-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1842255971980114461456381977992', 'a10': 0, 'a2': 1048576, 'a3': 6074010274, 'a4': 1099511627776, 'a5': 0, 'a6': 6369061397069824, 'a7': 0, 'a8': 1152921504606846976, 'a9': 24735935349600626275, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 81.07382815715273, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '20.0', 'prec': 14}, 'bad_lfactors': [[2, [1, -1048576]]], 'bad_primes': [2], 'central_character': '8.3', 'coefficient_field': '1.1.1.1', 'conductor': 8, 'conductor_radical': 2, 'degree': 2, 'euler_factors': [[1, -1048576], [1, -6074010274, 12157665459056928801], [1, 0, -9094947017729282379150390625], [1, 0, -6366805760909027985741435139224001], [1, -450820710293558904674, 452592555681759518058893560348969204658401], [1, 0, -361188648084531445929920877641340156544317601], [1, -3117739305616120485919874, 16517976926780506002833800829531584028976727363201], [1, 74150423297647257299970526, 1413006104539009638843035501053457425807904438071201], [1, 0, -2945190837423705167875564697729320458241471826430830401], [1, 0, -31327079986910989416247938623974919746509417027114485440801], [1, 0, -451302514611022222119906091571193923850834154614488607763201], [1, 0, -534649250915012063273309653845946926220190993810950712361813601], [1, -285742786287632550836163214308674, 32460430015431999968619493682032835511850959272235390105491169601], [1, 926377740549510106243296356291998, 218141463858908869909615270212837010053304269297195114305378988001], [1, 0, -7654455761751330268890575447204214294134057054403947260546060444801], [1, 0, -935480596774678503001801362972812283024661354043792689825893575512801], [1, 492235218679638009843647087920634398, 68246512894550079052163515422746832731983773500978660478681746942325601], [1, 0, -258936575725713381876605656162686020810913039245684608619946288452090401], [1, 6518641394409502304672373517636338526, 11040585568500089406404363834296492635119570897676624567608785151541319201], [1, 0, -112288155707690524284921569184047598526949432199996966253201749159632164801], [1, 738290036686676385826765468506068926, 341125672472605815737240060891364026523290350856811222245874647291144654401], [1, 0, -8036809082503641618612682084624530392577487756904348192905795828229186428801], [1, -480922555951254276823727356015713034274, 57959375186337998161464929843210464026538099255933595673241672975683189751201], [1, -1801140186462463501498463511038980231874, 945366624540204596465924137849354245846140921259572676085974614185475142494401], [1, 8374973723762831390571681779668742419198, 29571228739913279498948663112125511966004786122340140758535526194999034006060801], [1, 0, -148886373358822087497126463801738296202951256788286744534662595050969228887804001], [1, 0, -326203779199907436766740454433356067287204248224700781926823975402404198696196801], [1, -54119024947414893700641354215625876274274, 1497445783920694873253605954725085018527510926336074313466818706592456466757996001], [1, 0, -3140942005398926371772028385862838092239539909405451295670621541688111654708253601], [1, 207068616813035571916843667087545206438526, 13278155163351753706317696533924544108513274407835339859871275831776558989263625601]], 'euler_factors_factorization': [[[[1, -1048576], 1]], [[[1, -6074010274, 12157665459056928801], 1]], [[[1, -95367431640625], 1], [[1, 95367431640625], 1]], [[[1, -79792266297612001], 1], [[1, 79792266297612001], 1]], [[[1, -450820710293558904674, 452592555681759518058893560348969204658401], 1]], [[[1, -19004963774880799438801], 1], [[1, 19004963774880799438801], 1]], [[[1, -3117739305616120485919874, 16517976926780506002833800829531584028976727363201], 1]], [[[1, 74150423297647257299970526, 1413006104539009638843035501053457425807904438071201], 1]], [[[1, -1716155831334586342923895201], 1], [[1, 1716155831334586342923895201], 1]], [[[1, -176994576151109753197786640401], 1], [[1, 176994576151109753197786640401], 1]], [[[1, -671790528819082282036142601601], 1], [[1, 671790528819082282036142601601], 1]], [[[1, -23122483666661158726686253786801], 