-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1345860506635362846136783578475', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [2.182549750066737, 0.0], 'a6': [0.0, 0.0], 'a7': [4.852497860358367, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.10698696055516, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 11, 13], 'central_character': '5148.1', 'coefficient_field': 'CDF', 'conductor': 5148, 'conductor_radical': 858, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.182549750066737, 0], [5.0, 0]], [[1.0, 0], [-4.852497860358367, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [3.9208698820329, 0], [17.0, 0]], [[1.0, 0], [2.4873983602248937, 0], [19.0, 0]], [[1.0, 0], [-6.103419632099637, 0], [23.0, 0]], [[1.0, 0], [-6.669948110291631, 0], [29.0, 0]], [[1.0, 0], [8.024289514132537, 0], [31.0, 0]], [[1.0, 0], [1.2509217717412695, 0], [37.0, 0]], [[1.0, 0], [-2.8524978603583677, 0], [41.0, 0]], [[1.0, 0], [1.9208698820329002, 0], [43.0, 0]], [[1.0, 0], [-8.955917492458005, 0], [47.0, 0]], [[1.0, 0], [-7.339896220583261, 0], [53.0, 0]], [[1.0, 0], [-1.133056956383987, 0], [59.0, 0]], [[1.0, 0], [-4.9559174924580045, 0], [61.0, 0]], [[1.0, 0], [-3.04949279368275, 0], [67.0, 0]], [[1.0, 0], [10.295813713041266, 0], [71.0, 0]], [[1.0, 0], [-2.12229886009142, 0], [73.0, 0]], [[1.0, 0], [-10.285969382166375, 0], [79.0, 0]], [[1.0, 0], [6.2068392641992745, 0], [83.0, 0]], [[1.0, 0], [4.30041456542402, 0], [89.0, 0]], [[1.0, 0], [1.2509217717412695, 0], [97.0, 0]], [[1.0, 0], [-16.127709146232174, 0], [101.0, 0]], [[1.0, 0], [-4.472953176967248, 0], [103.0, 0]], [[1.0, 0], [2.4729531769672484, 0], [107.0, 0]], [[1.0, 0], [15.827294580808156, 0], [109.0, 0]], [[1.0, 0], [0.8380526771007222, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 25, 'label': '2-5148-1.1-c1-0-25', 'leading_term': '3.2298367750444505147979883904979', '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/5148/2/a/r/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [3.2298367750444505, 3.2220364884863106, 3.198564502806178, 3.159216548694237, 3.103681877877712, 3.031585573222892, 2.9425435572389644, 2.83622661748409, 2.7124293732253784, 2.57114003594642, 2.412607009456222, 2.237398756456782, 2.046453850469067, 1.8411186718023105, 1.6231707509195246, 1.394826289692031, 1.158730894612832, 0.917933040541688, 0.6758402582131476, 0.43615851286923873, 0.20281572123702615, -0.020129158866778022, -0.22858954164288245, -0.418564719800372, -0.5862605895998628, -0.7282142901388777, -0.8414190782469513, -0.9234454613936146, -0.9725544074882225, -0.9877983611691462, -0.9691058375607944, -0.9173455495298819, -0.8343663618692632, -0.7230098591106544, -0.587092960561701, -0.43135880817353983, -0.26139507496995057, -0.08351987250099024, 0.09536345263573247, 0.2679401842141643, 0.42668314682282066, 0.5640719097396244, 0.6728264759408965, 0.7461487148709187, 0.7779640330134131, 0.7631552224138689, 0.6977801217263655, 0.5792646982469977, 0.4065634356156265, 0.18027950338905704, -0.09726190676329627, -0.4219924784363556, -0.7881358034177667, -1.1883007070277005, -1.6136330794491813, -2.054024345414973, -2.4983725556388756, -2.934889944647611, -3.351448754451953, -3.7359552573020935, -4.076740308010796, -4.362953496749927, -4.58494712829497, -4.734635883029769, -4.805818163092629, -4.7944458202309415, -4.698830206184466, -4.5197742655939885, -4.26062266646858, -3.927224672255344, -3.527807518922618, -3.0727613669455236, -2.5743403318979623, -2.0462875262342815, -1.5033953288585833, -0.9610150961478168, -0.43453309993977485, 0.061168503671211544, 0.5122455182318093, 0.9063996102518155, 1.233339740839616, 1.4851776671506667, 1.6567399750163139, 1.7457818314654372, 1.7530911039771742, 1.6824755698946376, 1.540630489533289, 1.3368886671674372, 1.0828600804592368, 0.7919730118534595, 0.4789331500999209, 0.15912113508249562, -0.15204770347239768, -0.43977528813337724, -0.6905169624920311, -0.8925742518225122, -1.0366176051664526, -1.1161147412441825, -1.1276436119290256, -1.0710734415821797, -0.9496026404477175, -0.7696484197672417, -0.5405894088858753, -0.27436921291886773, 0.015024643485840487, 0.3121858686755465, 0.600992794138761, 0.8653598079699564, 1.0900035459038173, 1.2611888970624991, 1.36741978918987, 1.4000412522975363, 1.3537224075479048, 1.226794699919808, 1.0214257226748236, 0.7436161314380478, 0.4030151155107487, 