Lfunction data - 12-920e6-1.1-c3e6-0-0

Formats: - HTML - YAML - JSON - 2025-11-13T21:10:20.012545

• 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': '1365475034959529565500394021538,1452602613016722926772997064208,1738624455983782731517071705365,2028241256041127272318945459995,2132146919321229633308116493816,2381071320524965453243807748895', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': -30, 'a6': 0, 'a7': 28, 'a8': 0, 'a9': -77, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25581345835.804546, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, 30, 375, 2500, 9375, 18750, 15625]], [23, [1, 138, 7935, 243340, 4197615, 38618058, 148035889]]], 'bad_primes': [2, 5, 23], 'central_character': '920.1', 'coefficient_field': '1.1.1.1', 'conductor': 606355001344000000, 'conductor_radical': 230, 'degree': 12, 'euler_factors': [[1], [1, -2, 81, -109, 3707, -5454, 122034, -147258, 2702403, -2145447, 43046721, -28697814, 387420489], [1, 30, 375, 2500, 9375, 18750, 15625], [1, -28, 1710, -44507, 1306009, -29404243, 574046808, -10085655349, 153650652841, -1796017986749, 23668601113710, -132931722278404, 1628413597910449], [1, 3, 6021, -26781, 15818535, -133642140, 25492860502, -177877688340, 28023499683135, -63148197112671, 18896477256237141, 12531744508246953, 5559917313492231481], [1, 28, 10909, 255007, 53813653, 1024588726, 152088784296, 2251021431022, 259748224623277, 2704221571610611, 254158810601145229, 1433205004394541196, 112455406951957393129], [1, -24, 18030, -427891, 167973547, -3346966257, 1005505976060, -16443645220641, 4054473080887243, -50742685062177827, 10504678937252590830, -68698153236235579032, 14063084452067724991009], [1, 3, 21819, -265989, 273045711, -2946473628, 2316621912986, -20209862614452, 12845676027266391, -85831378044538431, 48292318219104566859, 45543381089624394897, 104127350297911241532841], [1, 138, 7935, 243340, 4197615, 38618058, 148035889], [1, -76, 96138, -6141574, 4443699358, -229233487192, 131290006644110, -5590775519125688, 2643216009651127918, -89096710539601677806, 34015045627807382663658, -655818344817462017512124, 210457284365172120330305161], [1, 381, 183933, 51276809, 14163826942, 2892542918421, 570209036379841, 86171746082680011, 12570448548071973502, 1355739455564894178839, 144877178810579323190013, 8940264818892825339311331, 699053619999045038539170241], [1, -131, 244110, -26876359, 27142443903, -2479299439834, 1757009562030548, -125583954525911602, 69640085126728134327, -3492898374997075884643, 1606964414145611012444910, -43681461101687805228592583, 16890053810563300749953435929], [1, 95, 296879, 24628819, 41954508060, 3095260524119, 3616955966486841, 213328450582805599, 199288286664874682460, 8063030406058740162059, 6698626436882412957541199, 147734339924196101534417095, 107178930967531784356353269521], [1, 202, 258690, 47154510, 25742273095, 5001826335900, 1831244225314684, 397680206488401300, 162726253939999866655, 23699508345501982611930, 10337156890943855889174690, 641768213891187043706690014, 252599333573498060811820806649], [1, 119, 253739, 36692102, 49887954357, 5785025024479, 5837170895173758, 600618653116483217, 537753002337426738453, 41063249470394983246234, 29482310732581503294293099, 1435538453747623820407125817, 1252453015827223091648143056289], [1, -137, 594084, -64786529, 164474180415, -13341277950754, 29237327999867368, -1986209437474403258, 3645465131114359088535, -213780229633433051866357, 291849054876452900853743844, -10019789808796920902254877509, 10888439761782913818722623349689], [1, 39, 811376, 13330213, 323695705039, -637831310, 81542978014641968, -130997156616490, 13653657575844752716999, 115479579480779710372007, 1443598084421519097692038256, 14250981675864062604551813061, 75047496554032956760519149093721], [1, 573, 1025951, 373972257, 406395107231, 101577722520254, 101990059148671426, 23056213035369773174, 20937628063019858104391, 4373286208024915236426237, 2723231984529582816715588271, 345224927538578151378465150273, 136753052840548005895349735207881], [1, 563, 264282, -228527999, -47606117265, 28011216293194, 73923412251272732, 8424737445989907022, -4306372349139599047785, -6217454865309957251721053, 2162545317554180751878870202, 1385576265369633803527084824209, 740195513856780056217081017732809], [1, 83, 1110819, -90983595, 584388344916, -143175567191021, 221791879833116245, -51244110428905517131, 74860312903862876895636, -4171461420724575664646445, 18228187372275885183326453379, 487476094628995948370988435733, 2102085018129621311776010144838961], [1, 1799, 3398133, 3709985452, 3923214415051, 2966055630106073, 2141537576603911750, 1153846063056974200241, 593716618067594801475739, 218412730223830525348401676, 77824205234364082306156990293, 16027805558797800250750396977743, 3465863721549107204083472585375569], [1, 1636, 2299646, 2035527108, 1747092049727, 1118492713318528, 843572321238202820, 551460528881853726592, 424696160929104832692767, 243961172559683485141891452, 135889556977945340127017269886, 47663910314344589999176825129564, 14364405059580771582276370834385761], [1, 1191, 2724018, 2654381901, 3546479899927, 2693775614251522, 2624824158961399580, 1540265877146035009814, 1159487462627787135844063, 496210830150479158509446103, 291170305100252198793517946898, 72791915374145201556647258699037, 34946659039493167390823397237402409], [1, 1370, 3801174, 3684694266, 5887444836831, 4432302017051644, 5245947803892614644, 3124635520658880419036, 2925949935469944380184591, 1290956231797351890882111594, 938853500281781750906096133654, 238545191601069021529057067313130, 122749609618842355502421774953773681], [1, 3021, 6979511, 11215812145, 15510026381711, 17665892352020490, 18254400207027091298, 16123182970595596669770, 12919417771675495127453519, 8526608740664079920523160465, 4842680390833630472877241904951, 1913051842382240735236736658825453, 577951262543040979328274795306257089], [1, 1333, 4312370, 3173337617, 6501747368815, 2482403870066614, 6422128496726013772, 2557623189733502470814, 6901735846114154290907815, 3470632616968185014747312917, 4859286455190202264287743356370, 1547571617508208047377552416650833, 1196147475686664860781049986817531801], [1, 839, 4477891, 3202014101, 9893639288011, 5783636494373558, 13376743587806837922, 6319935755587334912666, 11813522712879075006613819, 4177902133227906330943864883, 6384401843360523084210378183331, 1307134662528041483058279297069473, 1702433061239903677780481956434843889], [1, 321, -306652, -509873433, 2201167150751, -300261924460766, -1209891013041983224, -367833768727190162938, 3303358352625009054588599, -937381510067140416874512531, -690639055138014398158145764252, 885649124569622183219006055835203, 3379932275732534791891466777752413049], [1, 1553, 5664411, 6627552337, 15097313346687, 14004474745005338, 24077689358283816698, 18136200924549517864802, 25319705887130076360133767, 14394336379882471647743992093, 15932089329243627136792953496491, 5656775259894718657772088973489397, 4717120417286669419611030657597553321], [1, 3447, 4085148, -994087185, -5558393848361, 