Formats: - HTML - YAML - JSON - 2026-03-13T12:01:14.753392
Query: /api/lfunc_lfunctions/?_offset=0
Show schema

{'Lhash': '1446138700958148892095097415151', 'a10': 0, 'a2': 0, 'a3': 27, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 397, 'a8': 0, 'a9': 729, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 69.01622508595531, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -27]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '300.101', 'coefficient_field': '1.1.1.1', 'conductor': 300, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1, -27], [1], [1, -397, 117649], [1, 0, -1771561], [1, -4033, 4826809], [1, 0, -24137569], [1, 2269, 47045881], [1, 0, -148035889], [1, 0, -594823321], [1, 59221, 887503681], [1, -89206, 2565726409], [1, 0, -4750104241], [1, 42587, 6321363049], [1, 0, -10779215329], [1, 0, -22164361129], [1, 0, -42180533641], [1, -357839, 51520374361], [1, -585397, 90458382169], [1, 0, -128100283921], [1, 638066, 151334226289], [1, 204622, 243087455521], [1, 0, -326940373369], [1, 0, -496981290961], [1, 1608263, 832972004929], [1, 0, -1061520150601], [1, 1126946, 1194052296529], [1, 0, -1500730351849], [1, -2307311, 1677100110841], [1, 0, -2081951752609]], 'euler_factors_factorization': [[1], [[[1, -27], 1]], [1], [[[1, -397, 117649], 1]], [[[1, -1331], 1], [[1, 1331], 1]], [[[1, -4033, 4826809], 1]], [[[1, -4913], 1], [[1, 4913], 1]], [[[1, 2269, 47045881], 1]], [[[1, -12167], 1], [[1, 12167], 1]], [[[1, -24389], 1], [[1, 24389], 1]], [[[1, 59221, 887503681], 1]], [[[1, -89206, 2565726409], 1]], [[[1, -68921], 1], [[1, 68921], 1]], [[[1, 42587, 6321363049], 1]], [[[1, -103823], 1], [[1, 103823], 1]], [[[1, -148877], 1], [[1, 148877], 1]], [[[1, -205379], 1], [[1, 205379], 1]], [[[1, -357839, 51520374361], 1]], [[[1, -585397, 90458382169], 1]], [[[1, -357911], 1], [[1, 357911], 1]], [[[1, 638066, 151334226289], 1]], [[[1, 204622, 243087455521], 1]], [[[1, -571787], 1], [[1, 571787], 1]], [[[1, -704969], 1], [[1, 704969], 1]], [[[1, 1608263, 832972004929], 1]], [[[1, -1030301], 1], [[1, 1030301], 1]], [[[1, 1126946, 1194052296529], 1]], [[[1, -1225043], 1], [[1, 1225043], 1]], [[[1, -2307311, 1677100110841], 1]], [[[1, -1442897], 1], [[1, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 23255766, 'index': 26, 'label': '2-300-3.2-c6-0-26', 'leading_term': '4.21809544435116268502304089112115265969106666924966595100000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/300/7/g/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [4.218095444351163, 4.198392798115687, 4.13958166525438, 4.042548421304684, 3.9087569134301403, 3.7402283909558003, 3.539513608528555, 3.309657309460298, 3.0541553658487364, 2.776904927592634, 2.4821480149921795, 2.174409079337532, 1.8584271522971816, 1.5390833070205476, 1.2213242600928647, 0.9100830516889131, 0.6101978487961685, 0.3263300200655317, 0.06288272713498604, -0.1760786377268988, -0.3869027681928091, -0.5664240651510681, -0.7120280868278708, -0.8217093532045427, -0.8941200627060589, -0.9286083459642063, -0.9252447849854402, -0.8848360678610433, -0.8089248298678893, -0.6997749509624936, -0.5603418356274006, -0.3942274908898269, -0.2056205379030464, 0.000778363736061996, 0.21984483852936104, 0.4461316533518703, 0.6739805291336981, 0.8976429618735571, 1.111407767204146, 1.309732752103671, 1.4873776489627997, 1.6395352320407925, 1.7619573847982266, 1.8510728081771686, 1.9040930628169614, 1.919103728980635, 1.8951376511363949, 1.8322275118584042, 1.7314353515255392, 1.594857112908004, 1.4256008368512612, 1.2277377575516863, 1.006226230999485, 0.7668091627764533, 0.5158863636134784, 0.2603640326933521, 0.007484327520541718, -0.23536129815223203, -0.46083064444693395, -0.661836281550369, -0.8317526394423125, -0.964618937212855, -1.055332024843455, -1.099823181222083, -1.0952130589045352, -1.039939295741322, -0.9338518276375041, -0.7782716312748561, -0.5760094903787293, -0.33134239762736967, -0.04994635404078848, 0.2612144196849514, 0.5940405235063286, 0.9394899804978474, 1.2878063691953645, 1.6287771651861678, 1.952015782274047, 2.24725975834616, 2.5046766721882325, 2.7151687437876206, 2.8706666957633376, 2.964403364367501, 2.991157763799456, 2.947460836849262, 2.831754967400003, 2.644500474474217, 2.388223730588995, 2.0675032154562927, 1.6888916853122111, 