(13:20) gp > (13:20) gp > \p180
   realprecision = 183 significant digits (180 digits displayed)
(13:20) gp > (13:20) gp > \rList
? L=[x^2+x-1,x^3+x^2-2*x-1,x^2-2,x^5+x^4-4*x^3-3*x^2+3*x+1,x^2-3,x^6+x^5-5*x^4-4*x^3+6*x^2+3*x-1,x^2+x-1,x^2-2,x^2-3,x^2-13,x^2-17,x^2-21,x^2-24,x^2-28,x^2-29,x^2-33,x^2-37,x^2-40,x^2-41,x^2-44,x^3+x^2-2*x-1,x^3-9*x^2+14*x-1,x^3-354315*x^2+39645147398*x-1424861898171643];for(i=2,40,k=nfinit(L[i]);print("k=nfinit(",L[i],")");forprime(r=2,37,a=idealprincipal(k,r);print(r,"  ",idealfactor(k,a)));k=zetakinit(L[i]);for(j=1,18,a=round(zetak(k,1-2*j)*37!)/37!;print("z(1-",2*j,")=",a,"  ",factor(denominator(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])
37  Mat([[37, [37, 0, 0]~, 1, 3, [1, 0, 0]~], 1])
z(1-2)=-1/21  [3, 1; 7, 1]
z(1-4)=79/210  [2, 1; 3, 1; 5, 1; 7, 1]
z(1-6)=-7393/63  [3, 2; 7, 1]
z(1-8)=142490119/420  [2, 2; 3, 1; 5, 1; 7, 1]
z(1-10)=-1141452324871/231  [3, 1; 7, 1; 11, 1]
z(1-12)=2101941875088322867/8190  [2, 1; 3, 2; 5, 1; 7, 1; 13, 1]
z(1-14)=-5589087133015782866737/147  [3, 1; 7, 2]
z(1-16)=196210654771718649388061754983/14280  [2, 3; 3, 1; 5, 1; 7, 1; 17, 1]
z(1-18)=-38746229519570895574625913188448091/3591  [3, 3; 7, 1; 19, 1]
z(1-20)=194530316743193504738135306900338932340229/11550  [2, 1; 3, 1; 5, 2; 7, 1; 11, 1]
z(1-22)=-23518697248282245943905832963281144323974983973/483  [3, 1; 7, 1; 23, 1]
z(1-24)=4032222871166671567558267339270905870778751618513341627/16380  [2, 2; 3, 2; 5, 1; 7, 1; 13, 1]
z(1-26)=-43572916213590401338264590214819357048102430056970149704781/21  [3, 1; 7, 1]
z(1-28)=1194089697312559886180765426309942647979398288525057312408625805285251/42630  [2, 1; 3, 1; 5, 1; 7, 2; 29, 1]
z(1-30)=-12571803511139506277546193662338777041927305831095982842136650566411789737953/21483  [3, 2; 7, 1; 11, 1; 31, 1]
z(1-32)=524593197721878004128074038057347681941806656692550020768994456077596565747791967303/28560  [2, 4; 3, 1; 5, 1; 7, 1; 17, 1]
z(1-34)=-17725090082230954879967443748662313102060531752364945964209151256529495969384067713808041/21  [3, 1; 7, 1]
z(1-36)=958701643492633236702246155351371972979738625422460183404444752508275969194707626956442493475867873661/17272710  [2, 1; 3, 3; 5, 1; 7, 1; 13, 1; 19, 1; 37, 1]
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]
37  Mat([[37, [37, 0]~, 1, 2, [1, 0]~], 1])
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)=22620741302181663024236570255435200710817/3480  [2, 3; 3, 1; 5, 1; 29, 1]
z(1-30)=487857934646005911764739665381199198181718311/2772  [2, 2; 3, 2; 7, 1; 11, 1]
z(1-32)=102010928071772976385504537152795193127593261481587/16320  [2, 6; 3, 1; 5, 1; 17, 1]
z(1-34)=3434757869192636734100930146655497570361814688585871/12  [2, 2; 3, 1]
z(1-36)=88459896110093779093586793692246545522548443631029537081731931/5314680  [2, 3; 3, 3; 5, 1; 7, 1; 19, 1; 37, 1]
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])
37  Mat([[37, [37, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~], 1])
  ***   not enough memory
(13:25) gp > (13:25) gp > default(parisize,1000000000)
   parisize = 1000000000
  ***   not enough memory
(13:27) gp > (13:27) gp > defualt(parisize,100000000)
  ***   unknown function or error in formal parameters: defualt(parisize,100
                                                        ^-------------------