45220821636650, 7333838739900283160, 65248987877057375050, -11572307814286268132123849, -2986279593752725821791381505, 17707168373701868695620878303388, 21558469991922538705108675325163879, 9024267965168278308669913635234402529]], 'euler_factors_factorization': [[1], [[[1, -2, 81, -109, 3707, -5454, 122034, -147258, 2702403, -2145447, 43046721, -28697814, 387420489], 1]], [[[1, 5], 6]], [[[1, -28, 1710, -44507, 1306009, -29404243, 574046808, -10085655349, 153650652841, -1796017986749, 23668601113710, -132931722278404, 1628413597910449], 1]], [[[1, 3, 6021, -26781, 15818535, -133642140, 25492860502, -177877688340, 28023499683135, -63148197112671, 18896477256237141, 12531744508246953, 5559917313492231481], 1]], [[[1, 28, 10909, 255007, 53813653, 1024588726, 152088784296, 2251021431022, 259748224623277, 2704221571610611, 254158810601145229, 1433205004394541196, 112455406951957393129], 1]], [[[1, -24, 18030, -427891, 167973547, -3346966257, 1005505976060, -16443645220641, 4054473080887243, -50742685062177827, 10504678937252590830, -68698153236235579032, 14063084452067724991009], 1]], [[[1, 3, 21819, -265989, 273045711, -2946473628, 2316621912986, -20209862614452, 12845676027266391, -85831378044538431, 48292318219104566859, 45543381089624394897, 104127350297911241532841], 1]], [[[1, 23], 6]], [[[1, -76, 96138, -6141574, 4443699358, -229233487192, 131290006644110, -5590775519125688, 2643216009651127918, -89096710539601677806, 34015045627807382663658, -655818344817462017512124, 210457284365172120330305161], 1]], [[[1, 381, 183933, 51276809, 14163826942, 2892542918421, 570209036379841, 86171746082680011, 12570448548071973502, 1355739455564894178839, 144877178810579323190013, 8940264818892825339311331, 699053619999045038539170241], 1]], [[[1, -131, 244110, -26876359, 27142443903, -2479299439834, 1757009562030548, -125583954525911602, 69640085126728134327, -3492898374997075884643, 1606964414145611012444910, -43681461101687805228592583, 16890053810563300749953435929], 1]], [[[1, 95, 296879, 24628819, 41954508060, 3095260524119, 3616955966486841, 213328450582805599, 199288286664874682460, 8063030406058740162059, 6698626436882412957541199, 147734339924196101534417095, 107178930967531784356353269521], 1]], [[[1, 202, 258690, 47154510, 25742273095, 5001826335900, 1831244225314684, 397680206488401300, 162726253939999866655, 23699508345501982611930, 10337156890943855889174690, 641768213891187043706690014, 252599333573498060811820806649], 1]], [[[1, 119, 253739, 36692102, 49887954357, 5785025024479, 5837170895173758, 600618653116483217, 537753002337426738453, 41063249470394983246234, 29482310732581503294293099, 1435538453747623820407125817, 1252453015827223091648143056289], 1]], [[[1, -137, 594084, -64786529, 164474180415, -13341277950754, 29237327999867368, -1986209437474403258, 3645465131114359088535, -213780229633433051866357, 291849054876452900853743844, -10019789808796920902254877509, 10888439761782913818722623349689], 1]], [[[1, 39, 811376, 13330213, 323695705039, -637831310, 81542978014641968, -130997156616490, 13653657575844752716999, 115479579480779710372007, 1443598084421519097692038256, 14250981675864062604551813061, 75047496554032956760519149093721], 1]], [[[1, 573, 1025951, 373972257, 406395107231, 101577722520254, 101990059148671426, 23056213035369773174, 20937628063019858104391, 4373286208024915236426237, 2723231984529582816715588271, 345224927538578151378465150273, 136753052840548005895349735207881], 1]], [[[1, 563, 264282, -228527999, -47606117265, 28011216293194, 73923412251272732, 8424737445989907022, -4306372349139599047785, -6217454865309957251721053, 2162545317554180751878870202, 1385576265369633803527084824209, 740195513856780056217081017732809], 1]], [[[1, 83, 1110819, -90983595, 584388344916, -143175567191021, 221791879833116245, -51244110428905517131, 74860312903862876895636, -4171461420724575664646445, 18228187372275885183326453379, 487476094628995948370988435733, 2102085018129621311776010144838961], 1]], [[[1, 1799, 3398133, 3709985452, 3923214415051, 2966055630106073, 2141537576603911750, 1153846063056974200241, 593716618067594801475739, 218412730223830525348401676, 77824205234364082306156990293, 16027805558797800250750396977743, 3465863721549107204083472585375569], 1]], [[[1, 1636, 2299646, 2035527108, 1747092049727, 1118492713318528, 843572321238202820, 551460528881853726592, 424696160929104832692767, 243961172559683485141891452, 135889556977945340127017269886, 47663910314344589999176825129564, 14364405059580771582276370834385761], 1]], [[[1, 1191, 2724018, 2654381901, 3546479899927, 2693775614251522, 2624824158961399580, 1540265877146035009814, 1159487462627787135844063, 496210830150479158509446103, 291170305100252198793517946898, 72791915374145201556647258699037, 34946659039493167390823397237402409], 1]], [[[1, 1370, 3801174, 3684694266, 5887444836831, 4432302017051644, 5245947803892614644, 3124635520658880419036, 2925949935469944380184591, 1290956231797351890882111594, 938853500281781750906096133654, 238545191601069021529057067313130, 122749609618842355502421774953773681], 1]], [[[1, 3021, 6979511, 11215812145, 15510026381711, 17665892352020490, 18254400207027091298, 16123182970595596669770, 12919417771675495127453519, 8526608740664079920523160465, 4842680390833630472877241904951, 1913051842382240735236736658825453, 577951262543040979328274795306257089], 1]], [[[1, 1333, 4312370, 3173337617, 6501747368815, 2482403870066614, 6422128496726013772, 2557623189733502470814, 6901735846114154290907815, 3470632616968185014747312917, 4859286455190202264287743356370, 1547571617508208047377552416650833, 1196147475686664860781049986817531801], 1]], [[[1, 839, 4477891, 3202014101, 9893639288011, 5783636494373558, 13376743587806837922, 6319935755587334912666, 11813522712879075006613819, 4177902133227906330943864883, 6384401843360523084210378183331, 1307134662528041483058279297069473, 1702433061239903677780481956434843889], 1]], [[[1, 321, -306652, -509873433, 2201167150751, -300261924460766, -1209891013041983224, -367833768727190162938, 3303358352625009054588599, -937381510067140416874512531, -690639055138014398158145764252, 885649124569622183219006055835203, 3379932275732534791891466777752413049], 1]], [[[1, 1553, 5664411, 6627552337, 15097313346687, 14004474745005338, 24077689358283816698, 18136200924549517864802, 25319705887130076360133767, 14394336379882471647743992093, 15932089329243627136792953496491, 5656775259894718657772088973489397, 4717120417286669419611030657597553321], 1]], [[[1, 3447, 4085148, -994087185, -5558393848361, 45220821636650, 7333838739900283160, 65248987877057375050, -11572307814286268132123849, -2986279593752725821791381505, 17707168373701868695620878303388, 21558469991922538705108675325163879, 9024267965168278308669913635234402529], 1]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 0, 'label': '12-920e6-1.1-c3e6-0-0', '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}], 'nu_real_doubled': [3, 3, 3, 3, 3, 3], 'order_of_vanishing': 6, 'origin': 