2018年6月14日木曜日

180614

Ruby


A305756(2)

-1728<=b<=0 のとき、f(b) > 1 となるものについて
(q*(j(q)+b))^(1/f(b)) を出力してみた。

require 'prime'

def power0(a, n)
  return 1 if n == 0
  k = power0(a, n >> 1)
  k *= k
  return k if n & 1 == 0
  return k * a
end

# x > 0
def sigma(x, i)
  sum = 1
  pq = i.prime_division
  pq.each{|a, n| sum *= (power0(a, (n + 1) * x) - 1) / (power0(a, x) - 1)}
  sum
end

def A000521(n)
  s3 = [0] + (1..n + 1).map{|i| sigma(3, i)}
  s5 = [0] + (1..n + 1).map{|i| sigma(5, i)}
  ary = [1]
  (0..n).each{|i| ary << (1..i + 1).inject(0){|s, j| s + (504 * s5[j] - 240 * (i - j) * s3[j]) * ary[-j]} / (i + 1)}
  ary
end

def A008683(n)
  ary = n.prime_division
  return (-1) ** (ary.size % 2) if ary.all?{|i| i[1] == 1}
  0
end

# ary[0] = 1
def inverse_Euler_transform(ary, n)
  c = [0]
  (1..n).each{|i| c << (1..i - 1).inject(i * ary[i]){|s, j| s - ary[j] * c[-j]}}
  m_ary = [0] + (1..n).map{|i| A008683(i)}
  a = [0]
  (1..n).each{|i|
    s = 0
    (1..i).each{|j|
      s += m_ary[i / j] * c[j] if i % j == 0
    }
    # aryの要素が整数なら、s / iは整数
    a << s / i
  }
  a
end

def A305762(n)
  n = -n if n < 0
  return 24 if n == 0
  s = 1
  s *= 3 if n % 9 == 0
  n.prime_division.each{|i|
    s *= 2 ** [3, (i[1] - 1)].min if i[0] == 2
  }
  s
end

def s(f_ary, g_ary, n)
  s = 0
  (1..n).each{|i| s += i * f_ary[i] * g_ary[i] ** (n / i) if n % i == 0}
  s
end

def A(f_ary, g_ary, n)
  ary = [1]
  a = [0] + (1..n).map{|i| s(f_ary, g_ary, i)}
  (1..n).each{|i| ary << (1..i).inject(0){|s, j| s + a[j] * ary[-j]} / i}
  ary
end

n = 5
N = -1728
a = A000521(n)
a0 = Array.new(n + 1, 1)
N.upto(0){|i|
  a[1] = 744 + i
  i_ary = inverse_Euler_transform(a, n)
  f = A305762(i)
  if f > 1
    p ['(q*(j(q)-' + (-i).to_s + '))^(1/' + f.to_s + ')' , A(i_ary.map{|j| j / f}, a0, n)]
  end
}

