-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1641230654372059077648569645963,1715255885429512076926105265587', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 5, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.03420060467464, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [13, [1, -6, 13]]], 'bad_primes': [2, 13], 'central_character': '416.1', 'coefficient_field': '1.1.1.1', 'conductor': 173056, 'conductor_radical': 26, 'degree': 4, 'euler_factors': [[1], [1, 0, -5, 0, 9], [1, 2, 11, 10, 25], [1, 0, -5, 0, 49], [1, -4, 26, -44, 121], [1, -6, 13], [1, -6, 43, -102, 289], [1, 0, 38, 0, 361], [1, -12, 82, -276, 529], [1, 0, -22, 0, 841], [1, 0, -62, 0, 961], [1, 6, 83, 222, 1369], [1, 0, 18, 0, 1681], [1, 0, -5, 0, 1849], [1, 0, -45, 0, 2209], [1, 0, -70, 0, 2809], [1, -20, 218, -1180, 3481], [1, 0, -22, 0, 3721], [1, 24, 278, 1608, 4489], [1, 0, -117, 0, 5041], [1, 0, -110, 0, 5329], [1, 0, 158, 0, 6241], [1, 32, 422, 2656, 6889], [1, 0, -162, 0, 7921], [1, 0, 130, 0, 9409], [1, 0, -202, 0, 10201], [1, 8, 222, 824, 10609], [1, 0, -70, 0, 11449], [1, 30, 443, 3270, 11881], [1, 12, 262, 1356, 12769]], 'euler_factors_factorization': [[1], [[[1, 0, -5, 0, 9], 1]], [[[1, 1, 5], 2]], [[[1, 0, -5, 0, 49], 1]], [[[1, -2, 11], 2]], [[[1, -6, 13], 1]], [[[1, -3, 17], 2]], [[[1, 0, 19], 2]], [[[1, -6, 23], 2]], [[[1, 0, -22, 0, 841], 1]], [[[1, 0, -31], 2]], [[[1, 3, 37], 2]], [[[1, -8, 41], 1], [[1, 8, 41], 1]], [[[1, 0, -5, 0, 1849], 1]], [[[1, 0, -45, 0, 2209], 1]], [[[1, 0, -70, 0, 2809], 1]], [[[1, -10, 59], 2]], [[[1, -12, 61], 1], [[1, 12, 61], 1]], [[[1, 12, 67], 2]], [[[1, 0, -117, 0, 5041], 1]], [[[1, -16, 73], 1], [[1, 16, 73], 1]], [[[1, 0, 79], 2]], [[[1, 16, 83], 2]], [[[1, 0, -162, 0, 7921], 1]], [[[1, -8, 97], 1], [[1, 8, 97], 1]], [[[1, 0, -101], 2]], [[[1, 4, 103], 2]], [[[1, 0, -70, 0, 11449], 1]], [[[1, 15, 109], 2]], [[[1, 6, 113], 2]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 14, 'label': '4-416e2-1.1-c1e2-0-14', '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/416/2/e/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [2.0875691943467856, 2.0843190255513133, 2.077496662172872, 2.0639821330679924, 2.0423631965453737, 2.0114036455684645, 1.9687574447627427, 1.911953640093326, 1.8387144267814812, 1.7471666503000916, 1.6359873231210846, 1.5046852222964981, 1.3539735880475088, 1.185855796866201, 1.0040075595649947, 0.8136853848757428, 0.6220233451245679, 0.437707009653083, 0.27104664428253433, 0.13340592369381535, 0.036948382957470285, -0.006140343215299334, 0.01573120669622508, 0.11269039997745912, 0.2924971906708201, 0.5597687957169647, 0.9149995642571914, 1.354106957528602, 1.8677048119201327, 2.441171290754646, 3.054560981366535, 3.6832817467934813, 4.2989751070575215, 4.870691680795197, 5.366880578920996, 5.756713076674953, 6.013023440861684, 6.113223886957531, 6.042707446385132, 5.794718699828775, 5.373480934023338, 4.792516177796315, 4.076716570160963, 3.258967714766682, 2.3806245872032563, 1.4868201221590234, 0.6253102694164822, -0.1586116409654864, -0.8243058497066816, -1.3400093373585462, -1.684944932863144, -1.8514858847187847, -1.845901212797652, -1.6878045431688316, -1.4086081146680307, -1.0485129400477338, -0.6525819048794212, -0.2665208095842903, 0.06866544995706497, 0.3201901473711724, 0.4684508927839908, 0.5079663038776246, 0.4500051242133834, 0.31991843932414926, 