-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2034581927774766447921528921749', 'a10': [-2.3323252755578174e-60, -60.53386819369318], 'a2': [-1.6625077511098136, -2.288245611270737], 'a3': [3.387258068349183, 10.42490839312233], 'a4': [-2.4721359549995796, 7.608452130361228], 'a5': [17.314544778432463, 12.579753134584342], 'a6': [18.22340808482187, -25.082369417317036], 'a7': [27.35561773117077, 8.888379003475512], 'a8': [21.519952382846636, -6.9922563911811375], 'a9': [-31.674821239025, 23.01310469711912], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.274139187844576, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.6625077511098136, 2.288245611270737]]], [11, [[1.0, 0], [102.31837709220753, -64.59063174498932]]]], 'bad_primes': [2, 11], 'central_character': '22.19', 'coefficient_field': 'CDF', 'conductor': 22, 'conductor_radical': 22, 'conjugate': '3588403314878914786381682701772', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.6625077511098136, 2.288245611270737]], [[1.0, 0], [-3.387258068349183, -10.42490839312233], [-65.53037654437074, 47.610605435690324]], [[1.0, 0], [-17.314544778432463, -12.579753134584342], [193.13562148434215, 594.410322684471]], [[1.0, 0], [-27.35561773117077, -8.888379003475512], [1942.4498034942487, 1411.272390754228]], [[1.0, 0], [102.31837709220753, -64.59063174498932]], [[1.0, 0], [109.13780053397818, 150.21529549495676], [-8825.834376342873, 27163.125161905882]], [[1.0, 0], [-158.3588149432744, 217.9622098351632], [-25809.408387189982, -79433.19129748752]], [[1.0, 0], [-618.7882830990142, 201.05650097701334], [105431.90372393752, -76600.76186400739]], [[1.0, 0], [644.3120605810686, 0], [279841.0, 0]], [[1.0, 0], [505.9559865365297, 164.39506545266966], [572202.3487985072, 415729.3410266727]], [[1.0, 0], [-1188.3203859238497, 863.3652972694198], [285383.6836621458, -878320.6649854166]], [[1.0, 0], [367.01866076100885, -1129.567290060266], [-1516228.0991947458, -1101604.1962217137]], [[1.0, 0], [2142.6385584475365, -696.1854695476859], [2286088.671041946, -1660940.6423032312]], [[1.0, 0], [0, -1429.8140450074284], [-3418801.0, 0]], [[1.0, 0], [-409.37675455837194, -1259.9320980065356], [-3947744.856128538, 2868204.5276917876]], [[1.0, 0], [-1896.3999801441998, 1377.8152356832832], [2438292.7227926296, -7504293.371753099]], [[1.0, 0], [1015.9099664554135, -3126.64937901209], [-9803150.975976208, -7122406.092503974]], [[1.0, 0], [-2046.2952531246372, 2816.483790346734], [-4278600.170413417, -13168177.306636605]], [[1.0, 0], [-1553.8006831761684, 0], [20151121.0, 0]], [[1.0, 0], [3993.7572937874056, 2901.6345204681506], [7852641.284634958, 24167944.805063743]], [[1.0, 0], [3562.5183747066026, 1157.5323881338165], [22974659.5793554, 16692067.250847455]], [[1.0, 0], [2631.6963039646307, 3622.2192129477276], [-12036236.961280746, 37043728.34527405]], [[1.0, 0], [2119.1765854412893, -2916.796338487226], [-14665427.71350145, -45135545.43947713]], [[1.0, 0], [-9594.394555419449, 0], [62742241.0, 0]], [[1.0, 0], [10393.484043057488, -7551.308171426366], [27357052.32879514, -84196349.57797474]], [[1.0, 0], [1851.6245698839996, 2548.54258148855], [-32156432.350471772, 98967322.45933671]], [[1.0, 0], [3997.9701616106995, -12304.486948507138], [-91055575.46087238, -66155747.98432512]], [[1.0, 0], [7121.090369358858, -2313.782519659155], [106045624.82488735, -77046656.34418172]], [[1.0, 0], [0, 12658.021556909825], [-141158161.0, 0]], [[1.0, 0], [-6918.474164658088, -21292.87403894051], [-131908085.93698703, 