出力結果
["(q*(j(q)-1728))^(1/24)", [1, -41, -11128, -3785793, -1476507895, -618962022329]]
["(q*(j(q)-1724))^(1/2)", [1, -490, -21608, 158960, 276587553, 149085636778]]
["(q*(j(q)-1720))^(1/4)", [1, -244, -40083, -9440532, -2831354125, -922761308772]]
["(q*(j(q)-1719))^(1/3)", [1, -325, -39997, -7390755, -1890967644, -513025905518]]
["(q*(j(q)-1716))^(1/2)", [1, -486, -19656, 1194064, 819285921, 431766407718]]
["(q*(j(q)-1712))^(1/8)", [1, -121, -26633, -7470504, -2389119199, -784331895400]]
["(q*(j(q)-1710))^(1/3)", [1, -322, -38056, -6214728, -1216645674, -139079273096]]
["(q*(j(q)-1708))^(1/2)", [1, -482, -17720, 2205840, 1338365665, 694302663458]]
["(q*(j(q)-1704))^(1/4)", [1, -240, -37179, -7571440, -1713687669, -283666835376]]
["(q*(j(q)-1701))^(1/3)", [1, -319, -36133, -5067681, -573743964, 206655607606]]
["(q*(j(q)-1700))^(1/2)", [1, -478, -15800, 3194480, 1834291425, 937387013278]]
["(q*(j(q)-1696))^(1/8)", [1, -119, -24953, -6303016, -1655781279, -351981391976]]
["(q*(j(q)-1692))^(1/6)", [1, -158, -29596, -6650840, -1469579445, -166403151246]]
["(q*(j(q)-1688))^(1/4)", [1, -236, -34323, -5782988, -685932685, 273142608900]]
["(q*(j(q)-1684))^(1/2)", [1, -470, -12008, 5103120, 2758520353, 1367905758998]]
["(q*(j(q)-1683))^(1/3)", [1, -313, -32341, -2859447, 620561316, 817781722810]]
["(q*(j(q)-1680))^(1/8)", [1, -117, -23301, -5185508, -980507799, 25670123748]]
["(q*(j(q)-1676))^(1/2)", [1, -466, -10136, 6023504, 3187733601, 1556661022738]]
["(q*(j(q)-1674))^(1/3)", [1, -310, -30472, -1797720, 1173330006, 1085262129832]]
["(q*(j(q)-1672))^(1/4)", [1, -232, -31515, -4073832, 255429419, 753220471032]]
["(q*(j(q)-1668))^(1/2)", [1, -462, -8280, 6921520, 3595613025, 1728606331278]]
["(q*(j(q)-1665))^(1/3)", [1, -307, -28621, -763893, 1697408676, 1328709557854]]
["(q*(j(q)-1664))^(1/8)", [1, -115, -21677, -4117140, -361018999, 352317157412]]
["(q*(j(q)-1660))^(1/2)", [1, -458, -6440, 7797360, 3982604065, 1884370588298]]
["(q*(j(q)-1656))^(1/12)", [1, -76, -15361, -3002756, -232368064, 295009906344]]
["(q*(j(q)-1652))^(1/2)", [1, -454, -4616, 8651216, 4349148321, 2024570278918]]
["(q*(j(q)-1648))^(1/8)", [1, -113, -20081, -3097072, 204926241, 631514067376]]
["(q*(j(q)-1647))^(1/3)", [1, -301, -24973, 1221141, 2662154916, 1747439260258]]
["(q*(j(q)-1644))^(1/2)", [1, -450, -2808, 9483280, 4695683553, 2149809577218]]
["(q*(j(q)-1640))^(1/4)", [1, -224, -26043, -888032, 1892753675, 1504352077728]]
["(q*(j(q)-1638))^(1/3)", [1, -298, -23176, 2172888, 3104135766, 1924633932760]]
["(q*(j(q)-1636))^(1/2)", [1, -446, -1016, 10293744, 5022643681, 2260680453758]]
["(q*(j(q)-1632))^(1/8)", [1, -111, -18513, -2124464, 719530401, 866677460400]]
["(q*(j(q)-1629))^(1/3)", [1, -295, -21397, 3097815, 3520053156, 2081620850182]]