'ModularForm/GL2/Q/holomorphic/920/4/a/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.009765625', 'prec': 37}, 'plot_values': [0.0, 2.4049144956387526e-09, 1.537284822733493e-07, 1.7475361993320707e-06, 9.791113045432522e-06, 3.721467639438695e-05, 0.00011062971214050276, 0.00027750441940189053, 0.000614590683341648, 0.0012374049188122592, 0.0023105365268562047, 0.0040585326954703784, 0.006777087638647852, 0.010844250788211218, 0.01673137039945419, 0.025013440514457936, 0.03637854857516947, 0.05163612514492633, 0.07172369318656528, 0.097711860517807, 0.13080742919622307, 0.17235407618649937, 0.22383055568451055, 0.28684627507843785, 0.3631339984646367, 0.45453983122715846, 0.5630109465591558, 0.6905794627058235, 0.8393435583774315, 1.0114456887849597, 1.209048060229803, 1.4343062519996577, 1.6893427724269194, 1.9762154889915828, 2.2968843966971733, 2.6531774485300743, 3.0467554984315863, 3.4790785746579425, 3.951378132941386, 4.464619570678221, 5.019466690747256, 5.6162493884809965, 6.254933229918662, 6.935096521998518, 7.655920992741095, 8.416162178046239, 9.214128797445463, 10.047669780516657, 10.914167099021961, 11.810541966170854, 12.733281704520277, 13.678430989724733, 14.641598400984124, 15.617976344370575, 16.602369367819755, 17.58923408350591, 18.572756340547162, 19.54686259592885, 20.505254763413102, 21.441465816963188, 22.34891119416911, 23.220962390027886, 24.051068241240316, 24.83277075377998, 25.559758004812593, 26.225927683656018, 26.825446783458954, 27.352840287185636, 27.803131525928844, 28.171840610782773, 28.45501833510136, 28.649289961914715, 28.751901808117406, 28.76079275020902, 28.674723901723674, 28.493225936056362, 28.216579715210543, 27.845826732553164, 27.382773625382924, 26.83002316336786, 26.191061512065623, 25.470127291634384, 24.672144744197375, 23.802684317996558, 22.86791736867936, 21.874600310584267, 20.83008900505339, 19.742163364472574, 18.618920856748606, 17.468698000101345, 16.299994096783095, 15.121407849598265, 13.941609215831798, 12.769159056633741, 11.612394687054309, 10.479348246361722, 9.377664189246593, 8.314533806258607, 7.29666349329016, 6.330136585092874, 5.420336496852612, 4.571897654256768, 3.788661342467717, 3.073654143042815, 2.4290857572302684, 1.8562940148540679, 1.35573645348636, 0.9270031084695038, 0.5688416119351513, 0.27919605627094757, 0.05525506347802761, -0.1065122697069931, -0.21029327582268195, -0.2608553731106835, -0.2634629749193303, -0.2237896624058805, -0.14783032441729646, -0.04180561951255378, 0.08794012097573875, 0.23504092109264743, 0.3932095780671892, 0.5563336534898146, 0.7185644402366197, 0.8744112918814072, 1.0188260476537827, 1.1472770264295404, 1.255813533262299, 1.3411192161163323, 1.400553072442436, 1.4321844608235517, 1.4348114527933984, 1.4079650128623233, 1.3519003980302398, 1.2675744301751541, 1.1566135869938738, 1.0212668751052014, 0.8643460844893308, 0.6891562814917537, 0.4994159576029149, 0.29917125511342174, 0.09270766189694568, -0.11555131736056748, -0.32114672022956303, -0.5196864847155609, -0.7069460499240153, -0.8789644483764933, -1.0321338724157305, -1.1632899918236088, -1.269790708869907, -1.3495819952197887, -1.401251947345368, -1.42407132055334, -1.418020699887709, -1.3838046293800625, -1.3228463160946646, -1.2372663389610201, -1.1298453789317773, -1.0039717403263606, -0.8635751072884933, -0.7130428143947982, -0.5571235000326338, -0.40081981383181553, -0.24927159435894694, -0.10763178116017806, 0.019063061084709385, 0.12602659008320036, 0.20885611842932483, 0.2636633911070855, 0.28720036774968066, 0.2769772746119413, 0.23137023986776611, 0.1497159707276415, 0.03239110978125134, -0.1191262912554973, -0.3022145410249212, -0.5130862544668302, -0.7467893769938031, -0.9972307964813104, -1.2572243264492142, -1.5185629049283673, -1.7721103392944448, -2.0079174002754803, -2.2153596879587387, -2.3832934058626805, -2.500231372411795, -2.554527219550306, -2.534574428988224, -2.4290147796083397, -2.22694649863988, -1.9181403704885642, -1.4932486361786446, -0.9440104867450155, -0.2634517121200228, 0.5539356656295047, 1.5120593469056893, 2.6130772218483367, 3.8572688107296216, 5.242935308818895, 6.76632641888171, 8.421628288368181, 10.201049396700785, 12.094801390931712, 14.091134727855222, 16.176423986910855, 18.3352987021218, 20.550862024536325, 22.80500564901006, 25.078512172560867, 27.35123620489302, 29.602358199089235, 31.81069173595568, 33.95498815000612, 36.01443042494463, 37.96873194086346, 39.79834806947638, 41.484810113934095, 43.010940991185905, 44.36114740793071, 45.52192340758146, 46.481785007693304, 47.23141470443386, 47.763771513532745, 48.07412087638519, 48.16019610764656, 48.02253153715694, 47.664202058156235, 47.09068339090616, 46.30967355289582, 45.33096601178619, 44.16640004368963, 42.83000603036984, 41.33752341016999, 39.705968247092535, 37.95337289581055, 36.09853187202982, 34.16084590335947, 32.16033031403889, 30.116973250281465, 28.050365479760814, 25.97945721843721, 23.92234209636553, 21.896159888050608, 19.916984666218898, 17.99941604612586, 16.15639372069567, 14.399107934170384, 12.73697298667757, 11.177602182807858, 9.72683489639504, 8.388641087555483, 7.165158129203214, 6.056805737739824, 5.062403326811078, 4.179298087842541, 3.403545435301211, 2.7300279573068433, 2.152640270042105, 1.6644906371187917, 1.2580863863012033, 0.9255337228834277, 0.6587319871592101, 0.4495395780350446, 0.28994395701196307, 0.17221089817952642, 0.08901925747423929, 0.033575295234388826, -0.0002970081986920126, -0.0180894607357458, -0.02456603448959685, -0.023741449487724452, -0.018882115860943547, -0.01252852171034867, -0.006536699906399562, -0.002135573003588003, 1.70720276999453e-06, -0.00032443083472126895, -0.002929615267422064, -0.007339075321167227, -0.012881576962922262, -0.018780883836134604, -0.024241447011325048, -0.028525322769240434, -0.03101782312965489, -0.03127987067132874, -0.02908561829994262, -0.024444163179481785, -0.01760477250065173, -0.00904576920010539, 0.0005522493127661444, 0.01034764761731126, 0.01939173695558922, 0.02669337167112897, 0.031291572934945944, 0.03233331441572311, 0.02915334092091156, 0.021352718858560722, 0.008872641505487963, -0.00793918739164102, -0.02827276422778281, -0.050813506015687966, -0.07371586791270217, -0.09459507325429571, -0.11053821941941838, -0.11813390115565689, -0.11352253805961865, -0.0924669272796994, -0.05044219958063538, 0.017257443154471593, 0.1154022826761296, 0.2486958684635069, 0.4216332063984237, 0.6383530985838061, 0.9024879946675741, 1.2170227916407301, 1.5841858325661011, 2.005317351749939, 2.48075302535967, 3.0097296661188673, 3.590312102537523, 4.219368682912405, 4.892628381807477, 5.604657526632112, 6.3488809738960175, 7.117647704631485, 7.902332509503961, 8.693498227796361, 9.481180071216622, 10.254967458478333, 11.004149988092177, 11.717922921412953, 12.385597775139676, 12.996861396206503, 13.542186171439466, 14.01287167910698, 14.401178234149977, 14.700506521875974, 14.905525153375546, 15.012365305898404, 15.018943206677061, 14.92480471489615, 