-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1090424961078908481949437335412,3327703455453820779328774272632,3864981155923801717504895815022,4884587312533140388355016419594', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': -2, 'a5': 0, 'a6': 0, 'a7': -8, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.12190887035483554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 2, 0, 1]], [37, [1, -16, 138, -592, 1369]]], 'bad_primes': [2, 37], 'central_character': '74.1', 'coefficient_field': '1.1.1.1', 'conductor': 29986576, 'conductor_radical': 74, 'degree': 8, 'euler_factors': [[1, 0, 2, 0, 1], [1, 2, 3, 8, 25, 24, 27, 54, 81], [1, 0, -5, 0, 9, 0, -125, 0, 625], [1, 8, 52, 200, 646, 1400, 2548, 2744, 2401], [1, -6, 47, -180, 801, -1980, 5687, -7986, 14641], [1, 0, -37, 0, 633, 0, -6253, 0, 28561], [1, 0, -8, 0, -162, 0, -2312, 0, 83521], [1, 0, -16, 0, 30, 0, -5776, 0, 130321], [1, 0, -77, 0, 2493, 0, -40733, 0, 279841], [1, 0, -101, 0, 4185, 0, -84941, 0, 707281], [1, 0, -25, 0, 1653, 0, -24025, 0, 923521], [1, -16, 138, -592, 1369], [1, -30, 491, -5220, 39501, -214020, 825371, -2067630, 2825761], [1, 0, -100, 0, 6198, 0, -184900, 0, 3418801], [1, 12, 200, 1548, 14526, 72756, 441800, 1245876, 4879681], [1, -12, 224, -1764, 18270, -93492, 629216, -1786524, 7890481], [1, 0, -176, 0, 13950, 0, -612656, 0, 12117361], [1, 0, -13, 0, 5169, 0, -48373, 0, 13845841], [1, 2, 175, 308, 16681, 20636, 785575, 601526, 20151121], [1, 0, 116, 0, 13446, 0, 584756, 0, 25411681], [1, -10, 235, -1780, 25333, -129940, 1252315, -3890170, 28398241], [1, 0, -85, 0, 11973, 0, -530485, 0, 38950081], [1, -24, 380, -4824, 51606, -400392, 2617820, -13722888, 47458321], [1, 0, -284, 0, 36006, 0, -2249564, 0, 62742241], [1, 0, -184, 0, 20478, 0, -1731256, 0, 88529281], [1, -12, 416, -3492, 63774, -352692, 4243616, -12363612, 104060401], [1, 0, -361, 0, 53373, 0, -3829849, 0, 112550881], [1, -6, 347, -1656, 53385, -177192, 3972803, -7350258, 131079601], [1, 0, -364, 0, 56886, 0, -4324684, 0, 141158161], [1, 0, 40, 0, 7038, 0, 510760, 0, 163047361]], 'euler_factors_factorization': [[[[1, 0, 1], 2]], [[[1, 1, 1, 3, 9], 2]], [[[1, 0, -5, 0, 9, 0, -125, 0, 625], 1]], [[[1, 2, 7], 4]], [[[1, -3, 19, -33, 121], 2]], [[[1, 0, -37, 0, 633, 0, -6253, 0, 28561], 1]], [[[1, 0, -8, 0, -162, 0, -2312, 0, 83521], 1]], [[[1, 0, -16, 0, 30, 0, -5776, 0, 130321], 1]], [[[1, 0, -77, 0, 2493, 0, -40733, 0, 279841], 1]], [[[1, 0, -101, 0, 4185, 0, -84941, 0, 707281], 1]], [[[1, 0, -25, 0, 1653, 0, -24025, 0, 923521], 1]], [[[1, -8, 37], 2]], [[[1, -15, 133, -615, 1681], 2]], [[[1, 0, -50, 0, 1849], 2]], [[[1, 6, 82, 282, 2209], 2]], [[[1, -6, 94, -318, 2809], 2]], [[[1, 0, -176, 0, 13950, 0, -612656, 0, 12117361], 1]], [[[1, 0, -13, 0, 5169, 0, -48373, 0, 13845841], 1]], [[[1, 1, 87, 67, 4489], 2]], [[[1, 0, 58, 0, 5041], 2]], [[[1, -5, 105, -365, 5329], 2]], [[[1, 0, -85, 0, 11973, 0, -530485, 0, 38950081], 1]], [[[1, -12, 118, -996, 6889], 2]], [[[1, 0, -142, 0, 7921], 2]], [[[1, 0, -184, 0, 20478, 0, -1731256, 0, 88529281], 1]], [[[1, -6, 190, -606, 10201], 2]], [[[1, 0, -361, 0, 53373, 0, -3829849, 0, 112550881], 1]], [[[1, -3, 169, -321, 11449], 2]], [[[1, -20, 109], 2], [[1, 20, 109], 2]], [[[1, 0, 40, 0, 7038, 0, 510760, 0, 163047361], 1]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 1, 'label': '8-74e4-1.1-c1e4-0-1', '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}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/74/2/b/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.03125', 'prec': 24}, 'plot_values': [0.2885874323798437, 0.2895746440741251, 0.29020222426311565, 0.29079835796780285, 0.2916846344371145, 0.2931006758750747, 0.2949694542224117, 0.2971241229257905, 0.2993815577799491, 0.30155797369313225, 0.3035256687037074, 0.30515602549999793, 0.3062978301706469, 