-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1598442601711199158513848077217', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 8, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.694863227153103, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '576.127', 'coefficient_field': '1.1.1.1', 'conductor': 576, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[1], [1], [1, -8, 25], [1, 0, -49], [1, 0, -121], [1, -10, 169], [1, -16, 289], [1, 0, -361], [1, 0, -529], [1, 40, 841], [1, 0, -961], [1, -70, 1369], [1, 80, 1681], [1, 0, -1849], [1, 0, -2209], [1, -56, 2809], [1, 0, -3481], [1, -22, 3721], [1, 0, -4489], [1, 0, -5041], [1, -110, 5329], [1, 0, -6241], [1, 0, -6889], [1, -160, 7921], [1, 130, 9409], [1, 40, 10201], [1, 0, -10609], [1, 0, -11449], [1, 182, 11881], [1, 224, 12769]], 'euler_factors_factorization': [[1], [1], [[[1, -8, 25], 1]], [[[1, -7], 1], [[1, 7], 1]], [[[1, -11], 1], [[1, 11], 1]], [[[1, -10, 169], 1]], [[[1, -16, 289], 1]], [[[1, -19], 1], [[1, 19], 1]], [[[1, -23], 1], [[1, 23], 1]], [[[1, 40, 841], 1]], [[[1, -31], 1], [[1, 31], 1]], [[[1, -70, 1369], 1]], [[[1, 80, 1681], 1]], [[[1, -43], 1], [[1, 43], 1]], [[[1, -47], 1], [[1, 47], 1]], [[[1, -56, 2809], 1]], [[[1, -59], 1], [[1, 59], 1]], [[[1, -22, 3721], 1]], [[[1, -67], 1], [[1, 67], 1]], [[[1, -71], 1], [[1, 71], 1]], [[[1, -110, 5329], 1]], [[[1, -79], 1], [[1, 79], 1]], [[[1, -83], 1], [[1, 83], 1]], [[[1, -160, 7921], 1]], [[[1, 130, 9409], 1]], [[[1, 40, 10201], 1]], [[[1, -103], 1], [[1, 103], 1]], [[[1, -107], 1], [[1, 107], 1]], [[[1, 182, 11881], 1]], [[[1, 224, 12769], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-24e2-4.3-c2-0-12', 'leading_term': '2.52697792820141790094477781981797105529192033331384385000000000000000000000000000000000000', '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/576/3/g/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [2.526977928201418, 2.5202562823888224, 2.5000714998616473, 2.4663675753249183, 2.4190627706553247, 2.358066462431618, 2.283301647334604, 2.1947321030499976, 2.0923930167413096, 1.9764237654839596, 1.847101461119621, 1.704873849663967, 1.550390174476179, 1.3845286644568482, 1.2084193863942592, 1.0234612991240468, 0.8313324636412414, 0.6339924970508173, 0.4336765101531277, 0.2328799402530922, 0.034333884270339246, -0.1590292463352666, -0.3441196877525979, -0.5177435806636806, -0.676664919024676, -0.8176752936613501, -0.9376702314747739, -1.033730629366278, -1.1032074901733804, -1.1438078965515628, -1.1536799192040619, -1.1314939598915275, -1.076517888915624, -0.9886832623898352, -0.8686399066649321, -0.7177962442875762, -0.5383429143011628, -0.33325751347460086, -0.10628865512516966, 0.1380819937904971, 0.3947004846967456, 0.6578243257967079, 0.9212286494321691, 1.178333529066926, 1.422350398192136, 1.6464447525119965, 1.8439115695966215, 2.008359184880747, 2.1338967484047915, 2.215319881864529, 2.2482887879413718, 2.2294928587011094, 2.1567958086465655, 2.0293555375877705, 1.8477133197793505, 1.6138475228506073, 1.3311878793570393, 1.0045873535356347, 0.6402498457593341, 0.24561332846775588, -0.1708105269340285, -0.5996376369337869, -1.0308495561138755, -1.4540626214133767, -1.8588210973396981, -2.2349059601017713, -2.5726499033202783, -2.863248361334641, -3.099055877151966, -3.273857031193386, -3.38310142374221, -3.4240928850109142, -3.3961241740199113, -3.300549907165652, -3.1407922990705806, -2.9222764551175517, -2.6522943641422243, -2.33979932373402, -1.9951351997043467, -1.6297075761133153, -1.2556063871791625, -0.8851919295266103, -0.5306581267200042, -0.203588458667952, 