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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -2, 'A3': 0, 'A4': 2, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '677974156003934062', 'a10': [0.0, 0], 'a2': [-1.414213562373095, 0], 'a3': [0.0, 0], 'a4': [1.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 968.3857505130783, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]], [7, [1]], [11, [1, -1]]], 'bad_primes': [3, 5, 7, 11], 'central_character': '121275.1', 'coefficient_field': '1.1.1.1', 'conductor': 121275, 'conductor_radical': 1155, 'degree': 2, 'euler_factors': [[1, 2, 2], [1], [1], [1], [1, -1], [1, 3, 13], [1, 0, 17], [1, -1, 19], [1, -2, 23], [1, -8, 29], [1, 5, 31], [1, -3, 37], [1, 8, 41], [1, -11, 43], [1, 4, 47], [1, -6, 53], [1, -6, 59], [1, 6, 61], [1, 13, 67], [1, 12, 71], [1, 15, 73], [1, -1, 79], [1, 0, 83], [1, -8, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 109, 'label': '2-121275-1.1-c1-0-109', 'leading_term': '3.22624354539', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/Q/121275/s', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.6891652338590395, 0.7580475340112683, 0.05153295759077562, -0.7665751715100688, -0.6584199417356493, 0.508581569051344, 1.34174259430695, 0.3666500932443327, -1.701125202714776, -2.163543405513163, 0.120165911266191, 2.168337999034263, -0.08417381808031205, -5.827721446311485, -8.966689530568162, -5.625025623308131, 0.002321265270845601, 0.7907771881342996, -3.215752772425082, -4.627449731211645, 0.2340008193547391, 5.363778854843333, 3.864612574991007, -1.688173404750485, -3.446362534090332, -0.1335718414592225, 2.294331984496555, 0.9590109248947092, -0.488181168064434, 0.3484493585436716, 0.7369106119066579, -0.9632631748788244, -1.935102603329449, -0.6294532767100603, 0.320018606419421, -0.3616878017285325, -0.272343967597757, 1.126503019648028, 1.147124253460402, -0.2100181350345984, -0.08431588797912576, 0.6912835445098618, -0.9989938121943328, -2.940681616311889, -0.966761485633924, 1.744744714080173, 0.06493016600355264, -1.777409368114177, 2.157701824063126, 5.72106989469306, 0.7558724049153537, -5.647687061707715, -2.704831018950632, 3.267878255411323, 0.3954605453050184, -5.831705463047776, -3.474959125076265, 2.65169601560094, 1.472545906987796, -2.462180762778232, 0.4512669155974873, 5.367189798595332, 3.827012109437029, 0.05937357325365406, 0.3299407525128867, 1.092372052458708, -0.7331709274569451, -1.290520270450604, 0.2069853739415516, 0.1102061668010859, -0.6585090723522316, 0.37646831699772, 0.5569252424334009, -1.207670653390508, -1.050495180396342, 0.7946589606510235, 0.4929176373801325, -0.2518344933916114, 0.7994226234726427, -0.1258588492724094, -2.761440823642138, -1.197085354543603, 1.147946229446861, -3.325691549941794, -7.40860469512154, -1.780448370183921, 3.884169507828837, 0.4879642514220377, -0.8825257408429441, 5.523364755106826, 6.132101126281272, -1.026254521883136, -0.1211510330442312, 7.90076756562419, 6.873355359470741, -0.2247965252908419, 0.4890064793277909, 4.450605519731562, 2.011750685318377, -1.14671064747435, -0.2010594402806647, -0.6835411681642651, -2.444160069507663, -0.6531515704636258, 1.270564658967368, 0.06376736114837243, -0.2061609759975235, 0.8527571218436286, 0.119215903635972, -0.2556177481568162, 0.4027646565658544, -1.363027375685549, -2.858116488747341, -0.5321263482170308, 