["(q*(j(q)-1628))^(1/2)", [1, -442, 760, 11082800, 5330458785, 2357762783098]]
["(q*(j(q)-1624))^(1/4)", [1, -220, -23379, 591300, 2595457331, 1785480201684]]
["(q*(j(q)-1620))^(1/6)", [1, -146, -20476, -991400, 1600896075, 1323082260702]]
["(q*(j(q)-1616))^(1/8)", [1, -109, -16973, -1198476, 1184957321, 1061088587324]]
["(q*(j(q)-1612))^(1/2)", [1, -434, 4264, 12597456, 5890355041, 2512821463538]]
["(q*(j(q)-1611))^(1/3)", [1, -289, -17893, 4868289, 4276252836, 2338561063306]]
["(q*(j(q)-1608))^(1/4)", [1, -216, -20763, 1996712, 3225251115, 2010032598600]]
["(q*(j(q)-1604))^(1/2)", [1, -430, 5992, 13323440, 6143277153, 2571898051438]]
["(q*(j(q)-1602))^(1/3)", [1, -286, -16168, 5714376, 4617796566, 2440256825608]]
["(q*(j(q)-1600))^(1/8)", [1, -107, -15461, -318268, 1603332201, 1217895738748]]
["(q*(j(q)-1596))^(1/2)", [1, -426, 7704, 14028784, 6378736161, 2619386780778]]
["(q*(j(q)-1593))^(1/3)", [1, -283, -14461, 6534723, 4935799716, 2525230193710]]
["(q*(j(q)-1592))^(1/4)", [1, -212, -18195, 3329548, 3785357939, 2182551489852]]
["(q*(j(q)-1588))^(1/2)", [1, -422, 9400, 14713680, 6597142945, 2655808658918]]
["(q*(j(q)-1584))^(1/24)", [1, -35, -5884, -225255, 615732461, 488643706669]]
["(q*(j(q)-1580))^(1/2)", [1, -418, 11080, 15378320, 6798904545, 2681673242338]]
["(q*(j(q)-1576))^(1/4)", [1, -208, -15675, 4591152, 4278941579, 2307387496176]]
["(q*(j(q)-1575))^(1/3)", [1, -277, -11101, 8099277, 5503635876, 2648268936754]]
["(q*(j(q)-1572))^(1/2)", [1, -414, 12744, 16022896, 6984424161, 2697478744158]]
["(q*(j(q)-1568))^(1/8)", [1, -103, -12521, 1308168, 2307233441, 1430640850376]]
["(q*(j(q)-1566))^(1/3)", [1, -274, -9448, 8844024, 5754678486, 2687913689656]]
["(q*(j(q)-1564))^(1/2)", [1, -410, 14392, 16647600, 7154101153, 2703712141658]]
["(q*(j(q)-1560))^(1/4)", [1, -204, -13203, 5782868, 4709106675, 2388703185828]]
["(q*(j(q)-1557))^(1/3)", [1, -271, -7813, 9564111, 5984599716, 2713995231958]]
["(q*(j(q)-1556))^(1/2)", [1, -406, 16024, 17252624, 7308331041, 2700849283798]]
["(q*(j(q)-1552))^(1/8)", [1, -101, -11093, 2056076, 2596817001, 1492232151700]]
["(q*(j(q)-1548))^(1/6)", [1, -134, -12076, 3511720, 3494649675, 1874317586250]]
["(q*(j(q)-1544))^(1/4)", [1, -200, -10779, 6906040, 5078898731, 2430476622744]]
["(q*(j(q)-1540))^(1/2)", [1, -398, 19240, 18404400, 7572012385, 2669683201358]]
["(q*(j(q)-1539))^(1/3)", [1, -265, -4597, 10931385, 6383425956, 2728411105882]]
["(q*(j(q)-1536))^(1/8)", [1, -99, -9693, 2761564, 2847462921, 1527530951124]]
["(q*(j(q)-1532))^(1/2)", [1, -394, 20824, 18951536, 7682235681, 2642277000778]]
["(q*(j(q)-1530))^(1/3)", [1, -262, -3016, 11579112, 6553488726, 2718168569704]]
["(q*(j(q)-1528))^(1/4)", [1, -196, -8403, 7962012, 5391304115, 2436504914700]]
