Lfunction data - 4-10e2-1.1-c21e2-0-1

Formats: - HTML - YAML - JSON - 2025-04-07T19:35:04.827574

• lfunc_lfunctions •

  Column	Type
  A10	numeric
  A2	numeric
  A3	numeric
  A4	numeric
  A5	numeric
  A6	numeric
  A7	numeric
  A8	numeric
  A9	numeric
  Lhash	text
  a10	jsonb
  a2	jsonb
  a3	jsonb
  a4	jsonb
  a5	jsonb
  a6	jsonb
  a7	jsonb
  a8	jsonb
  a9	jsonb
  accuracy	smallint
  algebraic	boolean
  analytic_conductor	double precision
  analytic_normalization	numeric
  bad_lfactors	jsonb
  bad_primes	bigint[]
  central_character	text
  coeff_info	jsonb
  coefficient_field	text
  conductor	numeric
  conductor_radical	integer
  conjugate	text
  credit	text
  degree	smallint
  dirichlet_coefficients	jsonb
  euler_factors	jsonb
  euler_factors_factorization	jsonb
  gamma_factors	jsonb
  group	text
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  label	text
  leading_term	text
  load_key	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  origin	text
  plot_delta	numeric
  plot_values	jsonb
  positive_zeros	jsonb
  precision	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  root_number	text
  self_dual	boolean
  sign_arg	numeric
  spectral_label	text
  st_group	text
  symmetry_type	text
  trace_hash	bigint
  types	jsonb
  values	jsonb
  z1	numeric
  z2	numeric
  z3	numeric

  
  {'Lhash': '1007582480256126368314484983851,1882647287976310053152452664725', 'a10': -40000000000, 'a2': 2048, 'a3': 30972, 'a4': 3145728, 'a5': -19531250, 'a6': 63430656, 'a7': -439959356, 'a8': 4294967296, 'a9': -3214312218, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 781.0758596974906, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '10.5', 'prec': 14}, 'bad_lfactors': [[2, [1, -2048, 1048576]], [5, [1, 19531250, 95367431640625]]], 'bad_primes': [2, 5], 'central_character': '10.1', 'coefficient_field': '1.1.1.1', 'conductor': 100, 'conductor_radical': 10, 'degree': 4, 'euler_factors': [[1, -2048, 1048576], [1, -30972, 4173577002, -323978059403316, 109418989131512359209], [1, 19531250, 95367431640625], [1, 439959356, 1165225791399569298, 245737478658545162084819492, 311973482284542371301330321821976049], [1, -105191777184, 8234028698069986594486, -778445443242312797540386400569824, 54763699237492901685126120802225273763666521], [1, -308456648932, 405609014842664615811582, -76208696707959195024342654788136916, 61040881526285814362156628321386486455989674569], [1, -18393996100404, 208825011717392502633984838, -1270876762965253513176733122355707895668, 4773695331839566234818968439734627784374274207965089], [1, -23821216715800, 1035956287377312787535052438, -17013339177394069918283517809660348720200, 510095203738582479622335815880298130716653502143703561], [1, 82586042978868, 77146947665381262561749618002, 3259801942635761071751750752568073461086764, 1558005952997140033806173725098810522409738596181909282129], [1, 167038888446420, 2777767401182653647314031245758, 857384340578471742939243074395449956778618180, 26346074268992142099064516382762907506814419719803282255713641], [1, -5373084998145784, 46430479870606816647576677941326, -111897215981121253261870277733516807739723805704, 433701716541192355457229753999917360820651622584523552060436161], [1, -83725084127912164, 3220702700698569293188750157615598, -71629479938786776161097654974656738226655690252468, 731934824502651514621160916115101341995441470527191525223322819769], [1, 63222375005514036, 15760655031107517881866619597412406, 467016040657299076470191328021905963908681612920276, 54565982855941191947249368879497196495421462536627690767330656099281], [1, 113835841911164948, 1288902021152841619133031429646362, 2286212479385923251944678428852489801779196649508764, 403343566675122500462878634623535631588559593930513766350645748813849], [1, -13253549001226164, 249751699621383624758804273343838018, -1723404429175148388838602656880606417539246257648908, 16908692777708688563979281162874109375742132033178319498546247522565409], [1, 1445751023743904748, 678782388504569613867404006590887982, 2343617704282445120394447513376872530815486755777353244, 2627764996340071914932060028590629703016273743509013665720935053615458009], [1, 817060118931432840, 30605390446842697256692759826027300518, 12593494516226934046563946667850762818318945370874105560, 237566111385928825180581197186581724740035515556906717126291161106235417081], [1, 4580997169825849436, 32124045550183086220006871413102007646, 142195731160651598569443526091257811049520850448895834796, 963502998275379493962849646581354683437407419033192428674820139330228382121], [1, 28808031668773210556, 643317018166516874238150007062407026218, 6413342629619651892730332648700568900055018341589672366452, 