-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '5030627102569592420381283803388', 'a10': [-11.011231146732435, 19.07201180002549], 'a2': [0.8333519736180336, -2.2896157299734914], 'a3': [1.562835708096416, 2.560770303931763], 'a4': [-1.4836869065330605, -1.2449611360544506], 'a5': [-8.901035853627851, -1.5694927772479932], 'a6': [7.165572190514049, -1.444270233857827], 'a7': [-1.3260698548793035, 1.1127047261445329], 'a8': [4.353569070784258, -2.5135342749529204], 'a9': [-4.115089098997549, 8.004126542434943], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7356967137728017, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.562835708096416, -2.560770303931763]]]], 'bad_primes': [3], 'central_character': '27.23', 'coefficient_field': 'CDF', 'conductor': 27, 'conductor_radical': 3, 'conjugate': '4327217253498070388322768900071', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8333519736180336, 2.2896157299734914], [-3.064177772475912, -2.5711504387461575]], [[1.0, 0], [-1.562835708096416, -2.560770303931763]], [[1.0, 0], [8.901035853627851, 1.5694927772479932], [23.49231551964771, 8.550503583141719]], [[1.0, 0], [1.3260698548793035, -1.1127047261445329], [8.508760705679586, -48.255579897598196]], [[1.0, 0], [-8.66909293508912, 1.5285949827253493], [113.70280711509491, -41.38443734240592]], [[1.0, 0], [-4.317403393318281, 1.5714063244877516], [129.4615108871073, -108.63110603702515]], [[1.0, 0], [5.1681325507691485, 2.9838227193942353], [144.5, 250.28134169370276]], [[1.0, 0], [0.342748824012836, 0.5936583774247157], [-180.5, 312.63517076618234]], [[1.0, 0], [8.55456011380808, -10.194927748693912], [-91.85988598580616, -520.963301343458]], [[1.0, 0], [5.736747644429816, -15.761584614180416], [-644.2433766630605, -540.5843797463796]], [[1.0, 0], [20.068772243246432, 16.839699387488917], [166.87589873792007, 946.400250644732]], [[1.0, 0], [-22.158348954848268, 38.379386201637935], [-684.5, -1185.5887777808964]], [[1.0, 0], [-23.508305298466414, -64.58853797718193], [-1287.720708883002, 1080.5259718830725]], [[1.0, 0], [0.14211336201626143, 0.8059649263275734], [-1737.4916558331447, 632.3952450091615]], [[1.0, 0], [0.7555519330381553, 0.9004317305897215], [-383.58882446624915, 2175.4403264039674]], [[1.0, 0], [0, 46.1906590091138], [-2809.0, 0]], [[1.0, 0], [48.28333910503512, 8.5136554029138], [3271.070012955747, 1190.572118916653]], [[1.0, 0], [46.444331952246635, -38.971421811405314], [646.1448690986479, -3664.469648958426]], [[1.0, 0], [-85.1924320802865, 31.00750946196941], [3438.7735051610925, -2885.473579882875]], [[1.0, 0], [-51.038810099237544, -29.467270749912988], [2520.5, 4365.634060477355]], [[1.0, 0], [15.718016575202558, 27.224403302460587], [-2664.5, 4615.049376767273]], [[1.0, 0], [99.22579053374541, 36.115234225816444], [4780.883369505542, 4011.637472053692]], [[1.0, 0], [-50.50136291380235, 138.75135425735508], [-5277.28016864664, -4428.163843130569]], [[1.0, 0], [-2.881344581066517, 1.6635450695068232], [3960.5, -6859.787223376538]], [[1.0, 0], [-15.088753707312062, -85.57257458096821], [-8841.567868974613, 3218.067528551217]], [[1.0, 0], [-72.89718636338812, -86.87548373857744], [-1771.3850603803564, 10046.023888477534]], [[1.0, 0], [-8.316915471524009, 47.16757150895136], [-9969.199013917701, -3628.4917005420198]], [[1.0, 0], [0, -0.3116337318591817], [-11449.0, 0]], [[1.0, 0], [6.777577110629594, 0], [11881.0, 0]], [[1.0, 0], [29.492889895460877, 5.200392227633811], [11998.935074815265, 