1], [[1, 23122483666661158726686253786801], 1]], [[[1, -285742786287632550836163214308674, 32460430015431999968619493682032835511850959272235390105491169601], 1]], [[[1, 926377740549510106243296356291998, 218141463858908869909615270212837010053304269297195114305378988001], 1]], [[[1, -2766668711962335809450748011342401], 1], [[1, 2766668711962335809450748011342401], 1]], [[[1, -30585627290848204916791848989276401], 1], [[1, 30585627290848204916791848989276401], 1]], [[[1, 492235218679638009843647087920634398, 68246512894550079052163515422746832731983773500978660478681746942325601], 1]], [[[1, -508858109619679129936596364708525201], 1], [[1, 508858109619679129936596364708525201], 1]], [[[1, 6518641394409502304672373517636338526, 11040585568500089406404363834296492635119570897676624567608785151541319201], 1]], [[[1, -10596610576391421032662867140133202401], 1], [[1, 10596610576391421032662867140133202401], 1]], [[[1, 738290036686676385826765468506068926, 341125672472605815737240060891364026523290350856811222245874647291144654401], 1]], [[[1, -89648251976843595444986830377401534401], 1], [[1, 89648251976843595444986830377401534401], 1]], [[[1, -480922555951254276823727356015713034274, 57959375186337998161464929843210464026538099255933595673241672975683189751201], 1]], [[[1, -1801140186462463501498463511038980231874, 945366624540204596465924137849354245846140921259572676085974614185475142494401], 1]], [[[1, 8374973723762831390571681779668742419198, 29571228739913279498948663112125511966004786122340140758535526194999034006060801], 1]], [[[1, -12201900399479668244827490915525641902001], 1], [[1, 12201900399479668244827490915525641902001], 1]], [[[1, -18061112346694138117573133075817258818401], 1], [[1, 18061112346694138117573133075817258818401], 1]], [[[1, -54119024947414893700641354215625876274274, 1497445783920694873253605954725085018527510926336074313466818706592456466757996001], 1]], [[[1, -56044107677782919374398655242916531006801], 1], [[1, 56044107677782919374398655242916531006801], 1]], [[[1, 207068616813035571916843667087545206438526, 13278155163351753706317696533924544108513274407835339859871275831776558989263625601], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 33, 'label': '2-2e3-8.3-c40-0-33', 'leading_term': '9.16351946806152644257816481480147657101456667875422261400000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 40, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [40], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/8/41/d/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.08203125', 'prec': 34}, 'plot_values': [9.163519468061526, 9.10915976369718, 8.94736962406215, 8.68197906479005, 8.319249559135343, 7.867695127278411, 7.337839572304631, 6.741917283688954, 6.093526745124132, 5.407247313915257, 4.698230939275782, 3.9817812224164135, 3.2729325694806275, 2.5860421384817136, 1.934406835281652, 1.3299167856312835, 0.7827555266976458, 0.3011556598779151, -0.10878306538436476, -0.44320825348271453, -0.7005591047721464, -0.8815397740121415, -0.9890234560327836, -1.027890986780243, -1.0048097984880227, -0.9279609265341301, -0.8067233735081747, -0.6513264419808488, -0.472481609865019, -0.28100611041954576, -0.0874505741266717, 0.09825711433125797, 0.2671401873848104, 0.41146300761289106, 0.5249734481920935, 0.6030899786380158, 0.6430276537851093, 0.6438592517313216, 0.6065099755693066, 0.5336863536264218, 0.42974217126678316, 0.30048637215644886, 0.15293980912667263, -0.0049505597104924455, -0.1646300021064328, -0.31727574240336476, -0.4541462329650506, -0.5669277706631579, -0.6480663330980798, -0.6910729860304182, -0.6907920827956112, -0.6436227113146497, -0.5476854055507864, -0.40292797574683614, -0.21116636591966428, 0.023941349264359285, 0.2969874355279218, 0.6009707633662869, 0.9275119843304588, 1.267120680261666, 1.6095057084324902, 1.943918410192935, 2.259517132581038, 2.5457406751784384, 2.7926778497234115, 2.9914203456360915, 3.134386534475204, 3.2156047097844334, 3.2309455208910083, 3.1782949814938006, 3.0576613653716183, 