49561188616996901345349189252156955439051753759670367683995836545268981893289], [1, -51140957732016114984, 2157218440619039266169910340838120224606, -38476377764880669487339138342648533979869649366105822237464, 566044592922467932920289630256783944174352087720184706882390017513705742761841], [1, -14792322512082321412, 387306493896796427220489493655181191382, -19944191226316411485324744762702469436605370279360790010276, 1817858708606516392063752284490078897342614279715947003348265995414509863302929], [1, -25077766877525032720, 11203054443443268844042613144510070750558, -177606059160179602000643584057183613717160367595442717456880, 50157725483905227341761748890141694180076101090840037071925071763978352502147041], [1, 120090321897786074868, 3826541962025230167458574183763859414122, 2399650256121814573076512240593505869283315996883406971220444, 399282135658682469334331901689876886678820965774126540592961885129481494196023689], [1, -104228468137266844980, -33000838005370701606072611530973219718122, -9019376047271689666033173934908329348464316896758224062787220, 7488249032982960608606585095904734981347282237297075167277004918963148603698150321], [1, 260893520515229908796, 450218855490619179217341424115955462480198, 137616247945552544740706655569645756192846378961080262577838012, 278235691213844046805607971221988942088139032625098384397060765968745910963026076609], [1, -1530795108160169458284, 2897482267923056249850154091487128231274766, -1886539553619890460838149956620362167888475567445950030148254684, 1518789894633344114558187057241532359566305770497313080998093132114937103884488614201], [1, -3533951544934830051292, 6729520264789170214993749648837421567067922, -6574190875726652177613140727296715003845211592758370552772681476, 3460695893531817996658349481083474517849949869415850595461675555044106143967951861809], [1, -733521422666278262964, 8032069592248319814275139978740168379518938, -3037191203845926184852042472177689131439928052915706524295841148, 17144256780108035603880534575647498377121472595621714814881607371777034087912296215449], [1, -20959400980037179300, 9083071432840138115301373405463119058419518, -128036950867186545252862226415266616918186987358440286049703700, 37317531966144644223023469252436379373897973663646166843862654536796454569588761033481], [1, 809722632130867748748, 10072229624195728519784567090261138578535302, 10543470599293293226486710145087310499171547784098150951885835724, 169548763280838543075970667041682503721606000913649454670696321095954881733907235299169]], 'euler_factors_factorization': [[[[1, -1024], 2]], [[[1, -30972, 4173577002, -323978059403316, 109418989131512359209], 1]], [[[1, 9765625], 2]], [[[1, 439959356, 1165225791399569298, 245737478658545162084819492, 311973482284542371301330321821976049], 1]], [[[1, -105191777184, 8234028698069986594486, -778445443242312797540386400569824, 54763699237492901685126120802225273763666521], 1]], [[[1, -308456648932, 405609014842664615811582, -76208696707959195024342654788136916, 61040881526285814362156628321386486455989674569], 1]], [[[1, -18393996100404, 208825011717392502633984838, -1270876762965253513176733122355707895668, 4773695331839566234818968439734627784374274207965089], 1]], [[[1, -23821216715800, 1035956287377312787535052438, -17013339177394069918283517809660348720200, 510095203738582479622335815880298130716653502143703561], 1]], [[[1, 82586042978868, 77146947665381262561749618002, 3259801942635761071751750752568073461086764, 1558005952997140033806173725098810522409738596181909282129], 1]], [[[1, 167038888446420, 2777767401182653647314031245758, 857384340578471742939243074395449956778618180, 26346074268992142099064516382762907506814419719803282255713641], 1]], [[[1, -5373084998145784, 46430479870606816647576677941326, -111897215981121253261870277733516807739723805704, 433701716541192355457229753999917360820651622584523552060436161], 1]], [[[1, -83725084127912164, 3220702700698569293188750157615598, -71629479938786776161097654974656738226655690252468, 731934824502651514621160916115101341995441470527191525223322819769], 1]], [[[1, 63222375005514036, 15760655031107517881866619597412406, 467016040657299076470191328021905963908681612920276, 54565982855941191947249368879497196495421462536627690767330656099281], 1]], [[[1, 113835841911164948, 1288902021152841619133031429646362, 2286212479385923251944678428852489801779196649508764, 403343566675122500462878634623535631588559593930513766350645748813849], 1]], [[[1, -13253549001226164, 249751699621383624758804273343838018, -1723404429175148388838602656880606417539246257648908, 16908692777708688563979281162874109375742132033178319498546247522565409], 1]], [[[1, 1445751023743904748, 678782388504569613867404006590887982, 