["(q*(j(q)-1524))^(1/2)", [1, -390, 22392, 19479760, 7778555553, 2607568807878]]
["(q*(j(q)-1521))^(1/3)", [1, -259, -1453, 12203259, 6704745636, 2697209515006]]
["(q*(j(q)-1520))^(1/8)", [1, -97, -8321, 3425472, 3061103201, 1539056673248]]
["(q*(j(q)-1516))^(1/2)", [1, -386, 23944, 19989264, 7861348321, 2565980442818]]
["(q*(j(q)-1512))^(1/12)", [1, -64, -6121, 2287936, 2163544136, 1101438294912]]
["(q*(j(q)-1508))^(1/2)", [1, -382, 25480, 20480240, 7930986465, 2517923242558]]
["(q*(j(q)-1504))^(1/8)", [1, -95, -6977, 4048640, 3239631201, 1529210156512]]
["(q*(j(q)-1503))^(1/3)", [1, -253, 1619, 13381893, 6953086116, 2625781188610]]
["(q*(j(q)-1500))^(1/2)", [1, -378, 27000, 20952880, 7987838625, 2463798168378]]
["(q*(j(q)-1496))^(1/4)", [1, -188, -3795, 9877732, 5855604659, 2355631002996]]
["(q*(j(q)-1494))^(1/3)", [1, -250, 3128, 13936920, 7051275606, 2576585646232]]
["(q*(j(q)-1492))^(1/2)", [1, -374, 28504, 21407376, 8032269601, 2403995913398]]
["(q*(j(q)-1488))^(1/8)", [1, -93, -5661, 4631908, 3384901641, 1500276048876]]
["(q*(j(q)-1485))^(1/3)", [1, -247, 4619, 14469447, 7132871076, 2519221471654]]
["(q*(j(q)-1484))^(1/2)", [1, -370, 29992, 21843920, 8064640353, 2338897010098]]
["(q*(j(q)-1480))^(1/4)", [1, -184, -1563, 10740168, 6013176875, 2275450167528]]
["(q*(j(q)-1476))^(1/6)", [1, -122, -4396, 6953560, 4437876555, 1799129065398]]
["(q*(j(q)-1472))^(1/8)", [1, -91, -4373, 5176116, 3498730601, 1454425203500]]
["(q*(j(q)-1468))^(1/2)", [1, -362, 32920, 22663920, 8094625825, 2194281230378]]
["(q*(j(q)-1467))^(1/3)", [1, -241, 7547, 15468081, 7248420516, 2382337167658]]
["(q*(j(q)-1464))^(1/4)", [1, -180, 621, 11540780, 6124716531, 2172974019804]]
["(q*(j(q)-1460))^(1/2)", [1, -358, 34360, 23047760, 8092943265, 2115475583398]]
["(q*(j(q)-1458))^(1/3)", [1, -238, 8984, 15934728, 7283428566, 2303948207560]]
["(q*(j(q)-1456))^(1/8)", [1, -89, -3113, 5682104, 3582895521, 1393717074424]]
["(q*(j(q)-1452))^(1/2)", [1, -354, 35784, 23414416, 8080605921, 2032795962018]]
["(q*(j(q)-1449))^(1/3)", [1, -235, 10403, 16379955, 7303950756, 2219653381582]]
["(q*(j(q)-1448))^(1/4)", [1, -176, 2757, 12280912, 6192914315, 2051148109200]]
["(q*(j(q)-1444))^(1/2)", [1, -350, 37192, 23764080, 8057955553, 1946573708318]]
["(q*(j(q)-1440))^(1/24)", [1, -29, -1468, 1973223, 1326571565, 521171586067]]
["(q*(j(q)-1436))^(1/2)", [1, -346, 38584, 24096944, 8025330081, 1857130648858]]
["(q*(j(q)-1432))^(1/4)", [1, -172, 4845, 12961908, 6220401779, 1912758317892]]
["(q*(j(q)-1431))^(1/3)", [1, -229, 13187, 17207229, 7303574436, 2035420362706]]
["(q*(j(q)-1428))^(1/2)", [1, -342, 39960, 24413200, 7983063585, 1764779202198]]
["(q*(j(q)-1424))^(1/8)", [1, -85, -677, 6582780, 3669149801, 1235424159812]]
["(q*(j(q)-1422))^(1/3)", [1, -226, 14552, 17589816, 7283678166, 1936477622008]]
