Lfunction data - 14-405e7-1.1-c3e7-0-0

Formats: - HTML - YAML - JSON - 2025-09-22T22:05:03.482198

• 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
  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': '559616706508831041967960088098,589087196204845943755307995769,746366141552565370320368524280,1185354011697641570121271916888,1247680732397552627042966905607,1251954517532899558434358291671,2029226106367690886123805387635', 'a10': 70, 'a2': -2, 'a3': 0, 'a4': -8, 'a5': -35, 'a6': 0, 'a7': 22, 'a8': 18, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4448848926.195494, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, 35, 525, 4375, 21875, 65625, 109375, 78125]]], 'bad_primes': [3, 5], 'central_character': '405.1', 'coefficient_field': '1.1.1.1', 'conductor': 1787249410543828125, 'conductor_radical': 15, 'degree': 14, 'euler_factors': [[1, 2, 12, 22, 63, 12, 56, -864, 448, 768, 32256, 90112, 393216, 524288, 2097152], [1], [1, 35, 525, 4375, 21875, 65625, 109375, 78125], [1, -22, 830, -19134, 426701, -7825194, 165254493, -2430999116, 56682291099, -920626248906, 17218924460507, -264839189303934, 3940476053252690, -35825099154029878, 558545864083284007], [1, 23, 5151, 137494, 15125367, 360831273, 29040094313, 601859871012, 38652365530603, 639234610827153, 35664824193177597, 431515071228877174, 21517005320660018301, 127878098210321324063, 7400249944258160101211], [1, -96, 12191, -828700, 67939809, -3670430048, 227859076023, -10004745881352, 500606390022531, -17716464789556832, 720467661942239757, -19307123141000004700, 624007221734780418587, -10795719067387909740384, 247064529073450392704413], [1, 161, 24747, 2620018, 242733069, 19012626063, 1428967389431, 98461041404796, 7020516784274503, 458918573466860847, 28785199208309779293, 1526480748742243955698, 70836383255713411429371, 2264156596782903723552449, 69091933913008732880827217], [1, -279, 63455, -9627646, 1292727231, -139417672577, 13934197302465, -1188087181318116, 95574659297607435, -6559027233354505337, 417147174027611519949, -21309012527287648687006, 963318415680705326063045, -29051530733117236387662639, 714209495693373205673756419], [1, 96, 70730, 5128416, 2231256537, 129120969582, 42017720032537, 1973532783601374, 511229599635877679, 19114537520613328398, 4018833650024266733631, 112387310571163926541536, 18859110204396392801783110, 311438487349943835388835424, 39471584120695485887249589623], [1, -296, 154422, -29519614, 8749743807, -1202308386924, 280424950326131, -32104391095886106, 6839284113504008959, -715161067576286654604, 126933810659604754193283, -10444475827719128779270174, 1332536584781606837740226478, -62295356172090947617770327656, 5132842708382182842735812571629], [1, -244, 138953, -21581892, 6820038797, -643944456252, 180689501328357, -12932535760119704, 5382920934073083387, -571503075283193463612, 180319248913797187552787, -16999253132143831778527812, 3260568549552794644024481303, -170569083279766989403557538804, 20825506393391550743120420649631], [1, -404, 267991, -88433668, 32537859593, -8785146905212, 2408172804310695, -541287630181037208, 121981177056749633835, -22540283421647048143708, 4228676841914216018623661, -582154592144391741148240708, 89360598794674935961952327563, -6823581739467573502981188115316, 855531895666462872887391390111637], [1, -47, 321096, 12021155, 45171631701, 4630735558038, 4063682212222409, 491807687844214791, 280073041748580650689, 21996476613185805439158, 14788376166004950930557661, 271239214241698479638543555, 499335848550522857034686226696, -5037409755473993864748603667487, 7386879101213258109624223688656841], [1, -525, 461651, -177053890, 91552352643, -27963570378443, 10910759641065633, -2737206494978679516, 867481766782205282931, -176767880508400526352707, 46013536043808301580126049, -7075008075619140503219249890, 1466697711440992029278401740857, -132614650126086481926205923490725, 20083415214428110320965436874242043], [1, 164, 458970, 110392306, 108169816881, 25717707674850, 17081669577666257, 3320863886913274956, 1773470180562043800511, 277216708795484067775650, 121056138341473202284409727, 12826645757956882787445413746, 5536714992576024410523180976710, 205402294595664587030295461231396, 130033429462229783044185156533092847], [1, 506, 541623, 172442740, 132333548265, 35763427746966, 25492045997195975, 6232790423469661848, 3795179331924545170075, 792673527794653258084614, 436669424538837325685449245, 84714031499427521535957756340, 39612763617591348101036449058811, 5509550519462154392273647414942634, 1621038246414954860589967996431649253], [1, -85, 331341, -32993294, 125055414789, -9577822572435, 29633014670734625, -2027875987639118244, 6085998920060806547875, -403997667224123676785835, 1083354535417266020708492871, -58701583504017865350673596014, 121075244088781394037302622857559, -6379037207092801324644127672966285, 15413179794770734626518662321719325259], [1, -828, 1137794, -655662598, 472897824279, -204252976588544, 110585022303384087, -44527407364853870622, 25100698947444423451347, -10523189818190355543920384, 5530136244102034031709909339, -1740357344486590565693586177958, 685505848523261761203332246404394, -113231527751973748881349580752125468, 31040344686800426926132378247220037261], [1, -1093, 2017106, -1699166505, 1757369253407, -1166070992255454, 864466170577418349, -453458572496944446653, 259999438861376074900287, -105480895453628897206599726, 47811927039808716476356634429, -13903801882582440182487994129305, 4964217048551830484719900464335558, -809033696645460601445269552381960237, 222623423334106740048017938136372833267], [1, 328, 1276365, 268163756, 813660594393, 105690507940488, 374340014427629213, 36698946645864837192, 133980408903807199254043, 13538984074931217771293448, 37305118346601126104534883183, 4400482158498613760644686769196, 7496354524351065224608875358727115, 689483885946515790262531327507179208, 752359350923790893319063566949457370471], [1, -2085, 4050563, -4984423486, 5631570806793, -4895773027898939, 3922468709989734339, -2545861771312367695716, 1525907010154076483354763, -740898023263640744849007371, 331539509055864385937004333009, -114153506160426465391921371182206, 36087624328883098486425947878464491, -7226325859429888520514040340508061365, 1348279907365869037210940254745047725673], [1, -2110, 3466397, -4074662340, 4200201567425, -3637140873668514, 2929970636702454981, -2095116506829323507384, 1444589792749141701377259, -884143320351505977073165794, 503400861304581296519318658575, -240777954614457219934741297631940, 100991464377697520623090800182546003, -30308894675715428038603142460553955710, 7082211906170644040153959599814721217679], [1, 1290, 3282374, 3191089158, 4600431414309, 3678070946162670, 3902415474964514617, 2608484875033022043888, 2231350437183534919310579, 1202509888416094427609935230, 860005822931736383353089826527, 341095544793377611541353912134438, 200613174168173368441896296494536418, 45081190160946185934162182436249107610, 19982045332214679702896737836182611234883], [1, -3048, 5723102, -6323602086, 4534976524791, -780789931274556, -1899913405596725465, 2724235891150620996750, -1339380053630117954335585, -388037988014179309012088316, 1588858066123643901224854316319, -1561869031207273507560170068744806, 996509827111285634489773401499203598, -374140810118231499571381570059102179688, 86534669543385676516186776267386878120889], [1, -1787, 4084243, -4789169974, 7296823674929, -7118143615887349, 8621884508580027771, -7253857327779680859444, 7868961200099259685841883, -5929214359098246753936743221, 5547271987206968717072638344593, -3322929001968620421991613498298934, 2586351736473608092421547514614778099, -1032798906164414230059627059212281418043, 527480512638944839726474542256547576188897], [1, -2676, 8187623, -13764283128, 24682444043049, -30745954530190764, 40649724331582532407, -40002198566661245647632, 41881451628553814721464507, -32637450283259598002539249164, 26994825543738524918511096427149, -15509938750453562439503841928516728, 9505576121273373516499278207258772123, -3200890644937515167450089764723715099476, 1232391940347446492727576582468089832102101], [1, -1574, 4106005, -5041613656, 8792121865073, -9074266796227594, 12720590157889553325, -11110313281374700040496, 13900132321460177936167275, -10835149107352409889460221226, 11471724838506014167046642149559, -7188135557314366542789514221316696, 6397022002399822371447807014497904035, -2679629638391608388826478599428444281286, 1860294571709496226110032706809177658295303], [1, 2655, 9677348, 17271354393, 36214434403569, 48723301805829174, 73762751314366671175, 77404265925797309845761, 90362542158405689956235525, 73120537862307033376209042726, 66578760551826811560743372235483, 38898399093876166458806536250042793, 26700108362478455126261937122818349164, 8973720192069879872471844294932656645095, 4140562374860211619063098135818149338786107], [1, 286, 6447274, 1084040072, 20083558156703, 