14.731089621999544, 14.440496974297208, 14.057232937402437, 13.587008083558278, 13.037137113834387, 12.416171419560518, 11.733634440481792, 10.999819685546056, 10.225586586437599, 9.422204465043835, 8.601286893468446, 7.774343948402366, 6.952488738282379, 6.146233439688703, 5.365303946486532, 4.618514776732671, 3.9136978944081617, 3.2574352885561044, 2.6549454013688174, 2.1100444985417433, 1.6251432446086955, 1.201287231930785, 0.8382316554174355, 0.5344634228855001, 0.28731138438306886, 0.09309752792493284, -0.05269473347552508, -0.1552377607438501, -0.22017087570785304, -0.2534229456647279, -0.26101835910556137, -0.24888890498867705, -0.22269965580188175, -0.18769491050648301, -0.14856952207877608, -0.10936055953652338, -0.0733673153814365, -0.04310276049660631, -0.020276921850415217, -0.005811772732488565, 0.00011521351895388598, -0.001997733221509406, -0.011071424464236701, -0.025560998088965187, -0.043586310939282474, -0.06307182324477068, -0.08189021489134041, -0.09800659099917869, -0.10961544055882237, -0.11526483844585703, -0.11396314388807602, -0.10526397516936364, -0.08932621792743542, -0.06694554873085654, -0.03955589511902365, -0.009200450439781988, 0.021527253069487707, 0.04957061842538391, 0.07152341280972273, 0.08376510839219513, 0.08261335508100598, 0.06448857022360804, 0.02608479510365425, -0.035459914607233106, -0.12240038542836135, -0.23623457148673965, -0.3775725129502916, -0.5460306962813262, -0.7401566738367779, -0.9573882906897507, -1.1940563868827911, -1.4454171484298413, -1.7057259095110204, -1.9683525801882646, -2.2259285346235904, -2.4705337758079895, -2.6939244069259223, -2.887755846153279, -3.0438330690061113, -3.154363349707498, -3.212213977951505, -3.211170165297199, -3.146180904184593, -3.013554003824232, -2.8111225088345995, -2.538382347871427, -2.1965928664922374, -1.788826149628283, -1.319939144520279, -0.7965029260685016, -0.22669449286173268, 0.3798562430262429, 1.012264705716199, 1.6586586778316592, 2.3065565683398255, 2.94313773784659, 3.5555422190722736, 4.131198082904767, 4.658155409006376, 5.125459892871168, 5.523588711986009, 5.844608445393916, 6.08235423851733, 6.232609146549568, 6.293244832684949, 6.264329295596496, 6.148278410044065, 5.949640956665353, 5.6749275983730385, 5.332448518655886, 4.932076172062162, 4.485008684223522, 4.00356081103717, 3.500667579849955, 2.9894879329528643, 2.4830350807554615, 1.9938124899722236, 1.5334941072638402, 1.112641843455146, 0.7403271229134741, 0.4238753619017525, 0.1686899522139799, -0.0218608154769109, -0.1464942314115862, -0.20601349322126916, -0.2032604949746163, -0.14297198349361634, -0.031574061729508066, 0.12307073334854074, 0.31195207779541023, 0.5252259700434436, 0.7525788464117299, 0.9835965010306047, 1.2081241417076045, 1.416610152013436, 1.6004271431784516, 1.7521591843130482, 1.8658459955943891, 1.9371631603776356, 1.9635393799851382, 1.944213824205953, 1.880226751481198, 1.7743555756511167, 1.630963189744547, 1.4557907238051178, 1.2557074288607704, 1.038417522592105, 0.8121386770767965, 0.585275862065346, 0.3660581541512644, 0.1621944224320194, -0.019445526605876177, -0.17311711025582513, -0.29443867990435674, -0.3805739209121702, -0.4303659794192357, -0.4443977680015478, -0.42497808763792516, -0.37605679738615794, -0.30307166893123244, -0.21273189617529828, -0.11274534219556472, -0.011498546677059254, 0.08229883370840117, 0.15999232444461867, 0.21336943184824303, 0.23504057081133942, 0.218795115906776, 0.15992188723598197, 0.05548321628592372, -0.09547100556082046, -0.29176280323895115, -0.5300336632114125, -0.8047612510274728, -1.1083580319598059, -1.4313539781223006, -1.7626635387055476, -2.0899349991225367, -2.3999530963876676, -2.679061934209282, -2.913631994405121, -3.090557543218058, -3.197769185754236, -3.224697506171116, -3.1626895628501366, -3.0053750849898333, -2.7489903751053593, -2.392640626403739, -1.9384436004740846, -1.3915604653464044, -0.7600486136990501, -0.05474540401110091, 0.710947785638621, 1.521403359861501, 2.359173657433528, 3.205521395229971, 4.041168038899007, 4.846744832585826, 5.6033277588683825, 6.292979560945329, 6.899283650396102, 7.407933646263034, 7.807488567899825, 8.089525685781659, 8.248755028046745, 8.283163100123902, 8.194068734911374, 7.986189913882886, 7.667798223142102, 7.2500720121463225, 6.746607297035532, 6.172974556893516, 5.546230873779179, 4.884498844582958, 4.206448768426553, 3.53042242494121, 2.873803321628543, 2.2525006673042296, 1.6805278524332163, 1.169596193284877, 0.7287703326427311, 0.3641545262731767, 0.07879378254804882, -0.12727562946872187, -0.2568954656836085, -0.3155771262870063, -0.31119720111666677, -0.2535666488384735, -0.1539183580250951, -0.024364044955922853, 0.1226654807024516, 0.27498145237085214, 0.4211689330977963, 0.5511228036083673, 0.6564907412554043, 0.731026579949952, 0.7708410165943944, 0.7745384630560836, 0.743241920702803, 0.6804945216869336, 0.5920346364213989, 0.48545695557644825, 0.36977438711656146, 0.25490223067685297, 0.15108519365669604, 0.06827509867606252, 0.015503754866737874, 0.0002784264444635552, 0.028026518388248156, 0.10161494155712468, 0.2209641951480815, 0.38278737924988576, 0.5804728525334415, 0.8041194225009508, 1.0407300755782296, 1.2745635889474158, 1.4876388616583238, 1.6603854192899692, 1.7724150679587303, 1.8033906527248504, 1.733963243520254, 1.5467410934857078, 1.2272456192140606, 0.7648367905822371, 0.15356264135336162, -0.6071080094686842, -1.5117045545548107, -2.5483740116316436, -3.698763524103187, -4.938026716223146, -6.235081050248379, -7.553120456128493, -8.850363787353333, -10.081075046934933, -11.196869940927742, -12.147938886871533, -12.88447135106687, -13.35820515622437, -13.5240399079847, -13.341683336956226, -12.77722085266639, -11.804340972587058, -10.40551727574599, -8.573057178908478, -6.309927096514069, -3.6302326094771318, -0.5590375172310487, 2.867818098357218, 6.604107557551378, 10.593941055006912, 14.772781527960547, 19.06903672930631, 23.40667073263275, 27.706507630070757, 31.887855151759148, 35.87043073540479, 39.57637501479423, 42.93267517451147, 45.874561981078706, 48.346034883629116, 50.30081861618504, 51.70356536901149, 52.53076003523588, 52.771786909684444, 52.43081141729497, 51.524933520365416, 50.08309759496345, 48.14525825988944, 45.761147418829324, 42.98934548487137, 39.89690620348794, 36.55583538612238, 33.04067153018199, 29.426449395922912, 25.78676052815422, 22.192209840366534, 18.7093355938961, 15.397876672761958, 12.309160356864108, 9.485147514941518, 6.957808905014486, 4.748919451813736, 2.870204363602073, 1.3231005387666717, 0.09932922304306996, -0.8181065243667499, -1.4537005080065815, -1.8380435369594936, -2.006344131748827, -1.9968978556093318, -1.8494054139181264, -1.6033225388315642, -1.2963211953842406, -0.9629199826945759, -0.6333278702046097, -0.3324391972830448, -0.07911719980130753, 0.11421789747933833, 0.24170409307741486, 0.3038604744127543, 0.3071413139587003, 0.2632544575137021, 0.1882415646007443, 0.10137980913483523, 