-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1883615875533018455440050031666', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.745571016235191, -0.5125458956719999], 'a4': [0.0, 0.0], 'a5': [-0.8412535328311812, -0.5406408174555976], 'a6': [0.0, 0.0], 'a7': [0.28173255684142967, 1.9594929736144975], 'a8': [0.0, 0.0], 'a9': [1.9430613447189637, -1.2487297024951005], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9182796232447245, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.8412535328311812, 0.5406408174555976]]], [23, [[1.0, 0], [-0.9096319953545183, 0.41541501300188644]]]], 'bad_primes': [2, 5, 23], 'central_character': '1840.1039', 'coefficient_field': 'CDF', 'conductor': 1840, 'conductor_radical': 230, 'conjugate': '2079697733152080817653996932802', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.745571016235191, 0.5125458956719999], [0.8412535328311812, -0.5406408174555976]], [[1.0, 0], [0.8412535328311812, 0.5406408174555976]], [[1.0, 0], [-0.28173255684142967, -1.9594929736144975], [-0.9594929736144974, 0.28173255684142967]], [[1.0, 0], [0, 0], [0.6548607339452851, 0.7557495743542583]], [[1.0, 0], [0, 0], [0.9594929736144974, 0.28173255684142967]], [[1.0, 0], [0, 0], [0.14231483827328514, -0.9898214418809327]], [[1.0, 0], [0, 0], [0.14231483827328514, 0.9898214418809327]], [[1.0, 0], [-0.9096319953545183, 0.41541501300188644]], [[1.0, 0], [1.1018078118877825, 1.2715539987223625], [-0.14231483827328514, 0.9898214418809327]], [[1.0, 0], [0, 0], [-0.8412535328311812, -0.5406408174555976]], [[1.0, 0], [0, 0], [-0.41541501300188644, 0.9096319953545183]], [[1.0, 0], [-0.23944572094339864, -0.1538824210002601], [0.41541501300188644, 0.9096319953545183]], [[1.0, 0], [1.4502728128101159, -0.42583851982929477], [0.8412535328311812, -0.5406408174555976]], [[1.0, 0], [-1.081281634911195, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0.9594929736144974, -0.28173255684142967]], [[1.0, 0], [0, 0], [0.9594929736144974, 0.28173255684142967]], [[1.0, 0], [1.2566685458330675, 0.3689911778989208], [0.8412535328311812, 0.5406408174555976]], [[1.0, 0], [0.23407186752667444, 0.5125458956719999], [-0.6548607339452851, 0.7557495743542583]], [[1.0, 0], [0, 0], [0.6548607339452851, -0.7557495743542583]], [[1.0, 0], [0, 0], [0.14231483827328514, 0.9898214418809327]], [[1.0, 0], [0, 0], [0.9594929736144974, 0.28173255684142967]], [[1.0, 0], [-0.4740170175128286, 0.3046322396692123], [0.41541501300188644, -0.9096319953545183]], [[1.0, 0], [0.7971755722185702, -0.23407186752667444], [0.8412535328311812, -0.5406408174555976]], [[1.0, 0], [0, 0], [-0.41541501300188644, -0.9096319953545183]], [[1.0, 0], [1.6143537075597825, -1.0374821311956879], [0.41541501300188644, -0.9096319953545183]], [[1.0, 0], [-0.44918062442533513, 0.9835683711044663], [-0.6548607339452851, -0.7557495743542583]], [[1.0, 0], [1.0374821311956879, 0.3046322396692123], [0.8412535328311812, 0.5406408174555976]], [[1.0, 0], [-0.5440779606126109, -0.6278994385130887], [-0.14231483827328514, 0.9898214418809327]], [[1.0, 0], [0, 0], [0.6548607339452851, -0.7557495743542583]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-1840-460.119-c0-0-0', 'leading_term': '1.8668594093448265686821403377973', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1840/1/bq/a/1039/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.8668594093448265, 1.8775548888806939, 1.9064187754023403, 1.9512068789250674, 2.008529408716324, 2.074249384668975, 2.1438600430914976, 2.2127782399440385, 2.2765414922874703, 2.330927018624851, 2.372020375290239, 2.396257895968063, 2.400459548576981, 2.381861600033917, 2.3381531319958633, 2.2675169809876388, 2.1686736165983884, 2.040925345831494, 1.8841976905565847, 1.6990746063199749, 1.4868242656121842, 1.2494123469151324, 0.9895001159517917, 0.7104250384529915, 0.4161622129236787, 0.1112655476197733, -0.1992116829458952, -0.5098164945686995, -0.8148148409646194, -1.1083271958731895, -1.3844781852067554, -1.6375565933999245, -1.8621813453948868, -2.0534684450493743, -2.2071933653810096, -2.3199430674794237, -2.389251701347442, -2.4137141366778363, -2.3930718014396293, -2.328265879995718, -2.2214537399619645, -2.0759855076434683, -1.8963389743702714, -1.688012458166772, -1.457376824021689, -1.211489528805869, -0.9578752423047344, -0.7042792358991524, -0.45840125281249017, -0.22761890464881393, -0.018710705841721305, 0.1624104068058593, 0.31094187713117244, 0.42340355527885176, 0.49780640854111713, 0.5337684267411803, 0.5325697573097798, 0.49714108281768044, 0.4319816338342792, 0.34300594128775835, 0.23732138308710202, 0.12294165950459514, 0.008444415852338743, -0.09741581579958494, -0.18612550176173934, -0.24984469205811435, -0.281836447858188, -0.27687417967009326, -0.23160764612372153, -0.14486886801341445, -0.01790057774864306, 0.1455079490966741, 0.33898978479149594, 0.5536822764142705, 0.7784259077417244, 1.0000791140772864, 1.203942909914942, 1.3742839694669187, 1.4949397517007348, 1.5499846258803034, 1.5244319690571686, 1.4049440974527232, 1.1805198570375832, 0.8431288953162033, 