0.012558332578682548, -0.4120592669790086, -0.8530551042706418, -1.291347036619838, -1.707423383492327, -2.082255582342525, -2.3982109968001515, -2.6399222099699697, -2.795070025130993, -2.8550403892787544, -2.8154204732353576, -2.6763060039320004, -2.442400370612666, -2.1228956503214365, -1.7311360800642899, -1.2840751516359619, -0.8015478985706048, -0.30538955679631347, 0.1815598928197465, 0.636519206429819, 1.0378468280480104, 1.366086701694683, 1.6049268684192648, 1.7420219327586668, 1.7696361876230131, 1.6850722150291257, 1.4908597868945748, 1.194691417224831, 0.8091034141779031, 0.35091413082502904, -0.15955633635222774, -0.6994491587396487, -1.2444666431087053, -1.7700552338711728, -2.252612667758433, -2.6706579849308074, -3.0059039279620627, -3.244175261997649, -3.376123591625715, -3.397699033455212, -3.3103511748888828, -3.1209455217469726, -2.8413964164021346, -2.488032427979571, -2.0807246782661717, -1.6418216821925522, -1.19494531381936, -0.7637108157598046, -0.3704388420314316, -0.03492901516696284, 0.22663777119655082, 0.4026070214141358, 0.48651639724140927, 0.47748009912390477, 0.38026720709475237, 0.20506575310742675, -0.03305851490535001, -0.3149827101162399, -0.6185848804055336, -0.9199838923749962, -1.1948944478892698, -1.4200230857539635, -1.5744275638800513, -1.6407628473962215, -1.60634208499844, -1.4639502348658113, -1.2123609600051426, -0.8565233893861395, -0.4074034878221225, 0.11851589595711677, 0.700052806348217, 1.3124198665401505, 1.9285356180738575, 2.5204819801414984, 3.061026895446611, 3.525126325509238, 3.8913197167408398, 4.142937972244494, 4.269052639735396, 4.26510898840978, 4.1332031621642304, 3.8819837056107227, 3.5261793336208536, 3.0857766165349596, 2.5848920052693263, 2.0504010832376376, 1.5104029757146378, 0.9926085224579172, 0.5227464169047914, 0.12308161377419952, -0.18886519562930046, -0.40131911450996605, -0.5089113406559512, -0.5129556466328443, -0.4213209506277405, -0.24790393663239596, -0.011729859107043345, 0.264267483512048, 0.5547155033434401, 0.8334350790015468, 1.0751370046824238, 1.257079044653479, 1.3605809497960497, 1.3723020115130837, 1.2851988896611746, 1.0990998540968508, 0.8208541887892955, 0.46404101082623594, 0.04824863944370756, -0.4020377150968892, -0.8588774287691641, -1.2925612955802932, -1.6734434232167703, -1.9738073403266327, -2.169651572063366, -2.242283072721718, -2.1796169834471835, -1.9770976997705456, -1.6381782693966571, -1.1743214168071345, -0.6045144428177028, 0.045679884620814626, 0.7454853934282181, 1.4606102789934607, 2.1551815741890072, 2.7938013947274745, 3.3436010581697637, 3.7761677938102136, 4.069225172159419, 4.207962293217663, 4.185927410202003, 4.005427820445572, 3.677407950603011, 3.2208097484407787, 2.6614517579600196, 2.030493554139817, 1.362578600455056, 0.693769341744676, 0.05940206951326638, -0.5080051592649188], 'positive_zeros': ['1.06169673756558190021066408242730', '1.90252735602972131921879023584991', '2.52226535648290312354664401309716', '3.90366345384859803153865845006535', '4.64673023876810134162869466458193', '5.27866998927765262082192536507254', '5.94295837639668339578029734840897', '6.83626953472287045370225459176510', '7.44938950717695252164650908935952', '8.435670281935510611843415948311309'], 'prelabel': '2-5148-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.411473072590663, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06169673756558190021066408243', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.90252735602972131921879023585', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.52226535648290312354664401310', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 41.10698696055516, 'bad_primes': [2, 3, 11, 13], 'central_character': '1.1', 'conductor': 5148, 'conductor_radical': 858, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5148/2/a/r/1/3'], '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': '2-5148-1.1-c1-0-25', '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': '2-5148-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.411473072590663, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.06169673756558190021066408243', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1345860506635362846136783578475', 'Lhash_array': ['1345860506635362846136783578475'], 'label': '2-5148-1.1-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5148/2/a/r/1/3'}