0.023958760976294177, -0.022012592146816338, -0.01511579978097374, 0.06419896493730579, 0.23242784400475097, 0.5019719308382068, 0.8802820184956326, 1.36922639229819, 1.964713171491788, 2.656568813910562, 3.428686349781965, 4.2594395110977645, 5.122347389829385, 5.986982179932142, 6.820109784335839, 7.586876318984199, 8.252118306693397, 8.781736709836865, 9.144069618810825, 9.311235057202584, 9.260395458402796, 8.974696465539484, 8.444073228194696, 7.665858547266957, 6.645129830476294, 5.394743940105626, 3.9351852835700707, 2.29399383195811, 0.5050138996122873, -1.392559464873768, -3.3554275180642144, -5.337491665600006, -7.291285105916642, -9.169451204773017, -10.92618601327709, -12.518744899635374, -13.908781654808122, -15.063436445903626, -15.956457862166376, -16.568839025801168, -16.889350569948117, -16.91486434878237, -16.650211117776394, -16.107946360413674, -15.307874721002351, -14.276206533949926, -13.04467407191221, -11.649354627153885, -10.12948271378731, -8.526183370583897, -6.881011795213114, -5.234739665038546, -3.6261639280313247, -2.091039732669139, -0.6611750054854734, 0.6364171285086728, 1.7804276658000429, 2.755397871741163, 3.551751172033625, 4.165712706594043, 4.599053038863652, 4.858785882822536, 4.956882965684806, 4.909204833864378, 4.734579759778162, 4.453946248576541, 4.089494706779101, 3.6638851059548374, 3.1995476065753414, 2.717674767108735, 2.2375189023382074, 1.7758882549490826, 1.3467761664157927, 0.9611315460182899, 0.6267775584014565, 0.34833838597981276, 0.12739272659491266, -0.037238253167059615, -0.149118126356893, -0.21375551375487198, -0.2381313862391623, -0.23020318416085003, -0.19839486506667164, -0.15111388376023532, -0.09631771943095813, -0.04114750740030052, 0.00836315442111974, 0.04750472023136528, 0.07301347382049851, 0.08310176310789923, 0.07740420994814673, 0.05685093648271557, 0.02348275426919939, -0.019789780105811, -0.06946015132869252, -0.12171336926905094, -0.17271119652616884, -0.2188589008286874, -0.2570397662608796, -0.284809130587091, -0.3005338829923341, -0.30347291000918697, -0.29379684725299327, -0.2725481999083477, -0.24154631712062566, -0.20324400714027632, -0.16054756661745007, -0.11661090938396507, -0.07461606322753656, -0.037553779676611984, -0.008016492124352083, 0.011979822311240854, 0.02113897211969461, 0.018984822158401814, 0.005912603012675052, -0.016812316810764043, -0.04711358336630638, -0.08220920808507448, -0.1187570961867799, -0.1530333821649279, -0.18113879894738263, -0.19922481221799015, -0.20372944393960524, -0.19157922654249404, -0.1603618688143626, -0.10848797571492269, -0.035315733572718104, 0.05877119609213416, 0.17235132444831913, 0.30304190375564494, 0.4475746073324471, 0.6019053027393761, 0.7613735089081014, 0.9209075185782204, 1.0753318803273963, 1.2195801660922745, 1.348870953036326, 1.4589090682526218, 1.5460680261607345, 1.607604320562372, 1.6418459320223253, 1.6481487336307565, 1.626881604536648, 1.579389522860422, 1.5079411708488424, 1.415653783683426, 1.3063265415172902, 1.1841847052748204, 1.0536638606140987, 0.9192221523997098, 0.7851712954771937, 0.6554680066968608, 0.533569880296424, 0.4222759721891842, 0.3236437105483783, 0.23896588762764298, 0.16876035298288294, 0.11281372063086716, 0.07026903122069646, 0.03973135149776693, 0.01941028246350024, 0.007271566385110642, 0.0011944735797757358, -0.0008740733912976556, -0.000782027788669512, -5.8013720318314146e-05, 0.00017260307201399127, -0.000763666846748561, -0.0030779188052371355, -0.00654636451190442, -0.0105728136555581, -0.014281980943858475, -0.016636552443288648, -0.01656853411170188, -0.013114702003285897, -0.005545722769001617, 0.0065208425705042955, 0.023034443297402753, 0.04346103446732426, 0.06677404711232746, 0.09149050660048441, 0.11575304554697527, 0.13745643503113503, 0.15441339607816862, 0.16455094578987364, 0.16612672248739407, 0.1579526130718969, 0.139610502634108, 0.11164447545643089, 0.07571781616373459, 0.0347196474167942, -0.007191512095059262, -0.04461734691090332, -0.07102868745565243, -0.0789520910187243, -0.06022448771181312, -0.006322515947214504, 0.0912463838582227, 0.2405069678512162, 0.44855972161427476, 0.7211630032009568, 1.0622975924316949, 1.4737697514748456, 1.9548732266435034, 2.5021288426920196, 3.1091711061962632, 3.76690390643705, 4.463566431750184, 5.184915001549076, 5.91454912522429, 6.634359959773536, 7.325191458786277, 7.9679083642662505, 8.54386441332186, 9.035462449591915, 9.426834869168793, 9.704496625761987, 9.85815422165206, 9.881673139401183, 9.772909015115285, 9.533723846322177, 9.170003170951826, 8.691577755426936, 8.112125434642929, 7.4489184263518435, 6.721698603289169, 5.951798686426985, 5.161364910084004, 4.3725823333871645, 3.6067823852478615, 2.883695480930958, 2.2203722934239076, 1.6304974477663192, 1.1239687043367523, 0.7065451761592763, 0.3797231518113601, 0.14081449552239225, -0.016834025759786327, -0.10331951229041994, -0.1315125868193836, -0.11625011140020543, -0.0734252926101953, -0.019035595068250248, 0.03181418449335893, 0.06584283354914691, 0.07240959778627615, 0.04417305676536471, -0.022445304003857473, -0.12700688025426654, -0.26507711194704164, -0.42852725565765437, -0.6060999782877865, -0.7842183963794696, -0.9480006059989463, -1.0824394040150151, -1.1737376179857684, -1.2106752901203315, -1.185941622268008, -1.0973632921888197, -0.9489600087469001, -0.7517726442791545, -0.5243551790405003, -0.29289725364245245, -0.09094894976330056, 0.04127282447486447, 0.05799721222869965, -0.09057477080019158, -0.4563733141123827, -1.0912685737922112, -2.0446549465624493, -3.360901275155533, -5.076776994216902, -7.218997798399056, -9.801946090595756, -12.825697467524348, -16.274473007246662, -20.11558353158204, -24.29904904040713, -28.758123431893022, -33.41006225941478, -38.15765422552095, -42.89140001856821, -47.49231404451627, -51.83549210860807, -55.794601175522, -59.2455026233532, -62.070179317025094, -64.1608702202212, -65.42413195811514, -65.78486788621615, -65.19031672125908, -63.61168952005605, -61.04565434036018, -57.51542647311354, -53.07104660762891, -47.78888299390582, -41.769729071181125, -35.135505395618026, -28.025956758353157, -20.594847104524312, -13.005656642938106, -5.4264555121689755, 1.9767177405629823, 9.044394284860116, 15.62803114301164, 21.594310991737103, 26.829041094175583, 31.24103600813266, 34.76672345398032, 37.36982539570859, 39.041110885446095, 39.79799554192985, 39.68313048081206, 38.76284413970203, 37.125978042873214, 34.87788425980829, 32.13558793567669, 29.023279661691756, 25.667697344021953, 22.1940552911456, 18.722593118623188, 15.36296996224212, 12.210528038362062, 9.343704689606875, 6.822281803426759, 4.6865554034629175, 2.9573024822075222, 1.635815253824436, 0.7053645673066458, 0.13352498539433894, -0.12496629568962093, -0.12496568496990192, 0.07252157522375129, 0.4039429850942042, 0.8068134918992763, 1.2230590778915742, 1.6019360294647382, 1.9024188612983512, 2.0949959062151198, 2.162744564049431, 2.1016166076448264, 1.9199664804216765, 1.6373715382900451, 1.282828681704358, 