["(q*(j(q)-1420))^(1/2)", [1, -338, 41320, 24713040, 7931486305, 1669822486418]]
["(q*(j(q)-1416))^(1/4)", [1, -168, 6885, 13585112, 6209751339, 1760434409016]]
["(q*(j(q)-1413))^(1/3)", [1, -223, 15899, 17952063, 7251300516, 1833620347510]]
["(q*(j(q)-1412))^(1/2)", [1, -334, 42664, 24996656, 7870924641, 1572554426638]]
["(q*(j(q)-1408))^(1/8)", [1, -83, 499, 6979148, 3674600841, 1141422847876]]
["(q*(j(q)-1404))^(1/6)", [1, -110, 2564, 9429160, 4637383755, 1349588629026]]
["(q*(j(q)-1400))^(1/4)", [1, -164, 8877, 14151868, 6163476275, 1596653574828]]
["(q*(j(q)-1396))^(1/2)", [1, -326, 45304, 25515984, 7724134561, 1372214655878]]
["(q*(j(q)-1395))^(1/3)", [1, -217, 18539, 18616617, 7151034276, 1617974402554]]
["(q*(j(q)-1392))^(1/8)", [1, -81, 1647, 7340656, 3657111201, 1039735990800]]
["(q*(j(q)-1388))^(1/2)", [1, -322, 46600, 25752080, 7638539745, 1269685798018]]
["(q*(j(q)-1386))^(1/3)", [1, -214, 19832, 18919464, 7084096086, 1506052310056]]
["(q*(j(q)-1384))^(1/4)", [1, -160, 10821, 14663520, 6084030731, 1423743984864]]
["(q*(j(q)-1380))^(1/2)", [1, -318, 47880, 25972720, 7545227745, 1165931517438]]
["(q*(j(q)-1377))^(1/3)", [1, -211, 21107, 19203051, 7006577316, 1391949267358]]
["(q*(j(q)-1376))^(1/8)", [1, -79, 2767, 7668144, 3618265121, 931901982224]]
["(q*(j(q)-1372))^(1/2)", [1, -314, 49144, 26178096, 7444505761, 1061201387258]]
["(q*(j(q)-1368))^(1/12)", [1, -52, 1535, 5246980, 2530448960, 647622597720]]
["(q*(j(q)-1364))^(1/2)", [1, -310, 50392, 26368400, 7336677153, 955736432758]]
["(q*(j(q)-1360))^(1/8)", [1, -77, 3859, 7962452, 3559608201, 819362190748]]
["(q*(j(q)-1359))^(1/3)", [1, -205, 23603, 19713525, 6821627556, 1158764197282]]
["(q*(j(q)-1356))^(1/2)", [1, -306, 51624, 26543824, 7222041441, 849769238898]]
["(q*(j(q)-1352))^(1/4)", [1, -152, 14565, 15526888, 5835149099, 1059127391112]]
["(q*(j(q)-1350))^(1/3)", [1, -202, 24824, 19940952, 6715095126, 1040426716504]]
["(q*(j(q)-1348))^(1/2)", [1, -302, 52840, 26704560, 7100894305, 743524057838]]
["(q*(j(q)-1344))^(1/8)", [1, -75, 4923, 8224420, 3482647401, 703463355612]]
["(q*(j(q)-1341))^(1/3)", [1, -199, 26027, 20150199, 6599779236, 921397806406]]
["(q*(j(q)-1340))^(1/2)", [1, -298, 54040, 26850800, 6973527585, 637216916458]]
["(q*(j(q)-1336))^(1/4)", [1, -148, 16365, 15881292, 5670325619, 871363546236]]
["(q*(j(q)-1332))^(1/6)", [1, -98, 8804, 11033560, 4280590155, 723365031054]]
["(q*(j(q)-1328))^(1/8)", [1, -73, 5959, 8454888, 3388851041, 585459982376]]
["(q*(j(q)-1324))^(1/2)", [1, -290, 56392, 27100560, 6701283553, 425240378978]]
["(q*(j(q)-1323))^(1/3)", [1, -193, 28379, 20515233, 6344522916, 682594910410]]
["(q*(j(q)-1320))^(1/4)", [1, -144, 18117, 16185968, 5481556875, 682364359728]]
["(q*(j(q)-1316))^(1/2)", [1, -286, 57544, 27204464, 6556970721, 319962877918]]