0.3067671974554335, 0.3063234700123814, 0.3046856352875836, 0.3015351731357098, 0.296513872746613, 0.28922645343454445, 0.2792329595463334, 0.26604344227499005, 0.2491151403996764, 0.22785300469956152, 0.20160722172113654, 0.16967092204278036, 0.13128155325106322, 0.08563040792500756, 0.031859236719321934, -0.03093964351262595, -0.10371579745618131, -0.18744045463723324, -0.2831071347117339, -0.3917263228626611, -0.5143085049284525, -0.6518285181619439, -0.8052238151145585, -0.9753831586459851, -1.1631185256394116, -1.3691118918536602, -1.5939131770670147, -1.8379244647453281, -2.1013623730612645, -2.3841903525952075, -2.6861218356223975, -3.0066054431320293, -3.3447850736456015, -3.699429510936696, -4.068949272850069, -4.451392459174834, -4.8444164663835805, -5.245236946481127, -5.650667264077575, -6.057136775131496, -6.460692791063311, -6.856998333397132, -7.2413978935741365, -7.608966752306205, -7.954560338721314, -8.272888762567899, -8.558599539128139, -8.806355445820294, -9.01093700684627, -9.167406186448261, -9.271176982190886, -9.318100789593517, -9.304606163980077, -9.227933953003507, -9.086146842596872, -8.878181276361254, -8.603983116937913, -8.264760183166208, -7.8628743455063725, -7.401809442072386, -6.886245108850615, -6.322247580331181, -5.717006733151659, -5.0786835353918045, -4.416372797420446, -3.7401598038925203, -3.0607164816599224, -2.3890361995021463, -1.7362781497541004, -1.1136673509710961, -0.5320379971201897, -0.0015277607226301462, 0.46863734257130657, 0.870340156728309, 1.196930751331919, 1.4434466054737076, 1.6067696633704567, 1.6857865222399895, 1.6814908583301629, 1.5969899810355048, 1.4374783567252103, 1.2102118674179503, 0.924279391457953, 0.5903446717122495, 0.22038294020143412, -0.17259984347467455, -0.5750410706677958, -0.9732545338833423, -1.3538478702391084, -1.704173180894138, -2.012796780299107, -2.2698827377968747, -2.467553066689761, -2.6002796514638424, -2.665040047178694, -2.6613968209729397, -2.5915669190847885, -2.460506395093657, -2.275568973500255, -2.0461632291073637, -1.7834395495955069, -1.4999824487809876, -1.2090757502496046, -0.92408304714704, -0.6579175082753902, -0.42253676046263466, -0.22820875619170666, -0.08299459375980434, 0.007625080093148824, 0.04105047141267193, 0.017826234572137518, -0.058334694379763144, -0.18068165477137718, -0.33966694592844254, -0.523363372338527, -0.7180355876489936, -0.908804115755395, -1.0803877139008777, -1.2179334363162237, -1.3078404793104283, -1.338550229265603, -1.3012884938233842, -1.1906770770328359, -1.0051946577924518, -0.7474677620489684, -0.42434223750867633, -0.04673835489540397, 0.3706863970515727, 0.8101133238969184, 1.2514626454150106, 1.6732489354071158, 2.053553660654488, 2.3711937359011714, 2.6071515451824885, 2.7454199173955764, 2.7738567352282693, 2.685111734753421, 2.4775890906187343, 2.1553939267304267, 1.7282719326229643, 1.211508477159777, 0.6256065734090486, -0.004922402221631091, -0.6526533590853055, -1.288405699026224, -1.8827415732405228, -2.4075529214163116, -2.8373759800078147, -3.150717362263451, -3.3316400650889815, -3.3703981214306213, -3.2637963808919794, -3.015543821921054, -2.636703093448003, -2.1446136282526846, -1.5618014851480195, -0.9149990368602895, -0.23420653374783823, 0.4494752624119619, 1.105620001786928, 1.705924210420853, 2.2254873483443576, 2.6444426957423657, 2.948946029855811, 3.1317019778614013, 3.19216629658983, 3.1364194322820085, 2.9765339085233866, 2.7295980059418863, 2.4164707205061875, 2.0602752982302945, 1.6848232781201127, 1.3130357947431932, 0.9654176709573553, 0.6588442953455318, 0.4056423565941764, 0.21296724752670657, 0.08257047919051949, 0.011158173888241606, -0.008991564669144544, 0.010879019532894569, 0.05732362328196693, 0.11608971351476671, 0.17341600582030434, 0.2173372209292936, 0.23906499387671415, 0.2335901324800579, 