(12:10) gp > (12:10) gp > \rread ? k=nfinit(x^3+x^2-2*x-1);forprime(i=2,32,a=idealprincipal(k,i);print(i," ",idealfactor(k,a))) 2 Mat([[2, [2, 0, 0]~, 1, 3, [1, 0, 0]~], 1]) 3 Mat([[3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 1]) 5 Mat([[5, [5, 0, 0]~, 1, 3, [1, 0, 0]~], 1]) 7 Mat([[7, [-2, 1, 0]~, 3, 1, [-3, 3, 1]~], 3]) 11 Mat([[11, [11, 0, 0]~, 1, 3, [1, 0, 0]~], 1]) 13 [[13, [5, 1, 0]~, 1, 1, [5, -4, 1]~], 1; [13, [19, 1, 0]~, 1, 1, [2, -5, 1]~], 1; [13, [3, 1, 0]~, 1, 1, [4, -2, 1]~], 1] 17 Mat([[17, [17, 0, 0]~, 1, 3, [1, 0, 0]~], 1]) 19 Mat([[19, [19, 0, 0]~, 1, 3, [1, 0, 0]~], 1]) 23 Mat([[23, [23, 0, 0]~, 1, 3, [1, 0, 0]~], 1]) 29 [[29, [-7, 1, 0]~, 1, 1, [-4, 8, 1]~], 1; [29, [-3, 1, 0]~, 1, 1, [10, 4, 1]~], 1; [29, [11, 1, 0]~, 1, 1, [-8, -10, 1]~], 1] 31 Mat([[31, [31, 0, 0]~, 1, 3, [1, 0, 0]~], 1]) (12:10) gp > (12:10) gp > \rread ? k=nfinit(x^3+x^2-2*x-1);print("k=nfinit(x^3+x^2-2*x-1)");forprime(i=2,32,a=idealprincipal(k,i);print(i," ",idealfactor(k,a))) k=nfinit(x^3+x^2-2*x-1) 2 Mat([[2, [2, 0, 0]~, 1, 3, [1, 0, 0]~], 1]) 3 Mat([[3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 1]) 5 Mat([[5, [5, 0, 0]~, 1, 3, [1, 0, 0]~], 1]) 7 Mat([[7, [-2, 1, 0]~, 3, 1, [-3, 3, 1]~], 3]) 11 Mat([[11, [11, 0, 0]~, 1, 3, [1, 0, 0]~], 1]) 13 [[13, [5, 1, 0]~, 1, 1, [5, -4, 1]~], 1; [13, [19, 1, 0]~, 1, 1, [2, -5, 1]~], 1; [13, [3, 1, 0]~, 1, 1, [4, -2, 1]~], 1] 17 Mat([[17, [17, 0, 0]~, 1, 3, [1, 0, 0]~], 1]) 19 Mat([[19, [19, 0, 0]~, 1, 3, [1, 0, 0]~], 1]) 23 Mat([[23, [23, 0, 0]~, 1, 3, [1, 0, 0]~], 1]) 29 [[29, [-7, 1, 0]~, 1, 1, [-4, 8, 1]~], 1; [29, [-3, 1, 0]~, 1, 1, [10, 4, 1]~], 1; [29, [11, 1, 0]~, 1, 1, [-8, -10, 1]~], 1] 31 Mat([[31, [31, 0, 0]~, 1, 3, [1, 0, 0]~], 1]) (12:11) gp > (12:11) gp > \rread ? k=nfinit(x^2-2);print("k=nfinit(x^2-2)");forprime(i=2,32,a=idealprincipal(k,i);print(i," ",idealfactor(k,a))) k=nfinit(x^2-2) 2 Mat([[2, [0, 1]~, 2, 1, [0, 1]~], 2]) 3 Mat([[3, [3, 0]~, 1, 2, [1, 0]~], 1]) 5 Mat([[5, [5, 0]~, 1, 2, [1, 0]~], 1]) 7 [[7, [-3, 1]~, 1, 1, [3, 1]~], 1; [7, [3, 1]~, 1, 1, [-3, 1]~], 1] 11 Mat([[11, [11, 0]~, 1, 2, [1, 0]~], 1]) 13 Mat([[13, [13, 0]~, 1, 2, [1, 0]~], 1]) 17 [[17, [-6, 1]~, 1, 1, [6, 1]~], 1; [17, [6, 1]~, 1, 1, [-6, 1]~], 1] 19 Mat([[19, [19, 0]~, 1, 2, [1, 0]~], 1]) 23 [[23, [-5, 1]~, 1, 1, [5, 1]~], 1; [23, [5, 1]~, 1, 1, [-5, 1]~], 1] 29 Mat([[29, [29, 0]~, 1, 2, [1, 0]~], 1]) 31 [[31, [-8, 1]~, 1, 1, [8, 1]~], 1; [31, [8, 1]~, 1, 1, [-8, 1]~], 1] (12:12) gp > (12:12) gp > \rread ? k=nfinit(x^5+x^4-4*x^3-3*x^2+3*x+1);print("k=nfinit(x^5 + x^4 - 4*x^3 - 3*x^2 + 3*x + 1 )");forprime(i=2,32,a=idealprincipal(k,i);print(i," ",idealfactor(k,a))) k=nfinit(x^5 + x^4 - 4*x^3 - 3*x^2 + 3*x + 1 ) 2 Mat([[2, [2, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~], 1]) 3 Mat([[3, [3, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~], 1]) 5 Mat([[5, [5, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~], 1]) 7 Mat([[7, [7, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~], 1]) 11 Mat([[11, [-2, 1, 0, 0, 0]~, 5, 1, [5, 1, 2, 3, 1]~], 5]) 13 Mat([[13, [13, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~], 1]) 17 Mat([[17, [17, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~], 1]) 19 Mat([[19, [19, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~], 1]) 23 [[23, [-11, 1, 0, 0, 0]~, 1, 1, [2, 2, -10, -11, 1]~], 1; [23, [-10, 1, 0, 0, 0]~, 1, 1, [-7, -1, -9, 11, 1]~], 1; [23, [-6, 1, 0, 0, 0]~, 1, 1, [-4, -5, -8, 7, 1]~], 1; [23, [-4, 1, 0, 0, 0]~, 1, 1, [-6, -8, -7, 5, 1]~], 1; [23, [9, 1, 0, 0, 0]~, 1, 1, [-5, 6, -1, -8, 1]~], 1] 29 Mat([[29, [29, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~], 1]) 31 Mat([[31, [31, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~], 1]) (12:12) gp > (12:12) gp > \rread ? k=nfinit(x^2-3);print("k=nfinit(x^2-3)");forprime(i=2,32,a=idealprincipal(k,i);print(i," ",idealfactor(k,a))) k=nfinit(x^2-3) 2 Mat([[2, [1, 1]~, 2, 1, [1, 1]~], 2]) 3 Mat([[3, [0, 1]~, 2, 1, [0, 1]~], 2]) 5 Mat([[5, [5, 0]~, 1, 2, [1, 0]~], 1]) 7 Mat([[7, [7, 0]~, 1, 2, [1, 0]~], 1]) 11 [[11, [-5, 1]~, 1, 1, [5, 1]~], 1; [11, [5, 1]~, 1, 1, [-5, 1]~], 1] 13 [[13, [-4, 1]~, 1, 1, [4, 1]~], 1; [13, [4, 1]~, 1, 1, [-4, 1]~], 1] 17 Mat([[17, [17, 0]~, 1, 2, [1, 0]~], 1]) 19 Mat([[19, [19, 0]~, 1, 2, [1, 0]~], 1]) 23 [[23, [-7, 1]~, 1, 1, [7, 1]~], 1; [23, [7, 1]~, 1, 1, [-7, 1]~], 1] 29 Mat([[29, [29, 0]~, 1, 2, [1, 0]~], 1]) 31 Mat([[31, [31, 0]~, 1, 2, [1, 0]~], 1]) (12:13) gp > (12:13) gp > \l log = 0 (off) (13:11) gp > (13:11) gp > ******************************************************* *** unexpected character: ******************** ^------------------- (13:11) gp > (13:11) gp > \p180 realprecision = 183 significant digits (180 digits displayed) (13:11) gp > (13:11) gp > \rread1 ? L=[8,12,13,17,21,24,28,29,33,37,40,41,44];for(i=1,13,k=zetakinit(x^2-L[i]);print("k=zetakinit(x^2-",L[i],")");for(j=1,12,a=round(zetak(k,1-2*j)*(6*j)!)