2.8712114804034123, 2.623234167506673, 2.3200313255492433, 1.969739235057258, 1.5820853593955186, 1.1680880600517207, 0.7397086947351442, 0.3094673018948734, -0.10996554919306901, -0.5061871982459171, -0.8674775615947016, -1.1831959186923533, -1.4441461399536724, -1.6428975792201976, -1.7740501998323566, -1.8344342538058906, -1.82323693471115, -1.7420508097186194, -1.5948414275784697, -1.387834211694143, -1.129323490329137, -0.82940919650108, -0.4996692962865758, -0.15277828811038374, 0.19791592379324494, 0.5388429121839764, 0.8566733827109738, 1.1387800027577821, 1.3736797102713212, 1.5514422509009356, 1.6640506590031732, 1.705700864935718, 1.6730295337799612, 1.5652615591641752, 1.3842712757592468, 1.134554328770893, 0.8231101525779072, 0.4592380616922704, 0.05425294090597906, -0.3788706657851359, -0.8259147252405377, -1.2718806204969604, -1.7014835271176432, -2.099661762336876, -2.4520839301132824, -2.745636592035217, -2.968875696473279, -3.112426085933024, -3.1693150441252924, -3.1352279889489125, -3.008676996185733, -2.7910757659345484, -2.4867178210053873, -2.10265804495105, -1.648501012067578, -1.1361028151217711, -0.5791961431030578, 0.007048908801740366, 0.6065135013961929, 1.2026515795170676, 1.7790264210049032, 2.3198437448659703, 2.810462949951349, 3.2378687434797806, 3.591086743237816, 3.8615285567048008, 4.043254291086298, 4.133143346723922, 4.130967591777254, 4.039364493839482, 3.863711369838693, 3.6119054793845993, 3.2940580981324605, 2.922113840320788, 2.509409235766048, 2.070186801904674, 1.6190824989222556, 1.170605449364302, 0.7386291002079657, 0.3359125880081945, -0.026330054262154675, -0.33879700081762265, -0.5943885973294764, -0.7884096563873917, -0.9186768913471993, -0.9855279258133507, -0.9917321037961171, -0.9423071277325847, -0.8442492223047574, -0.7061879187074782, -0.5379795427400799, -0.3502559507634444, -0.15394688887427493, 0.04020452575226836, 0.2221133385200856, 0.3827918622999961, 0.5147381048455149, 0.6122572037790645, 0.6717021598345252, 0.6916233424559974, 0.6728198847665301, 0.6182900491286228, 0.5330817769465587, 0.4240487748128143, 0.2995214684734885, 0.16890581482084233, 0.04222614863643212, -0.07036918031759049, -0.1591187666384594, -0.21515404234669588, -0.23097825582303985, -0.20089739067806006, -0.12138345524587715, 0.008647022817252601, 0.18765331298652863, 0.4113998436121408, 0.673000569264654, 0.9630797010697779, 1.2700454048822827, 1.5804683588963695, 1.87955257934644, 2.1516818558374338, 2.3810216590039737, 2.5521536448025306, 2.6507180071455383, 2.664038016734073, 2.581701184960836, 2.3960726239303187, 2.1027183119727684, 1.700719052384075, 1.1928598260979588, 0.5856838453816202, -0.11059425656289126, -0.8823162124508057, -1.7127434322369222, -2.5825449329897885, -3.470393859610896, -4.3536519915010725, -5.209117792006075, -6.01381062603827, -6.745761880810025, -7.384782969359182, -7.913180626209622, -8.316391521405732, -8.58351097722881, -8.707694377707499, -8.686414576731163, -8.521564058789725, -8.219396576792596, -7.790309248930462, -7.248472390463539, -6.611320430546615, -5.898922867737019, -5.13325911530025, -4.3374250691373595, -3.5348021222738346, -2.7482210182759172, -1.999153298568578, -1.306962125538842, -0.6882419799968499, -0.15627321868042646, 0.27938713169048923, 0.6131624916656515, 0.8435521230148998, 0.9730618213628232, 1.0079737492358283, 0.957965947869546, 0.835598355055695, 0.6556877668939006, 0.4345988686240172, 0.18948201544858073, -0.0625092937445426, -0.30498744692498, -0.523053042105176, -0.7039393206864205, -0.8375509197643517, -0.916873769645756, -0.9382386153920711, -0.9014270903043214, -0.8096162386079911, -0.6691645717970489, -0.4892498326353106, -0.2813753178019614, -0.058767574309661674, 0.16430673604084817, 0.3732732472793084], 'positive_zeros': ['1.45328371370504805446593303464455', '2.49888384433323792077505047865351', '3.52480903071920779321212172692946', '4.50396560873164721928928611326813', '6.45861680537687427087680969951300', '7.74659680276416315582949594667279', '8.951924686108265668227164934610634', '10.49902902530454687279694806152713', '12.38037830603487849341591736506644', '13.43584524943433600033842998587394'], 