0.38826217925236683, -0.1846297298625027, -0.8718357908881762, -1.6652414653002408, -2.5523581933554387, -3.5165331556189785, -4.5373395592728585, -5.591139730755519, -6.651805282728134, -7.691570926550934, -8.681991499351138, -9.5949658325943, -10.403786540547488, -11.084171936043349, -11.615235304716252, -11.980347823386847, -12.167854537114879, -12.171607956671112, -11.991290845848166, -11.632508378833299, -11.106639713049782, -10.430449715290552, -9.625472610898221, -8.717190170810797, -7.734037169535607, -6.706275712091044, -5.664787154503901, -4.639835313690414, -3.6598571546308936, -2.7503369458877835, -1.9328169090015257, -1.2240917133211344, -0.6356259883078142, -0.17322368123057258, 0.16303395394855372, 0.3785781182863486, 0.4838800028797004, 0.4937395343399291, 0.42637124413522665, 0.3023340279354729, 0.14336016944616517, -0.028855152654434613, -0.19383996273790352, -0.33344396378943303, -0.4327902745035723, -0.48102871203754294, -0.4718492689560027, -0.40372726233015627, -0.2798862752045766, -0.10798069199692775, 0.10048450578468215, 0.3309638605242369, 0.5668650828453232, 0.7906686553759853, 0.9851077609866473, 1.134338471064523, 1.2250296884491036, 1.247306012627787, 1.1954843704994453, 1.0685565852647692, 0.8703844641297092, 0.6095906987514538, 0.2991469570670024, -0.04432104200472516, -0.4014740328737883, -0.7513920496314963, -1.0728334296196906, -1.3455445543433957, -1.5515400490551459, -1.6762730979378593, -1.7096204009146705, -1.64661594285162, -1.4878817110428235, -1.2397210475737437, -0.9138604807692593, -0.5268474739239573, -0.09913326329120557, 0.3461095157919823, 0.784366710624296, 1.191278053527603, 1.544156543419003, 1.8234361836307313, 2.0139542700463307, 2.1059822087079536, 2.0959322922959074, 1.9866863111157982, 1.7875143106460671, 1.5135769438046691, 1.1850311985145006, 0.825785181489389, 0.4619714529245305, 0.12022855741784111, -0.17410451183124118, -0.3987672659086804, -0.5362144710910507, -0.575000399665352, -0.5108127883172444, -0.3470778355937505, -0.09508230513334619, 0.22641224892499612, 0.592056663748424, 0.9712642513397588, 1.3299546836119207, 1.632595415635564, 1.8444224847261594, 1.933707439636043, 1.8739300476255227, 1.6457179822403702, 1.238425060635729, 0.6512383649127242, -0.10626921476982343, -1.0141923027817272, -2.0429672573885664, -3.154644182785372, -4.304695997122378, -5.444269100087722, -6.522750659506503, -7.490505211502423, -8.301619729457196, -8.916492618524197, -9.30410867682088, -9.44385871677807, -9.326788387425477, -8.956194291725657, -8.347524731890323, -7.527584909418327, -6.533089466806737, -5.40864611052716, -4.204290022884151, -2.972717453589241, -1.766386322213037, -0.634660483178152, 0.37882818746177305, 1.2384394802463303, 1.918270130945796, 2.40328167508962, 2.689747855011328, 2.785002753638514, 2.706516305159056, 2.48036754064412, 2.1392249094840725, 1.7199746115665346, 1.2611598985368864, 0.8004052124532721, 0.37199803877054854, 0.004788489596374153, -0.2794572377749711, -0.4671466252465709, -0.5533312249124, -0.5415396210156991, -0.4430005332034718, -0.27532709072177997, -0.06077147723156829, 0.17581074065008068, 0.4091274392307276, 0.6155806540599168, 0.7751982060468035, 0.8732196638290721, 0.9012174445232792, 0.8576702234144059, 0.7479485219465796, 0.5837182106571884, 0.3818132651468842, 0.162670993380151, -0.05154210759757157, -0.23896044648292974, -0.3800384274274977, -0.4593909490210737, -0.4673002285271667, -0.40075872425828607, -0.26395340922377547, -0.06814017751900249, 0.16909449776072555], 'positive_zeros': ['1.48591092466164564149388624913753', '2.93532223533742925427839506041146', '3.63725824264034833447181907532439', '4.10863810968350020015461460644719', '4.96284092967055379055375293542800', '6.88295233931080816453108398447036', '7.31441074379581097551158192448277', '7.82435363833509327427360210777796', '8.605919990283271892872491157245916', '9.388133441136257108482546120307158'], 'prelabel': '2-1840-460.119-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9582690766401285, 'root_angle': 0.053431193478514404, 'root_number': '0.98594471963910370753479931321941 + 0.16707187021090410932897957177277*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0267155967392572', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.48591092466164564149388624914', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.93532223533742925427839506041', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.63725824264034833447181907532', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.9182796232447245, 'bad_primes': [2, 5, 23], 'central_character': '460.119', 'conductor': 1840, 'conductor_radical': 230, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1840/1/bq/a/1039/2'], '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': '2-1840-460.119-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1840-460.119-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9582690766401285, 'root_angle': 0.026715596739257202, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.48591092466164564149388624914', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1883615875533018455440050031666', 'Lhash_array': ['1883615875533018455440050031666'], 'label': '2-1840-460.119-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1840/1/bq/a/1039/2'}