-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2036399348450905159894382290301', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-0.5, -0.8660254037844386], 'a6': [0, 0], 'a7': [-2.5, 0.8660254037844386], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20.122301309362665, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.5, 0.8660254037844386]]], [7, [[1.0, 0], [2.5, -0.8660254037844386]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '2520.361', 'coefficient_field': 'CDF', 'conductor': 2520, 'conductor_radical': 210, 'conjugate': '1768690206124601150122830346381', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [2.5, -0.8660254037844386]], [[1.0, 0], [-1.0, 1.7320508075688772], [-5.5, -9.526279441628825]], [[1.0, 0], [0, 0], [13.0, 0]], [[1.0, 0], [-2.0, 3.4641016151377544], [-8.5, -14.722431864335457]], [[1.0, 0], [-1.0, -1.7320508075688772], [-9.5, 16.454482671904334]], [[1.0, 0], [-0.5, -0.8660254037844386], [-11.5, 19.91858428704209]], [[1.0, 0], [9.0, 0], [29.0, 0]], [[1.0, 0], [2.0, -3.4641016151377544], [-15.5, -26.846787517317598]], [[1.0, 0], [2.0, 3.4641016151377544], [-18.5, 32.04293994002423]], [[1.0, 0], [1.0, 0], [41.0, 0]], [[1.0, 0], [-9.0, 0], [43.0, 0]], [[1.0, 0], [0, 0], [-23.5, 40.703193977868615]], [[1.0, 0], [5.0, -8.660254037844387], [-26.5, -45.89934640057525]], [[1.0, 0], [5.0, -8.660254037844387], [-29.5, -51.09549882328188]], [[1.0, 0], [4.5, 7.794228634059948], [-30.5, 52.827549630850754]], [[1.0, 0], [2.5, -4.330127018922194], [-33.5, -58.023702053557386]], [[1.0, 0], [14.0, 0], [71.0, 0]], [[1.0, 0], [6.0, -10.392304845413264], [-36.5, -63.21985447626402]], [[1.0, 0], [7.0, 12.12435565298214], [-39.5, 68.41600689897065]], [[1.0, 0], [11.0, 0], [83.0, 0]], [[1.0, 0], [7.5, 12.99038105676658], [-44.5, 77.07626093681505]], [[1.0, 0], [18.0, 0], [97.0, 0]], [[1.0, 0], [-1.5, 2.598076211353316], [-50.5, -87.4685657822283]], [[1.0, 0], [-6.5, -11.258330249197702], [-51.5, 89.20061658979718]], [[1.0, 0], [-4.5, -7.794228634059948], [-53.5, 92.66471820493493]], [[1.0, 0], [-0.5, 0.8660254037844386], [-54.5, -94.39676901250381]], [[1.0, 0], [2.0, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 37, 'label': '2-2520-7.4-c1-0-37', 'leading_term': '2.9876752361693418409636579987843798844423204', 'load_key': 'CMFs-workshop', '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': 'ModularForm/GL2/Q/holomorphic/2520/2/bi/a/361/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [8.860883997633214e-61, -0.1526189385285551, -0.30676747530620646, -0.4620046233732224, -0.617812382632452, -0.7735566666968429, -0.9284542533010206, -1.0815474875321256, -1.2316879538963263, -1.3775298173566233, -1.5175330644308853, -1.6499764827198442, -1.7729799101893124, -1.8845350576026196, -1.9825440425082799, -2.0648646515192395, -2.1293612509916957, -2.1739601805562514, -2.196708380576188, -2.1958339200839996, -2.169807007097109, -2.1173999827620205, -2.0377447309971948, -1.9303858837949686, -1.7953281769792981, -1.633076319500983, -1.4446657879121982, -1.2316830518723318, -0.9962738802351617, -0.7411385725401288, -0.46951320775627614, -0.18513629907000492, 0.1077994135399402, 0.40470991821574237, 0.70069710388761, 0.9906391838240833, 1.269292955554806, 1.5314060376022631, 1.7718367952350618, 1.9856792710678441, 2.1683900871123636, 2.3159139979900063, 2.4248045649040617, 2.4923362998362486, 2.5166046106491824, 2.496609969343816, 2.4323229337467787, 2.3247269801428434, 2.17583654984087, 1.988688271361514, 1.7673039826620456, 1.5166249311389053, 1.2424173555263511, 0.9511505318457364, 0.6498492704415083, 0.34592375522250035, 0.04698048977333602, -0.23938107294440372, -0.5057809212006635, -0.7452740029381746, -0.9515625345418034, -1.1191984939553299, -1.2437696211734324, -1.3220623912281242, -1.3521957892773375, -1.3337203065245617, -1.2676773840157525, -1.1566155454072198, -1.0045606579932713, -0.8169391141315332, -0.6004541958167264, -0.36291743006869825, -0.1130383131144951, 0.13982267587462494, 0.38593139077958505, 0.6154799622262321, 0.8189005385139922, 0.9871831084598709, 1.112187094483165, 1.1869361336044713, 1.205885546663113, 1.165152448306416, 1.0626992759598153, 0.8984627053767157, 0.6744214499066365, 0.39459827286418636, 0.06499362661275047, -0.30654939465535946, -0.7105467122629463, -1.1361370308860812, -1.5714008467584084, -2.0037255983852793, -2.420205866079454, -2.808065847663585, -3.155090052887155, -3.4500473347067313, -3.6830930635674455, -3.846134486166835, -3.9331451085595472, -3.9404152996454886, -3.866728198063279, -3.713452374437799, -3.484545481942763, -3.186466232070892, -2.827995353467984, -2.419969610468463, -1.9749363461405012, -1.5067392392676884, -1.030048893435417, -0.5598543829058419, -0.1109338492752183, 0.3026764234095063, 0.6681944064371155, 0.9745662918954672, 