0.19994502138788886, 0.1412604254618966, 0.06459625827725866, -0.020264025654718094, -0.10212278708850733, -0.1697116148819392, -0.21312285009619145, -0.2255842224296431, -0.20479898054268764, -0.1538832595823721, -0.08191151770809167, -0.0039628096720663916, 0.0595135582727195, 0.08391470904163818, 0.042272609617908546, -0.09254438313187721, -0.34536553094353073, -0.7361319144852961, -1.2773781142871292, -1.9721780085564014, -2.812555896982243, -3.778620763307177, -4.838900731501681, -5.9512132093656795, -7.06429514630623, -8.12064622611364, -9.061176239590912, -9.828332593432268, -10.369607879578568, -10.64199774479732, -10.61769576268694, -10.285037489324997, -9.649479939273805, -8.735004648784601, -7.585624661326845, -6.260607800907228, -4.830344530595557, -3.3727410757597758, -1.969348891260268, -0.6972063714684176, 0.37723399172868705, 1.2027670791237652, 1.7474907305004512, 2.0032778693326136, 1.9872644035918858, 1.741286439292557, 1.3298365041620501, 0.8364285771240613, 0.3578560820272305, -0.0027815865259327834, -0.14365896671303313, 0.027916506871180902, 0.5877279105623052, 1.5878238279832897, 3.0518535339472357, 4.971593876999556, 7.305184094504527, 9.978315518506369, 12.890216453823902, 15.91789496694515, 18.921996026354655, 21.75606766011098, 24.280948657543416, 26.369910320719505, 27.914677052445597, 28.83412948632639, 29.08624197493191, 28.664358812652562, 27.595042852263415, 25.938281745638754, 23.789056081162364, 21.26383734496481, 18.491046764722903, 15.60461160785933, 12.738685137934839, 10.014415218469178, 7.532401532089136, 5.3687873898149086, 3.573149539157344, 2.1655154206201366, 1.1377936294442847, 0.45762070820741785, 0.07350390647409646, -0.07919454838877174, -0.0713874248394073, 0.026521631732388744, 0.15087541877621274, 0.24969364714971928, 0.28599934182618275, 0.23952770591096564, 0.10668118844981647, -0.10148167745755339, -0.3623586746897852, -0.6458537561347226, -0.9193728328426343, -1.152122076029826, -1.3187187513338487, -1.402303813687643, -1.3970830703102108, -1.3077570124103823, -1.1481515745087683, -0.9393727716835508, -0.7073649754861033, -0.4784121264848533, -0.2755944316598369, -0.11612879450502239, -0.00940464032116611, 0.04445674237825758, 0.054160998627833835, 0.03549686041997757, 0.008663854488077358, -0.005141418489607785, 0.012424938076849136, 0.07322067247611333, 0.17970663536841047, 0.3230993957923395, 0.48291388710860406, 0.6281232318023593, 0.7200899801784423, 0.7165465772033447, 0.5765342797578762, 0.2659436023757493, -0.23708073939746077, -0.9379558613017241, -1.8224988353870022, -2.855593750495841, -3.9830983114512013, -5.134674515971168, -6.228169783024701, -7.1765337742799415, -7.898247338593656, -8.323290599563663, -8.39919754142781, -8.097907645682804, -7.423011042294395, -6.407714331368591, -5.112391378265999, -3.6215896835128176, -2.0390214306375873, -0.4763196605667087, 0.9565135580691401, 2.160106925380066, 3.055460794359329, 3.5911577985931578, 3.747134733289135, 3.536503035849656, 3.0057776812586607, 2.2282496217265497, 1.2960233258050033, 0.31150134000551544, -0.6218577466262541, -1.4111911467965004, -1.9831178686536461, -2.2901450759890603, -2.3146345359627767, -2.0698271109358726, -1.597299517748785, -0.96149832377845, -0.24133641952680665, 0.4789498132816336, 1.1190704515131908, 1.6119231667016187, 1.9124134891111968, 2.0010007674990904, 1.884918646111055, 1.597337291543303, 1.1938522916801628, 0.7438322247701937, 0.321637827443824, -0.0022865291901295855, -0.17054748990288077, -0.14667712862192678, 0.08009571402906893, 0.4927578449118726, 1.0476626682666461, 1.6793224778309424, 2.307312624721543, 2.8450421052662223, 3.210768374191536, 3.3366210201732116, 3.1760453618132356, 2.7098334569524316, 1.9502685849927042, 