-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '329194019974130607253962300915,1578012150496048397813012945969', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': -1, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.3637904678775588, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [1, 1, 1]], [5, [1]], [7, [1]]], 'bad_primes': [3, 5, 7], 'central_character': '3675.1', 'coefficient_field': '1.1.1.1', 'conductor': 13505625, 'conductor_radical': 105, 'degree': 4, 'euler_factors': [[1, 0, 1, 0, 1], [1, 1, 1], [1], [1], [1, 0, 1, 0, 1], [1, 2, 3, 2, 1], [1, 0, 1, 0, 1], [1, 1, 0, 1, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, -2, 3, -2, 1], [1, 1, 0, 1, 1], [1, 0, -2, 0, 1], [1, 4, 6, 4, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 1, 0, 1, 1], [1, 1, 0, 1, 1], [1, 0, -2, 0, 1], [1, -1, 0, -1, 1], [1, -1, 0, -1, 1], [1, 0, -2, 0, 1], [1, 0, 1, 0, 1], [1, 2, 3, 2, 1], [1, 0, 1, 0, 1], [1, -1, 0, -1, 1], [1, 0, 1, 0, 1], [1, -1, 0, -1, 1], [1, 0, -2, 0, 1]], 'euler_factors_factorization': [[[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, 1, 1], 1]], [1], [1], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, 1, 1], 2]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, 1], 2], [[1, -1, 1], 1]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, -1], 2], [[1, 1], 2]], [[[1, -1, 1], 2]], [[[1, 1], 2], [[1, -1, 1], 1]], [[[1, -1], 2], [[1, 1], 2]], [[[1, 1], 4]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, 1], 2], [[1, -1, 1], 1]], [[[1, 1], 2], [[1, -1, 1], 1]], [[[1, -1], 2], [[1, 1], 2]], [[[1, -1], 2], [[1, 1, 1], 1]], [[[1, -1], 2], [[1, 1, 1], 1]], [[[1, -1], 2], [[1, 1], 2]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, 1, 1], 2]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, -1], 2], [[1, 1, 1], 1]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, -1], 2], [[1, 1, 1], 1]], [[[1, -1], 2], [[1, 1], 2]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 0, 'label': '4-3675e2-1.1-c0e2-0-0', 'leading_term': '0.157860208259477114304022886317669738049683747343946404210887705600000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3675/1/u/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.025390625', 'prec': 37}, 'plot_values': [0.1578602082594771, 0.156556577117021, 0.15295682973879443, 0.14671396664932754, 0.1376618130453142, 0.12562154987709706, 0.11028119814039554, 0.09126977632493236, 0.06819190991947846, 0.040626907852496584, 0.008134526105065992, -0.029730142544255773, -0.07339262275703161, -0.12325246582435553, -0.17965534247883289, -0.24288795610136024, -0.3131455107698382, -0.3905296160514617, -0.47501450221904623, -0.5664476046413142, -0.6645170530442007, -0.7687554191753838, -0.878511337513984, -0.9929568645451183, -1.1110661320686244, -1.2316266975242594, -1.3532281664642933, -1.4742776018704364, -1.5930009377836734, -1.707462034692606, -1.815579380563494, -1.9151477624852964, -2.0038721564669126, -2.079390295342812, -2.1393247536932423, -2.18130400363598, -2.2030325099571493, -2.20230726610776, -2.177104269436007, -2.125587113661651, -2.0462065980249693, -1.9376978133693274, -1.7991879732198526, -1.630178651967586, -1.430655362977227, -1.2010522517897093, -0.9423556590025851, -0.6560496690954725, -0.34420506110970694, -0.00940565221938329, 0.34518618037383864, 0.7159205054417354, 1.0986260387037767, 1.4887144648871091, 1.8811853201097066, 2.2707373263166835, 2.651816768063959, 3.0187273860162067, 3.3657241951756243, 3.687111696879734, 3.9773816801564004, 4.231288336298252, 4.444024907668707, 4.6112639562324835, 4.729364112827825, 4.795364443798636, 4.807209390423692, 4.7636880016730965, 4.664662827714815, 4.5109477447480115, 4.304525432434545, 4.048361490798867, 3.746595462018948, 3.404293683427457, 3.0276007577836945, 2.6234387326837525, 2.1996094688959467, 1.764452817359421, 1.326895289747081, 0.8960843893916447, 0.48138497486761883, 