2163898991335460, 38848005140647582959, 3074454207667607504784, 50309293249287698711810811, 3629075238217428064613721860, 43619344987832020836374270184467, 3049041332555793226676204667604232, 23484082457799396226380481110408807826, 1349096439343987454008754768072900249806, 6108807736878338211809453421477901879741309], [1, -2878, 8889063, -16148831924, 31516523248773, -45383284808718306, 69439408720934270579, -81598691974597014627672, 100193914525209896215627363, -94485809346664482499681560354, 94676957578770289702335150079029, -69997485015690961318977593601669044, 55594603406384954357310541575841951191, -25971843203754304972352011442204610478462, 13021089174137413266744892374538813705886513]], 'euler_factors_factorization': [[[[1, 2, 12, 22, 63, 12, 56, -864, 448, 768, 32256, 90112, 393216, 524288, 2097152], 1]], [1], [[[1, 5], 7]], [[[1, -22, 830, -19134, 426701, -7825194, 165254493, -2430999116, 56682291099, -920626248906, 17218924460507, -264839189303934, 3940476053252690, -35825099154029878, 558545864083284007], 1]], [[[1, 23, 5151, 137494, 15125367, 360831273, 29040094313, 601859871012, 38652365530603, 639234610827153, 35664824193177597, 431515071228877174, 21517005320660018301, 127878098210321324063, 7400249944258160101211], 1]], [[[1, -96, 12191, -828700, 67939809, -3670430048, 227859076023, -10004745881352, 500606390022531, -17716464789556832, 720467661942239757, -19307123141000004700, 624007221734780418587, -10795719067387909740384, 247064529073450392704413], 1]], [[[1, 161, 24747, 2620018, 242733069, 19012626063, 1428967389431, 98461041404796, 7020516784274503, 458918573466860847, 28785199208309779293, 1526480748742243955698, 70836383255713411429371, 2264156596782903723552449, 69091933913008732880827217], 1]], [[[1, -279, 63455, -9627646, 1292727231, -139417672577, 13934197302465, -1188087181318116, 95574659297607435, -6559027233354505337, 417147174027611519949, -21309012527287648687006, 963318415680705326063045, -29051530733117236387662639, 714209495693373205673756419], 1]], [[[1, 96, 70730, 5128416, 2231256537, 129120969582, 42017720032537, 1973532783601374, 511229599635877679, 19114537520613328398, 4018833650024266733631, 112387310571163926541536, 18859110204396392801783110, 311438487349943835388835424, 39471584120695485887249589623], 1]], [[[1, -296, 154422, -29519614, 8749743807, -1202308386924, 280424950326131, -32104391095886106, 6839284113504008959, -715161067576286654604, 126933810659604754193283, -10444475827719128779270174, 1332536584781606837740226478, -62295356172090947617770327656, 5132842708382182842735812571629], 1]], [[[1, -244, 138953, -21581892, 6820038797, -643944456252, 180689501328357, -12932535760119704, 5382920934073083387, -571503075283193463612, 180319248913797187552787, -16999253132143831778527812, 3260568549552794644024481303, -170569083279766989403557538804, 20825506393391550743120420649631], 1]], [[[1, -404, 267991, -88433668, 32537859593, -8785146905212, 2408172804310695, -541287630181037208, 121981177056749633835, -22540283421647048143708, 4228676841914216018623661, -582154592144391741148240708, 89360598794674935961952327563, -6823581739467573502981188115316, 855531895666462872887391390111637], 1]], [[[1, -47, 321096, 12021155, 45171631701, 4630735558038, 4063682212222409, 491807687844214791, 280073041748580650689, 21996476613185805439158, 14788376166004950930557661, 271239214241698479638543555, 499335848550522857034686226696, -5037409755473993864748603667487, 7386879101213258109624223688656841], 1]], [[[1, -525, 461651, -177053890, 91552352643, -27963570378443, 10910759641065633, -2737206494978679516, 867481766782205282931, -176767880508400526352707, 46013536043808301580126049, -7075008075619140503219249890, 1466697711440992029278401740857, -132614650126086481926205923490725, 20083415214428110320965436874242043], 1]], [[[1, 164, 458970, 110392306, 108169816881, 25717707674850, 17081669577666257, 3320863886913274956, 1773470180562043800511, 277216708795484067775650, 121056138341473202284409727, 12826645757956882787445413746, 5536714992576024410523180976710, 205402294595664587030295461231396, 130033429462229783044185156533092847], 1]], [[[1, 506, 541623, 172442740, 132333548265, 35763427746966, 25492045997195975, 6232790423469661848, 3795179331924545170075, 792673527794653258084614, 436669424538837325685449245, 84714031499427521535957756340, 39612763617591348101036449058811, 5509550519462154392273647414942634, 1621038246414954860589967996431649253], 1]], [[[1, -85, 331341, -32993294, 125055414789, -9577822572435, 29633014670734625, -2027875987639118244, 6085998920060806547875, -403997667224123676785835, 1083354535417266020708492871, -58701583504017865350673596014, 121075244088781394037302622857559, -6379037207092801324644127672966285, 15413179794770734626518662321719325259], 1]], [[[1, -828, 1137794, -655662598, 472897824279, -204252976588544, 110585022303384087, -44527407364853870622, 25100698947444423451347, -10523189818190355543920384, 5530136244102034031709909339, -1740357344486590565693586177958, 685505848523261761203332246404394, -113231527751973748881349580752125468, 31040344686800426926132378247220037261], 1]], [[[1, -1093, 2017106, -1699166505, 1757369253407, -1166070992255454, 864466170577418349, -453458572496944446653, 259999438861376074900287, -105480895453628897206599726, 47811927039808716476356634429, -13903801882582440182487994129305, 4964217048551830484719900464335558, -809033696645460601445269552381960237, 222623423334106740048017938136372833267], 1]], [[[1, 328, 1276365, 268163756, 813660594393, 105690507940488, 374340014427629213, 36698946645864837192, 133980408903807199254043, 13538984074931217771293448, 37305118346601126104534883183, 4400482158498613760644686769196, 7496354524351065224608875358727115, 689483885946515790262531327507179208, 752359350923790893319063566949457370471], 1]], [[[1, -2085, 4050563, -4984423486, 5631570806793, -4895773027898939, 3922468709989734339, -2545861771312367695716, 1525907010154076483354763, -740898023263640744849007371, 331539509055864385937004333009, -114153506160426465391921371182206, 36087624328883098486425947878464491, -7226325859429888520514040340508061365, 1348279907365869037210940254745047725673], 1]], [[[1, -2110, 3466397, -4074662340, 4200201567425, -3637140873668514, 2929970636702454981, -2095116506829323507384, 1444589792749141701377259, -884143320351505977073165794, 503400861304581296519318658575, -240777954614457219934741297631940, 100991464377697520623090800182546003, -30308894675715428038603142460553955710, 7082211906170644040153959599814721217679], 1]], [[[1, 1290, 3282374, 3191089158, 4600431414309, 3678070946162670, 3902415474964514617, 2608484875033022043888, 2231350437183534919310579, 1202509888416094427609935230, 860005822931736383353089826527, 341095544793377611541353912134438, 200613174168173368441896296494536418, 45081190160946185934162182436249107610, 19982045332214679702896737836182611234883], 1]], [[[1, -3048, 5723102, -6323602086, 4534976524791, -780789931274556, -1899913405596725465, 2724235891150620996750, -1339380053630117954335585, -388037988014179309012088316, 1588858066123643901224854316319, -1561869031207273507560170068744806, 996509827111285634489773401499203598, -374140810118231499571381570059102179688, 86534669543385676516186776267386878120889], 1]], [[[1, -1787, 4084243, -4789169974, 7296823674929, -7118143615887349, 8621884508580027771, -7253857327779680859444, 7868961200099259685841883, -5929214359098246753936743221, 5547271987206968717072638344593, -3322929001968620421991613498298934, 2586351736473608092421547514614778099, -1032798906164414230059627059212281418043, 527480512638944839726474542256547576188897], 1]], [[[1, -2676, 8187623, -13764283128, 24682444043049, -30745954530190764, 40649724331582532407, -40002198566661245647632, 41881451628553814721464507, -32637450283259598002539249164, 26994825543738524918511096427149, -15509938750453562439503841928516728, 9505576121273373516499278207258772123, -3200890644937515167450089764723715099476, 1232391940347446492727576582468089832102101], 1]], [[[1, -1574, 4106005, -5041613656, 8792121865073, -9074266796227594, 12720590157889553325, -11110313281374700040496, 13900132321460177936167275, -10835149107352409889460221226, 11471724838506014167046642149559, -7188135557314366542789514221316696, 6397022002399822371447807014497904035, -2679629638391608388826478599428444281286, 1860294571709496226110032706809177658295303], 1]], [[[1, 2655, 9677348, 17271354393, 36214434403569, 48723301805829174, 73762751314366671175, 77404265925797309845761, 90362542158405689956235525, 73120537862307033376209042726, 66578760551826811560743372235483, 38898399093876166458806536250042793, 26700108362478455126261937122818349164, 8973720192069879872471844294932656645095, 4140562374860211619063098135818149338786107], 1]], [[[1, 286, 6447274, 1084040072, 