0.9392693576547048, -0.25563140696551484, -1.5475989248263826, -2.8399826086287647, -4.035846281183968, -5.046765546869232, -5.801845845991815, -6.257270859333821, -6.3967724785044915, -6.230859417534214, -5.7957150887540605, -5.151113659475529, -4.368854090572701, -3.5239399696546614, -2.687905976193507, -1.9230146884370085, -1.2741240856523617, -0.765942479244187, -0.40353286737125, -0.17466869069710092, -0.05350702449427766, -0.006555663155613791, 0.0010135521293666069, -0.00033435618843861677, 0.01099186265590436, 0.04512045928673595, 0.10037689824429558, 0.16513200753406979, 0.22153177552067893, 0.2504055637725743, 0.23655982149669602, 0.17353225915387532, 0.06680671464969182, -0.06489891058739873, -0.19071504854556903, -0.27155228491759514, -0.26561746037282663, -0.13501503517011879, 0.14700845084276093, 0.5891716753285513, 1.1782847696767058, 1.8775587733764523, 2.627849515189362, 3.353350104806254, 3.9694703137936598, 4.392084104406278, 4.548726599498465, 4.391855089106559, 3.9053174339341665, 3.1085353610241913, 2.058808317613, 0.8503682877858714, -0.3970433917973835, -1.550530428176709, -2.47725643825311, -3.059436347889462, -3.2107414020182734, -2.887605840280293, -2.09596256174388, -0.8930286771036958, 0.6165529266943064, 2.290510171240016, 3.9638760047703863, 5.469022909948004, 6.652671599425402, 7.3923066063676774, 7.61147082536447, 7.2920958795994295, 6.472940304839563, 5.244566851008571, 3.740268491233083, 2.1207745702135927, 0.5524605871432254, -0.8116855017710659, -1.8497770404748286, -2.4878473288799103, -2.7067311211667406, -2.542072116709749, -2.079300648109064, -1.4430306227672594, -0.7769664782645934, -0.22380392303930416, 0.09406052276294086, 0.09232262581579219, -0.26275748040971647, -0.9492672161982101, -1.8916200996560069, -2.971211448813207, -4.042968748705886, -4.954649932531633, -5.569048846769951, -5.789136667438191, -5.57127404640695, -4.933012038833592, -3.956600123233815, -2.786174297914321, -1.6071476588225688, -0.6242473500763007, -0.038376002850580314, -0.020624248336379075, -0.6866613135318981, -2.0803485111625633, -4.164684446936209, -6.820149459924905, -9.85559530977927, -13.026926448468986, -16.06168408547326, -18.689798592556407, -20.671797658693315, -21.8230013484648, -22.03400504171935, -21.286437513748755, -19.649361869445126, -17.269459651978313, -14.35597866076523, -11.159061874798306, -7.938898080158804, -4.939270478413132, -2.364352523826083, -0.3583439729404835, 1.0041637762464404, 1.7191403490905826, 1.847754753145767, 1.5043770636113851, 0.8359451063595035, 0.0018861082030935978, -0.8452864691511079, -1.5790402662943352, -2.110103716408387, -2.3912021258795813, -2.4175438625477326, -2.2233322262343105, -1.868388751433468, -1.4250305316315004, -0.9662417774495603, -0.5549565571680294, -0.2343955921865474, -0.02455489484801577, 0.07699076438639456, 0.09115072004444318, 0.05010055799800318, -0.011172235711247949, -0.06263315477884973, -0.08520337094616666, -0.07419602401028046, -0.03914965487551103, -0.00047722870670359767, 0.016251985892572242, -0.012805841277387956, -0.10295226236567559, -0.25563215248522486, -0.45644965403246057, -0.676014084038971, -0.8736463101529698, -1.0043226993251742, -1.0288507081576685, -0.92142006650143, -0.6760771487027043, -0.3116623689576179, 0.12679507155990438, 0.5735717022533929, 0.9498640270266185, 1.1739250709185305, 1.1747711939034702, 0.903531025693888, 0.3417946086639487, -0.49263970744318986, -1.5436902655592468, -2.723707334284326, -3.9232122318578333, -5.023679132422522, -5.914378063422215, -6.50591572791115, -6.740558943093161, -6.600577630608516, -6.114214250222093, -5.346950838586979, -4.390902699581786, -3.3534733051313186, -2.3444724420745686, -1.4574380613946132, -0.7579366265176577, -0.27743628113158786, -0.011774252227033388, 0.07523319485034044, 0.04178234775586023, -0.04515571794892659, -0.12441803258334004, -0.15408266644611118, -0.12113444730295522, -0.04600866712639548, 