0.09201024818949946, -0.2630263220412382, -0.5752611375768956, -0.836858823935552, -1.040921576629348, -1.1815782384546853, -1.2542334688018464, -1.2556442262555358, -1.1840941246486874, -1.0394324711522183, -0.8231658865384933, -0.5384361753596412, -0.190029457519767, 0.21572690848169504, 0.6710285432742167, 1.1667912406701633, 1.692770680923832, 2.2378581259178896, 2.7902302201161144, 3.3377374052510946, 3.8680529647177684, 4.369137881483909, 4.829355778121694, 5.237988317992059, 5.58528368122936, 5.862989076058283, 6.064305076965575, 6.184397460657495, 6.2202379060364175, 6.17105701027439, 6.03806286516331, 5.824801147936195, 5.536755897135052, 5.181590915818808, 4.768650310377212, 4.309067459843743, 3.815195014757117, 3.3005822361929766, 2.77937363890701, 2.2661710361249896, 1.7754455035478214, 1.321315176891885, 0.9170157427210042, 0.574637075897506, 0.30469259955442224, 0.11586555698925873, 0.01470753789538728, 0.005447308132347407, 0.08983445509380238, 0.26705961415028495, 0.5337420401654908, 0.883999876693984, 1.3095624829736112, 1.8000139792363181, 2.342994573026139, 2.9246215925588377, 3.529731069836971, 4.142460017039603, 4.746472033951156, 5.3256651751369395, 5.864324668088268, 6.347904848094988, 6.763058710025994, 7.098432208248646, 7.344533897438709, 7.494476919246178, 7.543671054422129, 7.490452574255462, 7.335603445408969, 7.082821521450776, 6.738094651823517, 6.309982017382044, 5.8088914951656685, 5.247165018160291, 4.6383228949978115, 3.9969690189909706, 3.3380736535413815, 2.6767350341846172, 2.027571033416382, 1.404389314836303, 0.8197480659200368, 0.2845951406697509, -0.19196027633637378, -0.6029794020656999, -0.9436936257921344, -1.211755875458457, -1.4070212130851336, -1.5316828352014966, -1.5898690783272356, -1.587650251260123, -1.5325093677165653, -1.433228960998033, -1.2993070082245353, -1.1407540263671538, -0.967530090691175, -0.78929847895869, -0.6149536422968476, -0.4523857956132633, -0.3081539199614252, -0.18731450791686186, -0.09327037841050069, -0.02770625215150975, 0.009383254611977882, 0.019626922529250017, 0.006093809873104688, -0.02690553588545841, -0.07411005234058796, -0.12961545428044036, -0.18721042790137465, -0.24074732509399213, -0.2844559247748403, -0.3133177692940764, -0.3232960669661479, -0.31164901013238744, -0.27703096278972494, -0.21968633866462456, -0.1414015082400549, -0.0455377464263822, 0.06315867369253346, 0.17870063357040053, 0.29415737324759367, 0.40196208076802, 0.4942605319295947, 0.5633389872058777, 0.6019566698075624, 0.6038268569799087, 0.5638658774203783, 0.47864626635785057, 0.3465076697743886, 0.1678999310630474, -0.05467531707728752, -0.31650074978443016, -0.6108719116352289, -0.9291559200650735, -1.261158780777058, -1.5954153514339795, -1.9196356297785668, -2.22119616448671, -2.487586366414229, -2.7070357223746293, -2.8688752472847145, -2.9642079181194054, -2.9861095946711598, -2.93023713739444, -2.7948168060959726, -2.5810885340333583, -2.293064682312089, -1.9377301349131733, -1.5245948652913583, -1.0656051602040284, -0.5745529104640609, -0.06669798492263414, 0.44187157458711857, 0.9348594633814222, 1.396338811838621, 1.8115273741935245, 2.167193054837273, 2.4524703132777237, 2.659003703466722, 2.7816830618783848, 2.818472237232854, 2.7709532308765485, 2.6438355666216267, 2.44523182881176, 2.1858948971987524, 1.8791944326197463, 1.5401756345451347, 1.1852604384479979, 0.8312541397911807, 0.4948470252701985, 0.19170770461425674, -0.06409882177163254, -0.26080319328993823, -0.38946036736854106, -0.4443326470385357, -0.4232316000084152, -0.32754911964542793, -0.16230705034924509, 0.06414567873771466, 0.34043254753464297, 0.6527079542825818, 0.9853010997581442, 1.3214031014347545, 1.6439867841218567, 1.936467290016089, 2.1837749382156453, 2.3728327432771743, 2.493625049650271, 2.539361875367091, 2.5073788807693678, 2.398909329173331, 2.2196739232308693, 1.9792482150127513, 1.6912513898984871, 1.3723686324341158, 1.0421183349031504, 0.7216523187428773, 0.4331594417963753, 0.19860969171177154, 0.038924926253539126, -0.027153135150550164, 0.016059226438226985, 0.1803406639562435, 0.47284619889059976, 0.8956561890497582, 