-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '506819068633979778896640747864', 'a10': [19.899775163946178, -43.13984445455951], 'a2': [1.3130996367993812, 4.04130513484826], 'a3': [-2.4270509831248424, 1.7633557568774194], 'a4': [-8.135780581788667, 5.910990591189664], 'a5': [-8.208229170274892, -7.591111505454808], 'a6': [-10.313218439267766, -7.492991796737106], 'a7': [-28.285304297192386, 0.0], 'a8': [-7.069291317193325, -5.136140784799986], 'a9': [2.7811529493745266, -8.559508646656383], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.425143250430549, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [2.4270509831248424, -1.7633557568774194]]], [5, [[1.0, 0], [8.208229170274892, 7.591111505454808]]]], 'bad_primes': [3, 5], 'central_character': '75.31', 'coefficient_field': 'CDF', 'conductor': 75, 'conductor_radical': 15, 'conjugate': '5075411183278081485049502501156', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.3130996367993812, -4.04130513484826], [-6.47213595499958, 4.702282018339785]], [[1.0, 0], [2.4270509831248424, -1.7633557568774194]], [[1.0, 0], [8.208229170274892, 7.591111505454808]], [[1.0, 0], [28.285304297192386, 0], [343.0, 0]], [[1.0, 0], [-15.815070784449567, -48.673782992561755], [-1076.8016195130551, 782.3421708012818]], [[1.0, 0], [7.929077645162081, -24.40319173349966], [-1777.4103366417594, -1291.3641992865635]], [[1.0, 0], [75.4922498361353, 54.848330040758036], [1518.2004933641167, 4672.54066455809]], [[1.0, 0], [-95.38990785259256, -69.30482479742102], [2119.5475644177645, 6523.296645268459]], [[1.0, 0], [29.19710770586256, 89.85945771946594], [-9843.309770559985, 7151.58316464252]], [[1.0, 0], [46.70405513676915, -33.93248228717002], [7536.615475810593, -23195.3173759225]], [[1.0, 0], [-32.79207257001336, -23.824835303552756], [9205.925279424058, 28332.924676948922]], [[1.0, 0], [126.40497000801723, -389.03449521080626], [-40979.13781607421, -29773.086384370643]], [[1.0, 0], [-31.45109347146622, 96.79651260329167], [-55758.26026931575, -40510.74737324954]], [[1.0, 0], [1.5619142915437016, 0], [79507.0, 0]], [[1.0, 0], [-265.6939429545242, 193.03794898989216], [32083.071406990166, -98741.54069131173]], [[1.0, 0], [-368.5775783033735, 267.78728550662686], [46005.523071559044, -141590.4409764736]], [[1.0, 0], [120.21197929213879, -369.974429638668], [-166155.10128773234, -120718.74733057583]], [[1.0, 0], [149.3307645384299, 459.5928356137198], [-183631.48640021993, 133416.08435059784]], [[1.0, 0], [122.4821536400597, 88.98849354119], [92940.87827919231, 286042.6110104793]], [[1.0, 0], [158.58633264466962, -115.21971502675736], [110600.58147373181, -340393.5888037147]], [[1.0, 0], [-186.19109639687375, -573.0372721492689], [-314721.3641007589, 228658.45549106103]], [[1.0, 0], [484.5689729802619, -352.05996662204086], [152357.4298896297, -468907.9537376462]], [[1.0, 0], [-654.3784652302163, -475.4337844006295], [176691.90016266805, 543801.752282857]], [[1.0, 0], [201.68894135198454, 620.734734429308], [-570331.9015075123, 414370.3815233725]], [[1.0, 0], [1258.643069442445, -914.4577175291411], [282031.4673071664, -868003.6038966466]], [[1.0, 0], [-557.1706996559541, 0], [1030301.0, 0]], [[1.0, 0], [-1081.8863761749637, 786.036462760717], [337671.2132123532, -1039245.1338816542]], [[1.0, 0], [-330.9615080964752, 0], [1225043.0, 0]], [[1.0, 0], [204.38292783345722, -629.0259722727092], [-1047700.4692083938, -761198.9474910692]], [[1.0, 