20083558156703, 2163898991335460, 38848005140647582959, 3074454207667607504784, 50309293249287698711810811, 3629075238217428064613721860, 43619344987832020836374270184467, 3049041332555793226676204667604232, 23484082457799396226380481110408807826, 1349096439343987454008754768072900249806, 6108807736878338211809453421477901879741309], 1]], [[[1, -2878, 8889063, -16148831924, 31516523248773, -45383284808718306, 69439408720934270579, -81598691974597014627672, 100193914525209896215627363, -94485809346664482499681560354, 94676957578770289702335150079029, -69997485015690961318977593601669044, 55594603406384954357310541575841951191, -25971843203754304972352011442204610478462, 13021089174137413266744892374538813705886513], 1]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 0, 'label': '14-405e7-1.1-c3e7-0-0', 'leading_term': '5.2320682304255811787901523351743024950545548924341886147519973405143438462511081895361446', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3, 3, 3, 3, 3, 3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/405/4/a/m', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.010044642857142858', 'prec': 67}, 'plot_values': [5.23206823042558, 5.19760219189247, 5.159665477852826, 5.114694761843733, 5.059243278008129, 4.99002841746668, 4.903996792797011, 4.7986988463190325, 4.6744610657358905, 4.5333362978338165, 4.377568169627312, 4.209429972719042, 4.031185906320025, 3.8450323471675185, 3.652684889954202, 3.4554664864476465, 3.2546230541266503, 3.051404142877486, 2.8470747971754764, 2.6429045105657734, 2.4402178833538297, 2.240395377251737, 2.044752988053025, 1.8545288147717955, 1.670856564202416, 1.4947521590417865, 1.327102046268959, 1.1686520331760757, 1.020017172021567, 0.8816813689971686, 0.7539956675872823, 0.6371802987304183, 0.5313279916032368, 0.43641074511879274, 0.3522786943066548, 0.278664626710635, 0.21519237763464774, 0.16138643892509266, 0.11668233703061034, 0.08043869734848763, 0.05194872966677456, 0.03045272199728755, 0.015151641291789667, 0.005220900864430415, -0.00017591287277620376, -0.001873541357658857, -0.0006922062308418265, 0.0025749047120979278, 0.007173617724968623, 0.012399756765402368, 0.01760897285663988, 0.022225247131444303, 0.025748045698776204, 0.027758202036329217, 0.027922079989616336, 0.025994038239270146, 0.021817195867853485, 0.015322556048424897, 0.006526677333433572, -0.004472478036076628, -0.017501318393732472, -0.03231780837085815, -0.04861993891351353, -0.06605525452910872, -0.08423093912541997, -0.10272533687221559, -0.12110001472281104, -0.13891190223349031, -0.15572546027157863, -0.17112458806236827, -0.18472366323196412, -0.19617846510239095, -0.20519664426069173, -0.21154618410004947, -0.2150624506778955, -0.21565364257133152, -0.21330423889049147, -0.2080767063587265, -0.20011159357448796, -0.1896253131299913, -0.17690503392455584, -0.16230154478706607, -0.14622004589228296, -0.12910894285501817, -0.11144683331970753, -0.09372766399440956, -0.07644444735824682, -0.06007119497726032, -0.045044156566849555, -0.031742593963197174, -0.020469281413309164, -0.011431178327136172, -0.0047207505191695, -0.000298328524931646, 0.002024181883152808, 0.0025975098324153324, 0.0019468160890834035, 0.0007806548175058053, -3.2631193616680803e-06, 0.0006841556973012125, 0.004121725156597539, 0.011772107880940135, 0.025271539830743227, 0.04641512433838741, 0.07713764145207465, 0.11948990252003235, 0.17561066853862928, 0.24769387388645436, 0.33795209101609824, 0.4485768630306853, 0.581695894910619, 0.739327755842139, 0.9233347497033862, 1.135374298143263, 1.3768488583193725, 1.6488581196621523, 1.9521523636421327, 2.287087845231119, 2.6535853961817066, 3.051093316237626, 3.4785559808772466, 3.9343865336977624, 4.416448048589439, 4.922042327010312, 5.447906787384323, 5.990220589278805, 6.544624548585657, 7.106247251441229, 7.669737311754813, 8.229309331007038, 8.778799761970346, 9.31173263480905, 9.821402577520177, 10.300964825433267, 10.743517071365892, 11.142198117950072, 11.490290854091276, 11.781330181515973, 12.00922279767774, 12.168376416223651, 12.253792076475516, 12.261169166372047, 12.187012031955847, 12.028726079248782, 11.784713204268536, 11.454477153036171, 11.038668289851666, 10.539125587426973, 9.958915350172804, 9.302353507133654, 8.575010662600794, 7.783718785176922, 6.9365189834593055, 6.042587078383915, 5.112158204946515, 4.156431061908966, 3.187449960050708, 2.217981415509055, 1.2613530537050412, 0.3312710491727316, -0.5583591061154215, -1.3936221031306575, -2.160794044124485, -2.8465640054136823, -3.4382550157552085, -3.9240263640905573, -4.293073528822501, -4.5358221956504625, -4.644112263550574, -4.611384199997394, -4.432884837719306, -4.105760428688865, -3.6291464515441865, -3.004246054958034, -2.2343812190767225, -1.3250231002244723, -0.2838413752003095, 0.8793769235972871, 2.152849432282401, 3.5229151365536633, 4.9741803284628565, 6.48969142619536, 8.05109407110899, 9.638892266656201, 11.232780537701693, 12.811920945872188, 14.355234358122823, 15.841706001612419, 17.250682461453216, 18.562201197544113, 19.75736011782934, 20.818666024159636, 21.73029728089123, 22.478361829319116, 23.051148356911185, 23.439374484090223, 23.636379473049146, 23.63828098226248, 23.44411820802255, 23.055863009174193, 22.47842542330962, 21.71967791085962, 20.79034686014262, 19.70385619312146, 18.476155058305146, 17.125518845962333, 15.672241521429235, 14.138385092994215, 12.547416328462722, 10.923789310055072, 9.29255193512902, 7.6789448638516795, 6.107997134930039, 4.60412854296932, 3.190729183499547, 1.8897044979601838, 0.7210980051786069, -0.29725298097961916, -1.150026572753999, -1.8246779564777758, -2.3116682980441934, -2.604673732181323, -2.700700558366629, -2.6001374642550585, -2.3067484824979108, -1.8276119730025324, -1.1730205615752418, -0.35629392327551374, 0.6064706319852092, 1.696694938522218, 2.8936612756325837, 4.174887107827966, 5.516502295947969, 6.8937163392062235, 8.281296023158433, 9.654031655269698, 10.98720258028337, 12.25702957531838, 13.441079826722031, 14.518690864400314, 15.471410777351913, 16.283311455841005, 16.94125849208243, 17.43513274808518, 17.757980234527516, 17.906109496798702, 17.879159505148742, 17.680109312081083, 17.31514129449328, 16.793461161888715, 16.127069784570516, 15.330482497883418, 14.420402195846329, 13.415355190273365, 12.335308466056041, 11.20119875295997, 10.034469503675055, 8.856616271329019, 7.6887260086119396, 6.551032244497377, 5.462499978004652, 4.440447089395639, 3.5001792199449144, 2.6546888814878806, 1.9144086905577211, 1.2870260778941096, 0.7773647559663164, 0.3873326672471381, 0.1159363380988584, -0.04064155896980146, -0.0888968806106621, -0.0377964601686575, 0.10148492581733533, 0.3158761794593317, 0.59076277726464, 0.9103748940473231, 1.2582008920148162, 1.6174094678490367, 1.971275445499739, 2.3035988210599334, 2.599106948312149, 2.8438334398586798, 3.0254678415972114, 3.13364196356597, 3.1601702129553986, 3.0992368999567694, 2.9475233980849955, 2.7042736784798342, 2.3712992589753217, 1.9528937890344014, 1.4556998050311927, 0.8885232558090901, 0.2620937518916598, -0.41122204659267036, -1.1177511902477524, -1.8428897804852893, -2.571502647200428, -3.2882965260597454, -3.9782037675955597, -4.626763486412336, -5.220501113248294, -5.747283823768188, -6.196610356264524, -6.559873823243203, -6.830538661126542, -7.004280595789707, -7.079092355174007, -7.055346315626649, -6.9357254614657595, -6.725120235458045, -6.430470608539077, -6.060550580108166, -5.625729142681431, -5.137722517692096, -4.609238189852942, -4.053614965002099, -3.4844637245137258, -2.915295387151786, -2.3591875074103066, -1.828483524493808, -1.3344657267610187, -0.8870610565624447, -0.4946082696801888, -0.16366945344623415, 0.10109945895656038, 0.2970018573585744, 0.423327875703864, 0.48133566709667286, 0.4741666218209549, 0.4067114039496562, 0.2854192368157944, 0.11802551202955898, -0.08669064277112132, -0.3191727805464928, -0.5693797319813505, -0.8270846869661832, -1.0821724736761567, -1.3249545490194106, -1.5465350009939887, -1.7389932829150685, -1.8955635460219895, -2.0107989589405215, -2.0806939915811733, -2.102762891541201, -2.076109183414807, -2.001507796984328, -1.88123722642776, -1.7189319236982246, -1.519430402235707, -1.2885923861406174, -1.0330932142979834, -0.760219891856115, -0.4776940850304604, -0.19332818635081328, 0.08524729758113571, 0.35081424207188366, 0.5967784829990059, 0.8173580710144485, 1.007723876212904, 1.1640890932356551, 1.2838477546861524, 1.3656265174254032, 1.4092811836306836, 1.415856695840636, 1.3874991356534572, 1.3273327227841578, 1.239307771091831, 1.1280504405654639, 0.9986776809142521, 0.8566006891168435, 0.7073157608480537, 0.5562023054654682, 0.4083349399741484, 0.26831446893438277, 0.14012434224396736, 