1.2607746546201073, 0.7931674886182273, 0.2974555237817216, -0.21391630399588954, -0.7277959115174217, -1.2307084611169583, -1.709261102253437, -2.150555357130197, -2.5425937279164077, -2.874666824494451, -3.137707502219385, -3.32459917344951, -3.4304266120057036, -3.452659185741566, -3.3912584904500216, -3.2487047621782623, -3.0299391420525206, -2.742221770819453, -2.3949087004837777, -1.9991536199528006, -1.5675432877961457, -1.113678234540937, -0.6517126293164541, -0.1958690991047699, 0.24005434628643013, 0.6431673672237963, 1.001942300244162, 1.306623667440852, 1.5495760029586494, 1.72555573850526, 1.8318954324103984, 1.8685917067895188, 1.8382917730427337, 1.7461772537472307, 1.5997480077834423, 1.408512681329539, 1.1835965792216323, 0.9372810174756302, 0.6824914228296459, 0.432253946006065, 0.19914212822015995, -0.005263893299641965, -0.17088310349686506, -0.2895825907929737, -0.35554993179627026, -0.3655718016966761, -0.31920511390937784, -0.2188311542528213, -0.06958786481400733, 0.12081952996341921, 0.3424241799067642, 0.5834090620055424, 0.8306089242533707, 1.0700831058964724, 1.2877360231141275, 1.4699594053183882, 1.6042687035998011, 1.6799055769525613, 1.6883790550326334, 1.6239198886803858, 1.4838256882378276, 1.268678618195194, 0.9824225169230386, 0.6322921474277745, 0.2285936245991993, -0.21565835916540288, -0.6852343603135339, -1.163296727192369, -1.6320949694752918, -2.0737214092379808, -2.4708950540106787, -2.8077394520047956, -3.0705195858472214, -3.2483037125742253, -3.333518475012842, -3.3223695323546165, -3.215105253933644, -3.0161074906126677, -2.7338008226717916, -2.3803796707980838, -1.9713608987062192, -1.524977659970705, -1.061437869207744, -0.6020774412450224, -0.16844400251424083, 0.21864915658066097, 0.5400567832353584, 0.7791804625355532, 0.9227514712503196, 0.9614800936734668, 0.8905390966882623, 0.7098559855696941, 0.42419693930617763, 0.04303459895421862, -0.4197982585827153, -0.946657138958107, -1.5168146694836107, -2.107339347991661, -2.6940861032598065, -3.252754627724468, -3.759967473104182, -4.194318138010804, -4.5373399598743624, -4.774349576757435, -4.895123957676143, -4.894377308435262, -4.77201323198916, -4.533137951452474, -4.187831706488587, -3.750687071248822, -3.240134346148308, -2.677584776617981, -2.0864316065599997, -1.4909563946199635, -0.9151932008705407, -0.38180588737542837, 0.0889663122362923, 0.4802426577777174, 0.7792674407590959, 0.9779704130525578, 1.0732923817624198, 1.0672589067574665, 0.966797729018604, 0.7833086442074773, 0.5320073462629464, 0.2310766302562847, -0.09933137254667407, -0.43819011658958407, -0.7647333821218704, -1.0595699128192237, -1.3057185817148909, -1.4895084260154048, -1.6012946169850744, -1.6359508661598, -1.5931104560125184, -1.477141433829519, -1.2968558321949006, -1.0649673213930495, -0.7973256738939131, -0.5119690588168502, -0.22804577126322748, 0.0353350792850011, 0.2602596299988626, 0.43110649039674626, 0.5355218669311792, 0.5652151944498549, 0.5165270562304258, 0.39073320529514177, 0.19406277742027514, -0.06257543801760822, -0.3641483780053415, -0.692309274215889, -1.0264219399059578, -1.3447443271314568, -1.6257067275326649, -1.8492132431535584, -1.9978922922286444, -2.0582231842282783, -2.0214712176021203, -1.8843731082628112, -1.6495274058225167, -1.3254602495755399, -0.9263545332837484, -0.47144932993111116, 0.01586476429361796, 0.5092109375114368, 0.980592989134866, 1.4018918437238659], 'positive_zeros': ['1.14080228471298342731741822162528', '2.06227224211623678837787118552562', '3.50187900956859998443671390843009', '4.38540583706417364227158082969548', '5.72398594822435853726354419863477', '7.02761702238040497799653042976207', '8.123241532980737018300444978874131', '8.586782077583325752919664268291629', '9.595242057166109947420286453477098', '10.83859781761554513856711293286289'], 'prelabel': '2-300-3.2-c6-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.307600440918865, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c6-0', 'trace_hash': 179724127718397737, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.14080228471298342731741822163', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.06227224211623678837787118553', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.50187900956859998443671390843', 'prec': 103}}