-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '472111600671867552619053515414', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [133.90336518870967, -77.3091439370983], 'a6': [0, 0], 'a7': [-2234.881045370244, -877.5578117963543], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 102.6594097354041, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2234.881045370244, 877.5578117963543]]]], 'bad_primes': [2, 3, 7], 'central_character': '252.73', 'coefficient_field': 'CDF', 'conductor': 252, 'conductor_radical': 42, 'conjugate': '935337108571752152893588121622', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-133.90336518870967, 77.3091439370983], [195312.5, -338291.17335329636]], [[1.0, 0], [2234.881045370244, 877.5578117963543]], [[1.0, 0], [3950.923127202026, -6843.199593112824], [-107179440.5, -185640236.47280544]], [[1.0, 0], [0, 4177.6430754308185], [-815730721.0, 0]], [[1.0, 0], [110619.75063227704, 63866.342805234424], [3487878720.5, 6041183154.544328]], [[1.0, 0], [-139247.1117698546, 80394.35746420345], [8491781520.5, -14708197040.280493]], [[1.0, 0], [-16422.380443453545, -28444.397309287047], [-39155492640.5, 67819302648.73526]], [[1.0, 0], [659559.5604265513, 0], [500246412961.0, 0]], [[1.0, 0], [5163.532445604447, 2981.1668474390945], [426445518720.5, 738625305083.9708]], [[1.0, 0], [-329534.27259593195, -570770.1029714065], [-1756239726960.5, 3041896437366.4785]], [[1.0, 0], [0, 1102084.272809809], [-7984925229121.0, 0]], [[1.0, 0], [-4571526.068385214, 0], [11688200277601.0, 0]], [[1.0, 0], [-1359051.7679748973, 784648.9040829438], [11905643330880.5, -20621179145878.59]], [[1.0, 0], [4310266.562060368, -7465600.679653789], [-31129845205680.5, -53918473527993.055]], [[1.0, 0], [18551096.998145267, 10710480.845642028], [73415218802160.5, 127158889014127.92]], [[1.0, 0], [-21659708.907388464, 12505238.768249664], [95853656498640.5, -166023403146900.03]], [[1.0, 0], [9657050.110539723, -16726501.442693442], [-203033838778320.5, -351664924419799.25]], [[1.0, 0], [9509184.65936376, 0], [645753531245761.0, 0]], [[1.0, 0], [-6916953.305576103, -3993504.8529464346], [403230045947040.5, 698414926718607.0]], [[1.0, 0], [1327774.498293007, 2299772.8920377637], [-758554404953280.5, 1313854769684258.8]], [[1.0, 0], [0, -53742115.84538775], [-2252292232139041.0, 0]], [[1.0, 0], [-33312144.340561535, 19232775.50230687], [1968294402851040.5, -3409185909991446.0]], [[1.0, 0], [0, 25675375.904235464], [-7837433594376961.0, 0]], [[1.0, 0], [-137264978.15709394, -79249972.0893063], [5414283528140400.0, 9377814157322450.0]], [[1.0, 0], [23686228.267452862, -13675250.266300833], [6333850406938080.0, -10970550712357564]], [[1.0, 0], [-80859671.90197548, -140053060.0175711], [-8590930899159600.0, 14879928801657808]], [[1.0, 0], [29516515.651236698, -51124104.77034393], [-9962813208450960.0, -17256098663355364]], [[1.0, 0], [-164112891.22178167, 0], [26584441929064320, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-252-7.3-c8-0-9', 'leading_term': '1.265514560091667368490167423536326182601811324541127074', 'load_key': 'CMFs-workshop', 'motivic_weight': 8, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [8], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/252/9/z/d/73/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.2655145600916673, 1.128659018538072, 0.9561268791206607, 0.751402699016099, 0.518639116306904, 0.2625754225269246, -0.011555418605723844, -0.2981296746458899, -0.5912438575053715, -0.8848318767273322, -1.172786233278333, -1.4490810530916667, -1.707894690052498, -1.9437295923801887, -2.1515271264821165, -2.32677509008758, -2.4656057232150896, -2.564882142222623, -2.6222712792345098, -2.636301606391358, -2.6064041606696886, -2.532935658704211, -2.417182799489947, -2.2613471924994815, -2.0685107151327577, -1.8425814910825415, -1.5882210837788937, -1.3107539093251404, -1.016060283218, -0.7104549159423919, -0.40055305500843924, -0.09312682557249968, 0.2050453612573214, 0.4873331935937132, 0.7474092853063427, 0.9794009435849341, 1.1780353016897247, 1.3387742447146922, 1.4579356439729476, 1.5327975907080593, 1.561682583433885, 1.544018974304605, 1.4803774151584193, 1.3724805574512375, 1.2231848438977677, 1.036433872505168, 0.8171835027068327, 0.5712995932053839, 0.3054299947427804, 0.02685314960984572, -0.2566936465629928, -0.5372026068166852, -0.8065961323175883, -1.0569349964620742, -1.2806288193548312, -1.470643339016144, -1.6206988431778644, -1.7254541316368683, -1.780670541993022, -1.783350895267037, -1.7318487019447446, -1.6259436082185599, -1.4668798464377195, -1.2573653679130166, -1.0015303602963548, -0.704844961289151, -0.3739971468848802, -0.016732963750337997, 0.35833754291237463, 0.7419642189274083, 1.1245049682499764, 1.4961917244258935, 1.8474069742103818, 2.168962988358529, 2.452375535809325, 2.69012371519877, 2.87588764801527, 3.0047561496569, 3.0733971290858895, 3.0801843571335525, 3.0252753714855767, 2.910636627968432, 2.740013529591943, 2.5188446257880224, 2.2541210265574363, 1.9541938664048453, 1.6285344236034063, 1.2874531918117293, 0.9417857533576871, 0.6025546583147505, 