-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '924734475087978527532409392353', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-10.372281323269014, 0.0], 'a6': [0.0, 0.0], 'a7': [5.116843969807043, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 76.46647536743987, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1296.1', 'coefficient_field': 'CDF', 'conductor': 1296, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [10.372281323269014, 0], [125.0, 0]], [[1.0, 0], [-5.116843969807043, 0], [343.0, 0]], [[1.0, 0], [-55.978250586152114, 0], [1331.0, 0]], [[1.0, 0], [-37.584219849035215, 0], [2197.0, 0]], [[1.0, 0], [23.64946809057887, 0], [4913.0, 0]], [[1.0, 0], [39.051595728263386, 0], [6859.0, 0]], [[1.0, 0], [-71.07334514211128, 0], [12167.0, 0]], [[1.0, 0], [-28.372281323269014, 0], [24389.0, 0]], [[1.0, 0], [12.883156030192957, 0], [29791.0, 0]], [[1.0, 0], [180.1031914565268, 0], [50653.0, 0]], [[1.0, 0], [-215.48356968036342, 0], [68921.0, 0]], [[1.0, 0], [61.233687939614086, 0], [79507.0, 0]], [[1.0, 0], [61.8776004174803, 0], [103823.0, 0]], [[1.0, 0], [492.30957436958033, 0], [148877.0, 0]], [[1.0, 0], [-789.630259964586, 0], [205379.0, 0]], [[1.0, 0], [-521.0895389432465, 0], [226981.0, 0]], [[1.0, 0], [304.42943266424504, 0], [300763.0, 0]], [[1.0, 0], [-270.39148944926194, 0], [357911.0, 0]], [[1.0, 0], [925.4643615543705, 0], [389017.0, 0]], [[1.0, 0], [-1289.0349288901255, 0], [493039.0, 0]], [[1.0, 0], [-713.8341015897845, 0], [571787.0, 0]], [[1.0, 0], [-404.80425527536903, 0], [704969.0, 0]], [[1.0, 0], [-75.02730502656054, 0], [912673.0, 0]], [[1.0, 0], [-1087.8776004174804, 0], [1030301.0, 0]], [[1.0, 0], [-1091.8179077886493, 0], [1092727.0, 0]], [[1.0, 0], [1029.1547871847902, 0], [1225043.0, 0]], [[1.0, 0], [-1776.515957282634, 0], [1295029.0, 0]], [[1.0, 0], [-1615.9372930463112, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 16, 'label': '2-6e4-1.1-c3-0-16', 'leading_term': '1.95772626318150615115231888690', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1296/4/a/i/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.9577262631815062, 1.942300140199358, 1.8962439956735253, 1.820223946629983, 1.7153482020112343, 1.5831636293483071, 1.4256500672861934, 1.2452115660064478, 1.0446635901997336, 0.8272151307520283, 0.5964446488370879, 0.3562688238180631, 0.11090319539087208, -0.1351860210785662, -0.37733941370030677, -0.6107713043624029, -0.8306459277488206, -1.0321622609462278, -1.210646486488201, -1.3616506439420535, -1.481055604349205, -1.5651761043463288, -1.6108652192887716, -1.6156153537148794, -1.577652598979928, -1.4960211666899272, -1.3706545658529194, -1.2024302623718954, -0.9932047497408089, -0.7458262743019618, -0.4641228980105025, -0.1528641428263322, 0.1823048645530999, 0.5349570539205198, 0.8980043275862349, 1.2638442627518283, 1.6245301816741264, 1.9719612189740103, 2.2980880952115004, 2.5951294533470928, 2.8557928666739003, 3.0734940194985256, 3.242567129612754, 3.358459455334802, 3.4179027355354634, 3.4190546680692253, 3.3616040520429995, 3.2468340050031523, 3.077638710090953, 2.858490432640182, 2.595355041912605, 2.295555942428868, 1.9675881114342375, 1.6208857963706977, 1.2655492834688473, 0.9120379351368304, 0.5708383362944369, 0.2521178146884179, -0.034625263042518346, -0.28090223373518747, -0.4795533566623071, -0.6250330224001246, -0.7136490194516255, -0.7437449713105135, -0.7158165836409324, -0.6325543220479165, -0.4988075266455656, -0.32146769139392944, -0.10927160646832819, 0.12747182302611867, 0.37722412569821545, 0.6276191784948649, 0.8659116688705818, 1.0794568261671769, 1.2562041636521715, 1.385186582312986, 1.4569854792436356, 1.4641525463479537, 1.40156978044873, 1.2667308637003716, 1.0599294895625508, 0.7843433456136173, 0.4460062266303887, 0.053665013397678464, -0.3814771407506801, -0.8461253020415698, -1.3253540736289762, -1.803150383527433, -2.2630183332582994, -2.6886232876614797, -3.06444980361093, -3.3764463940160576, -3.6126296221310725, -3.7636206952496503, -3.8230896026179773, -3.7880848930358226, -3.6592313314959455, -3.4407827756516247, -3.140523485535671, -2.769517492704227, -2.3417123404907803, -1.873410172345973, -1.382625484166909, -0.8883545635913696, -0.4097864241341753, 0.03451135575945962, 0.4273962759808971, 0.7539077849065187, 1.0019421320207036, 1.1628126424470624, 1.2316671494360272, 1.2077400901917403, 1.094423795425759, 0.8991514966372816, 