0.02701349834652072, -0.06859255297642587, -0.1451447302904731, -0.20198529231630477, -0.23932685391604647, -0.2581974148102888, -0.2603546463793293, -0.24817291473180644, -0.22450705978915836, -0.1925397391058495, -0.15561905546975854, -0.11709338966096187, -0.08015047188725928, -0.047667015096957234, -0.022075358336991074, -0.005253387430618863, 0.0015577420336698525, -0.0021955272286155614, -0.01636212716205888, -0.04010446180857455, -0.07195081005050577, -0.10988005510199583, -0.1514357448577439, -0.1938650512552351, -0.234277267699599, -0.26981618784726247, -0.2978348822732282, -0.3160689466249317, -0.3228008642332206, -0.3170071739590091, -0.2984815561693767, -0.2679284817227017, -0.22701689162600916, -0.17839103608243392, -0.12564821904623982, -0.0732723389829564, -0.02652383375347237, 0.008711120185571705, 0.026108918992176273, 0.019126480471104546, -0.01876518520436339, -0.09383457002171043, -0.21183088056134286, -0.37772657555176936, -0.5954745210794525, -0.8677843862000337, -1.195939393334161, -1.5796928595003028, -2.017151502038871, -2.504712009613385, -3.037077469100168, -3.6073078070049047, -4.206920955872764, -4.826087169346557, -5.453968974715532, -6.078911203844237, -6.688743502208028, -7.271093236295898, -7.8136887820225684, -8.304692532290025, -8.733091473721338, -9.089209377022405, -9.364891835753339, -9.55370592952464, -9.651071748149006, -9.654396630886191, -9.563159126260748, -9.379003318359771, -9.105937894799933, -8.750053147240205, -8.319195425903589, -7.822730480399275, -7.271278220502816, -6.6764156480792085, -6.050424581331351, -5.406120749596316, -4.756237450539151, -4.113012148238831, -3.4878754770478477, -2.8911742009371206, -2.3319390511685327, -1.8177374258722239, -1.3545533924912239, -0.9465788388657331, -0.5961775305490277, -0.30394024984032636, -0.0687945034739181, 0.11183913003523537, 0.24184909967929188, 0.32619141281901665, 0.370661655090828, 0.3816180006239514, 0.36569465336295404, 0.3295306521932238, 0.2795173941862756, 0.22156602468607722, 0.16091897468545374, 0.1020074351491152, 0.04835269685152635, 0.0025190975233525784, -0.033883389910265044, -0.060154192938529465, -0.07641059644503868, -0.08346071767208235, -0.08264937547198792, -0.07568676525689927, -0.06447142279815411, -0.05091751258205903, -0.03679643721926113, -0.02360354575973866, -0.012458128026108758, -0.004042508822554187, 0.001414187612173168, 0.0041067872400705275, 0.004579794334702484, 0.003611739568635447, 0.002064901422335647, 0.0007092868439245461, 3.166960855968758e-05, 4.2705606004292e-05, 9.603086263534749e-05, -0.0012663249384680265, -0.006428239475349921, -0.01876059616672897, -0.0426178386094152, -0.08326101396939219, -0.1467019929943254, -0.23946678941151633, -0.368279970117127, -0.5396764180574471, -0.7595523406282813, -1.0326746326264424, -1.3621575705649045, -1.7489328471296601, -2.191238512394543, -2.684152598973484, -3.2191995540596503, -3.784070723581797, -4.362493244948581, -4.934192296460613, -5.475025482599367, -5.957303333240946, -6.350297918652669, -6.620948757812316, -6.7347616957803345, -6.656910184525771, -6.353346217986929, -5.7920645338772525, -4.94447160325092, -3.7867881840960016, -2.301428639615345, -0.4783479033119293, 1.6837692033812366, 4.176562330481053, 6.981183756795373, 10.067758400861726, 13.39520727797895, 16.91123500364781, 20.552779404325324, 24.24716906818335, 27.913200078073352, 31.462597422086766, 34.80205380806654, 37.835177267780814, 40.464698984751216, 42.5952065042917, 44.13667307548396, 45.00662166379866, 45.132757274266666, 44.45525581652598, 42.9287528927341, 40.52427111760584, 37.23120215322404, 33.05968366532296, 28.040360581592477, 22.22399460528896, 15.68074493400425, 8.499186088103382, 0.7848465386362269, -7.34139074732433, -15.744884382285388, -24.28160652139147, -32.80184703645396, -41.153650878754355, -49.18636079927426, -56.754177127399295, -63.719633432287715, -69.95724908783676, -75.35722514873181, -79.82815953203857, -83.29918236741862, -85.72155909282574, -87.06980308555852, -87.34275202719896, -86.56339143061676, -84.77772089632484, -82.0531116802196, -78.47613050818346, -74.14991033282006, -69.19150131571033, -63.728439509000765, -57.89513249999086, -51.82871073842717, -45.66509134909387, -39.53531901281722, -33.562308286462674, -27.857740619876704, -22.51921331071864, -17.628337056377365, -13.248851983409228, -9.425591968715343, -6.184197965241225, -3.5314215237186923, -1.4559589480655328, 0.07002946596430162, 1.088905633005069, 1.6552786854016919, 1.833323158386328, 1.69387084368377, 1.3113702344593812, 0.7608533639572701, 0.11503582865090174, -0.5583481702791309, -1.198888967067924, -1.7554758262774748, -2.1878210429223204, -2.4674661613861817, -2.578261684407517, -2.5163251749668176, -2.2894943111172794, -1.9162860968996451, -1.4244502885290378, -0.8491637767598914, -0.23097613406707937, 0.38641416000580087, 0.9584609425489637, 1.442062059490882, 1.7977181889281932, 1.9914715105182539, 1.996554330881992, 1.794689465837378, 1.3769946465367482, 0.7444559599986215, -0.09207613919521467, -1.1123451166578937, -2.287532441924524, -3.581464017392038, -4.952127126112824, -6.353439923480945, -7.737270720863996, -9.055543859892483, -10.262180369128592, -11.314965523383835, -12.177259879319736, -12.81946952705394, -13.22026446111097, -13.367412550515438, -13.25830569018142, -12.899783843876119, -12.307662095615468, -11.505946212510851, -10.525726797050055, -9.403756872974036, -8.180844689305385, -6.900180835965061, -5.605305574005408, -4.338241379253068, -3.1377662359298295, -2.037844601548436, -1.0663667025233883, -0.24417102130767432, 0.41564294170689053, 0.9080629120477075, 1.236067916538638, 1.4101637307467418, 1.4475129656700467, 1.370797023827858, 1.206865657260989, 0.9852242463808059, 0.7363097217011406, 0.4897534069708311, 0.2727148027279933, 0.10836912799855995, 0.014601613657026224, 0.00296291880775823, 0.0779210808785611, 0.23647507892521835, 0.4681961562795421, 0.7556400806565223, 1.0751172192932763, 1.3977929491361485, 1.6910754059305508, 1.9202828156567213, 2.050508558734721, 2.048455758741298, 1.884282919652978, 1.5333636610914598, 0.9778773789906401, 0.20818657299322116, -0.7760493870392564, -1.965321706692213, -3.3400768801141307, -4.870912621677554, -6.519192984877248, -8.238088886655062, -9.974137922191609, -11.668901303750458, -13.261017949566037, -14.688426328547594, -15.890643249323336, -16.8110649885453, -17.399466062985624, -17.614053015790414, -17.42295108914819, -16.805686386287142, -15.75423177126355, -14.27360582607621, -12.382212804775458, -10.111586766491644, -7.505248338771962, -4.617412719920412, -1.5113562653221488, 1.7425402072412461, 5.068947876578993, 8.389951726263027, 11.62772016461634, 14.70698600293024, 17.557402597360422, 20.115674846732908, 22.32743509043137, 24.148894681773992, 25.548004531948433, 26.505144089321536, 27.013406504057457, 27.078479110951267, 26.71801257378742, 25.960753055210798, 24.845165568176, 23.417721164820286, 21.731059690049463, 19.84202656696534, 17.809650922919605, 15.693139410857956, 13.54993073735175, 11.433866475595863, 9.393659063718127, 7.47163346222295, 5.702761492702516, 4.113996874297902, 2.724004451856081, 1.543203562909813, 0.5741213284288125, -0.18798147968175305, -0.7542542443330807, -1.1412296278222078, -1.369675423431668, -1.4632907791729186, -1.447436061990173, -1.347920165399339, -1.1898771133373, -0.9967705668648754, -0.7895537815965079, -0.5860510356331918, -0.4005139115252641, -0.2434012749542419, -0.12136514651768597, -0.03742051269699859, 0.008723987610541783, 0.0201847635943026, 0.0023304123305492746, -0.03784610480355012, -0.09238215699802686, -0.15298966329763183, -0.21166219721346355, -0.2612059069944752, -0.2956597946701291, -0.31061628623070753, -0.30341591211104507, -0.27322126681113384, -0.22097257709571583, -0.14922204849089976, -0.06188511759480485, 0.03606814854342385, 0.13897260484337157, 0.24085506671700183, 0.33582352990157266, 0.41846014564190054, 0.4841187487095887, 0.5291626577292079, 0.5511477168319044, 0.5489398941522398, 0.522736024311195, 0.47402805366272344, 0.40545224240145616, 0.3205785620929627, 0.2236787162096947, 0.11947037039000889, 0.01285278205377746, -0.09137825540291207, -0.188801382371388, -0.2755909550076539, -0.3486829861191624, -0.40588860575361607, -0.4459522720098886, -0.4685663886673916, -0.4743367576207367, -0.4646634574187959, -0.44159327076195437, -0.40764843092258507, -0.365641415170799, -0.3184921520104196, -0.2690593488114486, -0.2199605757191635, -0.17343560653295548, -0.13125197197542207, -0.09465070666573813, -0.06433309658055156, -0.0404867966670621, -0.022840133225904946, -0.010747323030065056, -0.003296463972685908, 0.0005727885813478595, 0.0019519809353299876, 0.0018564766607536095, 0.0011357096582234624, 0.0004075632992852966, 2.229322313346107e-05, 5.8229690365761744e-05, 0.0003487511677618796, 0.0005374579560737632, 