0.019049722303477006, -0.0016520912567755954, -0.19415672215020813, -0.6386383209299278, -1.3925704044980192, -2.47660201792195, -3.8645229687218317, -5.479901449054868, -7.2039942730149775, -8.886392021313908, -10.359831505179882, -11.461838292899252, -12.065397958940437, -12.090084988266037, -11.510279833152975, -10.363490182243945, -8.757385104680463, -6.84605944878694, -4.808432050633943, -2.829879724563617, -1.084373008285955, 0.295060401779303, 1.231771636057976, 1.7102747998935552, 1.7737275096080665, 1.5169278954981513, 1.069172847514696, 0.5725040617982452, 0.15957631855245377, -0.06487412138381835, -0.0385271711353545, 0.2508996412416207, 0.7678147014203419, 1.437673213209832, 2.160041542412499, 2.8262434115956387, 3.3413620460504627, 3.6365601255094515, 3.6770223781085307, 3.4668621922481107, 3.049832546363208, 2.495052658694535, 1.8828515274356865, 1.2918903133127149, 0.7871675576068619, 0.40795071040118935, 0.16431041259396298, 0.0400219393663842, 0.00015114577923894154, 0.002340881291916338, 0.009738333029786368, 0.002221765190335755, -0.016444715476280063, -0.017377664382389576, 0.048078875433095324, 0.23704754773043443, 0.5999660541340712, 1.1645196738598513, 1.9212723703354335, 2.8148576487966674, 3.7465148390825207, 4.582210205703445, 5.168106784999285, 5.355492855351028, 5.035412897308517, 4.158751693287556, 2.752660480212624, 0.9321525191525545, -1.1005863839956702, -3.0826217923510457, -4.7217411941896845, -5.735355863101135, -5.901148538975341, -5.098087719130871, -3.334782737442218, -0.7671948157804734, 2.298790116004716, 5.438683777550883, 8.153527369226396, 9.92614288207183, 10.292264133294355, 8.9034356391029, 5.57799074293138, 0.33959496109137877, -6.565243983237995, -14.690367912611043, -23.42778127707354, -32.06631109375998, -39.88399198041566, -46.219613088594066, -50.533462398668796, -52.47158670218029, -51.93793817332794, -49.06705130801372, -44.190125196554234, -37.805202643399724, -30.544623154120636, -23.0624870929968, -15.95714225993792, -9.72151941319063, -4.708520799164089, -1.088233606409991, 1.1491950172868588, 2.1645470898652084, 2.227216001878699, 1.6667640367868641, 0.8178190165818172, -0.029434387083417782, -0.6664750739202925, -0.9850111838283846, -0.9784984130117241, -0.7278486692069618, -0.373645857131111, -0.0800245023461248, 0.0007972821048512197, -0.2404363365643861, -0.8493257765256478, -1.8004839110812576, -3.0014771145692127, -4.30832972339054, -5.555132508766156, -6.579781973647592, -7.246638327989845, -7.467702975647539, -7.221901958284576, -6.549482492538432, -5.54048628477168, -4.320670327185611, -3.034701626905752, -1.81945911703788, -0.7849822153241879, -0.0027815169550639385, 0.4994363695712327, 0.7362783800978604, 0.7559944066847851, 0.627623686876385, 0.4263434965841984, 0.21982667481521254, 0.05836895366697886, -0.03068396622516831, -0.043224034723806655, 0.006213202202244446, 0.09122000238104039, 0.1815901972007286, 0.2519622767311832, 0.28649362694976793, 0.28049052222490106, 0.23989972831262435, 0.1787125220086444, 0.1131582256721939, 0.05701940927451673, 0.018596143007817537, -0.0006133792747189353, -0.005147017989838664, -0.002643177321111129, -0.0001284101416057994, -0.000661318000251577, -0.001413667507433584, 0.005970775648818373, 0.03261029336145714, 0.08776380424535127, 0.17356331252886542, 0.28038038634522555, 0.38450673880248676, 0.450494403315323, 0.4362995338571558, 0.3013256088357487, 0.017684334216160204, -0.41616226815908114, -0.9694446282770629, -1.5769346897420016, -2.141196879979909, -2.5422718280595773, -2.6579967712584467, -2.38526775401111, -1.661529848805604, -0.4852028394790443, 1.0729004422300494, 2.8690419013009447, 4.697182345136067, 6.313914783782345, 7.470342602558247, 7.947048888019896, 7.590713066350797, 6.349581411328993, 4.284726083643902, 