0.28061761637508525, -0.013686889035701148, -0.27088499349325146, -0.48269219048198236, -0.64230605702082, -0.7446563053434042, -0.7866025892921139, -0.7670719528293695, -0.6871296010770455, -0.5499787529041468, -0.3608876371974576, -0.12704415062236488, 0.14265877781430827, 0.4379015577450953, 0.7472720795157104, 1.058645452266372, 1.3595972359714175, 1.6378365031052622, 1.8816439391821196, 2.080299559081347, 2.2244845202850803, 2.3066419792845334, 2.3212829679492097, 2.265224846123071, 2.1377519773216425, 1.9406908175058568, 1.678394524288495, 1.3576353899224551, 0.9874067658103179, 0.5786395579031015, 0.14384170333613228, -0.3033278409512673, -0.7485362840412166, -1.1772887214338685, -1.5754559862337918, -1.9297991138929944, -2.2284705062787316, -2.461472240664101, -2.621053097960275, -2.7020277642003414, -2.7020042415114767, -2.621508711311441, -2.464000817078413, -2.23577644587455, -1.9457594355355028, -1.6051880516735577, -1.2272063901044152, -0.8263748886760774, -0.41811770560298733, -0.01812767961897328, 0.35824820953393144, 0.6966186275038017, 0.9841282825461163, 1.209984910632126, 1.3659104406934548, 1.4464965134493, 1.4494479968334362, 1.3757023813928402, 1.2294177961585653, 1.0178276741657606, 0.7509656073370844, 0.4412694367770803, 0.10307889331948654, -0.2479540963977408, -0.5955192092392287, -0.9233391697629917, -1.2158701938284722, -1.4589817716329212, -1.6405863632828956, -1.7511910860458861, -1.7843462219811799, -1.7369692829541084, -1.6095282988423523, -1.406073756612982, -1.1341149829289014, -0.8043434673663956, -0.43021238045878035, -0.02738805289605385, 0.38690484641684536, 0.7946175454537423, 1.1776598519335546, 1.518697525046444, 1.8019292266702478, 2.0138081339077507, 2.1436750591435185, 2.184273222231067, 2.1321195416851952, 1.9877132794484595, 1.7555698463690272, 1.4440752594675925, 1.0651648028986662, 0.6338375210339187, 0.16752589241268598, -0.3146529681586011, -0.7927322972790071, -1.2467800088570067, -1.6577925484314584, -2.008557295880501, -2.284443251834608, -2.4740823552069804, -2.5699082099409694, -2.5685250819695318, -2.4708875132864305, -2.2822794664739336, -2.0120911776544474, -1.6734014330590776, -1.2823823447342726, -0.8575524319503023, -0.41891148317480853, 0.013003113939038356, 0.4180944624813537, 0.7776721710876602, 1.0753596177990152, 1.2978978656506215, 1.4358059183565715, 1.483863335853459, 1.4413893406199874, 1.3123020766112512, 1.1049521946387997, 0.8317359334050659, 0.508503810713613, 0.15379139108921028, -0.21209217255629242, -0.5680744975461601, -0.8933802940601945, -1.168589444663237, -1.3766399148647952, -1.5037244905463352, -1.5400348574615583, -1.4803134797710358, -1.324182796636047, -1.0762320216341559, -0.7458537864448324, -0.3468354329607146, 0.1032777021710355, 0.5840177911501969, 1.0729889978517129, 1.546972396284729, 1.983086386765987, 2.3599439929948143, 2.658747702217071, 2.864264841686646, 2.965631805055177, 2.9569435323833106, 2.83759513812008, 2.6123549702083206, 2.2911620579716745, 1.8886551738561177, 1.4234548561141322, 0.9172329702758905, 0.39361601272007224, -0.12302226372645639, -0.6088167317385605, -1.0416497041666979, -1.4023071265316345, -1.6754900968713025, -1.8506265264019615, -1.9224376703262018, -1.8912267484064724, -1.7628713141990597, -1.5485166773820187, -1.2639837130689924, -0.9289199463222108, -0.5657370293927193, -0.198389839308592, 0.14893827976038862, 0.4531736752843171], 'positive_zeros': ['0.37243038467135028281951216893618', '1.95674817507699207403755588209029', '3.06843874032464523081167967058525', '4.19034136234666608457813439661173', '5.68442460753204632615197450310891', '6.34283763245255591160741764860690', '7.52019819826220690555533112849975', '8.690404144015235067338493123339271', '9.518461419261189731728590383619437', '10.44165580998872261185614725524729'], 'prelabel': '2-252-7.3-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.13209799278531, 'root_angle': -0.2545783522790814, 'root_number': '0.6968634484445423603955870702918081160716992143671125317 - 0.7172038303174214446170559467980014305512741411901099551*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1272891761395407', 'prec': 64}, 'spectral_label': 'c8-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.37243038467135028281951216894', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.95674817507699207403755588209', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.06843874032464523081167967059', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 102.6594097354041, 'bad_primes': [2, 3, 7], 'central_character': '7.3', 'conductor': 252, 'conductor_radical': 42, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/252/9/z/d/73/3'], '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': '2-252-7.3-c8-0-9', 'motivic_weight': 8, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [8], 'order_of_vanishing': 0, 'prelabel': '2-252-7.3-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.13209799278531, 'root_angle': -0.1272891761395407, 'self_dual': False, 'spectral_label': 'c8-0', 'z1': {'__RealLiteral__': 0, 'data': '0.37243038467135028281951216894', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '472111600671867552619053515414', 'Lhash_array': ['472111600671867552619053515414'], 'label': '2-252-7.3-c8-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/252/9/z/d/73/3'}