2343617704282445120394447513376872530815486755777353244, 2627764996340071914932060028590629703016273743509013665720935053615458009], 1]], [[[1, 817060118931432840, 30605390446842697256692759826027300518, 12593494516226934046563946667850762818318945370874105560, 237566111385928825180581197186581724740035515556906717126291161106235417081], 1]], [[[1, 4580997169825849436, 32124045550183086220006871413102007646, 142195731160651598569443526091257811049520850448895834796, 963502998275379493962849646581354683437407419033192428674820139330228382121], 1]], [[[1, 28808031668773210556, 643317018166516874238150007062407026218, 6413342629619651892730332648700568900055018341589672366452, 49561188616996901345349189252156955439051753759670367683995836545268981893289], 1]], [[[1, -51140957732016114984, 2157218440619039266169910340838120224606, -38476377764880669487339138342648533979869649366105822237464, 566044592922467932920289630256783944174352087720184706882390017513705742761841], 1]], [[[1, -14792322512082321412, 387306493896796427220489493655181191382, -19944191226316411485324744762702469436605370279360790010276, 1817858708606516392063752284490078897342614279715947003348265995414509863302929], 1]], [[[1, -25077766877525032720, 11203054443443268844042613144510070750558, -177606059160179602000643584057183613717160367595442717456880, 50157725483905227341761748890141694180076101090840037071925071763978352502147041], 1]], [[[1, 120090321897786074868, 3826541962025230167458574183763859414122, 2399650256121814573076512240593505869283315996883406971220444, 399282135658682469334331901689876886678820965774126540592961885129481494196023689], 1]], [[[1, -104228468137266844980, -33000838005370701606072611530973219718122, -9019376047271689666033173934908329348464316896758224062787220, 7488249032982960608606585095904734981347282237297075167277004918963148603698150321], 1]], [[[1, 260893520515229908796, 450218855490619179217341424115955462480198, 137616247945552544740706655569645756192846378961080262577838012, 278235691213844046805607971221988942088139032625098384397060765968745910963026076609], 1]], [[[1, -1530795108160169458284, 2897482267923056249850154091487128231274766, -1886539553619890460838149956620362167888475567445950030148254684, 1518789894633344114558187057241532359566305770497313080998093132114937103884488614201], 1]], [[[1, -3533951544934830051292, 6729520264789170214993749648837421567067922, -6574190875726652177613140727296715003845211592758370552772681476, 3460695893531817996658349481083474517849949869415850595461675555044106143967951861809], 1]], [[[1, -733521422666278262964, 8032069592248319814275139978740168379518938, -3037191203845926184852042472177689131439928052915706524295841148, 17144256780108035603880534575647498377121472595621714814881607371777034087912296215449], 1]], [[[1, -20959400980037179300, 9083071432840138115301373405463119058419518, -128036950867186545252862226415266616918186987358440286049703700, 37317531966144644223023469252436379373897973663646166843862654536796454569588761033481], 1]], [[[1, 809722632130867748748, 10072229624195728519784567090261138578535302, 10543470599293293226486710145087310499171547784098150951885835724, 169548763280838543075970667041682503721606000913649454670696321095954881733907235299169], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 1, 'label': '4-10e2-1.1-c21e2-0-1', 'leading_term': '8.4829909070207078519261226190760127286406111741993310197061004198012860862657917239944705', 'load_key': 'CMFs-workshop', 'motivic_weight': 21, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [21, 21], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/10/22/a/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [8.482990907020708, 8.41891924301577, 8.296362671199319, 8.070871426708774, 7.750459572874154, 7.353370823449221, 6.886075549463756, 6.354027648908288, 5.767463456303709, 5.137964141009444, 4.4770681679426625, 3.796562291462996, 3.108799528152087, 2.4260673453927257, 1.7604228551370986, 1.1233600062809288, 0.5257182082517146, -0.02263500631997075, -0.5129241746397796, -0.9376821280797818, -1.290847298115258, -1.5678919797520854, -1.7658819281094524, -1.883515530697054, -1.9211276834682434, -1.8806509246094183, -1.7655525732059258, -1.580734059330298, -1.3323965776615185, -1.0278998759561777, -0.675558520657186, -0.28448428334478315, 0.13567835820647361, 0.5749013127065868, 1.0230838944207474, 1.4701698963425804, 1.9064866648091972, 2.3228101462742523, 2.7107111196501803, 3.0625534472969576, 3.371826128278671, 3.6330664891112168, 3.8421583005769615, 3.996178820811232, 4.093646648561743, 4.134298723201464, 4.119276525630329, 4.050845686968004, 3.932515107809073, 