductor_radical': 14, 'degree': 4, 'euler_factors': [[1, 1, 2], [1, 0, 6, 0, 9], [1, 0, -10, 0, 25], [1, 0, 7], [1, 0, 6, 0, 121], [1, 0, -26, 0, 169], [1, 0, -34, 0, 289], [1, 0, 38, 0, 361], [1, 0, -18, 0, 529], [1, 4, 62, 116, 841], [1, 0, 62, 0, 961], [1, -12, 110, -444, 1369], [1, 0, -82, 0, 1681], [1, 0, -58, 0, 1849], [1, 0, 94, 0, 2209], [1, 20, 206, 1060, 2809], [1, 0, 118, 0, 3481], [1, 0, -122, 0, 3721], [1, 0, 118, 0, 4489], [1, 0, -114, 0, 5041], [1, 0, -146, 0, 5329], [1, 0, 94, 0, 6241], [1, 0, 166, 0, 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'5.61837662151843458306893694869288', '6.62673790339788372172641120178176', '7.916820437477627041447330894699777', '8.288881670273938005137198112079121', '9.195135941073282046423675747515529', '9.487120310487436012715062545611031', '10.77438049141535870105484223016142', '11.00726626863206248848760142427435', '11.80582065632319781891202715000038', '12.76869743899601511049677332802093', '13.24557983896369712639090803792653', '14.18991637382708731070571093951491', '14.46184169942106912708858944273228', '14.98415704814163214532725277146580', '16.20713218939645642377157653892898', '16.51354540129250993514876248336518', '17.28002321670383671839280006781909', '17.36103568531052980967719794656972'], 'prelabel': '4-28e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.47284365879176726, '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': 1261740712572831350, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.05576516303848460288434731668', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.67922456886986568351537135220', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.61837662151843458306893694869', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.04998851975120723, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 784, 'conductor_radical': 14, 'degree': 4, 'dirichlet_coefficients': [1, -1, 0, -1, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0, -1, 0, 6, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, -4, 0, 0, -5, 0, 0, 0, 6, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7, -10, 0, 0, -20, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, -18, 0, -12, 0, 0, 0, 0, 0, 0, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, -10], 'euler11': [1, 0, 6, 0, 121], 'euler13': [1, 0, -26, 0, 169], 'euler17': [1, 0, -34, 0, 289], 'euler19': [1, 0, 38, 0, 361], 'euler2': [1, 1, 2, 0, 0], 'euler23': [1, 0, -18, 0, 529], 'euler29': [1, 4, 62, 116, 841], 'euler3': [1, 0, 6, 0, 9], 'euler31': [1, 0, 62, 0, 961], 'euler37': [1, -12, 110, -444, 1369], 'euler41': [1, 0, -82, 0, 1681], 'euler43': [1, 0, -58, 0, 1849], 'euler47': [1, 0, 94, 0, 2209], 'euler5': [1, 0, -10, 0, 25], 'euler53': [1, 20, 206, 1060, 2809], 'euler59': [1, 0, 118, 0, 3481], 'euler61': [1, 0, -122, 0, 3721], 'euler67': [1, 0, 118, 0, 4489], 'euler7': [1, 0, 7, 0, 0], 'euler71': [1, 0, -114, 0, 5041], 'euler73': [1, 0, -146, 0, 5329], 'euler79': [1, 0, 94, 0, 6241], 'euler83': [1, 0, 166, 0, 6889], 'euler89': [1, 0, -178, 0, 7921], 'euler97': [1, 0, -194, 0, 9409], 'euler_factors': [[1, 1, 2, 0, 0], [1, 0, 6, 0, 9], [1, 0, -10, 0, 25], [1, 0, 7, 0, 0], [1, 0, 6, 0, 121], [1, 0, -26, 0, 169], [1, 0, -34, 0, 289], [1, 0, 38, 0, 361], [1, 0, -18, 0, 529], [1, 4, 62, 116, 841], [1, 0, 62, 0, 961], [1, -12, 110, -444, 1369], [1, 0, -82, 0, 1681], [1, 0, -58, 0, 1849], [1, 0, 94, 0, 2209], [1, 20, 206, 1060, 2809], [1, 0, 118, 0, 3481], [1, 0, -122, 0, 3721], [1, 0, 118, 0, 4489], [1, 0, -114, 0, 5041], [1, 0, -146, 0, 5329], [1, 0, 94, 0, 6241], [1, 0, 166, 0, 6889], [1, 0, -178, 0, 7921], [1, 0, -194, 0, 9409]], 'index': 1, 'instance_types': ['HMF', 'ECNF', 'ECNF', 'ECNF', 'CMF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.28.1/holomorphic/2.2.28.1-1.1-a', 'EllipticCurve/2.2.28.1/1.1/a', 'EllipticCurve/2.0.7.1/16.1/CMa', 'EllipticCurve/2.0.7.1/16.5/CMa', 'ModularForm/GL2/Q/holomorphic/28/2/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': '4-28e2-1.1-c1e2-0-1', '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': '4-28e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.47284365879176726, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1261740712572831350, 'z1': {'__RealLiteral__': 0, 'data': '3.05576516303848460288434731668', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9955609
{'Lhash': '3873642543082248284211853638817,5931621833330563178449509137765', 'Lhash_array': ['3873642543082248284211853638817', '5931621833330563178449509137765'], 'label': '4-28e2-1.1-c1e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/28/2/d/a'}
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id: 9601417
{'Lhash': '_3873642543082248284211853638817', 'Lhash_array': ['_3873642543082248284211853638817'], 'label': '4-28e2-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/16.5/CMa'}
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id: 9600680
{'Lhash': '_3873642543082248284211853638817', 'Lhash_array': ['_3873642543082248284211853638817'], 'label': '4-28e2-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/16.1/CMa'}
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id: 9499864
{'Lhash': '_3873642543082248284211853638817', 'Lhash_array': ['_3873642543082248284211853638817'], 'label': '4-28e2-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.28.1/1.1/a'}
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id: 9499800
{'Lhash': '_3873642543082248284211853638817', 'Lhash_array': ['_3873642543082248284211853638817'], 'label': '4-28e2-1.1-c1e2-0-1', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.28.1/holomorphic/2.2.28.1-1.1-a'}