'prelabel': '2-2e3-8.3-c40-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.004100630110301, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c40-0', 'trace_hash': 450351787995337087, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.45328371370504805446593303464', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.49888384433323792077505047865', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.52480903071920779321212172693', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 81.07382815715273, 'bad_primes': [2], 'central_character': '8.3', 'conductor': 8, 'conductor_radical': 2, 'degree': 2, 'dirichlet_coefficients': [1, 1048576, 6074010274, 1099511627776, 0, 6369061397069824, 0, 1152921504606846976, 24735935349600626275, 0, 450820710293558904674, 6678444923493887770624, 0, 0, 0, 1208925819614629174706176, 3117739305616120485919874, 25937508145142826296934400, -74150423297647257299970526, 0, 0, 472719777116778822027444224, 0, 7002857064097526862969831424, 9094947017729282379150390625, 0, 76400540544307273903023847876, 0, 0, 0, 0, 1267650600228229401496703205376, 2738289626055054343014062620676, 3269186610125729154643917799424, 0, 27197448540801284227134285414400, 0, -77752354259753770470573894270976, 0, 0, 285742786287632550836163214308674, 0, -926377740549510106243296356291998, 495682613010003470086249354625024, 0, 0, 0, 7343027848843128327865453955252224, 6366805760909027985741435139224001, 9536743164062500000000000000000000, 18937180573965941731499187016785476, 0, 0, 80111773201787544040137134310424576, 0, 0, -450390432931358400867942474821184124, 0, -492235218679638009843647087920634398, 0, 0, 0, 0, 1329227995784915872903807060280344576, 0, 2871304782930304662780313726537957376, -6518641394409502304672373517636338526, 3427990618899196574059900750448820224, 0, 0, 0, 28518591801119247409751560462689894400, -738290036686676385826765468506068926, 0, 55242801627173321321606636047363281250, -81529252620275569624952491759082930176, 0, 0, 0, 0, 163326441407971123250497316958152231749, 299623027874340589625580678606932148224, 480922555951254276823727356015713034274, 0, 0, -971377465674443109164170720095238094848, 0, 519760891619577398649159003275289165824, 1801140186462463501498463511038980231874, 0, 0, 0, 0, 0, 0, 7699722769628532129519846246582556033024, -8374973723762831390571681779668742419198, 6676079717550944929176811092546946072576, 11151471944082506641055792362633424709350, 10000000000000000000000000000000000000000], 'euler11': [1, -450820710293558904674, 452592555681759518058893560348969204658401], 'euler13': [1, 0, -361188648084531445929920877641340156544317601], 'euler17': [1, -3117739305616120485919874, 16517976926780506002833800829531584028976727363201], 'euler19': [1, 74150423297647257299970526, 1413006104539009638843035501053457425807904438071201], 'euler2': [1, -1048576, 0], 'euler23': [1, 0, -2945190837423705167875564697729320458241471826430830401], 'euler29': [1, 0, -31327079986910989416247938623974919746509417027114485440801], 'euler3': [1, -6074010274, 12157665459056928801], 'euler31': [1, 0, -451302514611022222119906091571193923850834154614488607763201], 'euler37': [1, 0, -534649250915012063273309653845946926220190993810950712361813601], 'euler41': [1, -285742786287632550836163214308674, 32460430015431999968619493682032835511850959272235390105491169601], 'euler43': [1, 926377740549510106243296356291998, 218141463858908869909615270212837010053304269297195114305378988001], 'euler47': [1, 0, -7654455761751330268890575447204214294134057054403947260546060444801], 'euler5': [1, 0, -9094947017729282379150390625], 'euler53': [1, 0, -935480596774678503001801362972812283024661354043792689825893575512801], 'euler59': [1, 492235218679638009843647087920634398, 68246512894550079052163515422746832731983773500978660478681746942325601], 'euler61': [1, 0, -258936575725713381876605656162686020810913039245684608619946288452090401], 