/(6*j)!;print("z(1-",2*j,")=",a," ",factor(denominator(a))))) k=zetakinit(x^2-8) z(1-2)=1/12 [2, 2; 3, 1] z(1-4)=11/120 [2, 3; 3, 1; 5, 1] z(1-6)=361/252 [2, 2; 3, 2; 7, 1] z(1-8)=24611/240 [2, 4; 3, 1; 5, 1] z(1-10)=2873041/132 [2, 2; 3, 1; 11, 1] z(1-12)=27233033477/2520 [2, 3; 3, 2; 5, 1; 7, 1] z(1-14)=129570724921/12 [2, 2; 3, 1] z(1-16)=159549339299844787/8160 [2, 5; 3, 1; 5, 1; 17, 1] z(1-18)=853244674392953815867/14364 [2, 2; 3, 3; 7, 1; 19, 1] z(1-20)=1883014201750720442753521/6600 [2, 3; 3, 1; 5, 2; 11, 1] z(1-22)=570397367814021408569126923/276 [2, 2; 3, 1; 23, 1] z(1-24)=109511675519893842297200129361077/5040 [2, 4; 3, 2; 5, 1; 7, 1] k=zetakinit(x^2-12) z(1-2)=1/6 [2, 1; 3, 1] z(1-4)=23/60 [2, 2; 3, 1; 5, 1] z(1-6)=1681/126 [2, 1; 3, 2; 7, 1] z(1-8)=257543/120 [2, 3; 3, 1; 5, 1] z(1-10)=67637281/66 [2, 1; 3, 1; 11, 1] z(1-12)=18752521534133/16380 [2, 2; 3, 2; 5, 1; 7, 1; 13, 1] z(1-14)=15442193173681/6 [2, 1; 3, 1] z(1-16)=42783818174313146311/4080 [2, 4; 3, 1; 5, 1; 17, 1] z(1-18)=514802473837215246476827/7182 [2, 1; 3, 3; 7, 1; 19, 1] z(1-20)=2556248976935265966594188533/3300 [2, 2; 3, 1; 5, 2; 11, 1] z(1-22)=1742246443991808605483768362723/138 [2, 1; 3, 1; 23, 1] z(1-24)=9784043347352101537435984662493577693/32760 [2, 3; 3, 2; 5, 1; 7, 1; 13, 1] k=zetakinit(x^2-13) z(1-2)=1/6 [2, 1; 3, 1] z(1-4)=29/60 [2, 2; 3, 1; 5, 1] z(1-6)=33463/1638 [2, 1; 3, 2; 7, 1; 13, 1] z(1-8)=467669/120 [2, 3; 3, 1; 5, 1] z(1-10)=144547171/66 [2, 1; 3, 1; 11, 1] z(1-12)=47067236077919/16380 [2, 2; 3, 2; 5, 1; 7, 1; 13, 1] z(1-14)=45495767916691/6 [2, 1; 3, 1] z(1-16)=147939984968716630933/4080 [2, 4; 3, 1; 5, 1; 17, 1] z(1-18)=27159338094720360855345181/93366 [2, 1; 3, 3; 7, 1; 13, 1; 19, 1] z(1-20)=12174855335880619308295189279/3300 [2, 2; 3, 1; 5, 2; 11, 1] z(1-22)=9738560526887500711761231871273/138 [2, 1; 3, 1; 23, 1] z(1-24)=64184156678679131455067913889018026839/32760 [2, 3; 3, 2; 5, 1; 7, 1; 13, 1] k=zetakinit(x^2-17) z(1-2)=1/3 Mat([3, 1]) z(1-4)=41/30 [2, 1; 3, 1; 5, 1] z(1-6)=5791/63 [3, 2; 7, 1] z(1-8)=29950897/1020 [2, 2; 3, 1; 5, 1; 17, 1] z(1-10)=926010751/33 [3, 1; 11, 1] z(1-12)=514888471736531/8190 [2, 1; 3, 2; 5, 1; 7, 1; 13, 1] z(1-14)=850783423272511/3 Mat([3, 1]) z(1-16)=4730479106306885224897/2040 [2, 3; 3, 1; 5, 1; 17, 1] z(1-18)=114234320679904116390875557/3591 [3, 3; 7, 1; 19, 1] z(1-20)=1138395679632849871290948246451/1650 [2, 1; 3, 1; 5, 2; 11, 1] z(1-22)=1557165289072064053256624254503373/69 [3, 1; 23, 1] z(1-24)=298351132018971004567540400687875435236427/278460 [2, 2; 3, 2; 5, 1; 7, 1; 13, 1; 17, 1] k=zetakinit(x^2-21) z(1-2)=1/3 Mat([3, 1]) z(1-4)=77/30 [2, 1; 3, 1; 5, 1] z(1-6)=17971/63 [3, 2; 7, 1] z(1-8)=8529317/60 [2, 2; 3, 1; 5, 1] z(1-10)=6880084771/33 [3, 1; 11, 1] z(1-12)=5846032490154287/8190 [2, 1; 3, 2; 5, 1; 7, 1; 13, 1] z(1-14)=14745725203342771/3 Mat([3, 1]) z(1-16)=125121710284290710090149/2040 [2, 3; 3, 1; 5, 1; 17, 1] z(1-18)=4610784503383205352814427857/3591 [3, 3; 7, 1; 19, 1] z(1-20)=70115605861717430419952533689007/1650 [2, 1; 3, 1; 5, 2; 11, 1] z(1-22)=146351620074764895131354655029032393/69 [3, 1; 23, 1] z(1-24)=2516995799150646956921735521465227682859207/16380 [2, 2; 3, 2; 5, 1; 7, 1; 13, 1] k=zetakinit(x^2-24) z(1-2)=1/2 Mat([2, 1]) z(1-4)=87/20 [2, 2; 5, 1] z(1-6)=3623/6 [2, 1; 3, 1] z(1-8)=15540167/40 [2, 3; 5, 1] z(1-10)=16324877601/22 [2, 1; 11, 1] z(1-12)=2586338303951011/780 [2, 2; 3, 1; 5, 1; 13, 1] z(1-14)=59633825180769841/2 Mat([2, 1]) z(1-16)=660880926452517181569159/1360 [2, 4; 5, 1; 17, 1] z(1-18)=4544082991633386942201552461/342 [2, 1; 3, 2; 19, 1] z(1-20)=631781365642564377262812035249077/1100 [2, 2; 5, 2; 11, 1] z(1-22)=1722396914545775335671336811132998243/46 [2, 1; 23, 1] z(1-24)=5527184623827320720804884942579502766150331/1560 [2, 3; 