-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '443036875895917276306424761828,2675622625665951420531833987284', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -12, 'a8': 0, 'a9': -5, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 27.369859079893637, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 2, 9]]], 'bad_primes': [2, 3], 'central_character': '192.1', 'coefficient_field': '1.1.1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1, 2, 9], [1, 0, -18, 0, 625], [1, 12, 134, 588, 2401], [1, 0, -210, 0, 14641], [1, 20, 438, 3380, 28561], [1, 0, -66, 0, 83521], [1, 4, 726, 1444, 130321], [1, 0, -930, 0, 279841], [1, 0, -1394, 0, 707281], [1, 44, 2406, 42284, 923521], [1, -12, 2774, -16428, 1874161], [1, 0, -2210, 0, 2825761], [1, 164, 10422, 303236, 3418801], [1, 0, 190, 0, 4879681], [1, 0, -1746, 0, 7890481], [1, 0, -1554, 0, 12117361], [1, -172, 14838, -640012, 13845841], [1, 4, 8982, 17956, 20151121], [1, 0, 5406, 0, 25411681], [1, -164, 17382, -873956, 28398241], [1, -20, 12582, -124820, 38950081], [1, 0, -8370, 0, 47458321], [1, 0, -14690, 0, 62742241], [1, 188, 27654, 1768892, 88529281], [1, 0, -17810, 0, 104060401], [1, 268, 39174, 2843212, 112550881], [1, 0, -20306, 0, 131079601], [1, 20, 23862, 237620, 141158161], [1, 0, -20930, 0, 163047361]], 'euler_factors_factorization': [[1], [[[1, 2, 9], 1]], [[[1, 0, -18, 0, 625], 1]], [[[1, 6, 49], 2]], [[[1, 0, -210, 0, 14641], 1]], [[[1, 10, 169], 2]], [[[1, 0, -66, 0, 83521], 1]], [[[1, 2, 361], 2]], [[[1, 0, -930, 0, 279841], 1]], [[[1, 0, -1394, 0, 707281], 1]], [[[1, 22, 961], 2]], [[[1, -6, 1369], 2]], [[[1, 0, -2210, 0, 2825761], 1]], [[[1, 82, 1849], 2]], [[[1, 0, 190, 0, 4879681], 1]], [[[1, 0, -1746, 0, 7890481], 1]], [[[1, 0, -1554, 0, 12117361], 1]], [[[1, -86, 3721], 2]], [[[1, 2, 4489], 2]], [[[1, 0, 5406, 0, 25411681], 1]], [[[1, -82, 5329], 2]], [[[1, -10, 6241], 2]], [[[1, 0, -8370, 0, 47458321], 1]], [[[1, 0, -14690, 0, 62742241], 1]], [[[1, 94, 9409], 2]], [[[1, 0, -17810, 0, 104060401], 1]], [[[1, 134, 10609], 2]], [[[1, 0, -20306, 0, 131079601], 1]], [[[1, 10, 11881], 2]], [[[1, 0, -20930, 0, 163047361], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 0, 'label': '4-192e2-1.1-c2e2-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/192/3/e/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.3708804706142156, 0.35827363135576346, 0.3235404356417859, 0.2644996049738721, 0.18125741459020195, 0.07436472863873335, -0.05611911622690874, -0.21004550879790543, -0.386798434878878, -0.5853800803198472, -0.8042945161079719, -1.0415033826029687, -1.294208962568124, -1.558910253832182, -1.831217598190949, -2.105968588528389, -2.3771040304422417, -2.6378615485580976, -2.880770692752017, -3.0979122514006883, -3.2810781077554685, -3.4220687950716395, -3.5130438559897637, -3.546806529929105, -3.5173365349733148, -3.4199889179202634, -3.2521575516363757, -3.013301014939704, -2.7056398007691778, -2.33392402383003, -1.906032174200291, -1.4324207126640884, -0.9264810283368285, -0.40366285116528616, 0.11852927961201765, 0.6216720397091963, 1.086840378937146, 1.4958510392935265, 1.8320455047048516, 2.0814146259207624, 2.2335836316194535, 2.2825539545346314, 2.227626279527032, 2.0735194239467103, 1.8309202839384031, 1.5158381179927443, 1.1495079428923005, 0.7570055741127178, 0.3663668331073653, 