1.569208545065849, -1.526096599235494, -4.665036488234974, -7.492635580956536, -9.681029017562906, -10.976653988664633, -11.247103352569543, -10.491994877839575, -8.84000684173139, -6.534850863334658, -3.9047757270104, -1.3014884476004815, 0.9510125317739553, 2.6005042563225613, 3.5065550868814634, 3.6576593052333397, 3.162740519439074, 2.227626452488306, 1.119478785192395, 0.10979203978826566, -0.5767391769965494, -0.8012834068332123, -0.5362331058920156, 0.12716633302438277, 0.9967092732981714, 1.815838503142655, 2.31071085715692, 2.242264229780534, 1.4551687310671217, -0.08716308158135455, -2.2958187038968605, -4.963046908456006, -7.785456471502332, -10.410217167129787, -12.509642925394235, -13.82008191889422, -14.17438050619873, -13.533570239680987, -12.013090286423425, -9.840600412777556, -7.312690048443234, -4.754020865732944, -2.4743782210072647, -0.7080409175675447, 0.4180516372571179, 0.8934607634402771, 0.8151485873881734, 0.3616851527687018, -0.24790873122604568, -0.8008824523436219, -1.1358950450697904, -1.1735763735796656, -0.9302140452460222, -0.5137640011225845, -0.10105053437538478, 0.1016548371562237, -0.0981036994423296, -0.836906344337602, -2.1631833284574604, -4.022467316049006, -6.258787876811676, -8.634428160323301, -10.874802108374544, -12.709050812316258, -13.907612882911462, -14.31982281860772, -13.91103875823998, -12.753732365304536, -11.008040491792055, -8.897313304831304, -6.677748304165177, -4.588553423820366, -2.8166070832523857, -1.4749860560126467, -0.5946029986845847, -0.1315291141262186, 0.012963159046261868, -0.03503202703548847, -0.1530027026753786, -0.24766225314664272, -0.2688610986338996, -0.21272763058494357, -0.11297771588505708, -0.019148892316365455, 0.02736122712876761, 0.015410728599620938, -0.019697399165197225, 0.006751757927250465, 0.2185671506979453, 0.7572871736458108, 1.7490917959317929, 3.271468626307216, 5.327048189300561, 7.826910782146266, 10.585693061202162, 13.341140855532798, 15.78791943687905, 17.62114148151407, 18.58554570933537, 18.51735371761815, 17.374295734408665, 15.25019397643819, 12.367742259089402, 9.044550986251773, 5.650349297451663, 2.5556637534751325, 0.0732730690325271, -1.583040308454529, -2.3221838979864997, -2.1846510283736436, -1.332482116610552, -0.010543436420907196, 1.4964686197283623, 2.909315600098769, 4.0022034904722945, 4.631602027175696, 4.746906064802333, 4.388928833034696, 3.6771892567062627, 2.7716373478016623, 1.836921212214341, 1.0133068674357653, 0.3948890313146043, 0.015622236924280204, -0.14662112263021806, -0.15405871113818373, -0.08622068767744802, -0.015159271582791563, 0.015749481052554987, 0.004361372618194192, -0.009234180733116368, 0.046982560630574224, 0.25789451778221817, 0.6971023241168662, 1.405056426081635, 2.373434329028052, 3.537218898996569, 4.779215093858078, 5.954402888337077, 6.911181108238328, 7.513696791755121, 7.667991820764383, 7.351182101293743, 6.607091704666015, 5.53537675547031, 4.277358410287553, 2.99666013745039, 1.8441782047856008, 0.9332065256069053, 0.3242610326876519, 0.019271148157737103, -0.03227319199019722, 0.0824586287601499, 0.26122488753330975, 0.41132612604823865, 0.46898836193356136, 0.4098461878829672, 0.25118588934753233, 0.04441283271078308, -0.14327954957199082, -0.24813320351670964, -0.22766999592422033, -0.07572059285814975, 0.17427456590882823, 0.45615328261221394, 0.6848201069492664, 0.7750086201975683, 0.6634175505324809, 0.3254468233832701, -0.21629237556094402, -0.8946092219154966, -1.609424095448382, -2.2461468108270592, -2.6991243969112078, -2.8978391271000894, -2.8181929813340267, -2.4855207976347806, -1.9705198254487344, -1.3764974232470706, -0.8112034003639076, -0.363109860907985, -0.08383723977352038, 0.022047354415230275, -0.0038929894295936067, -0.0887320154879012, -0.15144850205618438, -0.13062355074230833, -0.009025557038544263, 