-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3283061052509111099807948190976,4044501897666894429067060515891', 'a10': 0, 'a2': 2, 'a3': 0, 'a4': 3, 'a5': 0, 'a6': 0, 'a7': -4, 'a8': 4, 'a9': -4, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.4287280699070375, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 1]], [41, [1, 2, 1]]], 'bad_primes': [2, 41], 'central_character': '82.1', 'coefficient_field': '1.1.1.1', 'conductor': 6724, 'conductor_radical': 82, 'degree': 4, 'euler_factors': [[1, -2, 1], [1, 0, 4, 0, 9], [1, 0, 2, 0, 25], [1, 4, 16, 28, 49], [1, 0, 4, 0, 121], [1, 0, 26, 0, 169], [1, -4, 6, -68, 289], [1, 8, 52, 152, 361], [1, -8, 54, -184, 529], [1, -8, 42, -232, 841], [1, 8, 70, 248, 961], [1, 0, 2, 0, 1369], [1, 2, 1], [1, -8, 70, -344, 1849], [1, 4, 48, 188, 2209], [1, -24, 250, -1272, 2809], [1, 8, 126, 472, 3481], [1, -12, 158, -732, 3721], [1, 8, 132, 536, 4489], [1, 4, 144, 284, 5041], [1, 16, 178, 1168, 5329], [1, 12, 176, 948, 6241], [1, -24, 278, -1992, 6889], [1, 12, 182, 1068, 7921], [1, 4, 166, 388, 9409], [1, 24, 314, 2424, 10201], [1, 8, 150, 824, 10609], [1, -24, 326, -2568, 11449], [1, -24, 362, -2616, 11881], [1, -8, 210, -904, 12769]], 'euler_factors_factorization': [[[[1, -1], 2]], [[[1, 0, 4, 0, 9], 1]], [[[1, 0, 2, 0, 25], 1]], [[[1, 4, 16, 28, 49], 1]], [[[1, 0, 4, 0, 121], 1]], [[[1, 0, 13], 2]], [[[1, -4, 6, -68, 289], 1]], [[[1, 8, 52, 152, 361], 1]], [[[1, -8, 54, -184, 529], 1]], [[[1, -8, 42, -232, 841], 1]], [[[1, 8, 70, 248, 961], 1]], [[[1, 0, 2, 0, 1369], 1]], [[[1, 1], 2]], [[[1, -8, 70, -344, 1849], 1]], [[[1, 4, 48, 188, 2209], 1]], [[[1, -12, 53], 2]], [[[1, 8, 126, 472, 3481], 1]], [[[1, -6, 61], 2]], [[[1, 8, 132, 536, 4489], 1]], [[[1, 4, 144, 284, 5041], 1]], [[[1, 16, 178, 1168, 5329], 1]], [[[1, 12, 176, 948, 6241], 1]], [[[1, -24, 278, -1992, 6889], 1]], [[[1, 12, 182, 1068, 7921], 1]], [[[1, 4, 166, 388, 9409], 1]], [[[1, 24, 314, 2424, 10201], 1]], [[[1, 8, 150, 824, 10609], 1]], [[[1, -24, 326, -2568, 11449], 1]], [[[1, -12, 109], 2]], [[[1, -8, 210, -904, 12769], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 5, 'label': '4-82e2-1.1-c1e2-0-5', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/82/2/a/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.6211033950866482, 1.6291458222874242, 1.644534242106443, 1.6730922709186176, 1.7141818616142843, 1.7659281687866684, 1.8280037506426754, 1.9003467403960708, 1.9822540826275115, 2.0728097120991515, 2.1710325189829733, 2.2758095027728356, 2.3857750654764436, 2.4993675574714778, 2.6148073567184533, 2.730119280480749, 2.8431074169591124, 2.9513965791685792, 3.052438758252732, 3.1435618349533736, 3.222007192808361, 3.284985924321512, 3.32975720144757, 3.353682729713887, 3.3543494498681596, 3.3296099972086592, 3.277748549513139, 3.1974912044180086, 3.0882061932230247, 2.9498663413297157, 2.7832668888190253, 2.589922863089444, 2.3722806501636473, 2.1335372333336204, 1.8778174864606754, 1.6099103015908547, 1.3353842492970307, 1.060247492600483, 0.7909814577564336, 0.5341459862402277, 0.2963244196298421, 0.08371044409836877, -0.09802258176651811, -0.24410441686405376, -0.35083936140768535, -0.4159043620701964, -0.4385058625888022, -0.41954338898803023, -0.3616836951846772, -0.2693568870774643, -0.1486799488605093, -0.007281671166339304, 