0.006693220459156032, -0.2934328645150212, -0.5079335785408334, -0.6151937956890164, -0.5996123957796452, -0.45339591140525004, -0.17718176783157188, 0.21895214126945733, 0.7160902735814528, 1.2867684255314737, 1.8967646116674848, 2.5068984931042704, 3.07557697432721, 3.5618734796124603, 3.9280639783247677, 4.143296350536016, 4.185218318615142, 4.043230339658611, 3.7184625047758035, 3.2255729773418245, 2.5907841884511447, 1.8515104015586101, 1.052812225390367, 0.24475923794155688, -0.5216938153742384, -1.1989589466692834, -1.7461155813325004, -2.1335215598410064, -2.3439348103014614, -2.3760181005995, -2.2424788295892846, -1.9713314373569222, -1.6011875496046362, -1.1799576962735487, -0.7584394663231486, -0.3871846548415244, -0.11023983912890739, 0.03822514018171583, 0.038101202302467066, -0.11494759148173543, -0.4086101298970317, -0.8152959655922084, -1.294543122430225, -1.7977293966819392, -2.27235231317309, -2.6689270816323556, -2.9448074150348775, -3.071032512050386, -3.0333554198395793, -2.836602055278598, -2.501606435871614, -2.065544089075715, -1.575201629774281, -1.0834805002371666, -0.641143826403417, -0.2915529131165819, -0.06393501536008116, 0.030459701251085512, 0.0009680983327654032, -0.12298345458665809, -0.2942505739354629, -0.4539937988204065, -0.5375301683229515, -0.4844956480988078, -0.24478003530543882, 0.2108251327850658, 0.8884270373094756, 1.7643609196109393, 2.78907622185623, 3.887656641718041, 4.969258558346237, 5.935072227247375, 6.6897400406675125, 7.153582866710177, 7.270750075515914, 7.020294125133589, 6.416528880616895, 5.513739112416079, 4.397300782215081, 3.1796296481255646, 1.984788903701265, 0.9375642298974848, 0.14757213078351433, -0.30293609828634316, -0.36880915733251046, -0.048675467865109644, 0.6155372986772338, 1.5420301517479127, 2.619071454878234, 3.7183808742663236, 4.709021999419543, 5.47555453282872, 5.928168667781963, 6.017698652755533, 5.735970648804711, 5.120961582810897, 4.246301146447866, 3.2145761766403216, 2.140757376754168, 1.1375663742321986, 0.3012074099339032, -0.30331189037791795, -0.6464710668424712, -0.7413145168036334, -0.6349802534739873, -0.40504317363478826, -0.14209598752334643, 0.06135380827873294, 0.12872056811999794, 0.00988186970836801, -0.3091885561431848, -0.80462187999966, -1.4170583115801834, -2.062038650443356, -2.641172581693599, -3.061056611833519, -3.244575798525468, -3.149310565135514, -2.769996378873345, -2.147100177361828, -1.3565826948813415, -0.5046351348932965, 0.29135456916154895, 0.9178816564993648, 1.2834733751599319, 1.3335331346824535, 1.0578096589693486, 0.49472988033235266, -0.27563764786617084, -1.1419988218417287, -1.9784974331175824, -2.6652272305220084, -3.1034792201682446, -3.235345674501555, -3.046900838214397, -2.5761813876463875, -1.900720350339135, -1.130231777119492, -0.38454877750236865, 0.22305852217799976, 0.605296789621405, 0.7148784937357142, 0.5504224346401452, 0.1573372408408818, -0.3822420022864622, -0.9637352172285104, -1.4783012835339806, -1.8341949459888682, -1.9697305310372197, -1.8685851865685918, -1.5573661209374017, -1.1054458311233202, -0.6070760892912852, -0.16677008937684556, 0.12351246812277222, 0.20205991631201523, 0.05078062487074258, -0.2984743200333806, -0.7684340061515154, -1.2489769824554888, -1.6158183710094027, -1.7565998401759275, -1.5896592330040489, -1.087948972331205, -0.2826917892108616, 0.7308534575308084, 1.8104290148571647, 2.7843029485724915, 3.480156004275609, 3.7556200705825433, 