1.212883051309589, 1.3767223229881471, 1.462400812971887, 1.4691255114270902, 1.3990357089662355, 1.2571319165655983, 1.0510921963095492, 0.7909809282867232, 0.4888594904623168, 0.15831252796144205, -0.1860927459004352, -0.5293936128400152, -0.8568422672046907, -1.1545150533460178, -1.4098954373860773, -1.61240610610976, -1.753867105993595, -1.8288594671974787, -1.834977225796521, -1.7729550449610736, -1.6466635852556717, -1.4629701948043659, -1.2314681639070018, -0.9640834795038915, -0.6745734776207827, -0.3779367831934216, -0.08975821552267726, 0.17448428381658998, 0.40012135024530426, 0.5739720964389091, 0.684972012529336, 0.7247202196499241, 0.6879202842062329, 0.5726928652262875, 0.38074359771224026, 0.1173756134517855, -0.2086572754745763, -0.5854537345973457, -0.9984143955088656, -1.4308209185273641, -1.8645217084036503, -2.2806960718402696, -2.6606644534407913, -2.986709591495765, -3.242872160183364, -3.415684808856119, -3.4948104991288167, -3.4735546284963243, -3.3492254920959215, -3.1233239771785075, -2.801550748236766, -2.393627250271456, -1.9129352774994728, -1.3759882429549044, -0.801755250046663, -0.2108662286407789, 0.3752675983315731, 0.9353791151477266, 1.4492749557055369, 1.8987268285039853, 2.268283004910602, 2.5459614629307676, 2.7237910634161895, 2.798173703628212, 2.7700483689617865, 2.644847037670589, 2.4322420763211117, 2.1456946448667598, 1.8018232386017514, 1.4196203606654165, 1.0195529989179273, 0.6225886778490884, 0.2491930406179635, -0.0816530548531685, -0.3533692117210041, -0.5525788300735007, -0.6697598444112218, -0.6997095156606216, -0.6417985997017581, -0.500000247396266, -0.28268991756036227, -0.0022238788246106574, 0.32568501651756765, 0.6827652419096434, 1.0491200611755152, 1.4042510957676395, 1.728121377871088, 2.002204570458297, 2.210466978443342, 2.3402316163338606, 2.3828788541834864, 2.334345817216084, 2.195396420309474, 1.9716452195109644, 1.6733306105768748, 1.3148456857425046, 0.9140476261515584, 0.4913782079928033, 0.06883821620730841, -0.33113326431801837, -0.6868180343099257, -0.978356960878352, -1.188807875107693, -1.3050671945758472, -1.318605532970679, -1.225976507252043, -1.0290691753171977, -0.7350874862074396, -0.35625415135339694, 0.09074926939160664, 0.5855802805606839, 1.105232721483017, 1.6251837350276794, 2.1206322091699676, 2.5677648476409685, 2.9449837043114866, 3.2340301702522702, 3.4209450294990327, 3.4968121103950396, 3.4582438854094004, 3.3075805816480064, 3.0527892870994897, 2.707065399738103, 2.288154729044584, 1.8174297629616512, 1.318767224233627, 0.8172852965854687, 0.3380071558967025, -0.09547780090152086, -0.4622826893093849, -0.7453524670661712, -0.9323912871001434, -1.016535599358423, -0.9967340214851484, -0.8778106038023687, -0.6702052079425118, -0.3894023820527054, -0.055077383219009506, 0.30999608999003747, 0.6812182355308131, 1.0335467264060059, 1.3429157681409272, 1.5876120601868497], 'positive_zeros': ['1.60643583341045968904385440329538', '2.85189617137491825838976769632837', '3.67890974132752309277195455037738', '4.37646315367087273935995257027715', '5.59907544177181933826568686563577', '6.26955698911630320483055034936012', '7.12597671835263987113451307539928', '7.58574843349104703752427644191155', '8.600156195859458894142793687161910'], 'prelabel': '2-2520-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.485788816848455, 'root_angle': -0.45965409389210776, 'root_number': '-0.9680403732843879069988040812939128198417627379257641738 - 0.2507944092108572498899676661099648234093800189274460869*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.45965409389210776', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.60643583341045968904385440330', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.85189617137491825838976769633', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.67890974132752309277195455038', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 20.122301309362665, 'bad_primes': [2, 3, 5, 7], 'central_character': '7.4', 'conductor': 2520, 'conductor_radical': 210, 'degree': 2, 'index': 37, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2520/2/bi/a/361/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, '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': '2-2520-7.4-c1-0-37', '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': '2-2520-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.485788816848455, 'root_angle': -0.45965409389210776, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.60643583341045968904385440330', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2036399348450905159894382290301', 'Lhash_array': ['2036399348450905159894382290301'], 'factors': ['2-2520-7.4-c1-0-37'], 'label': '2-2520-7.4-c1-0-37', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2520/2/bi/a/361/1'}