95836834.22100694]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-22-11.8-c4-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/22/5/d/a/19/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [1.2663111884068061, 1.195743860363975, 1.1136439885042373, 1.0182928101467221, 0.9074723090524667, 0.7786241879132322, 0.629043468050347, 0.45610423972912323, 0.25751443087080117, 0.031594902799870817, -0.22242452429936757, -0.5041033452429755, -0.8114988409269082, -1.1409056426994382, -1.486651947893211, -1.8409815033363788, -2.1940521164066262, -2.534080380387867, -2.8476578043460354, -3.1202550967569045, -3.336918744699333, -3.483147448305198, -3.5459161212135446, -3.5147933458051352, -3.383076272293979, -3.1488474113088363, -2.8158434222370925, -2.3940198238989705, -1.899700338887848, -1.3552175152783825, -0.7879834882230684, -0.22897591072381743, 0.2893179635694323, 0.7353904943555334, 1.0814605745369859, 1.3062419442583086, 1.3974509850065342, 1.3537504609305209, 1.1858357830270787, 0.9164175076614364, 0.5789395082725026, 0.2149933427815104, -0.12946287468606305, -0.40881234671340666, -0.5829909769441705, -0.6226520196960524, -0.513656129902722, -0.260249991243153, 0.11363031571135494, 0.5653359506324159, 1.036928828600198, 1.4609221728025332, 1.767884656484748, 1.8951455601588305, 1.7955899936118032, 1.4453905974003756, 0.8495218501031495, 0.04406629721906619, -0.9053515493722212, -1.9092033228123275, -2.8634139752356456, -3.6615154773694734, -4.2081720369474676, -4.432302019313579, -4.2978979867643385, -3.810796011135606, -3.020078635366069, -2.0134780578899787, -0.9069978109759443, 0.17012490063708674, 1.093178350733167, 1.7599342923987016, 2.1060490659556854, 2.1153459142776185, 1.8230483394087214, 1.3110407915495021, 0.6954791251920723, 0.10836772582212865, -0.32415690146534165, -0.5033569571069989, -0.3755682615842424, 0.05721232798611418, 0.7360149108239643, 1.553537686485336, 2.3716800316725064, 3.0452407061489555, 3.447777699057121, 3.4950080693119716, 3.1613335955328927, 2.486133285433486, 1.5682259800561196, 0.5490843395940901, -0.41242166082941173, -1.1691908229629335, -1.6134209780635498, -1.6970245171381206, -1.4406259275035413, -0.928957058448947, -0.29315422556227877, 0.3168023837434697, 0.7640531999173458, 0.9545865639863, 0.85824805765194, 0.5161147054144504, 0.03203955518689516, -0.4504613168506357, -0.7814918784759587, -0.8412129596650674, -0.5712900432655861, 0.006166115938094291, 0.7873266001511036, 1.60451913415132, 2.2604666899186556, 2.5721856153191585, 2.415178417473521, 1.757850049792181, 0.6776203235030716, -0.6462025704336696, -1.9627701951939487, -2.997985273437548, -3.511081341366407, -3.3474092862355547, -2.475551720394921, -0.999821662738009, 0.8556610636058488, 2.788866145351215, 4.479305004888291, 5.6523596221124555, 6.134333260258052, 5.885847987316186, 5.005953745924239, 3.7059878904757793, 2.2592897058202466, 0.9386273559722604, -0.043814024787194664, -0.579623543633932, -0.6803977028728414, -0.46359218783297773, -0.11224012445826656, 0.18052579144860004, 0.2672556993313523, 0.08726250460854969, -0.3181495768763651, -0.8205373301932193, -1.245263071479484, -1.427205119277157, -1.2654779208661773, -0.761201807482477, -0.026602337703107163, 0.7385928676594999, 1.2983495797496722, 1.4458969629332237, 1.0656999222598615, 0.17395275322262072, -1.0751430166800555, -2.421059640311541, -3.5598290706182416, -4.222269062252335, -4.24660232887368, -3.625100859330034, -2.5107362864999216, -1.1804088312521595, 0.036647347413078464, 0.8465784819019659, 1.070817007001725, 