0.7305246179213446, -0.6548581415541094, -0.1621749371602955, -1.060868389654502, -5.721883413208026, -4.520018017430293], 'positive_zeros': ['0.7636746506542952', '1.404590227565743', '2.046096799496780', '2.739842627551642', '3.245508984593413', '4.249857163919452', '4.563275527292437', '5.241060091321013', '5.920629817181529', '6.508470872534720', '7.119375536247939', '7.432116208937228', '7.879801987995405', '8.606724732087883', '8.896034805129284', '9.305192907886635', '9.953598302231016', '10.26939375308967', '10.64857230242041', '11.31775027033270', '11.75500341672442', '12.15024576775584', '12.77313513251621', '13.34318141426531', '13.76388827867476', '14.37432502490659', '14.82450942118740', '15.23043576630493', '16.00792662907354', '16.19604078152585', '16.66451914833516', '17.21006999527315', '17.52456475464007', '17.93180056446065', '18.33720450452086', '18.88089603736205', '19.34780513306700', '19.58260604325145', '19.98811270307828'], 'prelabel': '2-121275-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 31.118897000264617, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 677974156003934062, 'z1': {'__RealLiteral__': 0, 'data': '0.7636746506542952', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.404590227565743', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.046096799496780', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 968.3857505130783, 'bad_primes': [3, 5, 7, 11], 'central_character': '1.1', 'conductor': 121275, 'conductor_radical': 1155, 'degree': 2, 'dirichlet_coefficients': [1, -2, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, -3, 0, 0, -4, 0, 0, 1, 0, 0, -2, 2, 0, 0, 6, 0, 0, 8, 0, -5, 8, 0, 0, 0, 0, 3, -2, 0, 0, -8, 0, 11, 2, 0, -4, -4, 0, 0, 0, 0, -6, 6, 0, 0, 0, 0, -16, 6, 0, -6, 10, 0, -8, 0, 0, -13, 0, 0, 0, -12, 0, -15, -6, 0, 2, 0, 0, 1, 0, 0, 16, 0, 0, 0, -22, 0, 0, 8, 0, 0, 4, 0, 8, 0, 0, -2, 0, 0, 0], 'euler11': [1, -1, 0], 'euler13': [1, 3, 13], 'euler17': [1, 0, 17], 'euler19': [1, -1, 19], 'euler2': [1, 2, 2], 'euler23': [1, -2, 23], 'euler29': [1, -8, 29], 'euler3': [1, 0, 0], 'euler31': [1, 5, 31], 'euler37': [1, -3, 37], 'euler41': [1, 8, 41], 'euler43': [1, -11, 43], 'euler47': [1, 4, 47], 'euler5': [1, 0, 0], 'euler53': [1, -6, 53], 'euler59': [1, -6, 59], 'euler61': [1, 6, 61], 'euler67': [1, 13, 67], 'euler7': [1, 0, 0], 'euler71': [1, 12, 71], 'euler73': [1, 15, 73], 'euler79': [1, -1, 79], 'euler83': [1, 0, 83], 'euler89': [1, -8, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 2, 2], [1, 0, 0], [1, 0, 0], [1, 0, 0], [1, -1, 0], [1, 3, 13], [1, 0, 17], [1, -1, 19], [1, -2, 23], [1, -8, 29], [1, 5, 31], [1, -3, 37], [1, 8, 41], [1, -11, 43], [1, 4, 47], [1, -6, 53], [1, -6, 59], [1, 6, 61], [1, 13, 67], [1, 12, 71], [1, 15, 73], [1, -1, 79], [1, 0, 83], [1, -8, 89], [1, 2, 97]], 'index': 109, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/121275/s'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-121275-1.1-c1-0-109', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-121275-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 31.118897000264617, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 677974156003934062, 'z1': {'__RealLiteral__': 0, 'data': '0.7636746506542952', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '677974156003934062', 'Lhash_array': ['677974156003934062'], 'factors': ['2-121275-1.1-c1-0-109'], 'label': '2-121275-1.1-c1-0-109', 'type': 'ECQ', 'url': 'EllipticCurve/Q/121275/s'}