0.1459753300687551, 0.3013064170858662, 0.44850106147707414, 0.5772964964678712, 0.6780613652549342, 0.742123236545235, 0.7625578984312147, 0.7343475062363017, 0.6551512939142984, 0.5251826103552771, 0.347817362524914, 0.1291205329688401, -0.12183651372723861, -0.39379958442270446, -0.673380725937726, -0.946146103423968, -1.1970199041895198, -1.4114698872378255, -1.576151689718193, -1.6799727576399384, -1.7147699029379162, -1.6760297635229788, -1.5633397471670258, -1.3806031024337337, -1.136015555655429, -0.8417320969604808, -0.5132093083412722, -0.1684366736248566, 0.17336290900447376, 0.4926713602428338, 0.7714409137276016, 0.9938332217074227, 1.148112704502728, 1.2268084273435647, 1.2283124064993967, 1.1561926996859606, 1.02011004225778, 0.8342230081800731, 0.6172058263068328, 0.38995739245502853, 0.17477512810107224, -0.007168273395741746, -0.13713835003900748, -0.20098492737511456, -0.19035390617252004, -0.10387760076634542, 0.05237171252248468, 0.2649944747389743, 0.514070140488248, 0.7745298910611909, 1.018357789731676, 1.2167369336274838, 1.34329232351872, 1.376173041709613, 1.3015279752059392, 1.114570562743659, 0.8222301525319182, 0.4424494312630755, 0.005048380365121626, -0.45098798786551536, -0.8789231290043386, -1.2285530069827602, -1.4496326268652044, -1.49666191618357, -1.3332469731342893, -0.9359796685103089, -0.29807035337238746, 0.5689497091540767, 1.6340847855576204, 2.847972130892369, 4.145473206023914, 5.449187231669746, 6.675977562372698, 7.741470534837725, 8.569437505811365, 9.095151813036646, 9.275466468091983, 9.088882254739472, 8.543709220476263, 7.673477930881834, 6.541007863735575, 5.229206778515724, 3.840150289607736, 2.482925220261637, 1.2685822220631056, 0.297907424261961, -0.34525948930574374, -0.603114332373592, -0.4488424885079416, 0.10982350379393667, 1.0304319769035661, 2.2383824117406976, 3.6330960543432416, 5.09510940342622, 6.497925714089446, 7.716221124014102, 8.640558782763994, 9.182623532460706, 9.288738317251074, 8.938871510140151, 8.155132186494582, 6.993433293496521, 5.5448781614215505, 3.921678595149121, 2.251993188866502, 0.6639596205118351, -0.7228998051274568, -1.8108013533236602, -2.531191550819941, -2.8512510351692044, -2.7761040323597443, -2.3474252233774013, -1.6382580252884706, -0.7455409015410847, 0.22157946833224978, 1.1510477854481236, 1.9425125917492638, 2.513459246050887, 2.811933119831568, 2.815846165311147, 2.539792276563778, 2.0267639348144413, 1.347573453003077, 0.5874653150586225, -0.160152281526505, -0.8075238004575584, -1.2803599018917278, -1.5272637627500536, -1.5243656561370216, -1.2775386883291089, -0.8206974407358977, -0.21124230895765966, 0.4781261291862088, 1.1672580695820909, 1.7803210030495338, 2.252069309532683, 2.538640818260127, 2.618272750559935, 2.4971315858527947, 2.203289809233176, 1.7860841564140406, 1.305494136453237, 0.8267259059281546, 0.40936986585462953, 0.10121539832782611, -0.06840310932604997, -0.09132006603199706, 0.019211294721827827, 0.23154708842349345, 0.500716382696689, 0.7763024434109809, 1.0090198013117497, 1.1598801627157997, 1.2037964976994784, 1.135721968118541, 0.968514833027331, 0.7333817152412871, 0.47246155350388847, 0.23408981611353577, 0.06354276760441094, -0.003364415354237566, 0.05314432552544936, 0.23335941079577296, 