0.15620453778041765, 0.004665965039445169, -0.08583771407895992, -0.07048808053137044, 0.0858585521787854, 0.4030628127144484, 0.8816985990392759, 1.501309812316442, 2.220899575920934, 2.981814103808058, 3.714012503742211, 4.342050687368959, 4.7959286910853836, 5.016710468222314, 4.968418938006626, 4.639297174978701, 4.0502685761153545, 3.2492545559599164, 2.3128670368169155, 1.3341685925483866, 0.4172804879359637, -0.33776905983738, -0.8442178346567628, -1.0410957106622516, -0.9004489959240329, -0.4323957457961426, 0.3151064601895033, 1.2602132552051863, 2.2972670876785455, 3.3067534359107627, 4.1728607171702, 4.7929300465323506, 5.096141745533061, 5.045518636051523, 4.650370758443933, 3.957181409412886, 3.0513040602840986, 2.0386696893758316, 1.0377591011728504, 0.15916542632415936, -0.5058043264091409, -0.8990087717764086, -1.00182112535644, -0.8367897232192071, -0.4631934767438154, 0.032730860808490886, 0.5525376305296487, 0.999580919089067, 1.2972364406541945, 1.3973369142938796, 1.292446963582362, 1.0119492757035666, 0.6220521065842461, 0.21001093251307063, -0.12708946244585187, -0.30216059578478255, -0.2521506116836514, 0.04872559416765275, 0.5831844558776889, 1.2910583918775669, 2.0785865811244353, 2.8302868531749823, 3.431187930989628, 3.7805636108094944, 3.8165579868175885, 3.5196856690839136, 2.927063841691874, 2.1191882211730335, 1.2169358378955568, 0.3556168651404112, -0.3311740555396107, -0.7374203046434407, -0.8008853130097656, -0.5150357731816209, 0.06870289235290314, 0.8486685701945584, 1.6901482383316244, 2.4457991235281904, 2.9848813359527275, 3.210479195892899, 3.084604373271344, 2.6274787786831855, 1.924061621122071, 1.1019352017262325, 0.31670353250140465, -0.28058838069102515, -0.5671629649566603, -0.4728910097747979, 0.0061689604989283485, 0.8054509814983887, 1.8020688685976576, 2.833570000287541, 3.729806300698357, 4.336696542170643, 4.552620013049889, 4.336532701909502, 3.727870647305784, 2.828236666632714, 1.7946676808022641, 0.8022650480544518, 0.019327364864764603, -0.4278697011208088, -0.4761762061490128, -0.13822004278006392, 0.5003054396149615, 1.2953225176695646, 2.0744624019626663, 2.664013871081841, 2.930284493377972, 2.794160950500788, 2.259161426892464, 1.3972189135999806, 0.34833008538063354, -0.7180377355436895, -1.6258442430762947, -2.232773920334455, -2.4528876815021703, -2.274082086984829, -1.757884070002104, -1.0260960635196614, -0.2328735076844632, 0.4644262232172951, 0.9436631436416071, 1.13592156044221, 1.0480761070021498, 0.7514622667303835, 0.37393111245525734, 0.06415417981169225, -0.037330731063257516, 0.16640528626624515, 0.7060177822453249, 1.5353706352828875, 2.5391417538918555, 3.551759234494625, 4.396360889034915, 4.912709865048561, 5.003685527279042, 4.642409565534328, 3.8957443481758327, 2.895916505607688, 1.828410159802008, 0.8818030707530451, 0.21642169367725667, -0.07489054121042618, 0.015553742916213179, 0.4078627620615741, 0.9530780501660011, 1.4648157257395888, 1.7663574110355547, 1.7257207450465732, 1.2981635338333892, 0.530166619551167, -0.43479201417834107, -1.3931873816296165, -2.1159431583272172, -2.402130742941421, -2.123346051095397, -1.2547810090688807, 0.11195361400405204, 1.7822366016337794, 3.496085187668532, 4.970711768240345, 5.968389207599454, 6.326440090340768, 6.010961803103778, 5.09987277593895, 3.789586956021467, 2.3332805464889397, 