-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '223546338347949026771479361941', 'a10': [2.2016438827302496, 0.39085062829228107], 'a2': [0.0, -1.0], 'a3': [-1.2939724686552445, -1.2939724686552445], 'a4': [-1.0, 0.0], 'a5': [-0.39085062829228107, 2.2016438827302496], 'a6': [-1.2939724686552445, 1.2939724686552445], 'a7': [-2.6708733584255624, -2.6708733584255624], 'a8': [0.0, 1.0], 'a9': [0.0, 0.3487294992754958], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.9544648747873756, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [0.39085062829228107, -2.2016438827302496]]], [37, [[1.0, 0], [0.7709434346800754, 6.033709159424548]]]], 'bad_primes': [2, 5, 37], 'central_character': '370.327', 'coefficient_field': 'CDF', 'conductor': 370, 'conductor_radical': 370, 'conjugate': '2240861289320213348291637268675', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0]], [[1.0, 0], [1.2939724686552445, 1.2939724686552445], [0, 3.0]], [[1.0, 0], [0.39085062829228107, -2.2016438827302496]], [[1.0, 0], [2.6708733584255624, 2.6708733584255624], [0, 7.0]], [[1.0, 0], [0, -1.2958671734302252], [-11.0, 0]], [[1.0, 0], [0, -6.926119226129563], [-13.0, 0]], [[1.0, 0], [4.850710662054962, 0], [17.0, 0]], [[1.0, 0], [-4.695551505697151, -4.695551505697151], [0, 19.0]], [[1.0, 0], [0, 3.339586850910939], [-23.0, 0]], [[1.0, 0], [3.739550714412916, -3.739550714412916], [0, -29.0]], [[1.0, 0], [0.14691626526485949, 0.14691626526485949], [0, 31.0]], [[1.0, 0], [0.7709434346800754, 6.033709159424548]], [[1.0, 0], [0, -6.383513709360278], [-41.0, 0]], [[1.0, 0], [0, -2.5119527494157183], [-43.0, 0]], [[1.0, 0], [2.936860412942373, 2.936860412942373], [0, 47.0]], [[1.0, 0], [1.3097067319975244, -1.3097067319975244], [0, -53.0]], [[1.0, 0], [4.700388009009419, 4.700388009009419], [0, 59.0]], [[1.0, 0], [7.819654925326217, 7.819654925326217], [0, 61.0]], [[1.0, 0], [3.107893497986888, -3.107893497986888], [0, -67.0]], [[1.0, 0], [5.591243163903329, 0], [71.0, 0]], [[1.0, 0], [0.1349803295720994, 0.1349803295720994], [0, 73.0]], [[1.0, 0], [10.808036632095297, 10.808036632095297], [0, 79.0]], [[1.0, 0], [8.746517680526184, -8.746517680526184], [0, -83.0]], [[1.0, 0], [3.8382941656700718, -3.8382941656700718], [0, -89.0]], [[1.0, 0], [-13.251378913841503, 0], [97.0, 0]], [[1.0, 0], [0, -13.788957062894282], [-101.0, 0]], [[1.0, 0], [-10.683262733203511, 0], [103.0, 0]], [[1.0, 0], [7.62668817335341, 7.62668817335341], [0, 107.0]], [[1.0, 0], [-3.393948990031095, -3.393948990031095], [0, 109.0]], [[1.0, 0], [4.289554943761699, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-370-185.142-c1-0-0', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/370/2/g/e/327/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.24349421267698243, 0.07533119746850692, -0.1157873638915225, -0.3369243286418942, -0.5947166872061834, -0.89425987151687, -1.2381649329932656, -1.62580383305203, -2.052731802955667, -2.510292368886895, -2.9854402137954366, -3.4608383937975082, -3.9152913432330703, -4.324562952472414, -4.6626019795813685, -4.903158238736912, -5.021726089043556, -4.997701268422101, -4.816588602238247, -4.4720579121809685, -3.967620250944759, -3.317692688096345, -2.547842247244825, -1.6940509182299606, -0.8009234205723303, 0.08113678165709179, 0.8996382504897382, 1.6043312726788446, 2.15177737088789, 2.509696292369867, 2.6605886489846986, 2.60414923763265, 2.3580664306280923, 1.9569465411435718, 1.449299549947887, 0.8927557354805424, 0.34792524678156245, -0.12846740777908888, -0.4903783295004469, -0.7082964762530622, -0.7733143997455829, -0.6987321796020942, -0.5187767891756218, -0.2843768191885256, -0.05633962319850812, 0.10331925116144311, 0.1408064294355036, 0.01943819901255932, -0.2733618321349164, -0.7221488471392911, -1.2834710077667544, -1.8901414694036927, -2.4594802403266303, -2.9046026352449683, -3.1472768968465226, -3.130497485936525, -2.8288017229087745, -2.25454183792736, -1.4588130939235768, -0.5264821412727554, 0.4343390900287483, 1.3071039062633438, 1.9838594181115927, 2.38190479300411, 2.4573567786281076, 2.2132122382852852, 1.7002424839848922, 1.0101421467901146, 0.26162757423845767, -0.4185696541636173, -0.9168606724372032, -1.152588228866114, -1.0929364363456058, -0.7600839179368957, -0.22891373102480186, 0.3848287480697966, 0.9443305975616556, 1.31632275094783, 1.3963019306725264, 1.1297857372805296, 0.5254711984882784, -0.34259037335575343, -1.3448278606239006, -2.3168459627913993, -3.0877367517755907, -3.511145047752702, -3.493429197733405, -3.013489754851453, -2.1301189189155383, -0.9748730604728402, 0.26887312901181887, 1.3973552189749223, 2.222818494636767, 2.608157256205337, 2.493095615715235, 1.906559371700096, 0.9623556971931053, -0.16156866383097163, -1.2567750231712702, -2.1246821179759037, -2.6158510064708786, -2.6603733975422, -2.2830439978890933, -1.5998500593157032, -0.7959764615950743, -0.08928125953628144, 