0.8924453235866849, 0.5066000631683972, 0.16686958143627478, -0.08711961093632817, -0.2207654699792593, -0.20732528937522382, -0.03037819519302688, 0.31421765513909883, 0.8170340432187291, 1.4545057035910023, 2.189127740242879, 2.9704310427443414, 3.736718270946236, 4.417462154379438, 4.93626972902859, 5.214323231431167, 5.174136727595556, 4.743476236751936, 3.859243304097946, 2.470913278923452, 0.5437356814705133, -1.938543891147929, -4.971654824842778, -8.529597483584666, -12.564689066502263, -17.008205527118815, -21.771644064345708, -26.748964593747633, -31.819625234578965, -36.85274206150014, -41.71197241027602, -46.2594549448912, -50.360345365536844, -53.88751826003909, -56.72639594298168, -58.77963294919281, -59.97053281342573, -60.24523849464112, -59.574655381929375, -57.95588743794477, -55.41303085128051, -51.99607057963345, -47.778746835451244, -42.85594733760578, -37.340835497401415, -31.361587481040615, -25.05711144267859, -18.572247870395707, -12.05177580682344, -5.6368114184600975, 0.5388019619576476, 6.352260353875242, 11.694986516181636, 16.47584305372648, 20.62517924641526, 24.094309009382197, 26.855274306547987, 28.900334087170997, 30.240919432065407, 30.906693868462554, 30.945323919397634, 30.417923438586442, 29.395313673735085, 27.955005987902258, 26.17824527944576, 24.14761624689444, 21.94542354027604, 19.64949391343737, 17.330687304516637, 15.05137034363412, 12.864364218110868, 10.812551961342086, 8.92890638567884, 7.235912389487367, 5.746065680378028, 4.462886682879391, 3.38217078281517, 2.4933826011136726, 1.781134337667673, 1.2264572127448345, 0.808219637655641, 0.5044693567459645, 0.29359049771427836, 0.15525306263096753, 0.07113493594635659, 0.025397185733951725, 0.004959612261098454, -0.0004317934250402292, 0.0016784007390855155, 0.006190621423526931, 0.010078702112915613, 0.01195440424569341, 0.011608104648801323, 0.009563445778237478, 0.006678956240976353, 0.003822553438564563, 0.0016367632668382063, 0.0004039868903049119, 1.2059567096478603e-05, 1.2131857035365737e-05, -0.0002456882338350432, -0.0014191618120265035, -0.003947862358906033, -0.007820406761966565, -0.012360284608405905, -0.01605436159660818, -0.01644503753605753, -0.010102179200213867, 0.007319950247566119, 0.04093935690875165, 0.09641633183728325, 0.17964658117301877, 0.2963942316588552, 0.4518983914542008, 0.6505042764590984, 0.8952741832351097, 1.187629485144741, 1.5270606756216758, 1.9109365356235921, 2.3344270815710093, 2.790669461651127, 3.270842484108945, 3.7643683087501456, 4.259286984068576, 4.742656905214242, 5.201097336092527, 5.621613368650821, 5.991940583180179, 6.301031232895236, 6.539504923148861, 6.69998906777929, 6.777536018738639, 6.770168890104481, 6.678689930898821, 6.506528744510162, 6.259498562716582, 5.945527371591496, 5.574405709354082, 5.157637162074849, 4.707651904416684, 4.2371298760840315, 3.7585048404073573, 3.2835172114096327, 2.822879248800398, 2.3860642018130362, 1.9807969226262447, 1.6128519221576614, 1.2860232744201485, 1.0021896079962376, 0.7614816114753593, 0.5624907386564587, 0.4024630272175398, 0.2776106036816743, 0.18345495917281748, 0.11516319103311129, 0.06785282637178093, 0.036856288922329276, 0.017929878457550143, 0.007412823816528831, 0.002321344875608201, 0.00037685243216114265, -2.4145111419407053e-05, 0.00011193719730463543, 0.00026259197469702373, 0.0002557243698231265, 0.00013168177803870389, 1.6580791491798663e-05, 2.090496717404268e-05, 0.00017457034216754943, 0.0004060147685405598, 0.0005685857520379671, 0.0005128020622579445, 0.00019842793969137318, -0.0001639873834072411, 4.404718064446868e-05, 0.0020055572066837836, 0.007606345113083341, 0.019536871418564777, 0.04134088316548848, 0.07739792357255758, 0.13283740168054178, 0.21337116741027995, 0.3250450080185562, 0.4739164488539657, 0.6656695992273285, 0.9052042117953065, 1.1962697718631654, 1.5410373346815518, 1.9397020939439564, 2.3901523881614053, 2.8877306864809826, 3.4251765242143835, 3.9928633593739518, 4.578856126234897, 5.169136581292981, 5.7480164287786755, 6.298703499207477, 6.804033169333529, 7.247612072306475, 7.614242164242634, 7.89050004978653, 8.06544669175892, 8.13116531782023, 8.083362528506342, 7.922192107865875, 7.651846312478637, 7.280339204023154, 6.819204101178062, 6.282997708008562, 5.6888458473557995, 5.056052949682895, 4.404740376882117, 3.754790524267277, 3.124922827684424, 2.5318847210363886, 1.9898116742241099, 1.5097681036849395, 1.0990411211052011, 0.7608980807528967, 0.49468576072699727, 0.2961536594517668, 0.15798944347789187, 0.07051590194437517, 0.02247745525914119, 0.0020148167390201797, -0.0023184158961546196, -0.0005809368233059853, -0.0005713561789529889, -0.007111934691747462, -0.02154127093206848, -0.041473620713307686, -0.060855422423039394, -0.07033122116994574, -0.057911087312213616, -0.009914040577902364, 0.08784147631637601, 0.24867808492543994, 0.4835978368265091, 0.7998077105487638, 1.1993414014022996, 1.6778489840895754, 2.2236704247880215, 2.8172542659761826, 3.4309851556663333, 4.02950177956325, 4.570504381272855, 5.006085771972871, 5.28446818454389, 5.352136006522202, 5.156306232844244, 4.6476113049645855, 3.782888917554913, 2.527935115361651, 0.8599583314839657, -1.2302535238727226, -3.7365911654475483, -6.636440242203964, -9.890227835817424, -13.441984797164894, -17.220327358055155, -21.140129467171977, -25.104942617912624, -29.010049079551525, -32.74634704414395, -36.20517817813567, -39.281871246661545, -41.87962340647471, -43.91344957373734, -45.31389911102331, -46.03061460836107, -46.03546913740547, -45.32301367848465, -43.91076418819251, -41.838969751007845, -39.16954238444669, -35.98397109301539, -32.38052035774492, -28.469573484880975, -24.3692581051623, -20.201049105246163, -16.08499102756142, -12.134956804339089, -8.45376925924864, -5.1293163857148825, -2.2316111015297944, 0.18942023061180902, 2.1052796751035934, 3.509543376441083, 4.417995074214201, 4.86638645791236, 4.907688803741748, 4.608746372663866, 4.046461197904972, 3.303796897619944, 2.4656649968942643, 1.6140230518028058, 0.8239735141340646, 0.16029243799048018, -0.3254957890205225, -0.5973731215013985, -0.6364464312099148, -0.44113424634489995, -0.02585439723878483, 0.5811316385859053], 