1.0060046875344248, 0.036596622161780286, -0.4294361191911981, -0.36037252370477063, 0.1626092666318812, 0.9660467816605881, 1.8303426134684317, 2.5333448234456952, 2.9101984763909314, 2.874245822199526, 2.447725017782134, 1.7357468273341436, 0.9109474945103937, 0.15808578538351362, -0.3639303338293264, -0.5636026651213727, -0.4352110406016779, -0.05631025090327393, 0.4360891573603163, 0.8822972754590899, 1.148132479814139, 1.1553011162843099, 0.9121359024598127, 0.503496723667224, 0.0776514359913389, -0.1999272223265597, -0.1881776552095768, 0.18652885735485814, 0.9052643687822016, 1.8540394057121303, 2.8485938227917935, 3.6710966892834276, 4.1338247121755645, 4.113554413628295, 3.6058254946666928, 2.712512918749952, 1.6441956905169848, 0.656352661658812, 0.0038510327277970252, -0.13073040825404614, 0.3196868507093424, 1.2817041935480993, 2.5531094674263035, 3.83993286534197, 4.8290004692475845, 5.245950799316061, 4.939446700308801, 3.896885049435876, 2.277780840252486, 0.3584326329296293, -1.5049264859592828, -2.9689655317213823, -3.7674187242095214, -3.773827165729341, -3.0247626445985785, -1.711058628927692, -0.12737564301043663, 1.3857044650354116, 2.5336332653039615, 3.1090464411168797, 3.0577810994432935, 2.4541760437324065, 1.4996974838001447, 0.44484106159093123, -0.4589830359676658, -1.0295399740238156, -1.1884292135540577, -0.9708637199044069, -0.5061152361153409, 0.027766997212521603, 0.4607556913876125, 0.675630080566886, 0.6467680356880009, 0.4340347614071732, 0.1676878734753015, -0.004617706721790957, 0.03482520375366363, 0.3267038578433401, 0.8136445054464184, 1.3455302428083018, 1.7200893793566485, 1.7312561999056115, 1.2440705255620874, 0.22796486219246476, -1.200796447810334, -2.809290386288486, -4.278364895366097, -5.282971538026713, -5.565671078909493, -5.0008069438399385, -3.6351269128387864, -1.6805001562067037, 0.5288655272447983, 2.60225282170434, 4.193735394253642, 5.0537453732895035, 5.110778391123633, 4.444977877758127, 3.2933682789988223, 1.9540082040177529, 0.7330363335075374, -0.14590252814341348, -0.5799877233101622, -0.6032044016916943, -0.35785659373037626, -0.039101298000235346, 0.17812764996026045, 0.19502583164954326, 0.03318888047482781, -0.1754412740766662, -0.21965308645610232, 0.12061304997882666, 1.0010855030746038, 2.453026596416267, 4.352126922508574, 6.429007713423503, 8.33089996175419, 9.686160382349758, 10.221287480227192, 9.798404722541326, 8.495076208127946, 6.55124556829384, 4.354641396072564, 2.319702332965185, 0.8138485841690407, 0.05986704194741811, 0.09564730332397596, 0.7718980762928495, 1.8021540477805256, 2.8367770666713796, 3.5676416202738044, 3.787695590250321, 3.4601789294343908, 2.6926137449656298, 1.7189684595588246, 0.8068375675208093, 0.19127546942793855, 0.0011588703946543845, 0.23058505450289926, 0.7463740959330408, 1.3382285040576478, 1.7813805664720275, 1.91921019269274, 1.6974987074930226, 1.1976755059617898, 0.5930982427882494, 0.10633313832998952, -0.07429659489578452, 0.14605060179980833, 0.7291257992386724, 1.5091486170079274, 2.232604638419054, 2.6410773814587025, 2.5359040513568334, 1.8644406632033852, 0.7222248922347291, -0.6393562982458196, -1.8971359716955112, -2.7260798309920022, -2.8999515806848213, -2.3507803728576273, -1.1959102804154207, 0.29638004395241263, 1.7652700873082732, 2.873779334691388, 3.3695835069412863, 3.1858995408697868, 