0], [601.1879541550481, -1850.2662692510628], [-1167328.1941326286, -848113.5771770526]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-75-25.6-c3-0-1', '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/75/4/g/b/31/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.6973241699042139, 0.46787134470104524, 0.24893036006532265, 0.04021313016749679, -0.15823758507042193, -0.3459450715783254, -0.521933263396172, -0.684703201518081, -0.8322537336733501, -0.9621472546770178, -1.0716198327881798, -1.157733599424805, -1.2175676266101418, -1.248441548061848, -1.248163849596232, -1.2152941182319743, -1.1494057520759544, -1.0513329339902533, -0.9233833630344107, -0.7694966581666753, -0.5953278478293803, -0.4082362650672453, -0.21716275460718742, -0.03238255009644157, 0.13487244414622684, 0.27292002955211947, 0.37025106083770387, 0.41624725812502866, 0.40195976177265896, 0.3209039487649518, 0.1698167167699934, -0.050684356585084835, -0.335603793224226, -0.675295432424616, -1.055469990498406, -1.4575265689723662, -1.859233729517675, -2.2357625958280773, -2.561047198063664, -2.809417593222393, -2.9574213390392203, -2.985721238586545, -2.8809347098687246, -2.6372654788928305, -2.2577740949137564, -1.755142021315795, -1.151805927120342, -0.47937436685459384, 0.2227129075254186, 0.9092647671603552, 1.5320753759391827, 2.043170346492263, 2.3983547539102554, 2.56080613340076, 2.504423364773401, 2.2166323079169583, 1.700364883768877, 0.9749716218456703, 0.07589764193470641, -0.9469550203190498, -2.0321462555487195, -3.1107479733270935, -4.111260853149606, -4.965032775236359, -5.61173921773967, -6.0044467884463435, -6.113784898418776, -5.930801012470503, -5.468171038570601, -4.759572439372791, -3.857192947659521, -2.827527579619999, -1.7457932637133728, -0.6894448789633217, 0.26860938364523484, 1.0664369800899776, 1.6585055773101824, 2.01953206817548, 2.1463285776114387, 2.0574161703342737, 1.7904107601945274, 1.3974306797620828, 0.939003893695421, 0.47713723409156067, 0.06832586744629669, -0.2426894353970893, -0.42767539754544787, -0.4775862577930963, -0.4028241538922748, -0.23102372425217832, -0.0026152824037989886, 0.23528682685127913, 0.43588867535774956, 0.5596873128348968, 0.5804511388002399, 0.48935006844096673, 0.29659250100098206, 0.03024216770536222, -0.26773353995630694, -0.5477388480515082, -0.7603485644578344, -0.8645657652430834, -0.8353411261731092, -0.6691852872568804, -0.3869019494386286, -0.03281783856297067, 0.329652070478036, 0.6257468464132261, 0.7795463587564232, 0.7253195952801885, 0.41848400815207004, -0.15544051887536317, -0.9753391984303968, -1.983547157903959, -3.0899451418234034, -4.1809427008073445, -5.132482208792686, -5.8255662485867346, -6.16234793406738, -6.080606503840148, -5.56450687551959, -4.649920477510177, -3.423231101747051, -2.0133882051216823, -0.5778927417658175, 0.7157200451466884, 1.710629158391372, 2.281012097153563, 2.349105067325465, 1.896602997367385, 0.9686471893092514, -0.3303889822986682, -1.8489917112002758, -3.4070408815764583, -4.818407766982608, -5.914604334898575, -6.566254637368321, -6.6994032534439745, -6.304361023803427, -5.435825660664282, -4.204258827795567, -2.759770058206117, -1.270859822061538, 0.09886254322915856, 1.212569635868937, 1.9775164572633581, 2.355262191845463, 2.363425704367114, 2.068910005163316, 1.5738684142762738, 0.9968228427915979, 0.45209596603519125, 0.030956950087555703, -0.21244018178128135, -0.2680785432029499, -0.1690237902959493, 0.017355955049579132, 0.2042126781639338, 0.30335410741151536, 