0.6330931910811948, 0.31067435154750217, -0.05106387234196182, -0.4332362695302542, -0.8159832914446938, -1.1793995688518868, -1.5044780334077583, -1.7740245703600315, -1.9734983943881348, -2.0917358191867024, -2.1215197366788883, -2.0599637762989986, -1.9086885136298364, -1.6737768773053787, -1.3655066160195157, -0.9978688218623213, -0.5878925096039349, -0.15480555791779563, 0.2809286229216004, 0.6986520278698578, 1.0785788125866906, 1.4028334874986297, 1.6564063143087278, 1.8279746303844082, 1.9105445400641712, 1.9018756646830486, 1.8046620806160638, 1.6264547145207218, 1.3793237179296551, 1.0792730408014493, 0.7454328506963328, 0.3990678765791251, 0.062450498906678475, -0.24234416623989177, -0.4946583539528721, -0.6764217103063465, -0.7732072116326859, -0.7751134037360109, -0.6774213383865156, -0.48098550982194443, -0.19233151795495496, 0.17655155569364656, 0.6087197636062212, 1.0830631107167326, 1.575338014431363, 2.059392683799568, 2.5085229736200145, 2.896887703255783, 3.2009075806805787, 3.400571108700454, 3.4805743223114853, 3.4312288293013036, 3.249084079135638, 2.9372245206419425, 2.50521957818186, 1.9687232652148197, 1.3487397323216688, 0.6705900212003189, -0.03736732624775498, -0.7451944042314796, -1.422932208224482, -2.0421734543264325, -2.5775621768341233, -3.008135117653978, -3.318427651499528, -3.4992793218853566, -3.548290377146505, -3.4699001265378517, -3.2750794128149634, -2.9806518018259354, -2.6082799255188043, -2.1831734831252314, -1.7325924810795352, -1.2842322999213844, -0.8645852583891565, -0.4973759187110616, -0.2021641777664802, 0.0067987069872323756, 0.12139017764553697, 0.140060235020341, 0.06786898124164938, -0.08388789765394113, -0.2984463214794149, -0.5546899208906649, -0.8285492008983228, -1.0945994788789686, -1.3277597657414524, -1.504987024908356, -1.6068589175527812, -1.6189434343890559, -1.5328655279247478, -1.3469983938112127, -1.0667294285580626, -0.7042768116558993, -0.2780605706465769, 0.18833982367299412, 0.6675825846400152, 1.1302332126024293, 1.5466055737666387, 1.8886607312630455, 2.131844035410107, 2.2567426714838894, 2.2504550576247855, 2.1075797485437295, 1.830753938146834, 1.4306989584518017, 0.9257606966076783, 0.34096470887039954, -0.29336301255614633, -0.9433301775598631, -1.5734638822162086, -2.148826756304932, -2.637132216732478, -3.010725443226973, -3.2483031969179654, -3.3362603708693306, -3.2695733860037515, -3.05215891694541, -2.696679215081284, -2.2238004344951343, -1.6609456114645729, -1.0406170021295646, -0.3983911493761501, 0.22928761902538528, 0.807375129237767, 1.3044111491854027, 1.6944774529014803, 1.9588019552569453, 2.08690268478424, 2.0771946150868574, 1.937017070884147, 1.6820773326225913, 1.3353447011902924, 0.9254660789699543, 0.48480658413888905, 0.04724460172731109, -0.3541318454702657, -0.6892727447509087, -0.9332056797551701, -1.0677281805066328, -1.0826361559509814, -0.9764024064280933, -0.7562560944984892], 'positive_zeros': ['0.72948687510697993171544515694877', '1.84358428810393171001652714222434', '3.39093446666749378375077464386846', '4.01200807030069287981224628237525', '4.87079450314752286688131428848667', '6.14756749502821721631074983438235', '6.78886962675928966258991808274181', '7.69649474140189380710520573022797', '8.566084606082056203575166443185321', '9.055412383583005801301726148389926'], 'prelabel': '2-6e4-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.744511156573584, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.72948687510697993171544515695', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.84358428810393171001652714222', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.39093446666749378375077464387', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 76.46647536743987, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 1296, 'conductor_radical': 6, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1296/4/a/i/1/1'], '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': '2-6e4-1.1-c3-0-16', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-6e4-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.744511156573584, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.72948687510697993171544515695', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '924734475087978527532409392353', 'Lhash_array': ['924734475087978527532409392353'], 'label': '2-6e4-1.1-c3-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1296/4/a/i/1/1'}