2.4148364395930666, 1.3121611762404881, 0.18609814618527573, -0.6719144127395572, -1.0855001840832637, -1.037198007749085, -0.6639332023741538, -0.21011628376370015, 0.06425358633987628, -0.02313265527688103, -0.504224407096096, -1.22893111894414, -1.8955029262352936, -2.1303011341038993, -1.5909935423853339, -0.08484751606743389, 2.3670164643702543, 5.500797804241363, 8.854119763250468, 11.877203496292633, 14.031554937026106, 14.958054305519155, 14.506157879265452, 12.824629151013504, 10.25939778847747, 7.3163014271587095, 4.497301378074934, 2.2127155006989603, 0.6870983580087371, -0.0638069287255927, -0.19903323153978514, 0.018616253293312002, 0.31613342457455207, 0.4965337213548539, 0.4777455711922539, 0.30509779011831245, 0.09952334416040991, 0.00013350703227769673, 0.09277861239147646, 0.3697957375189233, 0.7240020727542051, 0.9883827496832732, 0.9914120848372584, 0.638042276813917, -0.05956458815256619, -0.9535849266356307, -1.8142533406473589, -2.386478820752377, -2.483194484930946, -2.0510274932632457, -1.2020171763222465, -0.18823074246192742, 0.6628892229494957, 1.0664834533723895, 0.8576470259967435, 0.09029826694125313, -0.9862716900336591, -1.9513810387903883, -2.346742915869623, -1.794368177655656, -0.1233412123539299, 2.561962419864509, 5.881662452820518, 9.268913593802093, 12.080248753904288, 13.790793931868489, 14.071193847368567, 12.929512120527274, 10.635770270578389, 7.708567811635329, 4.725559770858309, 2.2156785638205405, 0.5140368855644402, -0.29006661643241244, -0.3434178200515459, 0.04669157714317922, 0.5255704944948972, 0.8146903306994613, 0.7800236217551565, 0.4730484163755622, 0.0761269840126805, -0.16679933068645922, -0.05775233654872791, 0.4792269921594793, 1.3615253003331411, 2.373678485654754, 3.228860503393237, 3.680723161190451, 3.5844455661822834, 2.976185910448108, 2.03369664538671, 1.0467953065194908, 0.30098319729881984, -0.00262088942496538, 0.17992694240970533, 0.7263596162765519, 1.3898217922176395, 1.8946005027970734, 2.0238934211802255, 1.7205620122302954, 1.0933891042253379, 0.40919886884016504, -0.013232725616023186, 0.09640059245013811, 0.8497043295563418, 2.1442623343623124, 3.6691402118764262, 4.988295583616531, 5.649808400658988, 5.363297980000246, 4.03628062145209, 1.841062069775615, -0.7895883760778095], 'positive_zeros': ['1.29470269968441608072715738381038', '1.35309831046559301069422652712771', '2.92416774946599500699904970660033', '3.61102415332154168227078522061350', '4.06480225066723033621650033340203', '4.22324818397657834157527136280546', '5.28237839942400213115685528030003', '5.60103366058374838686862810103465', '6.45057159331266784874117649187092', '6.80857743730259293062239842643336', '7.34864537020561679716376479234195', '7.55506918318717107045340125087495', '8.342221936283905436847609548820810', '8.618797312506838930781956045142054', '9.279794348719621932061108838308524', '9.499410376287534354260725032362309', '10.25192866628245335004599790863663', '10.45332787133852351827811142107601', '11.02002109623427657805421566936635', '11.51934658035853730324972508151537'], 'prelabel': '4-416e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.8225742026280483, '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': 