3.768717128227979, 3.5648605315168034, 3.3269927958038745, 3.061794151447206, 2.7762449430279297, 2.4775733094283847, 2.1729500011481555, 1.869406315106524, 1.5735759103970974, 1.2916019527448508, 1.02894082854509, 0.7902778052460393, 0.5794015133855949, 0.3991457747609498, 0.25133689594895003, 0.13677582539354569, 0.05525335082050711, 0.005581778642827436, -0.014333261113012445, -0.007408348298037603, 0.022729652448705746, 0.07187784376325533, 0.13538938046771762, 0.20834856985466585, 0.2857017519962851, 0.3624593507882209, 0.4338049936351638, 0.49530718534483, 0.5429890500134449, 0.5735308014710135, 0.5842872559709007, 0.5734629105390833, 0.5400704696617576, 0.484063094637641, 0.406233965714302, 0.30829487881551737, 0.19272359856021343, 0.06278398993486448, -0.07766612858295985, -0.22421135350402258, -0.3720931261339031, -0.5162938302253719, -0.6517537485728722, -0.7734880504850261, -0.8767862670531894, -0.9573427109544318, -1.0114205713556417, -1.0359737185495597, -1.028761802566156, -0.9884412068689273, -0.914623555641623, -0.8079159131375656, -0.6699222171137853, -0.5032175129959764, -0.31129924296060846, -0.09848692225072517, 0.1301629300878601, 0.3690323943503841, 0.6120443151305174, 0.8529056278403333, 1.0852039589457012, 1.3027033676797835, 1.4994118909110736, 1.669908081654926, 1.8093579580025279, 1.913846646385614, 1.9803278237283133, 2.0069335117522145, 1.992845993079335, 1.9385606313217572, 1.8456786925795727, 1.7171029172459416, 1.5567587674864258, 1.3697099265357315, 1.1618241772234905, 0.9398053018901448, 0.7108270266084001, 0.48248793093039277, 0.26244173241984625, 0.05829162766061037, -0.12275306087920976, -0.27401839102045566, -0.3896544900179683, -0.464782473009568, -0.49570533901087765, -0.4800275668641789, -0.41677328632848254, -0.3064473955568596, -0.1510564857668231, 0.04591419227920344, 0.27957007118454685, 0.5437311793889722, 0.8310734998340886, 1.133358972601467, 1.4416209376271334, 1.7464926050646588, 2.0384018160089363, 2.3079777005896265, 2.5462169828077212, 2.7449376299946433, 2.8968803204214826, 2.996170164249383, 3.038322817658709, 3.020671979064914, 2.9422595015845867, 2.8041880360214204, 2.6093873770619607, 2.3628584611145795, 2.0713226640779765, 1.7433348677784475, 1.3888368100461135, 1.0191320047391286, 0.6463767397543019, 0.283426661639596, -0.05669203883965283, -0.3610375384951753, -0.6172543990346193, -0.8138881825498249, -0.940815663642432, -0.9895664282504567, -0.9536436842300404, -0.8287948001964469, -0.6131977613665106, -0.307623874031943, 0.08451848141046021, 0.5571776563820766, 1.1017473093696741, 1.7072510573695978, 2.360534388627435, 3.046655298474209, 3.7491343857577073, 4.450544621854621, 5.132762948635373, 5.777730062755061, 6.3676416692672335, 6.885829303813251, 7.3168316286830315, 7.647332386357963, 7.866061914279426, 7.964720361145547, 7.937676159312832, 7.782802908674878, 7.500963198017267, 7.096696370713812, 6.577500407594277, 5.954324380627095, 5.240685208998374, 4.4529412191304685, 3.6093014457113144, 2.729882755680709, 1.835684224299631, 0.9484566180499172, 0.08972109355027603, -0.7194968157831795, -1.4595275596400477, -2.1123895963227795, -2.662464240131485, -3.0968152435089977, -3.4056338934788055, -3.582468447384874, -3.6244216143532015, -3.5322227563157433, -3.3101891900480966, -2.966093398589525, -2.5109281948947424, -1.9585469207616277, -1.325296756549978, -0.6294387871418552, 0.1092696103094722, 0.8703396144699315, 1.6329318628310323, 2.376746969354817, 3.0822864579280553, 3.731793251999001, 4.309324512913165, 4.801659829023787, 5.198141985612826, 5.491474890757808, 5.677318472058834, 5.7549131018987545, 5.7264471102131855, 5.597467692093863, 5.376069668567077, 5.073081433691178, 4.701147500896165, 4.27470802621402, 3.8090620235751818, 3.3201861723727757, 2.8238682979796335, 2.335431657018171, 1.8690188620797836, 1.4372986635726022, 1.0509601425163186, 0.7184785619848427, 0.44585111554051826, 0.2364867241795352, 0.09118187589017751, 0.008177983822702246, -0.016656484306734266, 0.010414849565261303, 0.08132360881675754, 0.18660701444596536, 0.3158010774880223, 0.4579788220040301, 0.6021234327912189, 0.7377317024119926, 0.855087373962388, 0.9458560914827892, 1.0031971112571363, 1.0222767586504666, 1.0001837078814673, 0.9363005002994372, 0.8320195909298742, 0.6909350203408878, 0.518388457251157, 0.3214721631628792, 0.10846131523442565, -0.11134963798309701, -0.32825430580631726, -0.532414651802975, -0.7144282833434644, -0.8656553142223244, -0.9786734446667829, -1.047572383231853, -1.068244097678155, -1.038569798996772, -0.9585212267714177, -0.8301817659979296, -0.657667426788732, -0.44695031516590344, -0.2056396484482391, 0.057391700692889513, 0.33230060663914535, 