'positive_zeros': ['1.07716987213486723413594641398251', '1.14590141223077915419701561264785', '1.37153286218675604085788943349231', '1.60000023324720563906990631930440', '1.68196734883993683428649904929827', '1.87833407730511419390295660745911', '2.59754061067928649586787305112462', '2.67576300700063607284563373985837', '2.68293148110382910839099057216248', '2.81195201707861707396303171794624', '2.89606551655821439631084460524220', '2.99590893938077346615988920896941', '3.57032158720735069435598753201015', '3.71037664904740957358440748791430', '3.71585944389070178622977056204522', '3.86031698025225107990219900234073', '3.93040234366048363873909753644874', '4.20292868249716788914456660347578', '4.51040166762270446578713592279681', '4.56276092075088322524813829948912', '4.79380576008640825805848791055990', '4.90348335069356249737991405341076', '4.97465378152495280524072713397316', '5.18626741115818302032694583259066', '5.49159802789523151227873250723994', '5.55831904932220868181470520990690', '5.73055673139662243356929336329317', '5.73175702462688106949581519797739', '5.90057129225063563758407065144957', '6.11494157354305062236733830494115', '6.48529747705840487859636648728418', '6.60518313433629826245183968781693', '6.68370327282760759655966522842777', '6.70210849957537204128879831751564', '6.95577017839898307954184200323690', '7.21187154596492166825075322856745', '7.42912196530813108739303706398278', '7.51775304502066944894995322329055', '7.58365144952537211243089413604048', '7.75725577489018323576288664751325', '7.79591186889932104941632434728065', '7.914076296032283494399006211741367', '8.265606620353102662449529366911645', '8.291958679203636179963516616709059', '8.304174480293233280090974729570864', '8.393621380804630406116792482392538', '8.543209725234872527009931099188207', '8.594559838485291411548136393766108', '8.992825254421535291503945881187825', '9.046408426864991170069685566659620', '9.089079149070816529994091337222504', '9.253939854279693732115502055502034', '9.272951385894015350286341013920527', '9.626262253167823509138537972896585'], 'prelabel': '12-920e6-1.1-c3e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.367615435490738, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3e6-0', 'trace_hash': 943022525766121473, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.07716987213486723413594641398', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.14590141223077915419701561265', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.37153286218675604085788943349', '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': 25581345835.804546, 'bad_primes': [2, 5, 23], 'central_character': '1.1', 'conductor': 606355001344000000, 'conductor_radical': 230, 'degree': 12, 'dirichlet_coefficients': [1, 0, 2, 0, -30, 0, 28, 0, -77, 0, -3, 0, -28, 0, -60, 0, 24, 0, -3, 0, 56, 0, -138, 0, 525, 0, -207, 0, 76, 0, -381, 0, -6, 0, -840, 0, 131, 0, -56, 0, -95, 0, -202, 0, 2310, 0, -119, 0, -926, 0, 48, 0, 137, 0, 90, 0, -6, 0, -39, 0, -573, 0, -2156, 0, 840, 0, -563, 0, -276, 0, -83, 0, -1799, 0, 1050, 0, -84, 0, -1636, 0, 2334, 0, -1191, 0, -720, 0, 152, 0, -1370, 0, -784, 0, -762, 0, 90, 0, -3021, 0, 231, 0], 'euler11': [1, 3, 6021, -26781, 15818535, -133642140, 25492860502, -177877688340, 28023499683135, -63148197112671, 18896477256237141, 12531744508246953, 5559917313492231481], 'euler13': [1, 28, 10909, 255007, 53813653, 1024588726, 152088784296, 2251021431022, 259748224623277, 2704221571610611, 254158810601145229, 1433205004394541196, 112455406951957393129], 'euler17': [1, -24, 18030, -427891, 167973547, -3346966257, 1005505976060, -16443645220641, 4054473080887243, -50742685062177827, 10504678937252590830, -68698153236235579032, 14063084452067724991009], 'euler19': [1, 3, 21819, -265989, 273045711, -2946473628, 2316621912986, -20209862614452, 12845676027266391, -85831378044538431, 48292318219104566859, 45543381089624394897, 104127350297911241532841], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 138, 7935, 243340, 4197615, 38618058, 148035889, 0, 0, 0, 0, 0, 0], 'euler29': [1, -76, 96138, -6141574, 4443699358, -229233487192, 131290006644110, -5590775519125688, 2643216009651127918, -89096710539601677806, 34015045627807382663658, -655818344817462017512124, 210457284365172120330305161], 'euler3': [1, -2, 81, -109, 3707, -5454, 122034, -147258, 2702403, -2145447, 43046721, -28697814, 387420489], 'euler31': [1, 381, 183933, 51276809, 14163826942, 2892542918421, 570209036379841, 86171746082680011, 12570448548071973502, 1355739455564894178839, 144877178810579323190013, 8940264818892825339311331, 699053619999045038539170241], 'euler37': [1, -131, 244110, -26876359, 27142443903, -2479299439834, 1757009562030548, -125583954525911602, 69640085126728134327, -3492898374997075884643, 1606964414145611012444910, -43681461101687805228592583, 16890053810563300749953435929], 'euler41': [1, 95, 296879, 24628819, 41954508060, 3095260524119, 3616955966486841, 213328450582805599, 199288286664874682460, 8063030406058740162059, 6698626436882412957541199, 147734339924196101534417095, 107178930967531784356353269521], 'euler43': [1, 202, 258690, 47154510, 25742273095, 5001826335900, 1831244225314684, 397680206488401300, 162726253939999866655, 23699508345501982611930, 10337156890943855889174690, 641768213891187043706690014, 252599333573498060811820806649], 'euler47': [1, 119, 253739, 36692102, 49887954357, 5785025024479, 5837170895173758, 600618653116483217, 537753002337426738453, 41063249470394983246234, 29482310732581503294293099, 1435538453747623820407125817, 1252453015827223091648143056289], 'euler5': [1, 30, 375, 2500, 9375, 18750, 15625, 0, 0, 0, 0, 0, 0], 'euler53': [1, -137, 594084, -64786529, 164474180415, -13341277950754, 29237327999867368, -1986209437474403258, 3645465131114359088535, -213780229633433051866357, 291849054876452900853743844, -10019789808796920902254877509, 10888439761782913818722623349689], 'euler59': [1, 39, 811376, 13330213, 323695705039, -637831310, 81542978014641968, -130997156616490, 13653657575844752716999, 115479579480779710372007, 1443598084421519097692038256, 14250981675864062604551813061, 75047496554032956760519149093721], 'euler61': [1, 573, 1025951, 373972257, 406395107231, 101577722520254, 101990059148671426, 23056213035369773174, 20937628063019858104391, 4373286208024915236426237, 2723231984529582816715588271, 345224927538578151378465150273, 136753052840548005895349735207881], 'euler67': [1, 563, 264282, -228527999, -47606117265, 28011216293194, 73923412251272732, 8424737445989907022, -4306372349139599047785, -6217454865309957251721053, 2162545317554180751878870202, 1385576265369633803527084824209, 740195513856780056217081017732809], 'euler7': [1, -28, 1710, -44507, 1306009, -29404243, 574046808, -10085655349, 153650652841, -1796017986749, 23668601113710, -132931722278404, 1628413597910449], 'euler71': [1, 83, 1110819, -90983595, 584388344916, -143175567191021, 221791879833116245, -51244110428905517131, 74860312903862876895636, -4171461420724575664646445, 18228187372275885183326453379, 487476094628995948370988435733, 2102085018129621311776010144838961], 'euler73': [1, 1799, 3398133, 3709985452, 3923214415051, 2966055630106073, 2141537576603911750, 1153846063056974200241, 593716618067594801475739, 218412730223830525348401676, 77824205234364082306156990293, 16027805558797800250750396977743, 3465863721549107204083472585375569], 'euler79': [1, 1636, 2299646, 2035527108, 1747092049727, 1118492713318528, 843572321238202820, 551460528881853726592, 424696160929104832692767, 243961172559683485141891452, 135889556977945340127017269886, 47663910314344589999176825129564, 14364405059580771582276370834385761], 'euler83': [1, 1191, 2724018, 2654381901, 3546479899927, 2693775614251522, 2624824158961399580, 1540265877146035009814, 1159487462627787135844063, 496210830150479158509446103, 