1.4454129502012147, 2.1133037527847987, 2.885201320840958, 3.742035097105526, 4.660508770043114, 5.6137346654868745, 6.572509853249504, 7.506028447005245, 8.383605868742958, 9.175255118159809, 9.85367277963219, 10.394474763828882, 10.778211669453318, 10.990107164567002, 11.021863421529991, 10.87082420175908, 10.54136548988371, 10.043502422346101, 9.393730697772472, 8.613194806916841, 7.72794028115932, 6.766842399529121, 5.761331117782665, 4.743329090607308, 3.7446017163085643, 2.794960809828548, 1.9214547885990607, 1.1470569794771146, 0.48993362720490347, -0.037240889731532986, -0.4277224881343663, -0.6807161291449803, -0.8013677991799117, -0.8001895405692104, -0.6925443200941982, -0.49764926923103897, -0.23759696786412002, 0.06382176811961153, 0.3824205468169203, 0.6947076182544103, 0.9793036979078505, 1.2177001474775788, 1.3955550681281756, 1.502941469864064, 1.5353040018912796, 1.493118489297643, 1.38235551770302, 1.213585638439791, 1.0018928544524208, 0.7655647174236596, 0.5255101951535422, 0.30375050638548573, 0.12250018514292679, 0.0027077720011271017, -0.03696470509420574, 0.01868110868444481, 0.18052565443231816, 0.45440484868705405, 0.840671289751766, 1.3339880575525933, 1.9234868832647385, 2.5930385403921, 3.3220849736394102, 4.086236500536888, 4.858733123903638, 5.61114222534826, 6.315288665161687, 6.943795703594944, 7.472236621480548, 7.879283517621739, 8.148792327768819, 8.269395624909428, 8.236246449712288, 8.049998878611603, 7.718001659910053, 7.252733094245889, 6.672340332622719, 5.9987085121795625, 5.2573649594484655, 4.475443427195432, 3.681089715113325, 2.9016132916188195, 2.1626184408091595, 1.4866102850306486, 0.8921158672004875, 0.39293376722788637, -0.0025054593434122186, -0.291172352627127, -0.4756561997805087, -0.5635374186999795, -0.5671052552006552, -0.5022452076256547, -0.3876986590676624, -0.24372483770784018, -0.09105400327543248, 0.05038520435788712, 0.16259154558891087, 0.23043504098104592, 0.24260890423976064, 0.19206170986591006, 0.07655383971524349, -0.10148824790449926, -0.3349511415354462, -0.6126959927432992, -0.9200984895805151, -1.240051282155597, -1.5539666714373122, -1.8428719274301428, -2.088671482938442, -2.2750693869075995, -2.388824525890081, -2.4202761192337627, -2.364318846842566, -2.2203995680511945, -1.9929919590564926, -1.691055644023789, -1.3278918481996214, -0.9201830416407047, -0.4872409925730327, -0.04984779057857338, 0.37096229964365485, 0.7549841221685984, 1.0842829682819115, 1.3439268662542168, 1.523357925254567, 1.6165698332110225, 1.6231295825094358, 1.5477070339020296, 1.4005433497449364, 1.1963752471569322, 0.9542697303526206, 0.6961148658094195, 0.4458851659918763, 0.22796452230715547, 0.06604167099267298, -0.01843231504788851, -0.007423480399826948, 0.11254973960525383, 0.34949128594063, 0.7053810036894635, 1.1757964798327825, 1.7500033167570277, 2.4113163121604755, 3.137727065704079, 3.9030521893548586, 4.677870263130112, 5.431346426507458, 6.1321700422516985, 6.750806697247464, 7.2601143731806665, 7.63768551442347, 7.865877781305689, 7.933889882182366, 7.837062014470382, 7.5783841492457285, 7.16707624940654, 6.619345060994218, 5.956411843930545, 5.204488137433918, 4.392544486376942, 3.551633505531022, 2.7127587684668373, 1.9058003247368975, 1.157833155677771, 0.4919784631767834, -0.0735630639871453, -0.5264159075860654, -0.8601574486231404, -1.0747365806920914, -1.1758058742446909, -1.1745415976093974, -1.0863814938980436, -0.9302860020279633, -0.7271961082810011, -0.4989152497598839, -0.2666457146000155, -0.04976506107876463, 0.135235104890321, 0.2757775708871271, 0.36363951419589335, 0.39553241339901557, 0.37285299766406965, 0.3016715127255237, 0.19188806158417185, 0.05663334303273704, -0.08893911265142027, -0.22868665116440165, -0.34674038492096615, -0.42870575405970396, -0.4626686986472786, -0.4402439690492981, -0.3570857836102359, -0.21349023189694802, -0.014302931893619064, 0.23111999054100546, 0.5095568076397388, 0.8046472041753628, 1.097893081052653, 1.3699550648169574, 1.6017139455280667, 