0.6088103533628325, 0.8764985805580332, 1.1254355210508256, 1.3463858415385073, 1.5314689005396118, 1.6742070549934258, 1.7701237971701853, 1.8165963766820021, 1.8133175837884936, 1.7619438038632222, 1.6663693107579625, 1.5321965498433747, 1.366804438619567, 1.1786995850452548, 0.977396813293504, 0.7727324319931594, 0.5746096396908688, 0.3923635907977246, 0.23445027702483917, 0.1079459942017777, 0.01827079709440815, -0.031117239386794886, -0.038876578888128774, -0.005866629755131785, 0.06488727355363685, 0.16831747367520902, 0.2975731808393105, 0.4442998502849834, 0.5991164588605904, 0.7519675503002082, 0.8927712971498284, 1.0117442374077836, 1.1001386694317825, 1.150440936145722, 1.1570962982958664, 1.1165008195831854, 1.027609712489946, 0.891677785343091, 0.7126647246656954, 0.49672402270853, 0.2523535561487127, -0.010319876152537655, -0.2796495615907548, -0.543300754874264, -0.7885736513582016, -1.0032371626824381, -1.1759752925686209, -1.297101736781879, -1.3590085911610792, -1.3566565101762846, -1.2878953459342053, -1.1536610945319816, -0.9580531396261318, -0.7082208087534407, -0.4141202533420401, -0.08813140380104585, 0.25552640306062274, 0.6013523701813233, 0.9334462321163287, 1.236106849780762, 1.4949067546664023, 1.6971802010085706, 1.833138660663904, 1.8961073623651794, 1.883508425604597, 1.7967420522816118, 1.6418731811761393, 1.429112254792925, 1.173082214566071, 0.891924466992885, 0.6070908086470159, 0.3421703190409396, 0.122235232420476, -0.027459262903551374, -0.0824590335299948, -0.02035545501980651, 0.1780913441739568, 0.5279445168356094, 1.039066264613503, 1.7154901191080103, 2.5547443680150237, 3.547680917913442, 4.678363862982502, 5.924343799653522, 7.2572590379895, 8.643451549396634, 10.045329278017903, 11.42213876337373, 12.732024323967742, 13.932718567245637, 14.984126493702172, 15.848680369179691, 16.494192652519356, 16.893651459682474, 17.028040948954345, 16.8854255046489, 16.463438910637393, 15.76760931531109, 14.813270179911525, 13.623197605703929, 12.228789061633703, 10.667199629387452, 8.981753765134117, 7.218857115737934, 5.427731865216522, 3.65742914627985, 1.9560881178712122, 0.36837049184975695, -1.0654820150234694, -2.311526219174242, -3.342961052088244, -4.141156140114224, -4.696123319763516, -5.006662740467618, -5.080265382302467, -4.932481396221572, -4.586167808031039, -4.070304043592712, -3.4186247425517067, -2.6681894607180974, -1.8575576584656608, -1.0254487365450755, -0.20870300292510313, 0.5586608593321704, 1.2474149458263284, 1.833442222280926, 2.2993659487653293, 2.6341425004201335, 2.834146634793671, 2.9020684202341998, 2.847354065625304, 2.684565450219442, 2.433198923501071, 2.1157604816699522, 1.7571023113699484, 1.382511313210659, 1.016792299945084, 0.6826545092478451, 0.3998138501086252, 0.18389455455414527, 0.04581225851110126, -0.008700174894445393, 0.020770660557053396, 0.12945069631185782, 0.30781986715823484, 0.5422116085731447, 0.8158104588273419, 1.109490182709692, 1.4032313901182802, 1.676927334626073, 1.9120005053118125, 2.091919278741823, 2.2037539506451993, 2.2382143001353634, 2.190901253445978, 2.0617808079524425, 1.8559540034156432, 1.5826043898129916, 1.255212167426778, 0.8901249350788165, 0.5062599573652217, 0.12352769592140522, -0.2378258301474705, -0.5586829654520468, -0.8218450208099917, -1.0131493916352445, -1.1221402106783156, -1.1426801075631225, -1.0732765758985503, -0.9171393819062598, -0.682015240825492, -0.3797616570980026, -0.02565109944659625, 0.36236390977639166, 0.764799336187259, 1.1614428305481237, 1.5327781418704904, 1.860603269562494, 2.1294941973509287, 2.3270274875096018, 2.4450396826644547, 2.4793329988986965, 2.4305338831847134, 2.303276334469361, 2.1065540156441207, 1.8524925853886511, 1.556204057619206, 1.2343512279064963, 0.9046248122603573, 0.5843489014259312, 0.28978528527402714, 0.0350183324549236, -0.16867254810872503, -0.3134749712135915, -0.3953814972304407, -0.41432946724069275, -0.3740991486542805, -0.28198252678249036, -0.14819838883526015, 0.014750221585399124, 0.1930697023680259, 0.3723987326286177, 0.5390360139666002, 0.6804952505175357, 0.7867331136994686, 0.8503299152801647, 0.8674811846830106, 0.8376889524719526, 0.7643356792406872, 0.6538908889526436, 0.51598741693164, 0.36226842713838575, 0.2060100146199934, 0.060824156839588445, -0.06001239357594085, -0.14474170884333631, -0.1838478986816389, -0.17089909549498675, -0.10305614436348624, 0.018587108922637603, 0.18890676977479898, 0.3989406217913681, 0.636481211974254, 0.886559669406802, 1.1319559202817697, 1.3547265507256578, 1.5398428401596669, 1.6723439238691074, 1.7302061481580828, 1.7005594989760684], 