123489097273877693, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.29470269968441608072715738381', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.35309831046559301069422652713', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.92416774946599500699904970660', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 11.03420060467464, 'bad_primes': [2, 13], 'central_character': '1.1', 'conductor': 173056, 'conductor_radical': 26, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -2, 0, 0, 0, 5, 0, 4, 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 12, 0, -7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 5, 0, 0, 0, 0, 0, -8, 0, 0, 0, 20, 0, 0, 0, 0, 0, -12, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, -32, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0], 'euler11': [1, -4, 26, -44, 121], 'euler13': [1, -6, 13, 0, 0], 'euler17': [1, -6, 43, -102, 289], 'euler19': [1, 0, 38, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -12, 82, -276, 529], 'euler29': [1, 0, -22, 0, 841], 'euler3': [1, 0, -5, 0, 9], 'euler31': [1, 0, -62, 0, 961], 'euler37': [1, 6, 83, 222, 1369], 'euler41': [1, 0, 18, 0, 1681], 'euler43': [1, 0, -5, 0, 1849], 'euler47': [1, 0, -45, 0, 2209], 'euler5': [1, 2, 11, 10, 25], 'euler53': [1, 0, -70, 0, 2809], 'euler59': [1, -20, 218, -1180, 3481], 'euler61': [1, 0, -22, 0, 3721], 'euler67': [1, 24, 278, 1608, 4489], 'euler7': [1, 0, -5, 0, 49], 'euler71': [1, 0, -117, 0, 5041], 'euler73': [1, 0, -110, 0, 5329], 'euler79': [1, 0, 158, 0, 6241], 'euler83': [1, 32, 422, 2656, 6889], 'euler89': [1, 0, -162, 0, 7921], 'euler97': [1, 0, 130, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -5, 0, 9], [1, 2, 11, 10, 25], [1, 0, -5, 0, 49], [1, -4, 26, -44, 121], [1, -6, 13, 0, 0], [1, -6, 43, -102, 289], [1, 0, 38, 0, 361], [1, -12, 82, -276, 529], [1, 0, -22, 0, 841], [1, 0, -62, 0, 961], [1, 6, 83, 222, 1369], [1, 0, 18, 0, 1681], [1, 0, -5, 0, 1849], [1, 0, -45, 0, 2209], [1, 0, -70, 0, 2809], [1, -20, 218, -1180, 3481], [1, 0, -22, 0, 3721], [1, 24, 278, 1608, 4489], [1, 0, -117, 0, 5041], [1, 0, -110, 0, 5329], [1, 0, 158, 0, 6241], [1, 32, 422, 2656, 6889], [1, 0, -162, 0, 7921], [1, 0, 130, 0, 9409]], 'index': 14, 'instance_types': ['ECNF', 'HMF', 'CMF'], 'instance_urls': ['EllipticCurve/2.2.104.1/16.1/e', 'ModularForm/GL2/TotallyReal/2.2.104.1/holomorphic/2.2.104.1-16.1-e', 'ModularForm/GL2/Q/holomorphic/416/2/e/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-416e2-1.1-c1e2-0-14', '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': '4-416e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.8225742026280483, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 123489097273877693, 'z1': {'__RealLiteral__': 0, 'data': '1.29470269968441608072715738381', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 10650713
{'Lhash': '1641230654372059077648569645963,1715255885429512076926105265587', 'Lhash_array': ['1641230654372059077648569645963', '1715255885429512076926105265587'], 'label': '4-416e2-1.1-c1e2-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/416/2/e/a'}
-
id: 9463203
{'Lhash': '_1641230654372059077648569645963', 'Lhash_array': ['_1641230654372059077648569645963'], 'label': '4-416e2-1.1-c1e2-0-14', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.104.1/holomorphic/2.2.104.1-16.1-e'}
-
id: 9463214
{'Lhash': '_1641230654372059077648569645963', 'Lhash_array': ['_1641230654372059077648569645963'], 'label': '4-416e2-1.1-c1e2-0-14', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.104.1/16.1/e'}