0.08547901166088477, 0.3274606548892584, 0.5150936943075274, 0.6432442788937303, 0.7091430308823028, 0.7125361085899732, 0.6557426418090745, 0.5436127271906093, 0.38338390493762187, 0.18443804238202388, -0.0420353282296558, -0.28345909800610514, -0.5263581273417577, -0.756900830995387, -0.9614724997307172, -1.1272578902769352, -1.2428092977086789, -1.298575954351986, -1.2873712405369921, -1.2047558673998982, -1.0493178784753938, -0.8228339469752952, -0.5303009058076663, -0.17983158095737822, 0.21758538902708865, 0.6484562003388017, 1.097271583470555, 1.5470985317399724, 1.9802519484346046, 2.379019788978827, 2.726411964060268, 3.0069011559403673, 3.2071229312916048, 3.3165032027604675, 3.32778322861834, 3.237415908985583, 3.045812033323818, 2.7574211853859047, 2.380638984772728, 1.9275399510021245, 1.4134431862361434, 0.8563259274397943, 0.2761074458404766, -0.3061675962114107, -0.8692117282174386, -1.3924045427311307, -1.8566888452270018, -2.2454115812815068, -2.5450695056289865, -2.745922980995491, -2.8424465791840348, -2.833592111226379, -2.722848056237057, -2.5180887290086034, -2.2312164986003005, -1.8776104722432434, -1.47540479457297, -1.044628585100479, -0.6062470755701082, -0.18114929211836306, 0.21086869275930448, 0.5520745898319717, 0.8276756308286453, 1.0265537337749595, 1.1418207173037658, 1.1711624584113551, 1.1169509748006237, 0.9861148488365741, 0.7897706447261996, 0.5426303927829383, 0.2622121829001775, -0.03210821584599472, -0.32015761457394093, -0.5820835007533186, -0.799471645621135, -0.9564035840208371, -1.0403961422326178, -1.0431701271177827, -0.9612031790195649, -0.7960322951142503, -0.5542841612571154, -0.24742557019810374, 0.10875886768906402, 0.49493958395252663, 0.8892292212738693, 1.2683353276729563, 1.6088195949576418, 1.8883974159193953, 2.0872077213839995, 2.1889829815630777, 2.182053024203691, 2.060123832934324, 1.8227834301144936, 1.4757008063038841, 1.0304999421799736, 0.5043084426777046, -0.08100177050362363, -0.6998468732246182, -1.3241859623446013, -1.9249341831390954, -2.47345992043001, -2.9430856041388673, -3.310509845611756, -3.5570713728251033, -3.669782525659281, -3.6420716008047966, -3.4741885423626835, -3.1732465754482386, -2.752892405493004, -2.2326184487051295, -1.6367510370383132, -0.9931674632283901, -0.3318109681140135, 0.3169146773745926, 0.9237812890869459, 1.4623103862042441, 1.9101949579774022, 2.250486195706399, 2.472475141815289, 2.572216171332058, 2.5526595932459677, 2.4233832976585297, 2.199936975217329, 1.9028356064565342, 1.556260263068108, 1.1865424620976803, 0.8205222094041387, 0.48387853714182133, 0.19953415521258952, -0.013767485094284071, -0.14262379091715233, -0.17979933556781674, -0.12466267189930931, 0.016797136158476746, 0.23237934804426583, 0.5044843841311445, 0.8112837374873421, 1.128176951283052, 1.4294465459723198, 1.6900079159466208, 1.8871435644748162, 2.002110211118478, 2.02151347554808, 1.9383577675758155, 1.7526980160270291, 1.4718438712261288, 1.1100946002664527, 0.6880123860771995, 0.2312713084553566, -0.2308529488915346, -0.6672634591041915, -1.0469843276647546, -1.341144311054531, -1.524876240602022, -1.5790096653837136, -1.4914449663073726, -1.2581153792151618, -0.8834678751612675, -0.3804232295102215, 0.2301919275091745, 0.9207147788465223, 1.6581589937009007, 2.4060824842506743, 3.1266982688105505, 3.783099209907922, 4.341458182192077, 4.7730647910599595, 