3, 1; 5, 1; 13, 1] k=zetakinit(x^2-28) z(1-2)=2/3 Mat([3, 1]) z(1-4)=113/15 [3, 1; 5, 1] z(1-6)=88922/63 [3, 2; 7, 1] z(1-8)=37040933/30 [2, 1; 3, 1; 5, 1] z(1-10)=105911461682/33 [3, 1; 11, 1] z(1-12)=79934365069116923/4095 [3, 2; 5, 1; 7, 1; 13, 1] z(1-14)=716746659547868042/3 Mat([3, 1]) z(1-16)=5405796972572907220684141/1020 [2, 2; 3, 1; 5, 1; 17, 1] z(1-18)=708279012827664384120281835734/3591 [3, 3; 7, 1; 19, 1] z(1-20)=9573934977162438600250268080336723/825 [3, 1; 5, 2; 11, 1] z(1-22)=71052681874089832775706165545667272846/69 [3, 1; 23, 1] z(1-24)=1086207585206051133826593793036434968608347383/8190 [2, 1; 3, 2; 5, 1; 7, 1; 13, 1] k=zetakinit(x^2-29) z(1-2)=1/2 Mat([2, 1]) z(1-4)=157/20 [2, 2; 5, 1] z(1-6)=23537/14 [2, 1; 7, 1] z(1-8)=63987797/40 [2, 3; 5, 1] z(1-10)=8949528841/2 Mat([2, 1]) z(1-12)=53174446765203189/1820 [2, 2; 5, 1; 7, 1; 13, 1] z(1-14)=22252831377375190439/58 [2, 1; 29, 1] z(1-16)=12416846206191477000121109/1360 [2, 4; 5, 1; 17, 1] z(1-18)=290863760930388381994829535259/798 [2, 1; 3, 1; 7, 1; 19, 1] z(1-20)=2300464090518383947383826818643517/100 [2, 2; 5, 2] z(1-22)=100727578431619526478496202457697853993/46 [2, 1; 23, 1] z(1-24)=1101208363970191358787380920063859644073436829/3640 [2, 3; 5, 1; 7, 1; 13, 1] k=zetakinit(x^2-33) z(1-2)=1 matrix(0,2,j,k,0) z(1-4)=141/10 [2, 1; 5, 1] z(1-6)=74231/21 [3, 1; 7, 1] z(1-8)=84995021/20 [2, 2; 5, 1] z(1-10)=168313830831/11 Mat([11, 1]) z(1-12)=352647202814176591/2730 [2, 1; 3, 1; 5, 1; 7, 1; 13, 1] z(1-14)=2195713162447871431 matrix(0,2,j,k,0) z(1-16)=46003584335372550090866877/680 [2, 3; 5, 1; 17, 1] z(1-18)=4186134456578519540954338663877/1197 [3, 2; 7, 1; 19, 1] z(1-20)=157195404294629240579806320132627871/550 [2, 1; 5, 2; 11, 1] z(1-22)=810235667276450560661104858483703801973/23 Mat([23, 1]) z(1-24)=34410061486343846835304341132900205543844899231/5460 [2, 2; 3, 1; 5, 1; 7, 1; 13, 1] k=zetakinit(x^2-37) z(1-2)=5/6 [2, 1; 3, 1] z(1-4)=1129/60 [2, 2; 3, 1; 5, 1] z(1-6)=115865/18 [2, 1; 3, 2] z(1-8)=1193648689/120 [2, 3; 3, 1; 5, 1] z(1-10)=2988574807055/66 [2, 1; 3, 1; 11, 1] z(1-12)=1126138824426408037/2340 [2, 2; 3, 2; 5, 1; 13, 1] z(1-14)=61724704374047728655/6 [2, 1; 3, 1] z(1-16)=1625886902325466618525254353/4080 [2, 4; 3, 1; 5, 1; 17, 1] z(1-18)=983107522010748251749534394373935/37962 [2, 1; 3, 3; 19, 1; 37, 1] z(1-20)=8780152495032015611104972776926106659/3300 [2, 2; 3, 1; 5, 2; 11, 1] z(1-22)=56891811270123946109776919715889222866365/138 [2, 1; 3, 1; 23, 1] z(1-24)=433911874930178370627361990523141469876914594077/4680 [2, 3; 3, 2; 5, 1; 13, 1] k=zetakinit(x^2-40) z(1-2)=7/6 [2, 1; 3, 1] z(1-4)=1577/60 [2, 2; 3, 1; 5, 1] z(1-6)=1264807/126 [2, 1; 3, 2; 7, 1] z(1-8)=2150342537/120 [2, 3; 3, 1; 5, 1] z(1-10)=6273958190407/66 [2, 1; 3, 1; 11, 1] z(1-12)=19327071911053422827/16380 [2, 2; 3, 2; 5, 1; 7, 1; 13, 1] z(1-14)=176836590584822968807/6 [2, 1; 3, 1] z(1-16)=5443774185448827969118891369/4080 [2, 4; 3, 1; 5, 1; 17, 1] z(1-18)=727811089794971859689502345571069/7182 [2, 1; 3, 3; 7, 1; 19, 1] z(1-20)=40154912568352747611033023042162274187/3300 [2, 2; 3, 1; 5, 2; 11, 1] z(1-22)=304090330290887531809755216310777086459781/138 [2, 1; 3, 1; 23, 1] z(1-24)=18974436285039855244365922390662114802894020172307/32760 [2, 3; 3, 2; 5, 1; 7, 1; 13, 1] k=zetakinit(x^2-41) z(1-2)=4/3 Mat([3, 1]) z(1-4)=448/15 [3, 1; 5, 1] z(1-6)=733924/63 [3, 2; 7, 1] z(1-8)=324649814/15 [3, 1; 5, 1] z(1-10)=3970068530764/33 [3, 1; 11, 1] z(1-12)=6419998586927832328/4095 [3, 2; 5, 1; 7, 1; 13, 1] z(1-14)=123407242075130286004/3 Mat([3, 1]) z(1-16)=498892114387951583457289649/255 [3, 1; 5, 1; 17, 1] z(1-18)=560606297292308330570657275519348/3591 [3, 3; 7, 1; 19, 1] z(1-20)=666159673951002284358170884495203519568/33825 [3, 1; 5, 2; 11, 1; 41, 1] z(1-22)=258544809927042393527437248353417044884172/69 [3, 1; 23, 1] z(1-24)=4237305315191737531693797080486099851545364991834/4095 [3, 2; 5, 1; 7, 1; 13, 1] k=zetakinit(x^2-44) z(1-2)=7/6 [2, 1; 3, 1] z(1-4)=2153/60 [2, 2; 3, 1; 5, 1] z(1-6)=2130727/126 [2, 1; 3, 2; 7, 1] z(1-8)=4393611593/120 [2, 3; 3, 1; 5, 1] z(1-10)=15515203176007/66 [2, 1; 3, 1; 11, 1] z(1-12)=57833610972825439403/16380 [2, 2; 3, 2; 5, 1; 7, 1; 13, 1] z(1-14)=640284813520180963687/6 [2, 1; 3, 1] z(1-16)=23849907642936468917264806441/4080 [2, 4; 3, 1; 5, 1; 17, 1] z(1-18)=3858252593190828124973590079348989/7182 [2, 1; 3, 3; 7, 1; 19, 1] z(1-20)=257570454888069177671400223300084538443/3300 [2, 2; 3, 1; 5, 2; 11, 1] z(1-22)=2360181170214245276197461642177962807357701/138 [2, 1; 3, 1; 23, 1] z(1-24)=178195602951418769387248613782238554963197881783123/32760 [2, 3; 3, 2; 5, 1; 7, 1; 13, 1] ? (13:35) gp > (13:35) gp > \rread1 ? L=[8,12,13,17,21,24,28,29,33,37,40,41,44];for(i=1,13,k=zetakinit(x^2-L[i]);print("k=zetakinit(x^2-",L[i],")");for(j=1,20,a=round(zetak(k,1-2*j)*(6*j)!)