0.5172125209273155, 0.8669157505942403, 1.2315265677095677, 1.5554440629240425, 1.784871343857626, 1.8785555391191155, 1.8112565753850736, 1.5816683688949476, 1.2094678134406252, 0.7367949596932677, 0.21903804183213338, -0.28009563747242683, -0.7001885907245475, -0.9915757096969753, -1.123825475734364, -1.0901009571892302, -0.9085272466189441, -0.6193383201744129, -0.2791736609611372, 0.048977130423110325, 0.30422113702530423, 0.4405816747419524, 0.43188628051452, 0.28085579278025713, 0.015840229058437322, -0.3085448363739716, -0.6227837356630874, -0.8501437775928856, -0.9211141329224817, -0.7840333580978726, -0.41529856813280414, 0.17488401156878802, 0.941745522234719, 1.8107894941272404, 2.686168505062158, 3.4660126902214907, 4.053696384718091, 4.377303813255182, 4.394912301074684, 4.108928034364288, 3.5591409454128455, 2.825212323093437, 2.0080682464148434, 1.220747132031458, 0.5659107098257316, 0.12264229244843172, -0.0689556644180352, -0.014189506950648903, 0.23565923581308135, 0.591101106359755, 0.9381650022285405, 1.1591728676198112, 1.1514618115923494, 0.8510388119735343, 0.24314889669044862, -0.6249225787999746, -1.650681453571688, -2.6834719076874434, -3.547970392050857, -4.068831376409399, -4.099675165778353, -3.5514011182751677, -2.411108690936779, -0.755099869485934, 1.2527773847312869, 3.376986287249391, 5.330657951674588, 6.81998487850035, 7.568537584370329, 7.374797350530733, 6.120225816814403, 3.8168296145635243, 0.584862903812316, -3.328136124656624, -7.598910179892679, -11.841663556048116, -15.67153586187266, -18.736525092931757, -20.767557328251375, -21.60591624491087, -21.22004915986944, -19.708606638769414, -17.280560069093784, -14.228576465117984, -10.887544021491632, -7.590441995832481, -4.630612263576108, -2.2223233716118114, -0.48833462699908836, 0.5558558868985887, 0.9830692337423164, 0.9419008141137257, 0.618274027762056, 0.20673066481772823, -0.1257082938729503, -0.263327289165442, -0.15734225945537403, 0.1722402727671884, 0.645363677661845, 1.1447210990335666, 1.5369116821642839, 1.7073298952557092, 1.5744566618851297, 1.1175257553683575, 0.37012635773861596, -0.5728926715933897, -1.5820322667523323, -2.506388797001554, -3.206398207332727, -3.573532106290621, -3.551078288898635, -3.143085442825152, -2.4130758992110297, -1.4731377358862088, -0.4649495231113464, 0.4661064168215645, 1.1919819620058345, 1.6276558899166296, 1.738001796398461, 1.5483961957065502, 1.1313551990983624, 0.5976476888023131, 0.07046732439536137, -0.3340189287943237, -0.529173760728667, -0.47197349229605906, -0.16948462814813817, 0.3243074612757903, 0.9189936410713732, 1.5079672805099062, 1.984816697613503, 2.268821700684998, 2.3123165672279207, 2.1166420573720157, 1.7223989522071659, 1.2084498940636823, 0.6694319017573586, 0.202701604737999, -0.11349812639332905, -0.2319980450032282, -0.14531784685186516, 0.11500193422448057, 0.4856700588209685, 0.8864577300831504, 1.2344691917214345, 1.4638521042821309, 1.533535554062439, 1.4391802609270108, 1.2064690294018303, 0.8890521774400346, 0.5509914039747358, 0.255615099960375, 0.04927675052162049, -0.04686494288642054, -0.04064966122651046, 0.03508664627312243, 0.13235493819106364, 0.20291096091299907, 0.2118649821059435, 0.1520100857342573, 0.04792614729168571, -0.04286743491547372, -0.04120242029291874, 