0.17132822727609437, 0.3071340793593515, 0.24758879376384385, -0.17647095092972054, -1.115039852515438, -2.659457611719076, -4.8109382230579545, -7.462251924012857, -10.396193927191181, -13.308006227531209, -15.86115998617978, -17.731472180422525, -18.653581958274486, -18.473792138348415, -17.204437445131987, -15.003825757465208, -12.147384511196824, -8.994001128373784, -5.940098695475196, -3.3331555139053717, -1.4155624026639217, -0.29330213663120863, 0.07515488741017415, -0.1333138378762307, -0.6504529168388056, -1.1764580569026752, -1.4459354964383224, -1.2830924422889767, -0.6367759808218338, 0.40962765771826215, 1.6574888124150335, 2.8431628021776394, 3.700259464321531, 4.025194637332354, 3.7357640856527405, 2.9013548631746073, 1.7430794339647753, 0.6035458775093251, -0.11435311827118241, -0.025666525776030524, 1.1581229717358978, 3.5604180541403525, 7.1005586101503395, 11.492574857621811, 16.272604123225822, 20.862305355685272, 24.681209453161276, 27.227203841439522, 28.144963421534538, 27.290436777268265, 24.785868297112206, 20.96944751341909, 16.332212904089573, 11.449410018103423, 6.90056203141773, 3.16431665675228, 0.5536062486459896, -0.8168306784993286, -1.0328603043562055, -0.34368485309232577, 0.8966789961666555, 2.2986741061719442, 3.512718443460378, 4.287415133930729, 4.499186560522219, 4.158397708192165, 3.3915273031932154, 2.39320942256713, 1.3783695163616658, 0.539752132972524, 0.010411099038497785, -0.17126311383514267, -0.06420930007559461, 0.20464761130389403, 0.5074440705260845, 0.7499674207499678], 'positive_zeros': ['0.860193621872294310796872716452911', '2.62509516017638999425379875923573', '3.04893253332420279706449546079034', '3.77761671350164625409554474866234', '3.85325996899596242988396231978730', '4.34737798094927207572296928874737', '4.84351231959469134717944299118268', '5.32315482422903812575679653539712', '5.97832402100446085088432750212595', '6.02007695550803456404350041039465', '6.33636746403213413824536341217024', '6.59542030368139108942676692191673', '6.70025664105353145292165270197554', '7.48824916527483325333338914894425', '7.78092525267977142108962169786429', '7.84117264190993255120497014888631', '8.822974507471760822583719598981369', '8.899194145903140863029741060291120', '9.079728672022026253730412723330957', '9.566375257743002105551904355024597', '9.700846868135914281300537808868306', '9.736437178033479842865496534244490', '10.04927674140541890680663199484613', '10.60372255719571875243541001958686', '10.91633864637183167844453857724990', '11.19778113783628699812117761310847', '11.53096802022679387544575129822110', '11.61663988693689817395718213544293', '11.99360225742833307502145749866160', '12.64020750102322277673949082459330', '12.66999285057884744547093174535970', '12.69090853689407699925217616715432', '12.98493668412561973418339308322415', '13.14215444081536577234990046141126', '13.58372145412640746794111169644029', '13.83156345533807426231772609099838', '14.23068044913168063095737893912014', '14.51857667129917132603272307750547', '14.57429349606826310858075089622765', '15.03541603439504904094907466769774'], 'prelabel': '8-74e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.7686956321961737, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e4-0', 'trace_hash': 2230594572410133578, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.860193621872294310796872716453', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.62509516017638999425379875924', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.04893253332420279706449546079', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.12190887035483554, 'bad_primes': [2, 37], 'central_character': '1.1', 'conductor': 29986576, 'conductor_radical': 74, 'degree': 8, 'dirichlet_coefficients': [1, 0, -2, -2, 0, 0, -8, 0, 1, 0, 6, 4, 0, 0, 0, 3, 0, 0, 