0.00015633495962297976, -0.0012801827100653303, -0.004174146701768171, -0.008745567101235455, -0.014945943726276086, -0.022392705359311763, -0.0303320928634286, -0.037636443826682055, -0.042839161576437454, -0.044207947657429726, -0.039852521285356754, -0.027862398080189865, -0.006466214374177552, 0.025796502938051732, 0.06990284518263874, 0.1261866856461889, 0.19420633525793282, 0.27264884863073907, 0.35928312787301137, 0.45096364226704105, 0.5436914041854257, 0.6327375305064253, 0.7128288840299672, 0.7783942659767414, 0.8238320683274293, 0.843798450782799, 0.8335175637395061, 0.7890907787760073, 0.7077865781626185, 0.5882958666392951, 0.43090248517760216, 0.2375275850612908, 0.01178602263498901, -0.24105458158819076, -0.5142046290944957, -0.7995662857789565, -1.0880722444076714, -1.3702218600459972, -1.6363990000183692, -1.8772496826850307, -2.0841017082491082, -2.2493682013067886, -2.3669440664868717, -2.432731744503257, -2.4447850630835926, -2.403277286415351, -2.3104922797155707, -2.1707293102068084, -1.990122204094986, -1.7765094247857376, -1.5390054963242912, -1.2874224320222392, -1.0317531677188962, -0.7816848795297332, -0.546144731581393, -0.33294377093104766, -0.14840807847603513, 0.0030061870083396896, 0.11887922283366885, 0.19887312593508677, 0.24464795437342002, 0.2596583589074321, 0.24886216108734427, 0.2183757024337895, 0.17502535886927645, 0.12586177002167814, 0.07765200677119749, 0.036403194327949494, 0.006944462012574687, -0.007411388916954256, -0.005106042792122452, 0.013545859517087323, 0.046362833929412206, 0.08943680986614687, 0.13740223214808042, 0.18381641146703545, 0.22162626429482485, 0.24369222717047626, 0.2433352659787907, 0.21487298278782813, 0.15412408788834941, 0.05882852270651049, -0.07105773539570386, -0.23320264411740196, -0.42289154728387335, -0.6331805850655375, -0.8552024047707604, -1.078622355312152, -1.2922332709824278, -1.484634744548853, -1.6449626795383332, -1.7636256477080055, -1.8330014332105473, -1.8480496799273254, -1.8067910947108572, -1.7106121689039138, -1.5643669242514013, -1.3762557114826144, -1.1574731253032313, -0.9216288984984439, -0.6839658659090981, -0.4604120755882437, -0.26650637228889357, -0.11625353100531406, -0.020973207950314765, 0.011786568410823428, -0.02080493857603398, -0.11611327755557838, -0.2655449355055271, -0.4543516207461966, -0.6617743425198525, -0.8615523968205004, -1.0227716922533505, -1.111031038916436, -1.0899252464374014, -0.9227403080035499, -0.5743325123680935, -0.013057585562722135, 0.7874606150001501, 1.8465211648938897, 3.1747275627739646, 4.772716989067848, 6.630217850064715, 8.725624195830527, 11.026654306121149, 13.49071751329078, 16.0656897963106, 18.691378595768626, 21.301604066209993, 23.826382358708937, 26.19558927569337, 28.341427903886608, 30.20024799406591, 31.714959280709067, 32.837401304055675, 33.530744119629304, 33.77203508706178, 33.55335972522764, 32.88075251932038, 31.773905237547538, 30.26544781811968, 28.399857929161303, 26.232858578210926, 23.829493881254088, 21.25978892448318, 18.59585444710105, 15.909212291241522, 13.268221750684653, 10.735998942317192, 8.368883816964699, 6.213336303272212, 4.304432122382004, 2.6652784603514283, 1.3069761816221703, 0.22914057301883814, -0.578997155953542, -1.1375957192524646, -1.4745542282171449, -1.6233732834744175, -1.6209048350579751, -1.5051175973469235, -1.312998945006782, -1.078722143900252, -0.8320748142124202, -0.5972149426088555, -0.39191556930581495, -0.22730380639388947, -0.10807537928146922, -0.033129037780887806, 0.003440516403535623, 0.011055047858917082, 0.0011813939682260455, -0.014208981745110915, -0.024120270618615377, -0.019835717563716108, 0.0040607433401013545, 0.049036162976153756, 0.11239838505293108, 0.18756274476045665, 0.2648013482196962, 0.3324444060592558, 0.37847312581082115, 0.39241141807287716, 0.36739952664941966, 0.30231428779106895, 0.2037850605424795, 0.08794942798934531, -0.018195738772872713, -0.07597360842213692, -0.03484946913281389, 0.16702266152181094, 0.6014846916863167, 1.3483058177419631, 2.4924325539237886, 4.12058851661835, 6.317346945658982, 9.16082983112721, 12.718235398806959, 17.041654655205697, 22.16434770687776, 28.09700576770489, 34.82475029900265, 42.30497504744128, 50.46614996796225, 59.208228295965405, 68.40576192154835, 77.9094410357447, 87.54902483739063, 97.13763797176001, 106.47690749924158, 115.36319591476631, 123.59728474385938, 130.99043123562078, 137.3685870059005, 142.57793380893523, 146.4900544915706, 149.00655979286756, 150.066173890464, 149.64676624648152, 147.76342109215832, 144.4669582461178, 139.8418869568693, 134.0035287904463, 127.09659537094727, 119.29112850355006, 110.77276078145678, 101.73636546756751, 92.37938250875577, 82.89570025328597, 73.47101896660176, 64.27893337473854, 55.47329043091115, 47.18422163009415, 39.5157830966827, 32.54473085394098, 26.320669148023136, 20.867604113017073, 16.18440227852866, 12.247145454456602, 9.012641296837192, 6.42233096103197, 4.406582950197213, 2.8890265755946776, 1.7902997962167986, 1.031686208935249, 0.5384695020030518, 0.24265730327864482, 0.08501366884966997, 0.016383382685320486, -0.001745536529790976, 0.0026695801877455313, 0.011549103575161913, 0.015506584721660955, 0.012284135907608587, 0.004944676898344937, -4.1688250987384635e-05, 0.0053206404488895164, 0.028828641283168612, 0.07661773166875772, 0.15203878061165055, 0.254926537541988, 0.3812864606859757, 0.5233953230565062, 0.6702744036913367, 0.8084771311785854, 0.9231150356746686, 0.9990328170416045, 1.0220401482584658, 0.9801193760881628, 0.8644611831901956, 0.6702931259142728, 0.39744330115274423, 0.05059366936775046, -0.3608168826981196, -0.8230047908401037, -1.318543219497346, -1.8273178106487573, -2.3276537391023506, -2.7975521694504373, -3.216011223277843, -3.564277151302629, -3.8268491999929335, -3.9923683729874324, -4.0542219105395825, -4.01087041371841, -3.8659224710016935, -3.627919506126681, -3.3096460747499767, -2.9273044657382803, -2.499526781606844, -2.0462946344001787, -1.5878157171129057, -1.1434250083847306, -0.7304757942887411, -0.3634572047422619, -0.05333810858793637, 0.19285726117679228, 0.37216822782739256, 0.4856105738727602, 0.5378481109759942, 0.5366266143509729, 0.49204758047856956, 0.4157338955549753, 0.31993796212997794, 0.21667903186604695, 0.11694080972538919, 0.02998365249556556, -0.037166457179173884, -0.08003953226781141, -0.0968425942950403, -0.08837420328273896, -0.05773385067593731, -0.009876584762735865, 0.0489433350452015, 0.11179746271889628, 0.17172923007095825, 0.22238152931069613, 0.25857565145934197, 0.2767190672796726, 0.27506305592462155, 0.2538027352569772, 0.21500980852271226, 0.16240815329699407, 0.10102008730780898, 0.036664062493253255, -0.024630005352049813, -0.0772005522528616, -0.11630399020730879, -0.13859530231760536, -0.1425063413423973, -0.12849079336739289, -0.09909489414482921, -0.05883701787751929, -0.01392557513168647, 0.02816604034648229, 0.05924036321779743, 0.0710088378037586, 0.05576928435896095, 0.007062010838281569, -0.0797530319770174, -0.20703213857053632, -0.37452247995584487, -0.5791927190558411, -0.8152774566196674, -1.07452214602938, -1.3466489028011293, -1.619936622770673, -1.8819050894745137, -2.120063341471139, -2.3226900654841476, -2.479575120037733, -2.5826941337715854, -2.626808624889911, -2.6097542733709034, -2.5325662651385996, -2.3993918159414656, -2.2171967065962748, -1.995302089421314, -1.7447880326466563, -1.4778107270928633, -1.2067684781557944, -0.9434881337402106, -0.6984825995258734, -0.4803450655744133, -0.29530071425745497, -0.14694667087433902, -0.0361930183529682, 0.03860456724268528, 0.08130214250068339, 0.09745335524436705, 0.09368101879916481, 0.0769900360474515, 0.05408324319642574, 0.030741350646165507, 0.011321629556311441, -0.001561888870776463, -0.007142098223045069, -0.006367174270390387, -0.0015321131165563886, 0.00430814021781633, 0.008104695819744339, 0.007696991512519057, 0.0027384299319423615, -0.004417079650045858, -0.007956209555927254, 0.0019334366059589267, 0.039303096352724186, 0.12233101978582728, 0.27282124827174786, 0.515292823010883, 0.8756682131846014, 1.3795931035013969, 2.050476977213645, 2.9073985752965417, 3.963060042841791, 5.221733075677356, 6.677408823717744, 8.312342599541104, 10.096187093371007, 11.98567017324078, 13.925081273383219, 15.847869291481652, 17.67830907153134, 19.33398438790546, 20.729307460454844, 21.77910857149056, 22.402509740937873, 22.527232930991826, 22.094210688407134, 21.060643406112362, 19.40340571536562, 17.12130889022726, 14.236231396912453, 10.793598363498964, 6.861902084667285, 