0.6956098267701264, -0.12356812162233508, -1.1051257109352504, -1.920943578856726, -2.290628300894122, -2.0637730680468587, -1.266251492489863, -0.09628800940910649, 1.129784598435747, 2.0675367549504737, 2.444850679600453, 2.143638036087858, 1.2384994834157153, -0.020012749600292076, -1.273871845307479, -2.1588040235163737, -2.4091946408248655, -1.935918970495401, -0.8537867947634171, 0.5501498727377979, 1.8987152284858277, 2.8332904178014493, 3.116988046792011, 2.701626525222941, 1.7385181388402902, 0.5300001827067512, -0.5633502524367513, -1.231325903940163, -1.3052115007903944, -0.8036305271769171, 0.08042327291840101, 1.0463508034547215, 1.784484362215347, 2.0743847619151476, 1.851214863173387, 1.2191523988068875, 0.40840431698815954, -0.3087818834702889, -0.7138930331364706, -0.7164023487359955, -0.38039995575350827, 0.10617526345946235, 0.5093859126909418, 0.6468364580795618, 0.4694481623643994, 0.09609167623393083, -0.21498917480281837, -0.15229299648292727, 0.5318887177251541, 1.9129423775093974, 3.833294772745195, 5.915358237657658, 7.6504326447501025, 8.540415448705158, 8.249976042817943, 6.720768844116171, 4.208948551349869, 1.2301677531430373, -1.5747104696280416, -3.6141800160964133, -4.5080831973755755, -4.187159573265342, -2.899534792808314, -1.1229968592213981, 0.5880155878637519, 1.7710875171160942, 2.1861982738299552, 1.8673803184420663, 1.0821824088099021, 0.21660983256175212, -0.3720517191473208, -0.48230398803174934, -0.1316157105466532, 0.46439025070929735, 0.9863505100264321, 1.1423359307001193, 0.7860266461090815, -0.022592621140996694, -1.0368848217254225, -1.9163130998266873, -2.3574499829966773, -2.213559134117113, -1.5566606633270588, -0.6569673997104599, 0.11459481887807771, 0.42574751541241806, 0.11228239005412644, -0.7519183299278799, -1.8726561103253272, -2.837038028388414, -3.263274638632638, -2.9438359102185956], 'positive_zeros': ['1.60500214129071352138658893837616', '5.52454523381927311644732304080564', '7.31404049235551476448592852483632', '8.388748500202573781500003299253137', '10.02819391189421950331032921753440', '12.09992580929637120189009873233656', '13.57237910700832290360693529812625', '14.22022919674244182769324637337360', '16.09334042786587147317408251277469', '17.30754066371927228950325130095387'], 'prelabel': '2-22-11.8-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5080249294506294, 'root_angle': -0.20137228446417424, 'root_number': '0.8064754484470272 - 0.5912675799096094*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.100686142232', 'prec': 50}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.60500214129071352138658893838', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.52454523381927311644732304081', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.31404049235551476448592852484', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.274139187844576, 'bad_primes': [2, 11], 'central_character': '11.8', 'conductor': 22, 'conductor_radical': 22, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/22/5/d/a/19/2'], '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': '2-22-11.8-c4-0-0', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-22-11.8-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5080249294506294, 'root_angle': -0.10068614223208712, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '1.60500214129071352138658893838', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2034581927774766447921528921749', 'Lhash_array': ['2034581927774766447921528921749'], 'label': '2-22-11.8-c4-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/22/5/d/a/19/2'}