0.24338667461516889, -0.015439184312837514, -0.47240025892703735, -1.0851302794085924, -1.7763660392585732, -2.447419489491395, -2.9959329891002473, -3.334650083059191, -3.4076970682753713, -3.201278502182166, -2.7466833048081027, -2.114908002332949, -1.4037782735405897, -0.7198987104894788, -0.15880666284400155, 0.21286189214652512, 0.36967146606747003, 0.33160159216176743, 0.15912872292640393, -0.06011042186837635, -0.23066581260074262, -0.27092698207472876, -0.13274799833547504, 0.18509870439700044, 0.6327692650003814, 1.1159441499510818, 1.512562553759137, 1.6970290899081117, 1.567570159757041, 1.071503002980331, 0.22322559095770403, -0.8892144160899093, -2.111202945571766, -3.2420718625507434, -4.06625558045884, -4.390118185641532, -4.0780949178311205, -3.081518873098838, -1.4544484191909568, 0.6471432484469389, 2.9836367073261005, 5.26521157791255, 7.195364702724123, 8.517388485118854, 9.055903320094819, 8.746150268547272, 7.645701547739959, 5.926218147306263, 3.8463565607239842, 1.7102725930703302, -0.1812305467973618, -1.5785045124054722, -2.3215575201641054, -2.3626632137835166, -1.7693547224093944, -0.7076376710582828, 0.5911657199921341, 1.87360189337012, 2.909238693478435, 3.529531892830173, 3.653521159989264, 3.2961287541176736, 2.558255106453975, 1.6013747444489048, 0.61224278532151, -0.2349421472883209, -0.8113393924109108, -1.0549475888699082, -0.9770182898278598, -0.6528942491993038, -0.20002625192119253, 0.251476865645638, 0.5890099450176544, 0.741672529758272, 0.6933669484419507, 0.48228175863686207, 0.1873937349428122, -0.09441821441738431, -0.2749385055065208, -0.29835639853621465, -0.15639032289894744, 0.10893630963152284, 0.4156459985773317, 0.6628892868657273, 0.7577019545986099, 0.6408649619920337, 0.30530691142148614, -0.1979294273676455, -0.768303807161961, -1.2776653635983914, -1.600795427377608, -1.6476316748898896, -1.3893748493665048, -0.8716567899599534, -0.21058871263810514, 0.4287170194441707, 0.8674643310940141, 0.9551557178898898], 'positive_zeros': ['0.39980974926587139950799056507395', '2.89796315136488680068037719613389', '3.84937420887743082402952576872813', '5.96044643893770773155960676492699', '7.25972890046145550209948598579979', '9.213106718542406561128641209584854', '10.52396465683724012664607234761819', '11.25135494978307916911671486183696', '12.13796288244622726303469041552757', '13.13607456024868025910374389196170'], 'prelabel': '2-75-25.6-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.103602445908102, 'root_angle': 0.7551464505428257, 'root_number': '-0.71844640283666 + 0.6955823216924534*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.377573225271', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.39980974926587139950799056507', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.89796315136488680068037719613', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.84937420887743082402952576873', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.425143250430549, 'bad_primes': [3, 5], 'central_character': '25.6', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/4/g/b/31/6'], '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': '2-75-25.6-c3-0-1', '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': '2-75-25.6-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.103602445908102, 'root_angle': 0.37757322527141285, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.39980974926587139950799056507', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '506819068633979778896640747864', 'Lhash_array': ['506819068633979778896640747864'], 'label': '2-75-25.6-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/4/g/b/31/6'}