4367.255210125464]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-3e3-27.23-c2-0-3', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/27/3/f/a/23/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [1.1234083049392884, 1.1574380930560353, 1.2085376099860372, 1.2766390596323247, 1.360774032348006, 1.4591023038842468, 1.568924598297662, 1.6866670035761253, 1.8078474324248353, 1.927049066083287, 2.0379306763617357, 2.1333022567805537, 2.2052895895376454, 2.245604692724319, 2.2459307604254546, 2.1984200045945466, 2.09629061595746, 1.9344951575073097, 1.710417867135157, 1.4245438688410126, 1.0810309235279032, 0.6881061675999238, 0.2582084956369311, -0.19219609681055916, -0.6431821987539115, -1.0723442131736458, -1.456177852055609, -1.771808448989998, -1.9989596893170753, -2.1220058337586587, -2.1319069616816497, -2.0277975100052825, -1.8179907076984143, -1.5201815741567895, -1.1606828530122713, -0.7726120525565692, -0.393059757084213, -0.059400776735146515, 0.19495305064576168, 0.3449340010825498, 0.37781496527289055, 0.2962595436151578, 0.11988822409782023, -0.1150750881698479, -0.35833179831591866, -0.5502203417910059, -0.6283258074585355, -0.5353986179811087, -0.22772098950327022, 0.31713568741436815, 1.094295848851298, 2.0683660400144612, 3.1738420361724367, 4.3195611483087335, 5.3971079704972, 6.292504722074777, 6.899958539784568, 7.135986668878465, 6.951982254669432, 6.343285986513286, 5.353127472657094, 4.0703868166379475, 2.6209446399594487, 1.1533346902201438, -0.1796512043623719, -1.2409855256969442, -1.9281754962635016, -2.187866031143716, -2.0237978158228582, -1.4965304137957134, -0.7145696424973196, 0.18207009234260382, 1.0435128804584803, 1.7335047140256374, 2.150859907760283, 2.2451498931391156, 2.0237467004257526, 1.5487486420399734, 0.9240950192594096, 0.2750115448099597, -0.27652917157530316, -0.6357193585545444, -0.7535025063645461, -0.6359764900360932, -0.34242041816041996, 0.028033272682253804, 0.35870914510369095, 0.542299307235804, 0.5067699842513201, 0.23454456472857552, -0.22965501172632063, -0.7847504633836491, -1.292610991944163, -1.6073155829004517, -1.608517690729657, -1.2317159102788084, -0.4883940445076206, 0.5292606019082352, 1.6612843423115071, 2.708928305506118, 3.47439182550266, 3.8031552169313927, 3.619584615362189, 2.947334108736593, 1.9089239320524773, 0.7032257655889863, -0.4354539431226947, -1.2885380758452443, -1.703542898982746, -1.6320613098322503, -1.1459038999147402, -0.42639685640798314, 0.2722519888315154, 0.6785408725230274, 0.5664402624252436, -0.18874935958824107, -1.5746618766276355, -3.4354323530979136, -5.497342235662889, -7.421955145360395, -8.875557201084602, -9.59951398408416, -9.465477197210596, -8.502529666522246, -6.889722132773055, -4.915574876434671, -2.914035167656832, -1.1921142159338745, 0.03352777835165455, 0.676033622356589, 0.7848968189372246, 0.519067144675212, 0.0946613603725379, -0.2781690705978871, -0.4520094157261, -0.37737244034100637, -0.1072500813604082, 0.22931729932683928, 0.47611342672288215, 0.505976547664174, 0.267033204963457, -0.19563825848799538, -0.750303514195633, -1.218583527099878, -1.4336145162284748, -1.2985735802671552, -0.8266939374395558, -0.14852335055575805, 0.5185431628794565, 0.9320269218289647, 0.9007910180499471, 0.3536422269793408, -0.6218183038302321, -1.7847923121778821, -2.793839374399536, -3.2950676927413394, -3.023178679995445, -1.887059126586597, -0.014046650671526387, 2.2628394370645823, 4.475039155656243, 6.129944958830738, 6.8351242925088345, 6.401677920500806, 4.89761281024712, 2.6351266908720294, 