'euler67': [1, 6518641394409502304672373517636338526, 11040585568500089406404363834296492635119570897676624567608785151541319201], 'euler7': [1, 0, -6366805760909027985741435139224001], 'euler71': [1, 0, -112288155707690524284921569184047598526949432199996966253201749159632164801], 'euler73': [1, 738290036686676385826765468506068926, 341125672472605815737240060891364026523290350856811222245874647291144654401], 'euler79': [1, 0, -8036809082503641618612682084624530392577487756904348192905795828229186428801], 'euler83': [1, -480922555951254276823727356015713034274, 57959375186337998161464929843210464026538099255933595673241672975683189751201], 'euler89': [1, -1801140186462463501498463511038980231874, 945366624540204596465924137849354245846140921259572676085974614185475142494401], 'euler97': [1, 8374973723762831390571681779668742419198, 29571228739913279498948663112125511966004786122340140758535526194999034006060801], 'euler_factors': [[1, -1048576, 0], [1, -6074010274, 12157665459056928801], [1, 0, -9094947017729282379150390625], [1, 0, -6366805760909027985741435139224001], [1, -450820710293558904674, 452592555681759518058893560348969204658401], [1, 0, -361188648084531445929920877641340156544317601], [1, -3117739305616120485919874, 16517976926780506002833800829531584028976727363201], [1, 74150423297647257299970526, 1413006104539009638843035501053457425807904438071201], [1, 0, -2945190837423705167875564697729320458241471826430830401], [1, 0, -31327079986910989416247938623974919746509417027114485440801], [1, 0, -451302514611022222119906091571193923850834154614488607763201], [1, 0, -534649250915012063273309653845946926220190993810950712361813601], [1, -285742786287632550836163214308674, 32460430015431999968619493682032835511850959272235390105491169601], [1, 926377740549510106243296356291998, 218141463858908869909615270212837010053304269297195114305378988001], [1, 0, -7654455761751330268890575447204214294134057054403947260546060444801], [1, 0, -935480596774678503001801362972812283024661354043792689825893575512801], [1, 492235218679638009843647087920634398, 68246512894550079052163515422746832731983773500978660478681746942325601], [1, 0, -258936575725713381876605656162686020810913039245684608619946288452090401], [1, 6518641394409502304672373517636338526, 11040585568500089406404363834296492635119570897676624567608785151541319201], [1, 0, -112288155707690524284921569184047598526949432199996966253201749159632164801], [1, 738290036686676385826765468506068926, 341125672472605815737240060891364026523290350856811222245874647291144654401], [1, 0, -8036809082503641618612682084624530392577487756904348192905795828229186428801], [1, -480922555951254276823727356015713034274, 57959375186337998161464929843210464026538099255933595673241672975683189751201], [1, -1801140186462463501498463511038980231874, 945366624540204596465924137849354245846140921259572676085974614185475142494401], [1, 8374973723762831390571681779668742419198, 29571228739913279498948663112125511966004786122340140758535526194999034006060801]], 'index': 33, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8/41/d/a', 'ModularForm/GL2/Q/holomorphic/8/41/d/a/3/1'], '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': '2-2e3-8.3-c40-0-33', 'motivic_weight': 40, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [40], 'order_of_vanishing': 0, 'prelabel': '2-2e3-8.3-c40-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.004100630110301, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c40-0', 'trace_hash': 450351787995337087, 'z1': {'__RealLiteral__': 0, 'data': '1.45328371370504805446593303464', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 24591192
{'Lhash': '1842255971980114461456381977992', 'Lhash_array': ['1842255971980114461456381977992'], 'label': '2-2e3-8.3-c40-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8/41/d/a/3/1'}
-
id: 23651714
{'Lhash': '1842255971980114461456381977992', 'Lhash_array': ['1842255971980114461456381977992'], 'label': '2-2e3-8.3-c40-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8/41/d/a'}