'positive_zeros': ['0.794842427459680101765561788938816', '1.48514684380487484315958066096351', '3.10198697336722944316667572319487', '3.20267462228395308125262242872981', '4.05255449788773471739179722732984', '4.89552429151551962596653638970319', '6.01437335541878318939133969790558', '6.45860842729809545368635697469471', '7.63250874819259180382847280238821', '8.100065386988730858243015776922669', '9.426914530971558626016586784040245', '10.16505969652227915066826270463501', '11.53921826035046864923926285741631', '11.61423277013174624547472955210046', '12.44505953192757271287888041569510', '13.11501084736210432123292800820489', '14.16960218827182429796380241887163', '14.30191180182851090555111216749871', '15.13882234462509989118536923004375', '15.80904391050943419199518934071900'], 'prelabel': '4-10e2-1.1-c21e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.286561683051302, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c21e2-0', 'trace_hash': 280991840837278217, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.794842427459680101765561788939', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.48514684380487484315958066096', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.10198697336722944316667572319', 'prec': 103}}
• lfunc_search •

  Column	Type
  algebraic	boolean
  analytic_conductor	double precision
  bad_primes	bigint[]
  central_character	text
  conductor	numeric
  conductor_radical	bigint
  degree	smallint
  dirichlet_coefficients	numeric[]
  euler11	numeric[]
  euler13	numeric[]
  euler17	numeric[]
  euler19	numeric[]
  euler2	numeric[]
  euler23	numeric[]
  euler29	numeric[]
  euler3	numeric[]
  euler31	numeric[]
  euler37	numeric[]
  euler41	numeric[]
  euler43	numeric[]
  euler47	numeric[]
  euler5	numeric[]
  euler53	numeric[]
  euler59	numeric[]
  euler61	numeric[]
  euler67	numeric[]
  euler7	numeric[]
  euler71	numeric[]
  euler73	numeric[]
  euler79	numeric[]
  euler83	numeric[]
  euler89	numeric[]
  euler97	numeric[]
  euler_factors	numeric[]
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  is_instance_Artin	boolean
  is_instance_BMF	boolean
  is_instance_CMF	boolean
  is_instance_DIR	boolean
  is_instance_ECNF	boolean
  is_instance_ECQ	boolean
  is_instance_G2Q	boolean
  is_instance_HMF	boolean
  is_instance_MaassGL3	boolean
  is_instance_MaassGL4	boolean
  is_instance_MaassGSp4	boolean
  is_instance_NF	boolean
  label	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  self_dual	boolean
  spectral_label	text
  trace_hash	bigint
  z1	numeric

  
  {'algebraic': True, 'analytic_conductor': 781.0758596974906, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 100, 'conductor_radical': 10, 'degree': 4, 'dirichlet_coefficients': [1, 2048, 30972, 3145728, -19531250, 63430656, -439959356, 4294967296, -3214312218, -40000000000, 105191777184, 97429487616, 308456648932, -901036761088, -604921875000, 5497558138880, 18393996100404, -6582911422464, 23821216715800, -61440000000000, -13626421174032, 215432759672832, -82586042978868, 133023727091712, 286102294921875, 631719217012736, 95160354481476, -1383992465031168, -167038888446420, -1238880000000000, 5373084998145784, 6755399441055744, 3257999722942848, 37670904013627392, 8592956171875000, -10111351944904704, 83725084127912164, 48785851833958400, 9553519330721904, -83886080000000000, -63222375005514036, -27906910564417536, -113835841911164948, 330904718857469952, 62779535507812500, -169136216020721664, 13253549001226164, 170270370677391360, -971661556467634562, 585937500000000000, 569698847221712688, 970320717331562496, -1445751023743904748, 194888405978062848, -2054526898125000000, -1889611045589221376, 737790724121757600, -342095643538268160, -817060118931432840, -1902919680000000000, -4580997169825849436, 11004078076202565632, 1414166733414211608, 8070450532247928832, -6024543924453125000, 6672383432586952704, -28808031668773210556, 57862508564931674112, -2557854923141499696, 17598374240000000000, 51140957732016114984, -13805365855443222528, 14792322512082321412, 171468972293964111872, 8861160278320312500, 74935068416960102400, -46280106546368133504, 19565607589318459392, 25077766877525032720, -107374182400000000000, -83022254626380170949, -129479424011292745728, -120090321897786074868, -42865014626945335296, -359257736336015625000, -233135804234065813504, -5173528452962520240, 451795242813398974464, 104228468137266844980, 128572488720000000000, -135708388618040807792, -259793227807828475904, 166415188562571222048, 27143268354511183872, -465258138980468750000, 209228231488378503168, -260893520515229908796, -1989962867645715582976, -338119214635664834112, 900000000000000000000], 'euler11': [1, -105191777184, 8234028698069986594486, -778445443242312797540386400569824, 