3.5207320647002094, 2.761500074485813, 1.5402707870396797, -0.004534069727766698, -1.6819113882055436, -3.2744795761534347, -4.571261774792531, -5.404903408098279, -5.671562028875648, -5.356402045082949, -4.525474309698435, -3.3239629732923284, -1.9428167376435923, -0.5921618715371636, 0.5374937225406655, 1.3075657787455115, 1.651299487652815, 1.5888504121097464, 1.2156819250832978, 0.6896228526056589, 0.19557767006854218, -0.08615373817964568, -0.015677134323279163, 0.47944403011487996, 1.3906100389414044, 2.62703509498462, 4.0309906725629, 5.406582906352066, 6.549802552431004, 7.290706984324249, 7.513792164213759, 7.187713216724348, 6.358766020698027, 5.150881108412703, 3.7348951033666675, 2.302004163169365, 1.0296183595563009, 0.049040426627546686, -0.5682731886761245, -0.8259965839668192, -0.7868342536507269, -0.5626310480381561, -0.280228114496784, -0.058348053960814224, 0.020551978847407747, -0.07544202614970313, -0.32366371543976696, -0.6558902975171073, -0.9769855766132419, -1.192423159709003, -1.2301037549065346, -1.0660229082769554, -0.727273839183394, -0.29646835465942684, 0.11085268976251073, 0.3650676499854938, 0.35644962592502233, 0.01901873194840995, -0.648160159478373, -1.5769800506859333, -2.6359596456632, -3.657433600369112, -4.4621817245463795, -4.905083494160253, -4.893616827529695, -4.423484417066595, -3.568465246139286, -2.4834033624789464, -1.364351619966705, -0.42059085545490843, 0.17194249821121216, 0.30355117151970856, -0.04613384726517495, -0.8014380447984935, -1.8046656605895224, -2.847320327356367, -3.7064894799445702, -4.196273831180187, -4.193846424032029, -3.6767197457784393, -2.713294620164889, -1.4614180639790755, -0.12634306046749286, 1.0747937802814667, 1.9577393911944037, 2.4104703611672553, 2.4068516621758733, 2.018110672872204, 1.3846089634810563, 0.6919446818353178, 0.12236973684324845, -0.1817081820499514, -0.1495315150527471, 0.20294144066802233, 0.7808746729195464, 1.4333097483411754, 1.9903781122578688, 2.3078981269050325, 2.298613751288683, 1.9628657031312942, 1.3825582758866637, 0.7127905428625042, 0.13782038634038088, -0.16766837146030183, -0.08924835013843381, 0.3960661621629433, 1.2002539559197964, 2.1375295790998394, 2.9479153454863836, 3.3587308964801994, 3.1261027635211045, 2.1085848313684545, 0.2842073827946659, -2.214178700267967, -5.129856864589335, -8.11108677527158, -10.772541533865342, -12.768944210688094, -13.83964316896092, -13.876938470397711, -12.913602759494367, -11.143838671827165, -8.853736960719354, -6.392564659825037, -4.087981961444644, -2.2041918962739038, -0.8937357922006101, -0.18571636104053668, 0.003685846489879521, -0.16094154205525552, -0.4807540758201492, -0.7735015953139349, -0.909672360608038, -0.8416613087827147, -0.5986409314933416, -0.27454889786919284, 0.010042113495775828, 0.1433207208698332, 0.056959822849249345, -0.2529519290337294, -0.7243645452146259, -1.2457749785217027, -1.6840054377994875, -1.9254099679486025, -1.9003058686040888, -1.6127069442100714, -1.1315740904336022, -0.5837578293402562, -0.11409067029555948, 0.1482860288732456, 0.1280169118777777, -0.17338134663734014, -0.6744493040665348, -1.2307136587776388, -1.6677345023982293, -1.8303845954737497, -1.6177931270920265, -1.024593960157842, -0.1388500724642356, 0.8617921417479553, 1.7554955669568861, 2.3232254436568396, 2.4022003599382975, 1.9334276021975103, 