/(6*j)!;print("z(1-",2*j,")=",a," ",factor(denominator(a))))) k=zetakinit(x^2-8) z(1-2)=1/12 [2, 2; 3, 1] z(1-4)=11/120 [2, 3; 3, 1; 5, 1] z(1-6)=361/252 [2, 2; 3, 2; 7, 1] z(1-8)=24611/240 [2, 4; 3, 1; 5, 1] z(1-10)=2873041/132 [2, 2; 3, 1; 11, 1] z(1-12)=27233033477/2520 [2, 3; 3, 2; 5, 1; 7, 1] z(1-14)=129570724921/12 [2, 2; 3, 1] z(1-16)=159549339299844787/8160 [2, 5; 3, 1; 5, 1; 17, 1] z(1-18)=853244674392953815867/14364 [2, 2; 3, 3; 7, 1; 19, 1] z(1-20)=1883014201750720442753521/6600 [2, 3; 3, 1; 5, 2; 11, 1] z(1-22)=570397367814021408569126923/276 [2, 2; 3, 1; 23, 1] z(1-24)=109511675519893842297200129361077/5040 [2, 4; 3, 2; 5, 1; 7, 1] z(1-26)=3854553830778219905574569395190491/12 [2, 2; 3, 1] z(1-28)=3077609552434753667936167481742769368302633312052019443928476509346492616723495930737672627783573922560358013113278564096679992602121287315226624000000180945746491/473462876366479038142769654161447326857238040891721355302692290340437018755959552018555103281245250450882560000000000000000000 [2, 81; 3, 41; 5, 19; 7, 12; 11, 7; 13, 6; 17, 4; 19, 4; 23, 3; 29, 2; 31, 2; 37, 2; 41, 2; 43, 1; 47, 1; 53, 1; 59, 1; 61, 1; 67, 1; 71, 1; 73, 1; 79, 1; 83, 1] z(1-30)=4375842542128016245608965250685963516582926035350990748878748981521708825717963920744701002418367912074330030878203589291993600004963544736310314811994932819479693938343361837/24863458530361668434599995542144184384328842126762426021959950861099245135872577634440500901529312352867830883942400000000000000000000 [2, 86; 3, 44; 5, 20; 7, 13; 11, 8; 13, 6; 17, 4; 19, 3; 23, 3; 29, 3; 31, 2; 37, 1; 41, 2; 43, 2; 47, 1; 53, 1; 59, 1; 61, 1; 67, 1; 71, 1; 73, 1; 79, 1; 83, 1; 89, 1] *** precision loss in truncation (14:08) gp > (14:08) gp > \rread1 ? L=[8,12,13,17,21,24,28,29,33,37,40,41,44];for(i=3,13,k=zetakinit(x^2-L[i]);print("k=zetakinit(x^2-",L[i],")");for(j=1,18,a=round(zetak(k,1-2*j)*(6*j)!)/(6*j)!;print("z(1-",2*j,")=",a," ",factor(denominator(a))))) k=zetakinit(x^2-13) z(1-2)=1/6 [2, 1; 3, 1] z(1-4)=29/60 [2, 2; 3, 1; 5, 1] z(1-6)=33463/1638 [2, 1; 3, 2; 7, 1; 13, 1] z(1-8)=467669/120 [2, 3; 3, 1; 5, 1] z(1-10)=144547171/66 [2, 1; 3, 1; 11, 1] z(1-12)=47067236077919/16380 [2, 2; 3, 2; 5, 1; 7, 1; 13, 1] z(1-14)=45495767916691/6 [2, 1; 3, 1] z(1-16)=147939984968716630933/4080 [2, 4; 3, 1; 5, 1; 17, 1] z(1-18)=27159338094720360855345181/93366 [2, 1; 3, 3; 7, 1; 13, 1; 19, 1] z(1-20)=12174855335880619308295189279/3300 [2, 2; 3, 1; 5, 2; 11, 1] z(1-22)=9738560526887500711761231871273/138 [2, 1; 3, 1; 23, 1] z(1-24)=64184156678679131455067913889018026839/32760 [2, 3; 3, 2; 5, 1; 7, 1; 13, 1] z(1-26)=458886127252695004415215453937104183681/6 [2, 1; 3, 1] z(1-28)=4515001002940212304172873554675046472461556024734522816092510706676503095353285947327239390239991065288587808258501603715132665401253019109186756149248000000000101265233/1104746711521784422333129193043377096000222095414016495706282010794353043763905621376628574322905584385392640000000000000000000 [2, 81; 3, 40; 5, 19; 7, 13; 11, 7; 13, 6; 17, 4; 19, 4; 23, 3; 29, 2; 31, 2; 37, 2; 41, 2; 43, 1; 47, 1; 53, 1; 59, 1; 61, 1; 67, 1; 71, 1; 73, 1; 79, 1; 83, 1] *** precision loss in truncation (14:21) gp > (14:21) gp > \p180 (14:21) gp > (14:21) gp > \l log = 0 (off) (14:21) gp > (14:21) gp > \rread1 ? L=[8,12,13,17,21,24,28,29,33,37,40,41,44];for(i=3,13,k=zetakinit(x^2-L[i]);print("k=zetakinit(x^2-",L[i],")");for(j=1,13,a=round(zetak(k,1-2*j)*(6*j)!)