0.31372866848940245, 0.26066431005037594, -0.3139649962926005, -1.3728439629176314, -2.780375322129354, -4.327036108973569, -5.768837405177312, -6.87393988692698, -7.466884546401398, -7.461314917615396, -6.874449782785656, -5.820434982396073, -4.484237659019799, -3.081953362829734, -1.8163310049558061, -0.8373019675108594, -0.216075824737743, 0.06181511006958643, 0.08356892188813934, -0.020027676712839435, -0.11243101552550779, -0.08834027929091894, 0.09937744628718304, 0.4295307878516774, 0.8216693148687737, 1.1619006172737159, 1.338595493731117, 1.278372648002547, 0.9724073315120529, 0.48533446573268346, -0.05665147330880609, -0.49648183522887396, -0.6885113961074458, -0.5417038781370694, -0.05203497316360169, 0.6855109625798647, 1.4902923321011052, 2.1333853859123164, 2.3913236617228155, 2.103758585588793, 1.22068210566958, -0.17353363146462708, -1.8670780083106546, -3.5591994743703976, -4.92302296398944, -5.678987220301819, -5.661780836638377, -4.86429546249338, -3.446862091673128, -1.707907579878312, -0.021348032923267233, 1.245702388925773, 1.81607533328245, 1.5668886353028653, 0.5593946714762013, -0.9734210440757707, -2.679208602624913, -4.166601666195972, -5.094616083576113, -5.249792234131856, -4.592642368208887, -3.262444579623794, -1.539693475047779, 0.223997691217773, 1.6907178307414406, 2.614475581495784, 2.893445732909044, 2.58381041409488, 1.8728774672637991, 1.0198087870860841, 0.2806616313526777, -0.16169347810000428, -0.24390142425150807, -0.0326043052567853, 0.30297453660573564, 0.5478358166842549, 0.5107219568868225, 0.08616679193488765, -0.7089389274727635, -1.7350192689818216, -2.7661169831114076, -3.5526727921561063, -3.89287474954327, -3.691972134579249, -2.992139914550958, -1.9637369769028052, -0.8598312850676693, 0.053464793946803264, 0.5710854408401614, 0.6061503469638992, 0.21334204909798932, -0.4287399679765735, -1.071660609815971, -1.472335803500189, -1.4675219017266685, -1.0255905604751496, -0.2598159378225124, 0.6015847223015997, 1.2807625855937994, 1.5324017197796362, 1.2188544470942628, 0.3559107538490189, -0.8849625248879632, -2.219548630600511, -3.3273427481276108, -3.939833163381747, -3.915048223748855, -3.276494430103649, -2.204857017981132, -0.9847077441493188, 0.07813094884381512, 0.7440273287122019, 0.905648313505603, 0.6129065858233532, 0.04937437802818558, -0.5322988857518985, -0.8955964151070347, -0.898862048778391, -0.5420320160933855, 0.0344813952223186, 0.599652601244219, 0.9156152592125935, 0.8288977545942375, 0.33898811214813956, -0.38019283143290783, -1.0166089870175032, -1.2071157519129, -0.651530574534467, 0.7799241758425578, 2.9797015873010304, 5.60025641832492, 8.121429437341327, 9.97315506228156, 10.681664004441233, 9.998971882449453, 7.97858068185174, 4.974398960530298, 1.5610396978895118, -1.604195272898392, -3.940687184971113, -5.0820936398501315, -4.9552338921627355, -3.7801642831347935, -1.9938471402880529, -0.12134202926465255, 1.3673660324343702, 2.1740688369463332, 2.2311194090384645, 1.6892888316518506, 0.8433995060700431, 0.022719542298987358], 'positive_zeros': ['0.17634696682800565398427978326658', '3.11323308663633993505312138951818', '4.58866017228319490715324785701274', '5.53651240370616795746655242550209', '5.88629576372518561914933353708764', '7.44298557984077863744098136463548', '8.545437938584340951408709262783215', '9.297139888398845957515727925279363', '10.07904705316709307133486113117792', '11.22269931676098206194762723550537'], 'prelabel': '2-370-185.142-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7188556875978203, 'root_angle': -0.43701869673965776, 'root_number': '0.19657310343267786 - 0.9804891712848468*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.21850934837', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.17634696682800565398427978327', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.11323308663633993505312138952', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.58866017228319490715324785701', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.9544648747873756, 'bad_primes': [2, 5, 37], 'central_character': '185.142', 'conductor': 370, 'conductor_radical': 370, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/370/2/g/e/327/3'], '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': '2-370-185.142-c1-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-370-185.142-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7188556875978203, 'root_angle': -0.21850934836982888, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.17634696682800565398427978327', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '223546338347949026771479361941', 'Lhash_array': ['223546338347949026771479361941'], 'label': '2-370-185.142-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/370/2/g/e/327/3'}