54763699237492901685126120802225273763666521], 'euler13': [1, -308456648932, 405609014842664615811582, -76208696707959195024342654788136916, 61040881526285814362156628321386486455989674569], 'euler17': [1, -18393996100404, 208825011717392502633984838, -1270876762965253513176733122355707895668, 4773695331839566234818968439734627784374274207965089], 'euler19': [1, -23821216715800, 1035956287377312787535052438, -17013339177394069918283517809660348720200, 510095203738582479622335815880298130716653502143703561], 'euler2': [1, -2048, 1048576, 0, 0], 'euler23': [1, 82586042978868, 77146947665381262561749618002, 3259801942635761071751750752568073461086764, 1558005952997140033806173725098810522409738596181909282129], 'euler29': [1, 167038888446420, 2777767401182653647314031245758, 857384340578471742939243074395449956778618180, 26346074268992142099064516382762907506814419719803282255713641], 'euler3': [1, -30972, 4173577002, -323978059403316, 109418989131512359209], 'euler31': [1, -5373084998145784, 46430479870606816647576677941326, -111897215981121253261870277733516807739723805704, 433701716541192355457229753999917360820651622584523552060436161], 'euler37': [1, -83725084127912164, 3220702700698569293188750157615598, -71629479938786776161097654974656738226655690252468, 731934824502651514621160916115101341995441470527191525223322819769], 'euler41': [1, 63222375005514036, 15760655031107517881866619597412406, 467016040657299076470191328021905963908681612920276, 54565982855941191947249368879497196495421462536627690767330656099281], 'euler43': [1, 113835841911164948, 1288902021152841619133031429646362, 2286212479385923251944678428852489801779196649508764, 403343566675122500462878634623535631588559593930513766350645748813849], 'euler47': [1, -13253549001226164, 249751699621383624758804273343838018, -1723404429175148388838602656880606417539246257648908, 16908692777708688563979281162874109375742132033178319498546247522565409], 'euler5': [1, 19531250, 95367431640625, 0, 0], 'euler53': [1, 1445751023743904748, 678782388504569613867404006590887982, 2343617704282445120394447513376872530815486755777353244, 2627764996340071914932060028590629703016273743509013665720935053615458009], 'euler59': [1, 817060118931432840, 30605390446842697256692759826027300518, 12593494516226934046563946667850762818318945370874105560, 237566111385928825180581197186581724740035515556906717126291161106235417081], 'euler61': [1, 4580997169825849436, 32124045550183086220006871413102007646, 142195731160651598569443526091257811049520850448895834796, 963502998275379493962849646581354683437407419033192428674820139330228382121], 'euler67': [1, 28808031668773210556, 643317018166516874238150007062407026218, 6413342629619651892730332648700568900055018341589672366452, 49561188616996901345349189252156955439051753759670367683995836545268981893289], 'euler7': [1, 439959356, 1165225791399569298, 245737478658545162084819492, 311973482284542371301330321821976049], 'euler71': [1, -51140957732016114984, 2157218440619039266169910340838120224606, -38476377764880669487339138342648533979869649366105822237464, 566044592922467932920289630256783944174352087720184706882390017513705742761841], 'euler73': [1, -14792322512082321412, 387306493896796427220489493655181191382, -19944191226316411485324744762702469436605370279360790010276, 1817858708606516392063752284490078897342614279715947003348265995414509863302929], 'euler79': [1, -25077766877525032720, 11203054443443268844042613144510070750558, -177606059160179602000643584057183613717160367595442717456880, 50157725483905227341761748890141694180076101090840037071925071763978352502147041], 'euler83': [1, 120090321897786074868, 3826541962025230167458574183763859414122, 2399650256121814573076512240593505869283315996883406971220444, 399282135658682469334331901689876886678820965774126540592961885129481494196023689], 'euler89': [1, -104228468137266844980, -33000838005370701606072611530973219718122, -9019376047271689666033173934908329348464316896758224062787220, 7488249032982960608606585095904734981347282237297075167277004918963148603698150321], 'euler97': [1, 260893520515229908796, 450218855490619179217341424115955462480198, 137616247945552544740706655569645756192846378961080262577838012, 278235691213844046805607971221988942088139032625098384397060765968745910963026076609], 'euler_factors': [[1, -2048, 1048576, 0, 0], [1, -30972, 4173577002, -323978059403316, 109418989131512359209], [1, 19531250, 95367431640625, 0, 0], [1, 439959356, 1165225791399569298, 245737478658545162084819492, 311973482284542371301330321821976049], [1, -105191777184, 8234028698069986594486, -778445443242312797540386400569824, 