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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '1076447092899356583', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 535.2532148290469, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1]], [19, [1, 1]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '67032.1', 'coefficient_field': '1.1.1.1', 'conductor': 67032, 'conductor_radical': 798, 'degree': 2, 'euler_factors': [[1], [1], [1, -1, 5], [1], [1, -5, 11], [1, -2, 13], [1, 1, 17], [1, 1], [1, 4, 23], [1, -6, 29], [1, -10, 31], [1, 0, 37], [1, 0, 41], [1, 11, 43], [1, -9, 47], [1, 10, 53], [1, -4, 59], [1, -5, 61], [1, 4, 67], [1, 8, 71], [1, 13, 73], [1, -4, 79], [1, 4, 83], [1, 6, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 68, 'label': '2-67032-1.1-c1-0-68', 'leading_term': '7.96746534108', '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/67032/ca', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.845853407341079, 2.846556404626314, 2.45376275065388, 0.9741581684263948, -0.3062634730819808, -0.1114305962402498, 1.392454648949718, 2.426546383045292, 1.418754590995422, -0.9262741098092209, -2.016397601287582, -0.3614611816699699, 2.309495137190167, 2.910879681905753, 0.9465190789652267, -0.7396482163569662, 0.0909902353050151, 1.699153988309486, 0.7364702577205745, -2.605259065753633, -4.353571393705765, -2.33839748197745, 0.5848542397811634, 0.8271029568613921, -0.6508529377017515, -0.5301187597392873, 0.7799278496680838, -0.3738697509039599, -4.106901218777894, -5.559417562084988, -2.279139150870063, 1.481832402735817, 1.308456401767374, -0.545064237145606, 0.3986254521202737, 2.902224272576889, 2.570939634218711, 0.1026150452559993, -0.02376789069372118, 1.926207369240951, 1.375973473423107, -1.507396356833608, -1.372456926713339, 2.446049168057903, 4.089823452710975, 1.425724378368621, -0.5981133244514595, 0.2132838084925262, -0.644063469118454, -4.602462041198042, -5.885667693362848, -1.961299233120706, 1.37463229552668, 0.4633710814719041, -0.3801848213268456, 1.481882865138632, 1.920952996650817, -0.327455365782995, -0.002704074127506812, 3.755652903814449, 4.491753812970237, 0.8797262970282435, -0.4004443982980993, 2.07651103807371, 1.809217333777289, -2.118152568374176, -3.042754867354482, -0.1338734567391141, 0.6738959889431227, -0.6962563208059046, 0.4072389494234763, 1.72847486370305, -1.485364430951323, -4.894809539198532, -2.557030598511107, 1.008432042933006, 0.03108948055896551, -1.163300524024791, 1.429503867350894, 2.459453365803841, -0.6010129306911346, -1.268398646901804, 1.864445402491464, 1.709358993226363, -2.06674208708562, -2.419108084956336, 0.0319538287619179, -0.3941437218702384, -1.113204040581684, 1.970056626340653, 3.567525270538004, 0.2782903581826739, -1.040083365208343, 1.890799746946283, 1.487160128178487, -2.650439346903129, -2.199817821649449, 2.041120622150564, 2.293959636886501, 0.1055611321759261, 0.4918312483182149, -0.0728017005299456, -3.203293266425732, -2.15947309071314, 2.846612894439854, 3.201566058616933, -0.07882195629199513, 0.5405156402637318, 1.878531562677909, -1.660712410313703, -4.089160038776231, -1.100355729601387, 0.6540477177477431, -0.2537847832922127, 2.592703285991893, 6.299857226959777, 3.59184251134491, -0.6311967333364639, -0.005803054496818067, 0.4503220502367273], 'positive_zeros': ['1.167100864658853', '1.525017860613316', '2.402042098909046', '3.032716423364294', '3.855509302721101', '4.237348943839264', '4.812657959704212', '5.685491697231906', '6.135682656476954', '6.592024518651686', '6.966137970902194', '7.879040263925871', '8.405292844044275', '8.706728090418644', '9.514255674441670', '9.753717494451968', '10.36784871283247', '10.85119779395483', '11.62516553773140', '11.94906733977036', '12.18213328944339', '13.11022012440381', '13.56470169807678', '13.82503250820964', '14.46133648462682', '14.75024321320533', '15.57125466324687', '15.80506033134573', '16.37030484659755', '17.01265444025877', '17.36283991730961', '17.70404652176180', '18.16809913124430', '18.90008779332651', '19.25322631044047', '19.63822343703087'], 'prelabel': '2-67032-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.13554008077285, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1076447092899356583, 'z1': {'__RealLiteral__': 0, 'data': '1.167100864658853', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.525017860613316', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.402042098909046', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 535.2532148290469, 'bad_primes': [2, 3, 7, 19], 'central_character': '1.1', 'conductor': 67032, 'conductor_radical': 798, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 2, 0, 0, 0, -1, 0, -1, 0, 0, 0, -4, 0, -4, 0, 0, 0, 6, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11, 0, 0, 0, 9, 0, 0, 0, 0, 0, -10, 0, 5, 0, 0, 0, 4, 0, 5, 0, 0, 0, 2, 0, -4, 0, 0, 0, -8, 0, -13, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, -1, 0, 0, 0, -6, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0], 'euler11': [1, -5, 11], 'euler13': [1, -2, 13], 'euler17': [1, 1, 17], 'euler19': [1, 1, 0], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, -6, 29], 'euler3': [1, 0, 0], 'euler31': [1, -10, 31], 'euler37': [1, 0, 37], 'euler41': [1, 0, 41], 'euler43': [1, 11, 43], 'euler47': [1, -9, 47], 'euler5': [1, -1, 5], 'euler53': [1, 10, 53], 'euler59': [1, -4, 59], 'euler61': [1, -5, 61], 'euler67': [1, 4, 67], 'euler7': [1, 0, 0], 'euler71': [1, 8, 71], 'euler73': [1, 13, 73], 'euler79': [1, -4, 79], 'euler83': [1, 4, 83], 'euler89': [1, 6, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -1, 5], [1, 0, 0], [1, -5, 11], [1, -2, 13], [1, 1, 17], [1, 1, 0], [1, 4, 23], [1, -6, 29], [1, -10, 31], [1, 0, 37], [1, 0, 41], [1, 11, 43], [1, -9, 47], [1, 10, 53], [1, -4, 59], [1, -5, 61], [1, 4, 67], [1, 8, 71], [1, 13, 73], [1, -4, 79], [1, 4, 83], [1, 6, 89], [1, 2, 97]], 'index': 68, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/67032/ca'], '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': '2-67032-1.1-c1-0-68', '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': '2-67032-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.13554008077285, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1076447092899356583, 'z1': {'__RealLiteral__': 0, 'data': '1.167100864658853', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1076447092899356583', 'Lhash_array': ['1076447092899356583'], 'label': '2-67032-1.1-c1-0-68', 'type': 'ECQ', 'url': 'EllipticCurve/Q/67032/ca'}