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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': -4, 'A8': 0, 'A9': 1, 'Lhash': '1389226274891231526', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [-1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1278.245235556657, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, 1]], [23, [1, 1]], [29, [1, 1]]], 'bad_primes': [2, 3, 5, 23, 29], 'central_character': '160080.1', 'coefficient_field': '1.1.1.1', 'conductor': 160080, 'conductor_radical': 20010, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 1], [1, 4, 7], [1, 0, 11], [1, 2, 13], [1, 6, 17], [1, 4, 19], [1, 1], [1, 1], [1, -4, 31], [1, -6, 37], [1, 2, 41], [1, 4, 43], [1, 8, 47], [1, -10, 53], [1, 0, 59], [1, 10, 61], [1, 4, 67], [1, 8, 71], [1, 6, 73], [1, -16, 79], [1, -12, 83], [1, 6, 89], [1, 14, 97]], 'gamma_factors': [[], [0]], 'index': 19, 'label': '2-160080-1.1-c1-0-19', 'leading_term': '2.40825923132', '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/160080/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.4154433304813712, -0.1358000769384546, -1.80147847710838, -3.326020753024148, -2.7981936944714, 0.2030235466674239, 3.388569072432633, 3.748328091806524, 1.178388760159176, -0.9577754199607452, 0.04724743615424997, 2.49904028229986, 2.565087226441224, -0.09441609647638995, -1.698531957437508, -0.1642697958618415, 1.589548858108687, 0.5458319653746763, -1.090490995883524, 0.5266474985923896, 3.924566716638017, 4.144623382286062, 0.8831932113436178, -1.078012980942729, -0.02169323993165523, 0.5839423646606262, -0.4917677638361744, 0.08212833831207782, 2.546291518851138, 1.985405812660651, -2.273700267310269, -3.633421410283382, 0.4736880982608711, 3.232557878214737, 0.3046614447954032, -2.578745618586513, -0.7017002783780324, 1.187617688423639, -0.96578695419261, -2.624390103982949, -0.5984961795941612, 0.3404627378840506, -2.063240382793031, -2.468301505792155, 0.6271464248326284, 1.336391435413039, -1.353289238845625, -1.680143935929073, 0.4671037619772257, -0.08940614824518268, -1.930959028193968, -0.5283827455769124, 1.066959635407181, -0.1297996187709702, 2.025794754603154, 9.64905720269012, 12.29854960477312, 5.24783864121868, -0.8956486233245377, 0.123668228959483, 1.00550884444869, -1.453110695733321, -1.379189536590554, 0.971713327554776, 0.2810087877490851, -1.05852129602269, 0.3508612513588401, -0.0691932499030708, -3.120484268000158, -1.921126841131238, 2.304440391440493, 1.719188566443891, -0.6413324273516782, 2.211267443514709, 4.994989757438362, 2.017757203199723, -0.623135272691524, 0.05945972186999318, -1.109386256671991, -1.88732253466609, 2.380569474681105, 3.832286665338745, -2.482957378172077, -5.198466394231178, 0.7188951782950954, 3.80366198285235, 0.4661131109630083, -0.7305309365273938, 0.2924689323693289, -1.215512735212858, -1.579125060699795, 0.4741680865968226, -0.1412522323889306, -0.8763142114142406, 2.170909601096351, 2.293287686143801, -2.109462012987417, -1.969848693638238, 1.010497152450724, -1.699288336123282, -3.866984996017215, 1.082398275257723, 3.528707991864741, -0.2775039775331944, -0.850708142376315, 1.069126408076652, -0.962398703892458, -0.8629490625702542, 3.987111416955235, 4.082140016786962, 0.2188202047382899, 1.067063120678041, 2.417642217292749, -0.5562237821674882, -1.458855450321155, 0.0828720377413302, -0.8743994575131515, -0.2680392954360739, 2.192436231578209, -0.8236446159569758], 'positive_zeros': ['0.4696300876350462', '1.486088977120375', '2.354607235623152', '2.744995136165288', '3.491788968564770', '4.017037273003586', '4.563071473297381', '4.957462716969220', '5.820402114316169', '6.253603478939022', '6.642206561918448', '6.989964385088748', '7.624158448741702', '8.226200044803962', '8.767602219532655', '9.307072750953752', '9.670383927600652', '10.31511378794666', '10.55292774280415', '11.20056214078441', '11.63134091998999', '12.18492760624621', '12.48955505236079', '13.05189307131485', '13.47090142398688', '13.61668773652317', '14.68315779669237', '14.98785666677513', '15.36346123035830', '15.88243285420351', '16.28329720228612', '16.69866828964926', '16.99326987158517', '17.60445327484632', '18.13733953955384', '18.36090167100419', '19.14071245333207', '19.47435487475375', '19.59127162086079'], 'prelabel': '2-160080-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 35.752555650703584, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1389226274891231526, 'z1': {'__RealLiteral__': 0, 'data': '0.4696300876350462', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.486088977120375', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.354607235623152', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1278.245235556657, 'bad_primes': [2, 3, 5, 23, 29], 'central_character': '1.1', 'conductor': 160080, 'conductor_radical': 20010, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, -4, 0, 1, 0, 0, 0, -2, 0, 1, 0, -6, 0, -4, 0, 4, 0, -1, 0, 1, 0, -1, 0, -1, 0, 4, 0, 0, 0, 4, 0, 6, 0, 2, 0, -2, 0, -4, 0, -1, 0, -8, 0, 9, 0, 6, 0, 10, 0, 0, 0, 4, 0, 0, 0, -10, 0, -4, 0, 2, 0, -4, 0, 1, 0, -8, 0, -6, 0, -1, 0, 0, 0, 16, 0, 1, 0, 12, 0, 6, 0, 1, 0, -6, 0, 8, 0, -4, 0, 4, 0, -14, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 2, 13], 'euler17': [1, 6, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 1, 0], 'euler29': [1, 1, 0], 'euler3': [1, 1, 0], 'euler31': [1, -4, 31], 'euler37': [1, -6, 37], 'euler41': [1, 2, 41], 'euler43': [1, 4, 43], 'euler47': [1, 8, 47], 'euler5': [1, 1, 0], 'euler53': [1, -10, 53], 'euler59': [1, 0, 59], 'euler61': [1, 10, 61], 'euler67': [1, 4, 67], 'euler7': [1, 4, 7], 'euler71': [1, 8, 71], 'euler73': [1, 6, 73], 'euler79': [1, -16, 79], 'euler83': [1, -12, 83], 'euler89': [1, 6, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 1, 0], [1, 4, 7], [1, 0, 11], [1, 2, 13], [1, 6, 17], [1, 4, 19], [1, 1, 0], [1, 1, 0], [1, -4, 31], [1, -6, 37], [1, 2, 41], [1, 4, 43], [1, 8, 47], [1, -10, 53], [1, 0, 59], [1, 10, 61], [1, 4, 67], [1, 8, 71], [1, 6, 73], [1, -16, 79], [1, -12, 83], [1, 6, 89], [1, 14, 97]], 'index': 19, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/160080/d'], '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': '2-160080-1.1-c1-0-19', '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': '2-160080-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 35.752555650703584, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1389226274891231526, 'z1': {'__RealLiteral__': 0, 'data': '0.4696300876350462', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1389226274891231526', 'Lhash_array': ['1389226274891231526'], 'label': '2-160080-1.1-c1-0-19', 'type': 'ECQ', 'url': 'EllipticCurve/Q/160080/d'}