1.7758764908345657, 1.8777762089582049, 1.8969449174922017, 1.8273857906283681, 1.6687640964020773, 1.426008328596171, 1.1098539000225738, 0.735791337979602, 0.3238445314788309, -0.10295212497399722, -0.5194795837693315, -0.9002183974645751, -1.2206412255761565, -1.458706559747707, -1.5963658352463141, -1.620516251208209, -1.5242240969255256, -1.3069805109121362, -0.9752173333496955, -0.5417605268041884, -0.02598741996976567, 0.5476928478100576, 1.153096352736666, 1.7611557039413208, 2.332101125390296, 2.8310770367131366], 'positive_zeros': ['0.25968829259013651211178750589426', '1.24483209349006825236534939382438', '2.06296727126826652803087855644800', '2.37363935845580354016517679418192', '3.23452761038858395365596346527009', '3.24515126510555246084648002333137', '4.12803762927395620998288859809813', '4.63792981114622709091690035182315', '4.70315071050926586420988770748207', '5.03827274400745110159466885420890', '5.35160424173347701119444353122146', '5.89393948844653817684359059973133', '6.39153924256112075569056985683316', '6.56957402630262210893092052227713', '7.11963165890743106130832323055583', '7.15570208824648186719053758801753', '7.996012678339229751737792939322771', '8.195978817032358971181742351320187', '8.608269490605023682766841103989039', '8.653319836220177306224996332099863'], 'prelabel': '4-3675e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.3542761614332153, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c0e2-0', 'trace_hash': 1810964853757969304, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.25968829259013651211178750589', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.24483209349006825236534939382', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.06296727126826652803087855645', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.3637904678775588, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 13505625, 'conductor_radical': 105, 'degree': 4, 'dirichlet_coefficients': [1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0], 'euler11': [1, 0, 1, 0, 1], 'euler13': [1, 2, 3, 2, 1], 'euler17': [1, 0, 1, 0, 1], 'euler19': [1, 1, 0, 1, 1], 'euler2': [1, 0, 1, 0, 1], 'euler23': [1, 0, 1, 0, 1], 'euler29': [1, 0, -2, 0, 1], 'euler3': [1, 1, 1, 0, 0], 'euler31': [1, -2, 3, -2, 1], 'euler37': [1, 1, 0, 1, 1], 'euler41': [1, 0, -2, 0, 1], 'euler43': [1, 4, 6, 4, 1], 'euler47': [1, 0, 1, 0, 1], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, 1, 0, 1], 'euler59': [1, 0, 1, 0, 1], 'euler61': [1, 1, 0, 1, 1], 'euler67': [1, 1, 0, 1, 1], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 0, -2, 0, 1], 'euler73': [1, -1, 0, -1, 1], 'euler79': [1, -1, 0, -1, 1], 'euler83': [1, 0, -2, 0, 1], 'euler89': [1, 0, 1, 0, 1], 'euler97': [1, 2, 3, 2, 1], 'euler_factors': [[1, 0, 1, 0, 1], [1, 1, 1, 0, 0], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, 1, 0, 1], [1, 2, 3, 2, 1], [1, 0, 1, 0, 1], [1, 1, 0, 1, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, -2, 3, -2, 1], [1, 1, 0, 1, 1], [1, 0, -2, 0, 1], [1, 4, 6, 4, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 1, 0, 1, 1], [1, 1, 0, 1, 1], [1, 0, -2, 0, 1], [1, -1, 0, -1, 1], [1, -1, 0, -1, 1], [1, 0, -2, 0, 1], [1, 0, 1, 0, 1], [1, 2, 3, 2, 1]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3675/1/u/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': '4-3675e2-1.1-c0e2-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0], 'order_of_vanishing': 0, 'prelabel': '4-3675e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.3542761614332153, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 1810964853757969304, 'z1': {'__RealLiteral__': 0, 'data': '0.25968829259013651211178750589', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '329194019974130607253962300915,1578012150496048397813012945969', 'Lhash_array': ['329194019974130607253962300915', '1578012150496048397813012945969'], 'factors': ['2-3675-21.2-c0-0-1', '2-3675-21.11-c0-0-11'], 'label': '4-3675e2-1.1-c0e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3675/1/u/a'}