0.13878992524025413, 0.5698145985482876, 1.2911150660024235, 2.2947738133794764, 3.5177791620231518, 4.845367336532117, 6.127017033707006, 7.194068025763824, 7.895302061691121, 8.112776628803847, 7.7983182736201035, 6.969425437026854, 5.726350686665066, 4.222073595200564, 2.6529152770965476, 1.2150210534472679, 0.08057491872602915, -0.635684615438284, -0.8917645826605465, -0.72379395285364, -0.2361005083126244, 0.42042960424304554, 1.0810472055118894, 1.5954056164726909, 1.8626219235171473, 1.840976403852762, 1.5623524132482771, 1.1123022651554921, 0.6165569341209732, 0.20349557122838394, -0.022087492940430956, -0.007538977326642728, 0.23542725916104532, 0.6317194236871144, 1.061623171208319, 1.3888002672781017, 1.5018070488376005, 1.3436111115415168, 0.9460833027866122, 0.43126269978822485, 0.009332139685644718, -0.05853098579016679, 0.49683051590621746, 1.8969120848965932, 4.260346869379106, 7.566141549232978, 11.631710675925035, 16.1216778711798, 20.589564284667603, 24.525059965263974, 27.450621550509403, 28.966845252088945, 28.85815749531074, 27.088864140165125, 23.86405168326586, 19.55637341256129, 14.696845770211494, 9.857646671284737, 5.594230147234959, 2.3410894985974195, 0.3591728096198983, -0.3037837120261323, 0.18861634364632734, 1.4975451674411997, 3.175308777671766, 4.7401265048762085, 5.771262522874897, 5.9624530966568665, 5.190215856966508, 3.504082117789615, 1.1321537571464957, -1.5879799183474168, -4.258121712348003, -6.503564368263856, -8.031623723903634, -8.679497570739347, -8.434715320073764, -7.425135167594937, -5.88450360589756, -4.105687835112655, -2.374924871883228, -0.9333144256415735, 0.07692179227338766, 0.6087981739697352, 0.7228429441490483, 0.5427964788940148, 0.23128562473493933, -0.06249000811489363, -0.23198121375070943, -0.2375302797074725, -0.10970810245593296, 0.06565930063604951, 0.17497244061482337, 0.11043685309243113, -0.19483150010599398, -0.7480650808642332, -1.4842762214658103, -2.280513744188097, -2.976625726269335, -3.411319118078097, -3.4581461524138004, -3.0537268165619174, -2.216824623793601, -1.0466322426863652, 0.29464695265822677, 1.6090328700030514, 2.7076396794831856, 3.4362805571653503, 3.7177320783102696, 3.5488371024244567, 3.0137245688872634, 2.248473132429819, 1.4234658382213987, 0.6979127764158668, 0.19423746751431295, -0.027580825884517605, 0.023762456776715516, 0.27813043686569033, 0.6258482555954501, 0.944134396647308, 1.1309540926717996, 1.1228806502249586, 0.9148746609843061, 0.55175777925945, 0.12134530279068333, -0.27451004608748897, -0.5423711654602511, -0.621969435501767, -0.5002620962663716, -0.2152497379765076, 0.16117663284111175, 0.535671126031814, 0.798299056299642, 0.8724540035339607], 'positive_zeros': ['2.58987851377818515343201177612590', '3.19054942816160639424782225437799', '3.97049665509507487475106986467091', '4.96800621436173310389501551718416', '5.80970613597639718234982729358636', '6.10668064570171486137898034335491', '6.87569485664033031084846023606929', '7.39832926665039599439095721645068', '8.587271008673712693800179999138768', '8.802986449848110905891376609478032', '9.841007973617315997953823221716446', '10.36072055623948630057110844562120', '10.98613576177527262067132427299352', '11.45708666641992929035560991918544', '12.28054029136310314768439061781583', '12.43006960413634175283749753820674', '13.23854526427826292609453785409218', '13.26830258684954251367887342932051', '14.08919181679431614020214131364904', '14.61501708324602010139292220636809'], 