(13:27) gp > (13:27) gp > default(parisize,100000000)
   parisize = 100000000
  ***   not enough memory
(13:27) gp > (13:27) gp > defualt(parisize,10000000)
  ***   unknown function or error in formal parameters: defualt(parisize,100
                                                        ^-------------------
(13:28) gp > (13:28) gp > default(parisize,10000000)
   parisize = 10000000
(13:28) gp > (13:28) gp > \rList
? L=[x^2+x-1,x^3+x^2-2*x-1,x^2-2,x^5+x^4-4*x^3-3*x^2+3*x+1,x^2-3,x^6+x^5-5*x^4-4*x^3+6*x^2+3*x-1,x^2+x-1,x^2-2,x^2-3,x^2-13,x^2-17,x^2-21,x^2-24,x^2-28,x^2-29,x^2-33,x^2-37,x^2-40,x^2-41,x^2-44,x^3+x^2-2*x-1,x^3-9*x^2+14*x-1,x^3-354315*x^2+39645147398*x-1424861898171643];for(i=2,40,k=nfinit(L[i]);print("k=nfinit(",L[i],")");forprime(r=2,37,a=idealprincipal(k,r);print(r,"  ",idealfactor(k,a)));k=zetakinit(L[i]);for(j=1,18,a=round(zetak(k,1-2*j)*37!)/37!;print("z(1-",2*j,")=",a,"  ",factor(denominator(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])
37  Mat([[37, [37, 0, 0]~, 1, 3, [1, 0, 0]~], 1])
z(1-2)=-1/21  [3, 1; 7, 1]
z(1-4)=79/210  [2, 1; 3, 1; 5, 1; 7, 1]
z(1-6)=-7393/63  [3, 2; 7, 1]
z(1-8)=142490119/420  [2, 2; 3, 1; 5, 1; 7, 1]
z(1-10)=-1141452324871/231  [3, 1; 7, 1; 11, 1]
z(1-12)=2101941875088322867/8190  [2, 1; 3, 2; 5, 1; 7, 1; 13, 1]
z(1-14)=-5589087133015782866737/147  [3, 1; 7, 2]
z(1-16)=196210654771718649388061754983/14280  [2, 3; 3, 1; 5, 1; 7, 1; 17, 1]
z(1-18)=-38746229519570895574625913188448091/3591  [3, 3; 7, 1; 19, 1]
z(1-20)=194530316743193504738135306900338932340229/11550  [2, 1; 3, 1; 5, 2; 7, 1; 11, 1]
z(1-22)=-23518697248282245943905832963281144323974983973/483  [3, 1; 7, 1; 23, 1]
z(1-24)=4032222871166671567558267339270905870778751618513341627/16380  [2, 2; 3, 2; 5, 1; 7, 1; 13, 1]
z(1-26)=-43572916213590401338264590214819357048102430056970149704781/21  [3, 1; 7, 1]
z(1-28)=1194089697312559886180765426309942647979398288525057312408625805285251/42630  [2, 1; 3, 1; 5, 1; 7, 2; 29, 1]
z(1-30)=-12571803511139506277546193662338777041927305831095982842136650566411789737953/21483  [3, 2; 7, 1; 11, 1; 31, 1]
z(1-32)=524593197721878004128074038057347681941806656692550020768994456077596565747791967303/28560  [2, 4; 3, 1; 5, 1; 7, 1; 17, 1]
z(1-34)=-17725090082230954879967443748662313102060531752364945964209151256529495969384067713808041/21  [3, 1; 7, 1]
z(1-36)=958701643492633236702246155351371972979738625422460183404444752508275969194707626956442493475867873661/17272710  [2, 1; 3, 3; 5, 1; 7, 1; 13, 1; 19, 1; 37, 1]
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]
37  Mat([[37, [37, 0]~, 1, 2, [1, 0]~], 1])
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)=22620741302181663024236570255435200710817/3480  [2, 3; 3, 1; 5, 1; 29, 1]
z(1-30)=487857934646005911764739665381199198181718311/2772  [2, 2; 3, 2; 7, 1; 11, 1]
z(1-32)=102010928071772976385504537152795193127593261481587/16320  [2, 6; 3, 1; 5, 1; 17, 1]
z(1-34)=3434757869192636734100930146655497570361814688585871/12  [2, 2; 3, 1]
z(1-36)=88459896110093779093586793692246545522548443631029537081731931/5314680  [2, 3; 3, 3; 5, 1; 7, 1; 19, 1; 37, 1]
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])
37  Mat([[37, [37, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~], 1])
  ***   not enough memory
(13:33) gp > (13:33) gp > \q
Good bye!