0.09379900190523076, -2.200252328907242, -3.8064504419903327, -4.4767555232442735, -4.208212677430621, -3.2272789680638234, -1.911899533599015, -0.6753528711078999, 0.15320742125564452, 0.41619332316310015, 0.1580000815865958, -0.408692643297685, -0.9878442920388916, -1.3074957464518968, -1.2143873695648002, -0.7250950677282016, -0.017577995253020718, 0.6332111864610811, 0.9534517004537068, 0.7688740697126739, 0.06988697597352501, -0.9790620289656874, -2.089585112773328, -2.9423849637521706, -3.291862760006218, -3.0466537240843876, -2.2983388182422395, -1.2881888123570087, -0.3232240020464304, 0.3292477797195146, 0.5314588318289765, 0.31718312027761053, -0.12973760852772803, -0.5533778995887123, -0.7324231229208583, -0.5762406253971255, -0.17327525036349695, 0.22940432798302232, 0.3121914194456087, -0.19309267097440452, -1.3849554219900027, -3.1243132388296555, -5.046454850370029, -6.655838682318939, -7.4773173917442985, -7.2155359405147195, -5.8680486751344345, -3.7501757078557945, -1.4173792594004846, 0.49492812020442334, 1.4652800501057266, 1.2513642199329167, -0.02867453280846367, -1.9278832399953485, -3.8073561650252516, -5.035446927396809, -5.185141734891539, -4.165399485591931, -2.2439516724679467, 0.04476391254321626, 2.074523573336102, 3.325801614719327, 3.54174407047064, 2.791537548033334, 1.424050656746672, -0.06719678405161217, -1.21688780295218, -1.7368063470572042, -1.590487905447891, -0.9725714736974151, -0.20764617722859824, 0.38763396134385836, 0.624010358660393, 0.49565342841941007, 0.1551091442348671, -0.17695450694293774, -0.3249361715972717, -0.24350001189683054, -0.03645228828172241, 0.10017779635067485, -0.013129601928573067, -0.42705649420358033, -1.0003016618232046, -1.4205427751630058, -1.310511020325086, -0.38343624607118937, 1.4124007515783827, 3.821709345600068, 6.320800209214391, 8.26383305050829, 9.0910001052612], 'positive_zeros': ['3.96846504996240448051519862455896', '6.53983233447434020252870815730584', '7.47578717836839085902384681119839', '8.520630593858072071380667654624110', '11.22447499619343015503788936220542', '12.44515569715350319633409913092815', '13.96838490192263041016698776926585', '14.92814435503727244963783834840271', '15.74034832935604589883228089997834', '16.96377872496331911240563680471049'], 'prelabel': '2-3e3-27.23-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.857727645452099, 'root_angle': 0.23599796856445138, 'root_number': '0.7375174272786393 + 0.675328101340598*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.117998984282', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.96846504996240448051519862456', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.53983233447434020252870815731', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.47578717836839085902384681120', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.7356967137728017, 'bad_primes': [3], 'central_character': '27.23', 'conductor': 27, 'conductor_radical': 3, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/27/3/f/a/23/4'], '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': '2-3e3-27.23-c2-0-3', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-3e3-27.23-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.857727645452099, 'root_angle': 0.11799898428222569, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '3.96846504996240448051519862456', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '5030627102569592420381283803388', 'Lhash_array': ['5030627102569592420381283803388'], 'label': '2-3e3-27.23-c2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/27/3/f/a/23/4'}