["(q*(j(q)-1314))^(1/3)", [1, -190, 29528, 20671560, 6205429206, 563450282632]]
["(q*(j(q)-1312))^(1/8)", [1, -71, 6967, 8654696, 3279648801, 466516738600]]
["(q*(j(q)-1308))^(1/2)", [1, -282, 58680, 27294640, 6407567265, 215407421658]]
["(q*(j(q)-1305))^(1/3)", [1, -187, 30659, 20810787, 6059245476, 444873369454]]
["(q*(j(q)-1304))^(1/4)", [1, -140, 19821, 16442260, 5271001331, 493766109924]]
["(q*(j(q)-1300))^(1/2)", [1, -278, 59800, 27371280, 6253345825, 111750523478]]
["(q*(j(q)-1296))^(1/24)", [1, -23, 2120, 3043137, 1186512329, 156073834489]]
["(q*(j(q)-1292))^(1/2)", [1, -274, 60904, 27434576, 6094575201, 9161116498]]
["(q*(j(q)-1288))^(1/4)", [1, -136, 21477, 16651512, 5040758315, 307077341400]]
["(q*(j(q)-1287))^(1/3)", [1, -181, 32867, 21039021, 5747230116, 210530931058]]
["(q*(j(q)-1284))^(1/2)", [1, -270, 61992, 27484720, 5931520353, -92199338802]]
["(q*(j(q)-1280))^(1/8)", [1, -67, 8899, 8965692, 3020552201, 230034493748]]
["(q*(j(q)-1278))^(1/3)", [1, -178, 33944, 21128568, 5582193366, 95286418360]]
["(q*(j(q)-1276))^(1/2)", [1, -266, 63064, 27521904, 5764442401, -192176747062]]
["(q*(j(q)-1272))^(1/4)", [1, -132, 23085, 16815068, 4792868019, 123682413132]]
["(q*(j(q)-1269))^(1/3)", [1, -175, 35003, 21202095, 5411656356, -18347927018]]
["(q*(j(q)-1268))^(1/2)", [1, -262, 64120, 27546320, 5593598625, -290624270522]]
["(q*(j(q)-1264))^(1/8)", [1, -65, 9823, 9078560, 2873324001, 114397198912]]
["(q*(j(q)-1260))^(1/6)", [1, -86, 14324, 11861800, 3535526475, 69074980602]]
["(q*(j(q)-1256))^(1/4)", [1, -128, 24645, 16934272, 4529311499, -55154953344]]
["(q*(j(q)-1252))^(1/2)", [1, -254, 66184, 27557616, 5241623521, -482377954882]]
["(q*(j(q)-1251))^(1/3)", [1, -169, 37067, 21302169, 5055600036, -239885153894]]
["(q*(j(q)-1248))^(1/8)", [1, -63, 10719, 9164128, 2716022241, 1628237376]]
["(q*(j(q)-1244))^(1/2)", [1, -250, 67192, 27544880, 5060987553, -575425760582]]
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["(q*(j(q)-144))^(1/24)", [1, 25, 1016, -1006335, 269179961, -23230708151]]
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["(q*(j(q)-132))^(1/2)", [1, 306, 51624, -5050064, 644950881, 73472462478]]
["(q*(j(q)-128))^(1/8)", [1, 77, 3859, -2589012, 663324041, -67397940124]]
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["(q*(j(q)-124))^(1/2)", [1, 310, 50392, -4874640, 673611553, 46946205578]]
["(q*(j(q)-120))^(1/4)", [1, 156, 12717, -4374532, 944269875, -74553194772]]
["(q*(j(q)-117))^(1/3)", [1, 209, 21947, -5052369, 959652516, -52594116842]]
["(q*(j(q)-116))^(1/2)", [1, 314, 49144, -4684336, 695465121, 21953888518]]
["(q*(j(q)-112))^(1/8)", [1, 79, 2767, -2294704, 646752801, -91920784400]]
["(q*(j(q)-108))^(1/6)", [1, 106, 4724, -2891480, 774336075, -107141358150]]