/(6*j)!;print("z(1-",2*j,")=",a," ",factor(denominator(a))))) k=zetakinit(x^2-13) z(1-2)=1/6 [2, 1; 3, 1] z(1-4)=29/60 [2, 2; 3, 1; 5, 1] z(1-6)=33463/1638 [2, 1; 3, 2; 7, 1; 13, 1] z(1-8)=467669/120 [2, 3; 3, 1; 5, 1] z(1-10)=144547171/66 [2, 1; 3, 1; 11, 1] z(1-12)=47067236077919/16380 [2, 2; 3, 2; 5, 1; 7, 1; 13, 1] z(1-14)=45495767916691/6 [2, 1; 3, 1] z(1-16)=147939984968716630933/4080 [2, 4; 3, 1; 5, 1; 17, 1] z(1-18)=27159338094720360855345181/93366 [2, 1; 3, 3; 7, 1; 13, 1; 19, 1] z(1-20)=12174855335880619308295189279/3300 [2, 2; 3, 1; 5, 2; 11, 1] z(1-22)=9738560526887500711761231871273/138 [2, 1; 3, 1; 23, 1] z(1-24)=64184156678679131455067913889018026839/32760 [2, 3; 3, 2; 5, 1; 7, 1; 13, 1] z(1-26)=458886127252695004415215453937104183681/6 [2, 1; 3, 1] k=zetakinit(x^2-17) z(1-2)=1/3 Mat([3, 1]) z(1-4)=41/30 [2, 1; 3, 1; 5, 1] z(1-6)=5791/63 [3, 2; 7, 1] z(1-8)=29950897/1020 [2, 2; 3, 1; 5, 1; 17, 1] z(1-10)=926010751/33 [3, 1; 11, 1] z(1-12)=514888471736531/8190 [2, 1; 3, 2; 5, 1; 7, 1; 13, 1] z(1-14)=850783423272511/3 Mat([3, 1]) z(1-16)=4730479106306885224897/2040 [2, 3; 3, 1; 5, 1; 17, 1] z(1-18)=114234320679904116390875557/3591 [3, 3; 7, 1; 19, 1] z(1-20)=1138395679632849871290948246451/1650 [2, 1; 3, 1; 5, 2; 11, 1] z(1-22)=1557165289072064053256624254503373/69 [3, 1; 23, 1] z(1-24)=298351132018971004567540400687875435236427/278460 [2, 2; 3, 2; 5, 1; 7, 1; 13, 1; 17, 1] z(1-26)=202486631356500228172870771962665099345762137487118076548864537734830737703608728882553845557304998365879904496731782815455791257330122752000000000000000137/2831070294551574457864380289683011557182937394872062997512240706417208831308550191561271553294336000000000000000000 [2, 72; 3, 36; 5, 18; 7, 12; 11, 7; 13, 6; 17, 4; 19, 4; 23, 3; 29, 2; 31, 2; 37, 2; 41, 1; 43, 1; 47, 1; 53, 1; 59, 1; 61, 1; 67, 1; 71, 1; 73, 1] k=zetakinit(x^2-21) z(1-2)=1/3 Mat([3, 1]) z(1-4)=77/30 [2, 1; 3, 1; 5, 1] z(1-6)=17971/63 [3, 2; 7, 1] z(1-8)=8529317/60 [2, 2; 3, 1; 5, 1] z(1-10)=6880084771/33 [3, 1; 11, 1] z(1-12)=5846032490154287/8190 [2, 1; 3, 2; 5, 1; 7, 1; 13, 1] z(1-14)=14745725203342771/3 Mat([3, 1]) z(1-16)=125121710284290710090149/2040 [2, 3; 3, 1; 5, 1; 17, 1] z(1-18)=4610784503383205352814427857/3591 [3, 3; 7, 1; 19, 1] z(1-20)=70115605861717430419952533689007/1650 [2, 1; 3, 1; 5, 2; 11, 1] z(1-22)=146351620074764895131354655029032393/69 [3, 1; 23, 1] z(1-24)=2516995799150646956921735521465227682859207/16380 [2, 2; 3, 2; 5, 1; 7, 1; 13, 1] z(1-26)=59085321037165353837409112686613801037961337859890109735996242439812228210268533378869089224033500326492623388358045452289024388002077474816000000000000000001/3774760392735432610485840386244015409577249859829417330016320941889611775078066922081695404392448000000000000000000 [2, 74; 3, 35; 5, 18; 7, 12; 11, 7; 13, 6; 17, 4; 19, 4; 23, 3; 29, 2; 31, 2; 37, 2; 41, 1; 43, 1; 47, 1; 53, 1; 59, 1; 61, 1; 67, 1; 71, 1; 73, 1] k=zetakinit(x^2-24) z(1-2)=1/2 Mat([2, 1]) z(1-4)=87/20 [2, 2; 5, 1] z(1-6)=3623/6 [2, 1; 3, 1] z(1-8)=15540167/40 [2, 3; 5, 1] z(1-10)=16324877601/22 [2, 1; 11, 1] z(1-12)=2586338303951011/780 [2, 2; 3, 1; 5, 1; 13, 1] z(1-14)=59633825180769841/2 Mat([2, 1]) z(1-16)=660880926452517181569159/1360 [2, 4; 5, 1; 17, 1] z(1-18)=4544082991633386942201552461/342 [2, 1; 3, 2; 19, 1] z(1-20)=631781365642564377262812035249077/1100 [2, 2; 5, 2; 11, 1] z(1-22)=1722396914545775335671336811132998243/46 [2, 1; 23, 1] z(1-24)=5527184623827320720804884942579502766150331/1560 [2, 3; 3, 1; 5, 1; 13, 1] z(1-26)=5338208207873326167054719620447843225212804322070778271765737292436038675647011837948505903297702439889080900782553817875279201330187628183552000000000000134681/11324281178206297831457521158732046228731749579488251990048962825668835325234200766245086213177344000000000000000000 [2, 74; 3, 36; 5, 18; 7, 12; 11, 7; 13, 6; 17, 4; 19, 4; 23, 3; 29, 2; 31, 2; 37, 2; 41, 1; 43, 1; 47, 1; 53, 1; 59, 1; 61, 1; 67, 1; 71, 1; 73, 1] k=zetakinit(x^2-28) z(1-2)=2/3 Mat([3, 1]) z(1-4)=113/15 [3, 1; 5, 1] z(1-6)=88922/63 [3, 2; 7, 1] z(1-8)=37040933/30 [2, 1; 3, 1; 5, 1] z(1-10)=105911461682/33 [3, 1; 11, 1] z(1-12)=79934365069116923/4095 [3, 2; 5, 1; 7, 1; 13, 1] z(1-14)=716746659547868042/3 Mat([3, 1]) z(1-16)=5405796972572907220684141/1020 [2, 2; 3, 1; 5, 1; 17, 1] z(1-18)=708279012827664384120281835734/3591 [3, 3; 7, 1; 19, 1] z(1-20)=9573934977162438600250268080336723/825 [3, 1; 5, 2; 11, 1] z(1-22)=71052681874089832775706165545667272846/69 [3, 1; 23, 1] z(1-24)=1086207585206051133826593793036434968608347383/8190 [2, 1; 3, 2; 5, 1; 7, 1; 13, 1] z(1-26)=2747283322104654135617028768648610286449191699272171512487141058907481875897407747606459545523968949457829096524907467807922231988589757988864000000000000000001/114386678567740382135934557158909557865977268479679313030797604299685205305395967335808951648256000000000000000000 [2, 74; 3, 34; 5, 18; 7, 12; 11, 6; 13, 6; 17, 4; 19, 4; 23, 3; 29, 2; 31, 2; 37, 2; 41, 1; 43, 1; 47, 1; 53, 1; 59, 1; 61, 1; 67, 1; 71, 1; 73, 1] k=zetakinit(x^2-29) z(1-2)=1/2 Mat([2, 1]) z(1-4)=157/20 [2, 2; 5, 1] z(1-6)=23537/14 [2, 1; 7, 1] z(1-8)=63987797/40 [2, 3; 5, 1] z(1-10)=8949528841/2 Mat([2, 1]) z(1-12)=53174446765203189/1820 [2, 2; 5, 1; 7, 1; 13, 1] z(1-14)=22252831377375190439/58 [2, 1; 29, 1] z(1-16)=12416846206191477000121109/1360 [2, 4; 5, 1; 17, 1] z(1-18)=290863760930388381994829535259/798 [2, 1; 3, 1; 7, 1; 19, 1] z(1-20)=2300464090518383947383826818643517/100 [2, 2; 5, 2] z(1-22)=100727578431619526478496202457697853993/46 [2, 1; 23, 1] z(1-24)=1101208363970191358787380920063859644073436829/3640 [2, 3; 5, 1; 7, 1; 13, 1] z(1-26)=110919150464084763538113066372601256301698053462206518386465379965294918321249232883677031389738765543531166377578747020422864687978401436270592000000000000000001/1887380196367716305242920193122007704788624929914708665008160470944805887539033461040847702196224000000000000000000 [2, 73; 3, 35; 5, 18; 7, 12; 11, 7; 13, 6; 17, 4; 19, 4; 23, 3; 29, 2; 31, 2; 37, 2; 41, 1; 43, 1; 47, 1; 53, 1; 59, 1; 61, 1; 67, 1; 71, 1; 73, 1] k=zetakinit(x^2-33) z(1-2)=1 matrix(0,2,j,k,0) z(1-4)=141/10 [2, 1; 5, 1] z(1-6)=74231/21 [3, 1; 7, 1] z(1-8)=84995021/20 [2, 2; 5, 1] z(1-10)=168313830831/11 Mat([11, 1]) z(1-12)=352647202814176591/2730 [2, 1; 3, 1; 5, 1; 7, 1; 13, 1] z(1-14)=2195713162447871431 matrix(0,2,j,k,0) z(1-16)=46003584335372550090866877/680 [2, 3; 5, 1; 17, 1] z(1-18)=4186134456578519540954338663877/1197 [3, 2; 7, 1; 19, 1] z(1-20)=157195404294629240579806320132627871/550 [2, 1; 5, 2; 11, 1] z(1-22)=810235667276450560661104858483703801973/23 Mat([23, 1]) z(1-24)=34410061486343846835304341132900205543844899231/5460 [2, 2; 3, 1; 5, 1; 7, 1; 13, 1] z(1-26)=408001389311742473777636193955168683644475164201311254903880365495442007474897894739268211792118683780922887643149955805206165619880079849947136000000000000000001/257370026777415859805852753607546505198448854079278454319294609674291711937140926505570141208576000000000000000000 [2, 72; 3, 36; 5, 18; 7, 12; 11, 6; 13, 6; 17, 4; 19, 4; 23, 3; 29, 2; 31, 2; 37, 2; 41, 1; 43, 1; 47, 1; 53, 1; 59, 1; 61, 1; 67, 1; 71, 1; 73, 1] k=zetakinit(x^2-37) z(1-2)=5/6 [2, 1; 3, 1] z(1-4)=1129/60 [2, 2; 3, 1; 5, 1] z(1-6)=115865/18 [2, 1; 3, 2] z(1-8)=1193648689/120 [2, 3; 3, 1; 5, 1] z(1-10)=2988574807055/66 [2, 1; 3, 1; 11, 1] z(1-12)=1126138824426408037/2340 [2, 2; 3, 2; 5, 1; 13, 1] z(1-14)=61724704374047728655/6 [2, 1; 3, 1] z(1-16)=1625886902325466618525254353/4080 [2, 4; 3, 1; 5, 1; 17, 1] z(1-18)=983107522010748251749534394373935/37962 [2, 1; 3, 3; 19, 1; 37, 1] z(1-20)=8780152495032015611104972776926106659/3300 [2, 2; 3, 1; 5, 2; 11, 1] z(1-22)=56891811270123946109776919715889222866365/138 [2, 1; 3, 1; 23, 1] z(1-24)=433911874930178370627361990523141469876914594077/4680 [2, 3; 3, 2; 5, 1; 13, 1] z(1-26)=5355020192651038404595510712806190786312953062351438557312901872941537005323112092477672453440807649725845626315014905169507444613197208915804160000000000000033359/182649696422682223088024534818258810140834670636907290162080045575303795568293560745888487309312000000000000000000 [2, 73; 3, 36; 5, 18; 7, 12; 11, 7; 13, 6; 17, 4; 19, 4; 23, 3; 29, 2; 31, 1; 37, 2; 41, 1; 43, 1; 47, 1; 53, 1; 59, 1; 61, 1; 67, 1; 71, 1; 73, 1] k=zetakinit(x^2-40) z(1-2)=7/6 [2, 1; 3, 1] z(1-4)=1577/60 [2, 2; 3, 1; 5, 1] z(1-6)=1264807/126 [2, 1; 3, 2; 7, 1] z(1-8)=2150342537/120 [2, 3; 3, 1; 5, 1] z(1-10)=6273958190407/66 [2, 1; 3, 1; 11, 1] z(1-12)=19327071911053422827/16380 [2, 2; 3, 2; 5, 1; 7, 1; 13, 1] z(1-14)=176836590584822968807/6 [2, 1; 3, 1] z(1-16)=5443774185448827969118891369/4080 [2, 4; 3, 1; 5, 1; 17, 1] z(1-18)=727811089794971859689502345571069/7182 [2, 1; 3, 3; 7, 1; 19, 1] z(1-20)=40154912568352747611033023042162274187/3300 [2, 2; 3, 1; 5, 2; 11, 1] z(1-22)=304090330290887531809755216310777086459781/138 [2, 1; 3, 1; 23, 1] z(1-24)=18974436285039855244365922390662114802894020172307/32760 [2, 3; 3, 2; 5, 1; 7, 1; 13, 1] z(1-26)=346290505157639770793524389384806186031146142673933005838915222240690947571624713563880826811985849608602127512293029782293599604804939972706566144000000000000000001/1617754454029471118779645879818863746961678511355464570006994689381262189319171538035012316168192000000000000000000 [2, 74; 3, 36; 5, 18; 7, 11; 11, 7; 13, 6; 17, 4; 19, 4; 23, 3; 29, 2; 31, 2; 37, 2; 41, 1; 43, 1; 47, 1; 53, 1; 59, 1; 61, 1; 67, 1; 71, 1; 73, 1] k=zetakinit(x^2-41) z(1-2)=4/3 Mat([3, 1]) z(1-4)=448/15 [3, 1; 5, 1] z(1-6)=733924/63 [3, 2; 7, 1] z(1-8)=324649814/15 [3, 1; 5, 1] z(1-10)=3970068530764/33 [3, 1; 11, 1] z(1-12)=6419998586927832328/4095 [3, 2; 5, 1; 7, 1; 13, 1] z(1-14)=123407242075130286004/3 Mat([3, 1]) z(1-16)=498892114387951583457289649/255 [3, 1; 5, 1; 17, 1] z(1-18)=560606297292308330570657275519348/3591 [3, 3; 7, 1; 19, 1] z(1-20)=666159673951002284358170884495203519568/33825 [3, 1; 5, 2; 11, 1; 41, 1] z(1-22)=258544809927042393527437248353417044884172/69 [3, 1; 23, 1] z(1-24)=4237305315191737531693797080486099851545364991834/4095 [3, 2; 5, 1; 7, 1; 13, 1] z(1-26)=1205335113210720999099053080674507703268775833425444/3 Mat([3, 1]) k=zetakinit(x^2-44) z(1-2)=7/6 [2, 1; 3, 1] z(1-4)=2153/60 [2, 2; 3, 1; 5, 1] z(1-6)=2130727/126 [2, 1; 3, 2; 7, 1] z(1-8)=4393611593/120 [2, 3; 3, 1; 5, 1] z(1-10)=15515203176007/66 [2, 1; 3, 1; 11, 1] z(1-12)=57833610972825439403/16380 [2, 2; 3, 2; 5, 1; 7, 1; 13, 1] z(1-14)=640284813520180963687/6 [2, 1; 3, 1] z(1-16)=23849907642936468917264806441/4080 [2, 4; 3, 1; 5, 1; 17, 1] z(1-18)=3858252593190828124973590079348989/7182 [2, 1; 3, 3; 7, 1; 19, 1] z(1-20)=257570454888069177671400223300084538443/3300 [2, 2; 3, 1; 5, 2; 11, 1] z(1-22)=2360181170214245276197461642177962807357701/138 [2, 1; 3, 1; 23, 1] z(1-24)=178195602951418769387248613782238554963197881783123/32760 [2, 3; 3, 2; 5, 1; 7, 1; 13, 1] z(1-26)=237461991771821091923266842545384266993275185324022089421068915661417906311576616302984915160037724137874117852068749021624788680397318136180768768000000000000964829/97623113605226705443599320333896950247687496374898724052146231255765821769260351433147294941184000000000000000000 [2, 72; 3, 36; 5, 18; 7, 12; 11, 7; 13, 6; 17, 4; 19, 4; 23, 3; 29, 1; 31, 2; 37, 2; 41, 1; 43, 1; 47, 1; 53, 1; 59, 1; 61, 1; 67, 1; 71, 1; 73, 1] ? (14:44) gp > (14:44) gp > \q Good bye! (12:56) gp > (12:56) gp > \rread ? k=nfinit(x^2-21);print("k=nfinit(x^2-21)");forprime(i=2,32,a=idealprincipal(k,i);print(i," ",idealfactor(k,a))) k=nfinit(x^2-21) 2 Mat([[2, [2, 0]~, 1, 2, [1, 0]~], 1]) 3 Mat([[3, [-1, 2]~, 2, 1, [-1, -1]~], 2]) 5 [[5, [-2, 2]~, 1, 1, [0, 2]~], 1; [5, [0, 2]~, 1, 1, [-2, 2]~], 1] 7 Mat([[7, [-1, 2]~, 2, 1, [-1, 2]~], 2]) 11 Mat([[11, [11, 0]~, 1, 2, [1, 0]~], 1]) 13 Mat([[13, [13, 0]~, 1, 2, [1, 0]~], 1]) 17 [[17, [-3, 2]~, 1, 1, [1, 2]~], 1; [17, [1, 2]~, 1, 1, [-3, 2]~], 1] 19 Mat([[19, [19, 0]~, 1, 2, [1, 0]~], 1]) 23 Mat([[23, [23, 0]~, 1, 2, [1, 0]~], 1]) 29 Mat([[29, [29, 0]~, 1, 2, [1, 0]~], 1]) 31 Mat([[31, [31, 0]~, 1, 2, [1, 0]~], 1]) (12:56) gp > (12:56) gp > \rread ? k=nfinit(x^2-24);print("k=nfinit(x^2-24)");forprime(i=2,32,a=idealprincipal(k,i);print(i," ",idealfactor(k,a))) k=nfinit(x^2-24) 2 Mat([[2, [0, 1]~, 2, 1, [2, 1]~], 2]) 3 Mat([[3, [0, 2]~, 2, 1, [0, -1]~], 2]) 5 [[5, [-2, 2]~, 1, 1, [2, 2]~], 1; [5, [2, 2]~, 1, 1, [-2, 2]~], 1] 7 Mat([[7, [7, 0]~, 1, 2, [1, 0]~], 1]) 11 Mat([[11, [11, 0]~, 1, 2, [1, 0]~], 1]) 13 Mat([[13, [13, 0]~, 1, 2, [1, 0]~], 1]) 17 Mat([[17, [17, 0]~, 1, 2, [1, 0]~], 1]) 19 [[19, [-9, 2]~, 1, 1, [9, 2]~], 1; [19, [9, 2]~, 1, 1, [-9, 2]~], 1] 23 [[23, [-1, 2]~, 1, 1, [1, 2]~], 1; [23, [1, 2]~, 1, 1, [-1, 2]~], 1] 29 [[29, [-13, 2]~, 1, 1, [13, 2]~], 1; [29, [13, 2]~, 1, 1, [-13, 2]~], 1] 31 Mat([[31, [31, 0]~, 1, 2, [1, 0]~], 1]) (12:56) gp > (12:56) gp > \rread ? k=nfinit(x^2-28);print("k=nfinit(x^2-28)");forprime(i=2,32,a=idealprincipal(k,i);print(i," ",idealfactor(k,a))) k=nfinit(x^2-28) 2 Mat([[2, [1, 1]~, 2, 1, [1, 1]~], 2]) 3 [[3, [2, 2]~, 1, 1, [1, -1]~], 1; [3, [4, 2]~, 1, 1, [-1, -1]~], 1] 5 Mat([[5, [5, 0]~, 1, 2, [1, 0]~], 1]) 7 Mat([[7, [0, 2]~, 2, 1, [0, 2]~], 2]) 11 Mat([[11, [11, 0]~, 1, 2, [1, 0]~], 1]) 13 Mat([[13, [13, 0]~, 1, 2, [1, 0]~], 1]) 17 Mat([[17, [17, 0]~, 1, 2, [1, 0]~], 1]) 19 [[19, [-3, 2]~, 1, 1, [3, 2]~], 1; [19, [3, 2]~, 1, 1, [-3, 2]~], 1] 23 Mat([[23, [23, 0]~, 1, 2, [1, 0]~], 1]) 29 [[29, [-12, 2]~, 1, 1, [12, 2]~], 1; [29, [12, 2]~, 1, 1, [-12, 2]~], 1] 31 [[31, [-11, 2]~, 1, 1, [11, 2]~], 1; [31, [11, 2]~, 1, 1, [-11, 2]~], 1] (12:56) gp > (12:56) gp > \rread ? k=nfinit(x^2-29);print("k=nfinit(x^2-29)");forprime(i=2,32,a=idealprincipal(k,i);print(i," ",idealfactor(k,a))) k=nfinit(x^2-29) 2 Mat([[2, [2, 0]~, 1, 2, [1, 0]~], 1]) 3 Mat([[3, [3, 0]~, 1, 2, [1, 0]~], 1]) 5 [[5, [2, 2]~, 1, 1, [1, 2]~], 1; [5, [6, 2]~, 1, 1, [2, 2]~], 1] 7 [[7, [-2, 2]~, 1, 1, [0, 2]~], 1; [7, [0, 2]~, 1, 1, [-2, 2]~], 1] 11 Mat([[11, [11, 0]~, 1, 2, [1, 0]~], 1]) 13 [[13, [-5, 2]~, 1, 1, [3, 2]~], 1; [13, [3, 2]~, 1, 1, [-5, 2]~], 1] 17 Mat([[17, [17, 0]~, 1, 2, [1, 0]~], 1]) 19 Mat([[19, [19, 0]~, 1, 2, [1, 0]~], 1]) 23 [[23, [-12, 2]~, 1, 1, [10, 2]~], 1; [23, [10, 2]~, 1, 1, [11, 2]~], 1] 29 Mat([[29, [-1, 2]~, 2, 1, [-1, 2]~], 2]) 31 Mat([[31, [31, 0]~, 1, 2, [1, 0]~], 1]) (12:57) gp > (12:57) gp > \rread ? k=nfinit(x^2-33);print("k=nfinit(x^2-33)");forprime(i=2,32,a=idealprincipal(k,i);print(i," ",idealfactor(k,a))) k=nfinit(x^2-33) 2 [[2, [2, 1]~, 1, 1, [1, 1]~], 1; [2, [1, 1]~, 1, 1, [2, 1]~], 1] 3 Mat([[3, [-1, 2]~, 2, 1, [-1, -1]~], 2]) 5 Mat([[5, [5, 0]~, 1, 2, [1, 0]~], 1]) 7 Mat([[7, [7, 0]~, 1, 2, [1, 0]~], 1]) 11 Mat([[11, [-1, 2]~, 2, 1, [-1, 2]~], 2]) 13 Mat([[13, [13, 0]~, 1, 2, [1, 0]~], 1]) 17 [[17, [-5, 2]~, 1, 1, [3, 2]~], 1; [17, [3, 2]~, 1, 1, [-5, 2]~], 1] 19 Mat([[19, [19, 0]~, 1, 2, [1, 0]~], 1]) 23 Mat([[23, [23, 0]~, 1, 2, [1, 0]~], 1]) 29 [[29, [-3, 2]~, 1, 1, [1, 2]~], 1; [29, [1, 2]~, 1, 1, [-3, 2]~], 1] 31 [[31, [-9, 2]~, 1, 1, [7, 2]~], 1; [31, [7, 2]~, 1, 1, [-9, 2]~], 1] (12:57) gp > (12:57) gp > \rread ? k=nfinit(x^2-37);print("k=nfinit(x^2-37)");forprime(i=2,32,a=idealprincipal(k,i);print(i," ",idealfactor(k,a))) k=nfinit(x^2-37) 2 Mat([[2, [2, 0]~, 1, 2, [1, 0]~], 1]) 3 [[3, [1, 2]~, 1, 1, [0, -1]~], 1; [3, [3, 2]~, 1, 1, [1, -1]~], 1] 5 Mat([[5, [5, 0]~, 1, 2, [1, 0]~], 1]) 7 [[7, [-4, 2]~, 1, 1, [2, 2]~], 1; [7, [2, 2]~, 1, 1, [3, 2]~], 1] 11 [[11, [-3, 2]~, 1, 1, [1, 2]~], 1; [11, [1, 2]~, 1, 1, [-3, 2]~], 1] 13 Mat([[13, [13, 0]~, 1, 2, [1, 0]~], 1]) 17 Mat([[17, [17, 0]~, 1, 2, [1, 0]~], 1]) 19 Mat([[19, [19, 0]~, 1, 2, [1, 0]~], 1]) 23 Mat([[23, [23, 0]~, 1, 2, [1, 0]~], 1]) 29 Mat([[29, [29, 0]~, 1, 2, [1, 0]~], 1]) 31 Mat([[31, [31, 0]~, 1, 2, [1, 0]~], 1]) (12:57) gp > (12:57) gp > \rread ? k=nfinit(x^2-40);print("k=nfinit(x^2-40)");forprime(i=2,32,a=idealprincipal(k,i);print(i," ",idealfactor(k,a))) k=nfinit(x^2-40) 2 Mat([[2, [0, 1]~, 2, 1, [2, 1]~], 2]) 3 [[3, [-1, 2]~, 1, 1, [1, -1]~], 1; [3, [1, 2]~, 1, 1, [-1, -1]~], 1] 5 Mat([[5, [0, 2]~, 2, 1, [0, 2]~], 2]) 7 Mat([[7, [7, 0]~, 1, 2, [1, 0]~], 1]) 11 Mat([[11, [11, 0]~, 1, 2, [1, 0]~], 1]) 13 [[13, [-1, 2]~, 1, 1, [1, 2]~], 1; [13, [1, 2]~, 1, 1, [-1, 2]~], 1] 17 Mat([[17, [17, 0]~, 1, 2, [1, 0]~], 1]) 19 Mat([[19, [19, 0]~, 1, 2, [1, 0]~], 1]) 23 Mat([[23, [23, 0]~, 1, 2, [1, 0]~], 1]) 29 Mat([[29, [29, 0]~, 1, 2, [1, 0]~], 1]) 31 [[31, [-3, 2]~, 1, 1, [3, 2]~], 1; [31, [3, 2]~, 1, 1, [-3, 2]~], 1] (12:58) gp > (12:58) gp > \rread ? k=nfinit(x^2-41);print("k=nfinit(x^2-41)");forprime(i=2,32,a=idealprincipal(k,i);print(i," ",idealfactor(k,a))) k=nfinit(x^2-41) 2 [[2, [0, 1]~, 1, 1, [1, 1]~], 1; [2, [3, 1]~, 1, 1, [2, 1]~], 1] 3 Mat([[3, [3, 0]~, 1, 2, [1, 0]~], 1]) 5 [[5, [-2, 2]~, 1, 1, [0, 2]~], 1; [5, [0, 2]~, 1, 1, [-2, 2]~], 1] 7 Mat([[7, [7, 0]~, 1, 2, [1, 0]~], 1]) 11 Mat([[11, [11, 0]~, 1, 2, [1, 0]~], 1]) 13 Mat([[13, [13, 0]~, 1, 2, [1, 0]~], 1]) 17 Mat([[17, [17, 0]~, 1, 2, [1, 0]~], 1]) 19 Mat([[19, [19, 0]~, 1, 2, [1, 0]~], 1]) 23 [[23, [-9, 2]~, 1, 1, [7, 2]~], 1; [23, [7, 2]~, 1, 1, [-9, 2]~], 1] 29 Mat([[29, [29, 0]~, 1, 2, [1, 0]~], 1]) 31 [[31, [-15, 2]~, 1, 1, [13, 2]~], 1; [31, [13, 2]~, 1, 1, [-15, 2]~], 1] (12:58) gp > (12:58) gp > \rread ? k=nfinit(x^2-44);print("k=nfinit(x^2-44)");forprime(i=2,32,a=idealprincipal(k,i);print(i," ",idealfactor(k,a))) k=nfinit(x^2-44) 2 Mat([[2, [1, 1]~, 2, 1, [1, 1]~], 2]) 3 Mat([[3, [3, 0]~, 1, 2, [1, 0]~], 1]) 5 [[5, [-2, 2]~, 1, 1, [2, 2]~], 1; [5, [2, 2]~, 1, 1, [-2, 2]~], 1] 7 [[7, [-3, 2]~, 1, 1, [3, 2]~], 1; [7, [3, 2]~, 1, 1, [-3, 2]~], 1] 11 Mat([[11, [0, 2]~, 2, 1, [0, 2]~], 2]) 13 Mat([[13, [13, 0]~, 1, 2, [1, 0]~], 1]) 17 Mat([[17, [17, 0]~, 1, 2, [1, 0]~], 1]) 19 [[19, [-5, 2]~, 1, 1, [5, 2]~], 1; [19, [5, 2]~, 1, 1, [-5, 2]~], 1] 23 Mat([[23, [23, 0]~, 1, 2, [1, 0]~], 1]) 29 Mat([[29, [29, 0]~, 1, 2, [1, 0]~], 1]) 31 Mat([[31, [31, 0]~, 1, 2, [1, 0]~], 1]) (12:58) gp > (12:58) gp > \l log = 0 (off)