'prelabel': '4-82e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.8091806328468938, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1973444166290023075, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.58987851377818515343201177613', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.19054942816160639424782225438', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.97049665509507487475106986467', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.4287280699070375, 'bad_primes': [2, 41], 'central_character': '1.1', 'conductor': 6724, 'conductor_radical': 82, 'degree': 4, 'dirichlet_coefficients': [1, 2, 0, 3, 0, 0, -4, 4, -4, 0, 0, 0, 0, -8, 0, 5, 4, -8, -8, 0, 0, 0, 8, 0, -2, 0, 0, -12, 8, 0, -8, 6, 0, 8, 0, -12, 0, -16, 0, 0, -2, 0, 8, 0, 0, 16, -4, 0, 0, -4, 0, 0, 24, 0, 0, -16, 0, 16, -8, 0, 12, -16, 16, 7, 0, 0, -8, 12, 0, 0, -4, -16, -16, 0, 0, -24, 0, 0, -12, 0, 7, -4, 24, 0, 0, 16, 0, 0, -12, 0, 0, 24, 0, -8, 0, 0, -4, 0, 0, -6], 'euler11': [1, 0, 4, 0, 121], 'euler13': [1, 0, 26, 0, 169], 'euler17': [1, -4, 6, -68, 289], 'euler19': [1, 8, 52, 152, 361], 'euler2': [1, -2, 1, 0, 0], 'euler23': [1, -8, 54, -184, 529], 'euler29': [1, -8, 42, -232, 841], 'euler3': [1, 0, 4, 0, 9], 'euler31': [1, 8, 70, 248, 961], 'euler37': [1, 0, 2, 0, 1369], 'euler41': [1, 2, 1, 0, 0], 'euler43': [1, -8, 70, -344, 1849], 'euler47': [1, 4, 48, 188, 2209], 'euler5': [1, 0, 2, 0, 25], 'euler53': [1, -24, 250, -1272, 2809], 'euler59': [1, 8, 126, 472, 3481], 'euler61': [1, -12, 158, -732, 3721], 'euler67': [1, 8, 132, 536, 4489], 'euler7': [1, 4, 16, 28, 49], 'euler71': [1, 4, 144, 284, 5041], 'euler73': [1, 16, 178, 1168, 5329], 'euler79': [1, 12, 176, 948, 6241], 'euler83': [1, -24, 278, -1992, 6889], 'euler89': [1, 12, 182, 1068, 7921], 'euler97': [1, 4, 166, 388, 9409], 'euler_factors': [[1, -2, 1, 0, 0], [1, 0, 4, 0, 9], [1, 0, 2, 0, 25], [1, 4, 16, 28, 49], [1, 0, 4, 0, 121], [1, 0, 26, 0, 169], [1, -4, 6, -68, 289], [1, 8, 52, 152, 361], [1, -8, 54, -184, 529], [1, -8, 42, -232, 841], [1, 8, 70, 248, 961], [1, 0, 2, 0, 1369], [1, 2, 1, 0, 0], [1, -8, 70, -344, 1849], [1, 4, 48, 188, 2209], [1, -24, 250, -1272, 2809], [1, 8, 126, 472, 3481], [1, -12, 158, -732, 3721], [1, 8, 132, 536, 4489], [1, 4, 144, 284, 5041], [1, 16, 178, 1168, 5329], [1, 12, 176, 948, 6241], [1, -24, 278, -1992, 6889], [1, 12, 182, 1068, 7921], [1, 4, 166, 388, 9409]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/82/2/a/b'], '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': '4-82e2-1.1-c1e2-0-5', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-82e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.8091806328468938, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1973444166290023075, 'z1': {'__RealLiteral__': 0, 'data': '2.58987851377818515343201177613', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3283061052509111099807948190976,4044501897666894429067060515891', 'Lhash_array': ['3283061052509111099807948190976', '4044501897666894429067060515891'], 'label': '4-82e2-1.1-c1e2-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/82/2/a/b'}