54763699237492901685126120802225273763666521], [1, -308456648932, 405609014842664615811582, -76208696707959195024342654788136916, 61040881526285814362156628321386486455989674569], [1, -18393996100404, 208825011717392502633984838, -1270876762965253513176733122355707895668, 4773695331839566234818968439734627784374274207965089], [1, -23821216715800, 1035956287377312787535052438, -17013339177394069918283517809660348720200, 510095203738582479622335815880298130716653502143703561], [1, 82586042978868, 77146947665381262561749618002, 3259801942635761071751750752568073461086764, 1558005952997140033806173725098810522409738596181909282129], [1, 167038888446420, 2777767401182653647314031245758, 857384340578471742939243074395449956778618180, 26346074268992142099064516382762907506814419719803282255713641], [1, -5373084998145784, 46430479870606816647576677941326, -111897215981121253261870277733516807739723805704, 433701716541192355457229753999917360820651622584523552060436161], [1, -83725084127912164, 3220702700698569293188750157615598, -71629479938786776161097654974656738226655690252468, 731934824502651514621160916115101341995441470527191525223322819769], [1, 63222375005514036, 15760655031107517881866619597412406, 467016040657299076470191328021905963908681612920276, 54565982855941191947249368879497196495421462536627690767330656099281], [1, 113835841911164948, 1288902021152841619133031429646362, 2286212479385923251944678428852489801779196649508764, 403343566675122500462878634623535631588559593930513766350645748813849], [1, -13253549001226164, 249751699621383624758804273343838018, -1723404429175148388838602656880606417539246257648908, 16908692777708688563979281162874109375742132033178319498546247522565409], [1, 1445751023743904748, 678782388504569613867404006590887982, 2343617704282445120394447513376872530815486755777353244, 2627764996340071914932060028590629703016273743509013665720935053615458009], [1, 817060118931432840, 30605390446842697256692759826027300518, 12593494516226934046563946667850762818318945370874105560, 237566111385928825180581197186581724740035515556906717126291161106235417081], [1, 4580997169825849436, 32124045550183086220006871413102007646, 142195731160651598569443526091257811049520850448895834796, 963502998275379493962849646581354683437407419033192428674820139330228382121], [1, 28808031668773210556, 643317018166516874238150007062407026218, 6413342629619651892730332648700568900055018341589672366452, 49561188616996901345349189252156955439051753759670367683995836545268981893289], [1, -51140957732016114984, 2157218440619039266169910340838120224606, -38476377764880669487339138342648533979869649366105822237464, 566044592922467932920289630256783944174352087720184706882390017513705742761841], [1, -14792322512082321412, 387306493896796427220489493655181191382, -19944191226316411485324744762702469436605370279360790010276, 1817858708606516392063752284490078897342614279715947003348265995414509863302929], [1, -25077766877525032720, 11203054443443268844042613144510070750558, -177606059160179602000643584057183613717160367595442717456880, 50157725483905227341761748890141694180076101090840037071925071763978352502147041], [1, 120090321897786074868, 3826541962025230167458574183763859414122, 2399650256121814573076512240593505869283315996883406971220444, 399282135658682469334331901689876886678820965774126540592961885129481494196023689], [1, -104228468137266844980, -33000838005370701606072611530973219718122, -9019376047271689666033173934908329348464316896758224062787220, 7488249032982960608606585095904734981347282237297075167277004918963148603698150321], [1, 260893520515229908796, 450218855490619179217341424115955462480198, 137616247945552544740706655569645756192846378961080262577838012, 278235691213844046805607971221988942088139032625098384397060765968745910963026076609]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/10/22/a/d'], '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': '4-10e2-1.1-c21e2-0-1', 'motivic_weight': 21, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [21, 21], 'order_of_vanishing': 0, 'prelabel': '4-10e2-1.1-c21e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.286561683051302, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c21e2-0', 'trace_hash': 280991840837278217, 'z1': {'__RealLiteral__': 0, 'data': '0.794842427459680101765561788939', 'prec': 107}}
• lfunc_instances •

  Column	Type
  Lhash	text
  Lhash_array	text[]
  label	text
  type	text
  url	text

  
  {'Lhash': '1007582480256126368314484983851,1882647287976310053152452664725', 'Lhash_array': ['1007582480256126368314484983851', '1882647287976310053152452664725'], 'label': '4-10e2-1.1-c21e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/10/22/a/d'}