2.5310051255215873, -2.0909047228371005, -6.8812048148619835, -11.707812726618588, -16.434249587064528, -20.924972026993267, -25.050981010083728, -28.695924026342038, -31.760730803532383, -34.16759212452422, -35.86289180349784, -36.819025241254934, -37.03505394251083, -36.536551906985714, -35.37508198962083, -33.62419774706475, -31.375065215229203, -28.731760909187003, -25.80614744574308, -22.712616925358443, -19.563237702830882, -16.463160667263985, -13.505482727641786, -10.767639042239471, -8.309038827186948, -6.1698133434266325, -4.370712884206151, -2.9140374704158782, -1.785549948746944, -0.9570483842889277, -0.38974477734843344, -0.038049148626290774, 0.14655907788403325, 0.21183559534463617, 0.20149075156443144, 0.15254096736993183, 0.09344715028445681, 0.04315544359540182, 0.011090313034585646, -0.0019265731508651383, -0.0019267591104810626, 0.0006285552866621899, -0.00625790468350984, -0.03299831797494971, -0.08533349803315726, -0.16154820379708315, -0.250229910529134, -0.32878479558657087, -0.3628873264627283, -0.30697513491978584, -0.10578720082372296, 0.3031315850920447, 0.9860492646863868, 2.008894678141755, 3.4325967681482314, 5.308218969720927, 7.6723703445522835, 10.543304729901623, 13.917781944611859, 17.768341361597745, 22.041893485961673, 26.65962283888257, 31.518537986422473, 36.495991235824036, 41.4548050608864, 46.24729112250865, 50.72098959501423, 54.72512017144091, 58.11728087916738, 60.771281482966906, 62.58719521447917, 63.493192345825925, 63.447970563183546, 62.4429949355672, 60.50330930984246, 57.68719872650467, 54.08662920433332, 49.82265490356881, 45.03701245631147, 39.88537650918197, 34.53060579504687, 29.135877886645677, 23.858901602401, 18.844729664362994, 14.21897807498734, 10.082510197450066, 6.5083342932724255, 3.5401987145069063, 1.1927881138018288, -0.5470984471503845, -1.718152602929652, -2.3805331466090105, -2.610837409925089, -2.496443816380239, -2.129756338127999, -1.602688691838626, -1.0013513702417274, -0.4015200682231033, 0.134894392863911, 0.5622515074562207, 0.852269308150474, 0.993877119770727, 0.9920157547688562, 0.8653632524868939, 0.6432525548714383, 0.36206017432714244, 0.06130193117586621, -0.22017445660156523, -0.44769462137866073, -0.5937148724724988, -0.6399986329157746, -0.578900642387346, -0.41371079743701084, -0.15801226370046065, 0.16582219675655682, 0.5288519748265523, 0.8983188396543794, 1.2406846884104143, 1.5247037577595035, 1.724278784779529, 1.8208539855591754, 1.8051429015530598, 1.6780566369216108, 1.4507418882722682, 1.1437078376808354, 0.7850854740070015, 0.4081271753093255, 0.04819719901038496, -0.2605578476396242, -0.48862274907278896, -0.6143428015111767, -0.6267051011913042, -0.5274192474718231, -0.3320402222138098, -0.07010673181707738, 0.21573353928686922, 0.47165499050867055, 0.6355757464035259, 0.6409091585162247, 0.42092941521481714, -0.08657077830843467, -0.9348150236655952, -2.1637396078882922, -3.7961740518666875, -5.834971535959802, -8.261292651667329, -11.033945525308024, -14.090871590853622, -17.35097434222103, -20.71700649245303, -24.079890445441453, -27.32433296795115, -30.333683109094597, -32.9959156750143, -35.21115637829066, -36.89535976506038, -37.98410446515908, -38.43682733919874, -38.23791972586398, -37.39688589410026, -35.948396426834336, -33.952327785124254, -31.488475184460793, -28.652472757188757, -25.55031994372478, -22.29249114026195, -18.988730522981843, -15.743495541881227, -12.652291107175218, -9.796489104318775, -7.239902724142698, -5.026773886011632, -3.1813950639889197, -1.7088486838976824, -0.5968016181894554, 0.18189825705837123, 0.6665753215986367, 0.9051229819943568, 0.9500537877077161, 0.854702398462708, 0.6698173973313246, 0.44073632391205086, 0.20528187910587617, -0.007636177084637994, -0.17858628560215126, -0.29735776899384797, -0.36199308594339846, -0.37726301324128525, -0.35277497893785326, -0.30091239533400305, -0.23478528763957363, -0.1664076686775955, -0.10527333755931953, -0.05745283610563885, -0.025282963450744992, -0.007659938183213957, -0.0008975069152372681, -5.238639659416025e-05, -0.0005691305763189388, -6.385459060900558e-05, -4.701093206826755e-05, -0.007381787782835551, -0.03528861608618949, -0.10374360395107006, -0.23916358758622142, -0.4733218004017308, -0.8415043141649652, -1.3799883115115938, -2.122969898929311, -3.0991765208482915, -4.328539248689771, -5.818902847009356, -7.563168287991761, -9.53723288142745, -11.698751753133307, -13.986981795657666, -16.32407796541796, -18.618258860824707, -20.767074258101612, -22.66202500044637, -24.193885284219, -25.25847040173935, -25.762779957976353, -25.631396355133734, -24.81300625805197, -23.283806953852636, -21.050077267179805, -18.149593192836065, -14.651687015966345, -10.655686210244038, -6.287808774614959, -1.6959575013983985, 2.958134025582971, 7.50622476235703, 11.78122431353864, 15.625008470791732, 18.89597477792504, 21.476536913172172, 23.281139109095587, 24.259333271985536, 24.397410159711928, 23.718669278248456, 22.28186744357226, 20.178001876125986, 17.526257655213456, 14.468245636144765, 11.158530096407691, 7.755981416361244, 4.415613412008147, 1.2808662856657955, -1.523323754686314, -3.896343027566488, -5.766095000178637, -7.09227962885082, -7.867041066333452, -8.113576025857732, -7.883159838960375, -7.250627294977818, -6.308493516704776, -5.160639458821065, -3.915232629784005, -2.677684280931821, -1.5441789172956721, -0.5960526356561733, 0.10467194659390382, 0.5181849599598428, 0.6282414663669785, 0.44208367972397467, -0.011263630222019923, -0.6841090185045109, -1.5143712634507613, -2.430631557542512, -3.357601494111193, -4.221643375986342, -4.955921257121429, -5.504989064161084, -5.828394557959618, -5.903068368610822, -5.724459506333839, -5.306388139558781, -4.679653706862695, -3.8892939675579097, -2.991020207699962, -2.0470277724471035, -1.1214948676571197, -0.2760523302095634, 0.4344768628489225, 0.9658394712376972, 1.2872604773587915, 1.3832276664861214, 1.2542337357146411, 0.9164321889887679, 0.4002476024960133, -0.251963001510334, -0.989120746564875, -1.7551372497037405, -2.4927876339381325, -3.1475587155186138, -3.671231306447581, -4.024983757914656, -4.18190317297355, -4.128609112343429, -3.8656650551061955, -3.407164818092047, -2.7795082583654422, -2.019426871210565, -1.1713426831398621, -0.28431637153261347, 0.5911887810427414, 1.406637051718932, 2.118371275587351, 2.690115029767459, 3.095001293303859, 3.3168666291234783, 3.3506887551881768, 3.20260881693957, 2.8888901197734973, 2.434336934235876, 1.8703432452033744, 1.2326128852338358, 0.5586589373475008, -0.11449312316647438, -0.7523590605313527, -1.3250837013252417, -1.808943845900172, -2.1873152166724212, -2.4510537250705258, -2.5983502499320124, -2.6341417141892745, -2.569180753583369, -2.4188315694711617, -2.2016025361854625, -1.9375871355395966, -1.6469855279565604, -1.3487918870399291, -1.0597189845148556, -0.793414202354756, -0.5599197849282871, -0.3654869681546288, -0.21272754992388906, -0.10099559916077039, -0.02695799605872962, 0.014711417110887156, 0.030579354839012772, 0.02769802106425242, 0.01293542881990182, -0.007560136133429027, -0.02874502288623007, -0.04690292207630913, -0.05971436868161906, -0.06619383713274625, -0.06647241377394307, -0.06151262134750156, -0.05279471711068062, -0.04200709380394802, -0.030774458818873297, -0.02044994000945416, -0.011968305252321227, -0.005791980116246302, -0.0019411340940069907, -8.385880205720582e-05, 0.00033557538747597824, -4.5698257612471945e-05, -0.000640706689485551, -0.0010142639973446037, -0.0009412043701635596, -0.000414131198292174, 0.00039696609232316225, 0.0012220243720175857, 0.001787266299061358, 0.0019110784549030936, 0.0015734276337712944, 0.0009353018900072966], 'positive_zeros': ['0.44145974167335774490302015680540', '0.46470785885226256135455754199224', '0.58877907005147055154530428950912', '0.935079438675159345548818508351354', '0.984246551985948356398853228608466', '0.987617973996538241153943980658243', '1.60077714316732582054481276996704', '1.77040465006059863744687634367420', '2.17658793496912945396131150029200', '2.28402211704689360934952701558975', '2.69859825181607269717792927406536', '2.72549077903736379630300305386996', '2.93701824830953775772850386142726', '3.25031630265613507115998125630430', '3.33075536230368044243124874590519', '3.55269551529212876575052556695618', '3.76939229706880367161895096057315', '3.92329061184162276451883136559522', '3.93456176029549216490959517390587', '4.13546620660020685180015423952476', '4.16463209098446068639553574113889', '4.63407213640431552555192754310032', '4.76177786178245292897715376416343', '4.88855550172135036581938173550617', '4.95335014449579350470096944370371', '4.95968296431347293559009230132445', '4.97409491770830216879436917775046', '5.28584523359216844802227047045621', '5.55567766833519892440067741919046', '5.91574438080211578171159862907559', '5.98832554641626732896442875770077', '6.11086065053600724085465211272079', '6.20658727816745020862669101855048', '6.48222691434272075392756449812846', '6.61323815346549005315335532432926', '6.61830455565005486472325099456594', '6.76236213442568382226804571235074', '6.99577991457002789270435656883910', '7.29971375068235128540608158172923', '7.45045003874848915357626070349367', '7.47396556948554538029086414219862', '7.60018383782360534277601981076172', '7.75568253154504959856833798973974', '7.993417134269002912516042296421707', '8.047513787547059840775239215124840', '8.051906289324845442590047566924410', '8.087637699293025828699597807943086', '8.208801178120784637415400691613921', '8.407853250042967559280748385751217', '8.658262277153445364084444410767099', '8.772539296728125686840746225471626', '8.792799244282510171176000821966479', '8.904431114991664101436118648372732', '9.134622147112753285814281558174091', '9.146659809953380007680642174545567', '9.261352792702462619626225157435758', '9.635352754360351527528439237816392', '9.781951395298130911868815767378471', '9.804374744384881384319713696458780', '9.842522722574301190127635484123001', '9.962335153505604815756344112481764', '9.987023462173171780453155600818034', '10.58428834126319441926391763159628', '10.59374581461984949794635850554900', '10.64701009421490345600188301678293', '10.64978162521193277996202545335821', '10.81939904212213424802028127587890', '11.05107129385211003467575620360675', '11.16367822216126260023413695974042', '11.22165440255486708848627151629831'], 