5.0560682881066965, 5.176813411161577, 5.1306805439121375, 4.922372356485515, 4.565624039441637, 4.082351155087754], 'positive_zeros': ['1.26094887772972580207168534305298', '2.40265884343944723895058450400121', '3.72466989013489869440663708524527', '5.23051108084831153486045570307178', '5.86380711965561486322716731347219', '6.71657921466068649530501536807932', '7.904523949423743499712643620828016', '8.965550391680154665799488317946319', '9.680694201042961202167672155934875', '10.35662430577431868338505179068730'], 'prelabel': '2-24e2-4.3-c2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.961674295945226, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c2-0', 'trace_hash': 342354869520283642, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.26094887772972580207168534305', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.40265884343944723895058450400', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.72466989013489869440663708525', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 15.694863227153103, 'bad_primes': [2, 3], 'central_character': '4.3', 'conductor': 576, 'conductor_radical': 6, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 39, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 70, 0, 0, 0, -80, 0, 0, 0, 0, 0, 0, 0, 49, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 22, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, 110, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 128, 0, 0, 0, 160, 0, 0, 0, 0, 0, 0, 0, -130, 0, 0, 0], 'euler11': [1, 0, -121], 'euler13': [1, -10, 169], 'euler17': [1, -16, 289], 'euler19': [1, 0, -361], 'euler2': [1, 0, 0], 'euler23': [1, 0, -529], 'euler29': [1, 40, 841], 'euler3': [1, 0, 0], 'euler31': [1, 0, -961], 'euler37': [1, -70, 1369], 'euler41': [1, 80, 1681], 'euler43': [1, 0, -1849], 'euler47': [1, 0, -2209], 'euler5': [1, -8, 25], 'euler53': [1, -56, 2809], 'euler59': [1, 0, -3481], 'euler61': [1, -22, 3721], 'euler67': [1, 0, -4489], 'euler7': [1, 0, -49], 'euler71': [1, 0, -5041], 'euler73': [1, -110, 5329], 'euler79': [1, 0, -6241], 'euler83': [1, 0, -6889], 'euler89': [1, -160, 7921], 'euler97': [1, 130, 9409], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -8, 25], [1, 0, -49], [1, 0, -121], [1, -10, 169], [1, -16, 289], [1, 0, -361], [1, 0, -529], [1, 40, 841], [1, 0, -961], [1, -70, 1369], [1, 80, 1681], [1, 0, -1849], [1, 0, -2209], [1, -56, 2809], [1, 0, -3481], [1, -22, 3721], [1, 0, -4489], [1, 0, -5041], [1, -110, 5329], [1, 0, -6241], [1, 0, -6889], [1, -160, 7921], [1, 130, 9409]], 'index': 12, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/576/3/g/c', 'ModularForm/GL2/Q/holomorphic/576/3/g/c/127/1'], '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': '2-24e2-4.3-c2-0-12', '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': '2-24e2-4.3-c2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.961674295945226, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2-0', 'trace_hash': 342354869520283642, 'z1': {'__RealLiteral__': 0, 'data': '1.26094887772972580207168534305', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 24555289
{'Lhash': '1598442601711199158513848077217', 'Lhash_array': ['1598442601711199158513848077217'], 'label': '2-24e2-4.3-c2-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/576/3/g/c/127/1'}
-
id: 23595548
{'Lhash': '1598442601711199158513848077217', 'Lhash_array': ['1598442601711199158513848077217'], 'label': '2-24e2-4.3-c2-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/576/3/g/c'}