0.9762949352982373, -0.2902633597399163, -1.6073110934775612, -2.6892457932557874, -3.284097146971232, -3.240396927249997, -2.533151266473005, -1.2881818122941249, 0.2541639637211187, 1.778665439228391, 2.9675527582934484, 3.570168027864078, 3.4517619980587577, 2.6319389386975067, 1.2690872734659697, -0.3673372132838434, -1.9616158246923647, -3.2231930108807076, -3.941585818146573, -4.041692913984297, -3.5775515953937638, -2.7282410695693775, -1.7328062837701308, -0.8390773574356896, -0.23354162952490237, 0.0008372643569102916, -0.0967562603024702, -0.37915984283575815, -0.6322737272290045, -0.6392699786678908, -0.23454279432028713, 0.6372929327402221, 1.9116490305030975, 3.4035177303551736, 4.854841173814304, 5.994010614822309, 6.595769406611338, 6.548052205675637, 5.8635462866687025, 4.696109162790947, 3.284687872624862, 1.9108980214127025, 0.8175445388364494, 0.15675277367128393, -0.05089334805585604, 0.08277003807794896, 0.3420323116652684, 0.4701304565155816, 0.23190636620480418, -0.5096340347015922, -1.7625088770960413, -3.383628449426753, -5.113447594057079, -6.631286824008281, -7.623676094512482, -7.872249908615554, -7.287610958990175, -5.95702781640485, -4.103743898395344, -2.059842470419319, -0.1781340016331384, 1.235870930844827, 1.9889893725629346, 2.0400968253995786, 1.4929639920568032, 0.5682318775054244, -0.4590548435201831, -1.3300519890339912, -1.8545581718748385, -1.9616891563725027, -1.6907659783801203, -1.1836957279102187, -0.6235179216260379, -0.18953596609862466, -0.0007686471700416995, -0.0898549215828116, -0.39850635149309716, -0.8030906438194944, -1.1536273095245557, -1.3281913289502767, -1.2633071182585371, -0.9840889069250829, -0.5859040481908842, -0.21386077710143792, -0.009565852237078926, -0.06920015576304275, -0.40796763031942723, -0.9514376264335196, -1.5522222228013316, -2.0356019123132842, -2.2457529099572593, -2.1071253081254095, -1.6413862950826417, -0.9839337286451205, -0.3383919728429107, 0.06905116113618355, 0.0663124472818837, -0.40824325027587544, -1.2660979478455705, -2.27626323362463, -3.0976129127265053, -3.3725375813632628, -2.7918621416420004, -1.2130752146413266, 1.3226367219186392, 4.542163232344098, 8.012208361261889, 11.201807019636181, 13.595457882935115, 14.813001625673014, 14.664330616988659, 13.22708803550322, 10.781928463099634, 7.7946404429662985, 4.770026434276485, 2.1791918519811797, 0.3383326758263825, -0.6270152903183928, -0.7987365503642009, -0.41365745463266373, 0.2073446627389351, 0.7602332810707525, 1.0267268032386556, 0.9373127971650149, 0.560107067104534, 0.06906749877540284, -0.31665052823753864, -0.39752431340418876, -0.09680185557120008], 'positive_zeros': ['0.34949447096554236819794990157721', '2.11069408651266285238567965591627', '3.06375294348636723508846077755882', '3.46766842693641246302661146970942', '4.51940446466197251972109600854398', '5.35194265588145884900693417578719', '5.46015142984845819772878767786781', '6.59387133494967527884977702010568', '6.68819988717016081537271772799697', '7.09979244414894395021587982845870', '8.203195787830959945570876474766649', '8.380862154553730997341495473527461', '9.340386222186197727321680144535174', '9.727433502065386965565122863579363', '9.877753904053585087025537825215335', '10.66351050982243380319133115331861', '11.04149073009512687228756808992491', '11.72469184887904304875096522313504', '12.01950614117946585443493170285251', '12.65584047590198450828423606929952'], 