'prelabel': '14-405e7-1.1-c3e7-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.888330344025959, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e7-0', 'trace_hash': 115064121946566206, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44145974167335774490302015681', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.46470785885226256135455754199', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.58877907005147055154530428951', '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': 4448848926.195494, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 1787249410543828125, 'conductor_radical': 15, 'degree': 14, 'dirichlet_coefficients': [1, -2, 0, -8, -35, 0, 22, 18, 0, 70, -23, 0, 96, -44, 0, 41, -161, 0, 279, 280, 0, 46, -96, 0, 700, -192, 0, -176, 296, 0, 244, -8, 0, 322, -770, 0, 404, -558, 0, -630, 47, 0, 525, 184, 0, 192, -164, 0, -346, -1400, 0, -768, -506, 0, 805, 396, 0, -592, 85, 0, 828, -488, 0, -400, -3360, 0, 1093, 1288, 0, 1540, -328, 0, 2085, -808, 0, -2232, -506, 0, 2110, -1435, 0, -94, -1290, 0, 5635, -1050, 0, -414, 3048, 0, 2112, 768, 0, 328, -9765, 0, 1787, 692, 0, -5600], 'euler11': [1, 23, 5151, 137494, 15125367, 360831273, 29040094313, 601859871012, 38652365530603, 639234610827153, 35664824193177597, 431515071228877174, 21517005320660018301, 127878098210321324063, 7400249944258160101211], 'euler13': [1, -96, 12191, -828700, 67939809, -3670430048, 227859076023, -10004745881352, 500606390022531, -17716464789556832, 720467661942239757, -19307123141000004700, 624007221734780418587, -10795719067387909740384, 247064529073450392704413], 'euler17': [1, 161, 24747, 2620018, 242733069, 19012626063, 1428967389431, 98461041404796, 7020516784274503, 458918573466860847, 28785199208309779293, 1526480748742243955698, 70836383255713411429371, 2264156596782903723552449, 69091933913008732880827217], 'euler19': [1, -279, 63455, -9627646, 1292727231, -139417672577, 13934197302465, -1188087181318116, 95574659297607435, -6559027233354505337, 417147174027611519949, -21309012527287648687006, 963318415680705326063045, -29051530733117236387662639, 714209495693373205673756419], 'euler2': [1, 2, 12, 22, 63, 12, 56, -864, 448, 768, 32256, 90112, 393216, 524288, 2097152], 'euler23': [1, 96, 70730, 5128416, 2231256537, 129120969582, 42017720032537, 1973532783601374, 511229599635877679, 19114537520613328398, 4018833650024266733631, 112387310571163926541536, 18859110204396392801783110, 311438487349943835388835424, 39471584120695485887249589623], 'euler29': [1, -296, 154422, -29519614, 8749743807, -1202308386924, 280424950326131, -32104391095886106, 6839284113504008959, -715161067576286654604, 126933810659604754193283, -10444475827719128779270174, 1332536584781606837740226478, -62295356172090947617770327656, 5132842708382182842735812571629], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, -244, 138953, -21581892, 6820038797, -643944456252, 180689501328357, -12932535760119704, 5382920934073083387, -571503075283193463612, 180319248913797187552787, -16999253132143831778527812, 3260568549552794644024481303, -170569083279766989403557538804, 20825506393391550743120420649631], 'euler37': [1, -404, 267991, -88433668, 32537859593, -8785146905212, 2408172804310695, -541287630181037208, 121981177056749633835, -22540283421647048143708, 4228676841914216018623661, -582154592144391741148240708, 89360598794674935961952327563, -6823581739467573502981188115316, 855531895666462872887391390111637], 'euler41': [1, -47, 321096, 12021155, 45171631701, 4630735558038, 4063682212222409, 491807687844214791, 280073041748580650689, 21996476613185805439158, 14788376166004950930557661, 271239214241698479638543555, 499335848550522857034686226696, -5037409755473993864748603667487, 7386879101213258109624223688656841], 'euler43': [1, -525, 461651, -177053890, 91552352643, -27963570378443, 10910759641065633, -2737206494978679516, 867481766782205282931, -176767880508400526352707, 46013536043808301580126049, -7075008075619140503219249890, 1466697711440992029278401740857, -132614650126086481926205923490725, 20083415214428110320965436874242043], 'euler47': [1, 164, 458970, 110392306, 108169816881, 25717707674850, 17081669577666257, 3320863886913274956, 1773470180562043800511, 277216708795484067775650, 121056138341473202284409727, 12826645757956882787445413746, 5536714992576024410523180976710, 205402294595664587030295461231396, 130033429462229783044185156533092847], 'euler5': [1, 35, 525, 4375, 21875, 65625, 109375, 78125, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, 506, 541623, 172442740, 132333548265, 35763427746966, 25492045997195975, 6232790423469661848, 3795179331924545170075, 792673527794653258084614, 436669424538837325685449245, 84714031499427521535957756340, 39612763617591348101036449058811, 5509550519462154392273647414942634, 1621038246414954860589967996431649253], 'euler59': [1, -85, 331341, -32993294, 125055414789, -9577822572435, 29633014670734625, -2027875987639118244, 6085998920060806547875, -403997667224123676785835, 1083354535417266020708492871, -58701583504017865350673596014, 121075244088781394037302622857559, -6379037207092801324644127672966285, 15413179794770734626518662321719325259], 'euler61': [1, -828, 1137794, -655662598, 472897824279, -204252976588544, 110585022303384087, -44527407364853870622, 25100698947444423451347, -10523189818190355543920384, 5530136244102034031709909339, -1740357344486590565693586177958, 685505848523261761203332246404394, -113231527751973748881349580752125468, 31040344686800426926132378247220037261], 'euler67': [1, -1093, 2017106, -1699166505, 1757369253407, -1166070992255454, 864466170577418349, -453458572496944446653, 259999438861376074900287, -105480895453628897206599726, 47811927039808716476356634429, -13903801882582440182487994129305, 4964217048551830484719900464335558, -809033696645460601445269552381960237, 222623423334106740048017938136372833267], 'euler7': [1, -22, 830, -19134, 426701, -7825194, 165254493, -2430999116, 56682291099, -920626248906, 17218924460507, -264839189303934, 3940476053252690, -35825099154029878, 558545864083284007], 'euler71': [1, 328, 1276365, 268163756, 813660594393, 105690507940488, 374340014427629213, 36698946645864837192, 133980408903807199254043, 13538984074931217771293448, 37305118346601126104534883183, 4400482158498613760644686769196, 7496354524351065224608875358727115, 689483885946515790262531327507179208, 752359350923790893319063566949457370471], 'euler73': [1, -2085, 4050563, -4984423486, 5631570806793, -4895773027898939, 3922468709989734339, -2545861771312367695716, 1525907010154076483354763, -740898023263640744849007371, 331539509055864385937004333009, -114153506160426465391921371182206, 36087624328883098486425947878464491, -7226325859429888520514040340508061365, 1348279907365869037210940254745047725673], 'euler79': [1, -2110, 3466397, -4074662340, 4200201567425, -3637140873668514, 2929970636702454981, -2095116506829323507384, 1444589792749141701377259, -884143320351505977073165794, 503400861304581296519318658575, -240777954614457219934741297631940, 100991464377697520623090800182546003, -30308894675715428038603142460553955710, 7082211906170644040153959599814721217679], 'euler83': [1, 1290, 3282374, 3191089158, 4600431414309, 3678070946162670, 3902415474964514617, 2608484875033022043888, 2231350437183534919310579, 1202509888416094427609935230, 860005822931736383353089826527, 341095544793377611541353912134438, 200613174168173368441896296494536418, 45081190160946185934162182436249107610, 19982045332214679702896737836182611234883], 'euler89': [1, -3048, 5723102, -6323602086, 4534976524791, -780789931274556, -1899913405596725465, 