["(q*(j(q)-104))^(1/4)", [1, 160, 10821, -3916640, 925528331, -111776254176]]
["(q*(j(q)-100))^(1/2)", [1, 322, 46600, -4258320, 717549025, -22490145922]]
["(q*(j(q)-99))^(1/3)", [1, 215, 19403, -4491495, 946062756, -99084482918]]
["(q*(j(q)-96))^(1/8)", [1, 81, 1647, -1967216, 610370721, -109481000976]]
["(q*(j(q)-92))^(1/2)", [1, 326, 45304, -4022224, 717168801, -41451264902]]
["(q*(j(q)-90))^(1/3)", [1, 218, 18104, -4182168, 923395926, -117121263896]]
["(q*(j(q)-88))^(1/4)", [1, 164, 8877, -3404988, 876011315, -138442301100]]
["(q*(j(q)-84))^(1/2)", [1, 330, 43992, -3770480, 708760353, -57897032202]]
["(q*(j(q)-81))^(1/3)", [1, 221, 16787, -3853221, 889526436, -131137401794]]
["(q*(j(q)-80))^(1/8)", [1, 83, 499, -1605708, 552632201, -118637221252]]
["(q*(j(q)-76))^(1/2)", [1, 334, 42664, -3502896, 692008801, -71560456462]]
["(q*(j(q)-72))^(1/12)", [1, 56, -841, -910424, 368338856, -90759349968]]
["(q*(j(q)-68))^(1/2)", [1, 338, 41320, -3219280, 666595425, -82165675922]]
["(q*(j(q)-64))^(1/8)", [1, 85, -677, -1209340, 471953001, -117851051588]]
["(q*(j(q)-63))^(1/3)", [1, 227, 14099, -3135387, 786276516, -145369388990]]
["(q*(j(q)-60))^(1/2)", [1, 342, 39960, -2919440, 632197665, -89427850902]]
["(q*(j(q)-56))^(1/4)", [1, 172, 4845, -2215028, 675011699, -151227103044]]
["(q*(j(q)-54))^(1/3)", [1, 230, 12728, -2745960, 715928406, -144676462568]]
["(q*(j(q)-52))^(1/2)", [1, 346, 38584, -2603184, 588489121, -93053056282]]
["(q*(j(q)-48))^(1/8)", [1, 87, -1881, -777272, 366710241, -105484677624]]
["(q*(j(q)-45))^(1/3)", [1, 233, 11339, -2335833, 632442276, -138144913946]]
["(q*(j(q)-44))^(1/2)", [1, 350, 37192, -2270320, 535139553, -92738173982]]
["(q*(j(q)-40))^(1/4)", [1, 176, 2757, -1534032, 518561675, -132540496272]]
["(q*(j(q)-36))^(1/6)", [1, 118, -1996, -716840, 350254155, -105400701402]]
["(q*(j(q)-32))^(1/8)", [1, 89, -3113, -308664, 235242401, -79798468600]]
["(q*(j(q)-28))^(1/2)", [1, 358, 34360, -1554000, 398177185, -79029064102]]
["(q*(j(q)-27))^(1/3)", [1, 239, 8507, -1452399, 424049316, -105569557142]]
["(q*(j(q)-24))^(1/4)", [1, 180, 621, -793900, 321401331, -93679057116]]
["(q*(j(q)-20))^(1/2)", [1, 362, 32920, -1170160, 313884705, -64981667882]]
["(q*(j(q)-18))^(1/3)", [1, 242, 7064, -978552, 298122966, -78485818040]]
["(q*(j(q)-16))^(1/8)", [1, 91, -4373, 197324, 75849321, -38948581676]]
["(q*(j(q)-12))^(1/2)", [1, 366, 31464, -768944, 218591841, -45687631662]]
["(q*(j(q)-9))^(1/3)", [1, 245, 5603, -482925, 157019556, -43483167218]]
["(q*(j(q)-8))^(1/4)", [1, 184, -1563, 6712, 80899115, -31856903400]]
["(q*(j(q)-4))^(1/2)", [1, 370, 29992, -350160, 111949153, -20796259762]]
["(q*(j(q)-0))^(1/24)", [1, 31, -2848, 413823, -68767135, 12310047967]]

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