0, 0, 16, 0, 0, 0, 5, 0, -4, 16, 0, 0, 0, 0, -12, 0, 0, -2, 16, 0, 0, 0, 30, 0, 0, -12, 0, 0, -12, -6, 12, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -4, 0, 0, -2, 0, 0, 0, 0, 0, 10, 0, -10, 0, -48, 0, 0, 0, -4, 0, 24, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -10], 'euler11': [1, -6, 47, -180, 801, -1980, 5687, -7986, 14641], 'euler13': [1, 0, -37, 0, 633, 0, -6253, 0, 28561], 'euler17': [1, 0, -8, 0, -162, 0, -2312, 0, 83521], 'euler19': [1, 0, -16, 0, 30, 0, -5776, 0, 130321], 'euler2': [1, 0, 2, 0, 1, 0, 0, 0, 0], 'euler23': [1, 0, -77, 0, 2493, 0, -40733, 0, 279841], 'euler29': [1, 0, -101, 0, 4185, 0, -84941, 0, 707281], 'euler3': [1, 2, 3, 8, 25, 24, 27, 54, 81], 'euler31': [1, 0, -25, 0, 1653, 0, -24025, 0, 923521], 'euler37': [1, -16, 138, -592, 1369, 0, 0, 0, 0], 'euler41': [1, -30, 491, -5220, 39501, -214020, 825371, -2067630, 2825761], 'euler43': [1, 0, -100, 0, 6198, 0, -184900, 0, 3418801], 'euler47': [1, 12, 200, 1548, 14526, 72756, 441800, 1245876, 4879681], 'euler5': [1, 0, -5, 0, 9, 0, -125, 0, 625], 'euler53': [1, -12, 224, -1764, 18270, -93492, 629216, -1786524, 7890481], 'euler59': [1, 0, -176, 0, 13950, 0, -612656, 0, 12117361], 'euler61': [1, 0, -13, 0, 5169, 0, -48373, 0, 13845841], 'euler67': [1, 2, 175, 308, 16681, 20636, 785575, 601526, 20151121], 'euler7': [1, 8, 52, 200, 646, 1400, 2548, 2744, 2401], 'euler71': [1, 0, 116, 0, 13446, 0, 584756, 0, 25411681], 'euler73': [1, -10, 235, -1780, 25333, -129940, 1252315, -3890170, 28398241], 'euler79': [1, 0, -85, 0, 11973, 0, -530485, 0, 38950081], 'euler83': [1, -24, 380, -4824, 51606, -400392, 2617820, -13722888, 47458321], 'euler89': [1, 0, -284, 0, 36006, 0, -2249564, 0, 62742241], 'euler97': [1, 0, -184, 0, 20478, 0, -1731256, 0, 88529281], 'euler_factors': [[1, 0, 2, 0, 1, 0, 0, 0, 0], [1, 2, 3, 8, 25, 24, 27, 54, 81], [1, 0, -5, 0, 9, 0, -125, 0, 625], [1, 8, 52, 200, 646, 1400, 2548, 2744, 2401], [1, -6, 47, -180, 801, -1980, 5687, -7986, 14641], [1, 0, -37, 0, 633, 0, -6253, 0, 28561], [1, 0, -8, 0, -162, 0, -2312, 0, 83521], [1, 0, -16, 0, 30, 0, -5776, 0, 130321], [1, 0, -77, 0, 2493, 0, -40733, 0, 279841], [1, 0, -101, 0, 4185, 0, -84941, 0, 707281], [1, 0, -25, 0, 1653, 0, -24025, 0, 923521], [1, -16, 138, -592, 1369, 0, 0, 0, 0], [1, -30, 491, -5220, 39501, -214020, 825371, -2067630, 2825761], [1, 0, -100, 0, 6198, 0, -184900, 0, 3418801], [1, 12, 200, 1548, 14526, 72756, 441800, 1245876, 4879681], [1, -12, 224, -1764, 18270, -93492, 629216, -1786524, 7890481], [1, 0, -176, 0, 13950, 0, -612656, 0, 12117361], [1, 0, -13, 0, 5169, 0, -48373, 0, 13845841], [1, 2, 175, 308, 16681, 20636, 785575, 601526, 20151121], [1, 0, 116, 0, 13446, 0, 584756, 0, 25411681], [1, -10, 235, -1780, 25333, -129940, 1252315, -3890170, 28398241], [1, 0, -85, 0, 11973, 0, -530485, 0, 38950081], [1, -24, 380, -4824, 51606, -400392, 2617820, -13722888, 47458321], [1, 0, -284, 0, 36006, 0, -2249564, 0, 62742241], [1, 0, -184, 0, 20478, 0, -1731256, 0, 88529281]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/74/2/b/a'], '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': '8-74e4-1.1-c1e4-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-74e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.7686956321961737, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 2230594572410133578, 'z1': {'__RealLiteral__': 0, 'data': '0.860193621872294310796872716453', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1090424961078908481949437335412,3327703455453820779328774272632,3864981155923801717504895815022,4884587312533140388355016419594', 'Lhash_array': ['1090424961078908481949437335412', '3327703455453820779328774272632', '3864981155923801717504895815022', '4884587312533140388355016419594'], 'label': '8-74e4-1.1-c1e4-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/74/2/b/a'}