'prelabel': '4-192e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.2872737212055974, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c2e2-0', 'trace_hash': 402936552681280144, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.34949447096554236819794990158', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.11069408651266285238567965592', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.06375294348636723508846077756', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 27.369859079893637, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 0, 0, 0, -12, 0, -5, 0, 0, 0, -20, 0, 0, 0, 0, 0, -4, 0, 24, 0, 0, 0, 18, 0, 28, 0, 0, 0, -44, 0, 0, 0, 0, 0, 12, 0, 40, 0, 0, 0, -164, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 172, 0, 60, 0, 0, 0, -4, 0, 0, 0, 0, 0, 164, 0, -36, 0, 0, 0, 20, 0, -11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 240, 0, 88, 0, 0, 0, -188, 0, 0, 0], 'euler11': [1, 0, -210, 0, 14641], 'euler13': [1, 20, 438, 3380, 28561], 'euler17': [1, 0, -66, 0, 83521], 'euler19': [1, 4, 726, 1444, 130321], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -930, 0, 279841], 'euler29': [1, 0, -1394, 0, 707281], 'euler3': [1, 2, 9, 0, 0], 'euler31': [1, 44, 2406, 42284, 923521], 'euler37': [1, -12, 2774, -16428, 1874161], 'euler41': [1, 0, -2210, 0, 2825761], 'euler43': [1, 164, 10422, 303236, 3418801], 'euler47': [1, 0, 190, 0, 4879681], 'euler5': [1, 0, -18, 0, 625], 'euler53': [1, 0, -1746, 0, 7890481], 'euler59': [1, 0, -1554, 0, 12117361], 'euler61': [1, -172, 14838, -640012, 13845841], 'euler67': [1, 4, 8982, 17956, 20151121], 'euler7': [1, 12, 134, 588, 2401], 'euler71': [1, 0, 5406, 0, 25411681], 'euler73': [1, -164, 17382, -873956, 28398241], 'euler79': [1, -20, 12582, -124820, 38950081], 'euler83': [1, 0, -8370, 0, 47458321], 'euler89': [1, 0, -14690, 0, 62742241], 'euler97': [1, 188, 27654, 1768892, 88529281], 'euler_factors': [[1, 0, 0, 0, 0], [1, 2, 9, 0, 0], [1, 0, -18, 0, 625], [1, 12, 134, 588, 2401], [1, 0, -210, 0, 14641], [1, 20, 438, 3380, 28561], [1, 0, -66, 0, 83521], [1, 4, 726, 1444, 130321], [1, 0, -930, 0, 279841], [1, 0, -1394, 0, 707281], [1, 44, 2406, 42284, 923521], [1, -12, 2774, -16428, 1874161], [1, 0, -2210, 0, 2825761], [1, 164, 10422, 303236, 3418801], [1, 0, 190, 0, 4879681], [1, 0, -1746, 0, 7890481], [1, 0, -1554, 0, 12117361], [1, -172, 14838, -640012, 13845841], [1, 4, 8982, 17956, 20151121], [1, 0, 5406, 0, 25411681], [1, -164, 17382, -873956, 28398241], [1, -20, 12582, -124820, 38950081], [1, 0, -8370, 0, 47458321], [1, 0, -14690, 0, 62742241], [1, 188, 27654, 1768892, 88529281]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/192/3/e/c'], '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': '4-192e2-1.1-c2e2-0-0', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2], 'order_of_vanishing': 0, 'prelabel': '4-192e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.2872737212055974, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2e2-0', 'trace_hash': 402936552681280144, 'z1': {'__RealLiteral__': 0, 'data': '0.34949447096554236819794990158', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '443036875895917276306424761828,2675622625665951420531833987284', 'Lhash_array': ['443036875895917276306424761828', '2675622625665951420531833987284'], 'label': '4-192e2-1.1-c2e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/192/3/e/c'}