2724235891150620996750, -1339380053630117954335585, -388037988014179309012088316, 1588858066123643901224854316319, -1561869031207273507560170068744806, 996509827111285634489773401499203598, -374140810118231499571381570059102179688, 86534669543385676516186776267386878120889], 'euler97': [1, -1787, 4084243, -4789169974, 7296823674929, -7118143615887349, 8621884508580027771, -7253857327779680859444, 7868961200099259685841883, -5929214359098246753936743221, 5547271987206968717072638344593, -3322929001968620421991613498298934, 2586351736473608092421547514614778099, -1032798906164414230059627059212281418043, 527480512638944839726474542256547576188897], 'euler_factors': [[1, 2, 12, 22, 63, 12, 56, -864, 448, 768, 32256, 90112, 393216, 524288, 2097152], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 35, 525, 4375, 21875, 65625, 109375, 78125, 0, 0, 0, 0, 0, 0, 0], [1, -22, 830, -19134, 426701, -7825194, 165254493, -2430999116, 56682291099, -920626248906, 17218924460507, -264839189303934, 3940476053252690, -35825099154029878, 558545864083284007], [1, 23, 5151, 137494, 15125367, 360831273, 29040094313, 601859871012, 38652365530603, 639234610827153, 35664824193177597, 431515071228877174, 21517005320660018301, 127878098210321324063, 7400249944258160101211], [1, -96, 12191, -828700, 67939809, -3670430048, 227859076023, -10004745881352, 500606390022531, -17716464789556832, 720467661942239757, -19307123141000004700, 624007221734780418587, -10795719067387909740384, 247064529073450392704413], [1, 161, 24747, 2620018, 242733069, 19012626063, 1428967389431, 98461041404796, 7020516784274503, 458918573466860847, 28785199208309779293, 1526480748742243955698, 70836383255713411429371, 2264156596782903723552449, 69091933913008732880827217], [1, -279, 63455, -9627646, 1292727231, -139417672577, 13934197302465, -1188087181318116, 95574659297607435, -6559027233354505337, 417147174027611519949, -21309012527287648687006, 963318415680705326063045, -29051530733117236387662639, 714209495693373205673756419], [1, 96, 70730, 5128416, 2231256537, 129120969582, 42017720032537, 1973532783601374, 511229599635877679, 19114537520613328398, 4018833650024266733631, 112387310571163926541536, 18859110204396392801783110, 311438487349943835388835424, 39471584120695485887249589623], [1, -296, 154422, -29519614, 8749743807, -1202308386924, 280424950326131, -32104391095886106, 6839284113504008959, -715161067576286654604, 126933810659604754193283, -10444475827719128779270174, 1332536584781606837740226478, -62295356172090947617770327656, 5132842708382182842735812571629], [1, -244, 138953, -21581892, 6820038797, -643944456252, 180689501328357, -12932535760119704, 5382920934073083387, -571503075283193463612, 180319248913797187552787, -16999253132143831778527812, 3260568549552794644024481303, -170569083279766989403557538804, 20825506393391550743120420649631], [1, -404, 267991, -88433668, 32537859593, -8785146905212, 2408172804310695, -541287630181037208, 121981177056749633835, -22540283421647048143708, 4228676841914216018623661, -582154592144391741148240708, 89360598794674935961952327563, -6823581739467573502981188115316, 855531895666462872887391390111637], [1, -47, 321096, 12021155, 45171631701, 4630735558038, 4063682212222409, 491807687844214791, 280073041748580650689, 21996476613185805439158, 14788376166004950930557661, 271239214241698479638543555, 499335848550522857034686226696, -5037409755473993864748603667487, 7386879101213258109624223688656841], [1, -525, 461651, -177053890, 91552352643, -27963570378443, 10910759641065633, -2737206494978679516, 867481766782205282931, -176767880508400526352707, 46013536043808301580126049, -7075008075619140503219249890, 1466697711440992029278401740857, -132614650126086481926205923490725, 20083415214428110320965436874242043], [1, 164, 458970, 110392306, 108169816881, 25717707674850, 17081669577666257, 3320863886913274956, 1773470180562043800511, 277216708795484067775650, 121056138341473202284409727, 12826645757956882787445413746, 5536714992576024410523180976710, 205402294595664587030295461231396, 130033429462229783044185156533092847], [1, 506, 541623, 172442740, 132333548265, 35763427746966, 25492045997195975, 6232790423469661848, 3795179331924545170075, 792673527794653258084614, 436669424538837325685449245, 84714031499427521535957756340, 39612763617591348101036449058811, 5509550519462154392273647414942634, 1621038246414954860589967996431649253], [1, -85, 331341, -32993294, 125055414789, -9577822572435, 29633014670734625, -2027875987639118244, 6085998920060806547875, -403997667224123676785835, 1083354535417266020708492871, -58701583504017865350673596014, 121075244088781394037302622857559, -6379037207092801324644127672966285, 15413179794770734626518662321719325259], [1, -828, 1137794, -655662598, 472897824279, -204252976588544, 110585022303384087, -44527407364853870622, 25100698947444423451347, -10523189818190355543920384, 5530136244102034031709909339, -1740357344486590565693586177958, 685505848523261761203332246404394, -113231527751973748881349580752125468, 31040344686800426926132378247220037261], [1, -1093, 2017106, -1699166505, 1757369253407, -1166070992255454, 864466170577418349, -453458572496944446653, 259999438861376074900287, -105480895453628897206599726, 47811927039808716476356634429, -13903801882582440182487994129305, 4964217048551830484719900464335558, -809033696645460601445269552381960237, 222623423334106740048017938136372833267], [1, 328, 1276365, 268163756, 813660594393, 105690507940488, 374340014427629213, 36698946645864837192, 133980408903807199254043, 13538984074931217771293448, 37305118346601126104534883183, 4400482158498613760644686769196, 7496354524351065224608875358727115, 689483885946515790262531327507179208, 752359350923790893319063566949457370471], [1, -2085, 4050563, -4984423486, 5631570806793, -4895773027898939, 3922468709989734339, -2545861771312367695716, 1525907010154076483354763, -740898023263640744849007371, 331539509055864385937004333009, -114153506160426465391921371182206, 36087624328883098486425947878464491, -7226325859429888520514040340508061365, 1348279907365869037210940254745047725673], [1, -2110, 3466397, -4074662340, 4200201567425, -3637140873668514, 2929970636702454981, -2095116506829323507384, 1444589792749141701377259, -884143320351505977073165794, 503400861304581296519318658575, -240777954614457219934741297631940, 100991464377697520623090800182546003, -30308894675715428038603142460553955710, 7082211906170644040153959599814721217679], [1, 1290, 3282374, 3191089158, 4600431414309, 3678070946162670, 3902415474964514617, 2608484875033022043888, 2231350437183534919310579, 1202509888416094427609935230, 860005822931736383353089826527, 341095544793377611541353912134438, 200613174168173368441896296494536418, 45081190160946185934162182436249107610, 19982045332214679702896737836182611234883], [1, -3048, 5723102, -6323602086, 4534976524791, -780789931274556, -1899913405596725465, 2724235891150620996750, -1339380053630117954335585, -388037988014179309012088316, 1588858066123643901224854316319, -1561869031207273507560170068744806, 996509827111285634489773401499203598, -374140810118231499571381570059102179688, 86534669543385676516186776267386878120889], [1, -1787, 4084243, -4789169974, 7296823674929, -7118143615887349, 8621884508580027771, -7253857327779680859444, 7868961200099259685841883, -5929214359098246753936743221, 5547271987206968717072638344593, -3322929001968620421991613498298934, 2586351736473608092421547514614778099, -1032798906164414230059627059212281418043, 527480512638944839726474542256547576188897]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/405/4/a/m'], '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': '14-405e7-1.1-c3e7-0-0', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3, 3, 3, 3, 3, 3], 'order_of_vanishing': 0, 'prelabel': '14-405e7-1.1-c3e7-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.888330344025959, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e7-0', 'trace_hash': 115064121946566206, 'z1': {'__RealLiteral__': 0, 'data': '0.44145974167335774490302015681', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '559616706508831041967960088098,589087196204845943755307995769,746366141552565370320368524280,1185354011697641570121271916888,1247680732397552627042966905607,1251954517532899558434358291671,2029226106367690886123805387635', 'Lhash_array': ['559616706508831041967960088098', '589087196204845943755307995769', '746366141552565370320368524280', '1185354011697641570121271916888', '1247680732397552627042966905607', '1251954517532899558434358291671', '2029226106367690886123805387635'], 'factors': ['2-405-1.1-c3-0-1', '2-405-1.1-c3-0-2', '2-405-1.1-c3-0-3', '2-405-1.1-c3-0-12', '2-405-1.1-c3-0-13', '2-405-1.1-c3-0-15', '2-405-1.1-c3-0-35'], 'label': '14-405e7-1.1-c3e7-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/405/4/a/m'}