291170305100252198793517946898, 72791915374145201556647258699037, 34946659039493167390823397237402409], 'euler89': [1, 1370, 3801174, 3684694266, 5887444836831, 4432302017051644, 5245947803892614644, 3124635520658880419036, 2925949935469944380184591, 1290956231797351890882111594, 938853500281781750906096133654, 238545191601069021529057067313130, 122749609618842355502421774953773681], 'euler97': [1, 3021, 6979511, 11215812145, 15510026381711, 17665892352020490, 18254400207027091298, 16123182970595596669770, 12919417771675495127453519, 8526608740664079920523160465, 4842680390833630472877241904951, 1913051842382240735236736658825453, 577951262543040979328274795306257089], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -2, 81, -109, 3707, -5454, 122034, -147258, 2702403, -2145447, 43046721, -28697814, 387420489], [1, 30, 375, 2500, 9375, 18750, 15625, 0, 0, 0, 0, 0, 0], [1, -28, 1710, -44507, 1306009, -29404243, 574046808, -10085655349, 153650652841, -1796017986749, 23668601113710, -132931722278404, 1628413597910449], [1, 3, 6021, -26781, 15818535, -133642140, 25492860502, -177877688340, 28023499683135, -63148197112671, 18896477256237141, 12531744508246953, 5559917313492231481], [1, 28, 10909, 255007, 53813653, 1024588726, 152088784296, 2251021431022, 259748224623277, 2704221571610611, 254158810601145229, 1433205004394541196, 112455406951957393129], [1, -24, 18030, -427891, 167973547, -3346966257, 1005505976060, -16443645220641, 4054473080887243, -50742685062177827, 10504678937252590830, -68698153236235579032, 14063084452067724991009], [1, 3, 21819, -265989, 273045711, -2946473628, 2316621912986, -20209862614452, 12845676027266391, -85831378044538431, 48292318219104566859, 45543381089624394897, 104127350297911241532841], [1, 138, 7935, 243340, 4197615, 38618058, 148035889, 0, 0, 0, 0, 0, 0], [1, -76, 96138, -6141574, 4443699358, -229233487192, 131290006644110, -5590775519125688, 2643216009651127918, -89096710539601677806, 34015045627807382663658, -655818344817462017512124, 210457284365172120330305161], [1, 381, 183933, 51276809, 14163826942, 2892542918421, 570209036379841, 86171746082680011, 12570448548071973502, 1355739455564894178839, 144877178810579323190013, 8940264818892825339311331, 699053619999045038539170241], [1, -131, 244110, -26876359, 27142443903, -2479299439834, 1757009562030548, -125583954525911602, 69640085126728134327, -3492898374997075884643, 1606964414145611012444910, -43681461101687805228592583, 16890053810563300749953435929], [1, 95, 296879, 24628819, 41954508060, 3095260524119, 3616955966486841, 213328450582805599, 199288286664874682460, 8063030406058740162059, 6698626436882412957541199, 147734339924196101534417095, 107178930967531784356353269521], [1, 202, 258690, 47154510, 25742273095, 5001826335900, 1831244225314684, 397680206488401300, 162726253939999866655, 23699508345501982611930, 10337156890943855889174690, 641768213891187043706690014, 252599333573498060811820806649], [1, 119, 253739, 36692102, 49887954357, 5785025024479, 5837170895173758, 600618653116483217, 537753002337426738453, 41063249470394983246234, 29482310732581503294293099, 1435538453747623820407125817, 1252453015827223091648143056289], [1, -137, 594084, -64786529, 164474180415, -13341277950754, 29237327999867368, -1986209437474403258, 3645465131114359088535, -213780229633433051866357, 291849054876452900853743844, -10019789808796920902254877509, 10888439761782913818722623349689], [1, 39, 811376, 13330213, 323695705039, -637831310, 81542978014641968, -130997156616490, 13653657575844752716999, 115479579480779710372007, 1443598084421519097692038256, 14250981675864062604551813061, 75047496554032956760519149093721], [1, 573, 1025951, 373972257, 406395107231, 101577722520254, 101990059148671426, 23056213035369773174, 20937628063019858104391, 4373286208024915236426237, 2723231984529582816715588271, 345224927538578151378465150273, 136753052840548005895349735207881], [1, 563, 264282, -228527999, -47606117265, 28011216293194, 73923412251272732, 8424737445989907022, -4306372349139599047785, -6217454865309957251721053, 2162545317554180751878870202, 1385576265369633803527084824209, 740195513856780056217081017732809], [1, 83, 1110819, -90983595, 584388344916, -143175567191021, 221791879833116245, -51244110428905517131, 74860312903862876895636, -4171461420724575664646445, 18228187372275885183326453379, 487476094628995948370988435733, 2102085018129621311776010144838961], [1, 1799, 3398133, 3709985452, 3923214415051, 2966055630106073, 2141537576603911750, 1153846063056974200241, 593716618067594801475739, 218412730223830525348401676, 77824205234364082306156990293, 16027805558797800250750396977743, 3465863721549107204083472585375569], [1, 1636, 2299646, 2035527108, 1747092049727, 1118492713318528, 843572321238202820, 551460528881853726592, 424696160929104832692767, 243961172559683485141891452, 135889556977945340127017269886, 47663910314344589999176825129564, 14364405059580771582276370834385761], [1, 1191, 2724018, 2654381901, 3546479899927, 2693775614251522, 2624824158961399580, 1540265877146035009814, 1159487462627787135844063, 496210830150479158509446103, 291170305100252198793517946898, 72791915374145201556647258699037, 34946659039493167390823397237402409], [1, 1370, 3801174, 3684694266, 5887444836831, 4432302017051644, 5245947803892614644, 3124635520658880419036, 2925949935469944380184591, 1290956231797351890882111594, 938853500281781750906096133654, 238545191601069021529057067313130, 122749609618842355502421774953773681], [1, 3021, 6979511, 11215812145, 15510026381711, 17665892352020490, 18254400207027091298, 16123182970595596669770, 12919417771675495127453519, 8526608740664079920523160465, 4842680390833630472877241904951, 1913051842382240735236736658825453, 577951262543040979328274795306257089]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/920/4/a/b'], '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': '12-920e6-1.1-c3e6-0-0', '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}], 'nu_real_doubled': [3, 3, 3, 3, 3, 3], 'order_of_vanishing': 6, 'prelabel': '12-920e6-1.1-c3e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.367615435490738, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e6-0', 'trace_hash': 943022525766121473, 'z1': {'__RealLiteral__': 0, 'data': '1.07716987213486723413594641398', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '1365475034959529565500394021538,1452602613016722926772997064208,1738624455983782731517071705365,2028241256041127272318945459995,2132146919321229633308116493816,2381071320524965453243807748895', 'Lhash_array': ['1365475034959529565500394021538', '1452602613016722926772997064208', '1738624455983782731517071705365', '2028241256041127272318945459995', '2132146919321229633308116493816', '2381071320524965453243807748895'], 'factors': ['2-920-1.1-c3-0-34', '2-920-1.1-c3-0-35', '2-920-1.1-c3-0-48', '2-920-1.1-c3-0-55', '2-920-1.1-c3-0-58', '2-920-1.1-c3-0-64'], 'label': '12-920e6-1.1-c3e6-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/920/4/a/b'}