History of Weber class polynomials $W_D$

 Display properties:   number-header: $W_D(x)$-Numbers: []+Numbers:+- params:+    D: '-7'+  number: x - 1+  comment: $h(D)=1$; fundamental discriminant of $\mathbb{Q}(\sqrt{-7})$+- params:+    D: '-23'+  number: x^3 - x - 1+  comment: $h(D)=3$; fundamental discriminant of $\mathbb{Q}(\sqrt{-23})$+- params:+    D: '-31'+  number: x^3 - x^2 - 1+  comment: $h(D)=3$; fundamental discriminant of $\mathbb{Q}(\sqrt{-31})$+- params:+    D: '-47'+  number: x^5 - x^3 - 2*x^2 - 2*x - 1+  comment: $h(D)=5$; fundamental discriminant of $\mathbb{Q}(\sqrt{-47})$+- params:+    D: '-55'+  number: x^4 - 2*x^3 + x - 1+  comment: $h(D)=4$; fundamental discriminant of $\mathbb{Q}(\sqrt{-55})$+- params:+    D: '-71'+  number: x^7 - 2*x^6 - x^5 + x^4 + x^3 + x^2 - x - 1+  comment: $h(D)=7$; fundamental discriminant of $\mathbb{Q}(\sqrt{-71})$+- params:+    D: '-79'+  number: x^5 - 3*x^4 + 2*x^3 - x^2 + x - 1+  comment: $h(D)=5$; fundamental discriminant of $\mathbb{Q}(\sqrt{-79})$+- params:+    D: '-95'+  number: x^8 - 2*x^7 - 2*x^6 + x^5 + 2*x^4 - x^3 + x - 1+  comment: $h(D)=8$; fundamental discriminant of $\mathbb{Q}(\sqrt{-95})$+- params:+    D: '-103'+  number: x^5 - x^4 - 3*x^3 - 3*x^2 - 2*x - 1+  comment: $h(D)=5$; fundamental discriminant of $\mathbb{Q}(\sqrt{-103})$+- params:+    D: '-119'+  number: x^10 - 4*x^9 + 5*x^8 - 8*x^7 + 9*x^6 - 7*x^5 + 5*x^4 - 4*x^3 + 2*x^2 - x+    + 1+  comment: $h(D)=10$; fundamental discriminant of $\mathbb{Q}(\sqrt{-119})$+- params:+    D: '-127'+  number: x^5 - 3*x^4 - x^3 + 2*x^2 + x - 1+  comment: $h(D)=5$; fundamental discriminant of $\mathbb{Q}(\sqrt{-127})$+- params:+    D: '-143'+  number: x^10 - 6*x^9 + 12*x^8 - 13*x^7 + 9*x^6 - 3*x^5 - 3*x^4 + 6*x^3 - 6*x^2 ++    3*x - 1+  comment: $h(D)=10$; fundamental discriminant of $\mathbb{Q}(\sqrt{-143})$+- params:+    D: '-151'+  number: x^7 - 3*x^6 - x^5 - 3*x^4 - x^2 - x - 1+  comment: $h(D)=7$; fundamental discriminant of $\mathbb{Q}(\sqrt{-151})$+- params:+    D: '-167'+  number: x^11 - 2*x^10 - 4*x^9 - 9*x^8 - 7*x^7 - 11*x^6 - 6*x^5 - 10*x^4 - 4*x^3+    - 5*x^2 - x - 1+  comment: $h(D)=11$; fundamental discriminant of $\mathbb{Q}(\sqrt{-167})$+- params:+    D: '-175'+  number: x^6 - 4*x^5 + x + 1+  comment: $h(D)=6$; order of conductor $5$ in $\mathbb{Q}(\sqrt{-7})$+- params:+    D: '-191'+  number: x^13 - 6*x^12 + 10*x^11 - 16*x^10 + 22*x^9 - 19*x^8 + 11*x^7 - 5*x^6 - x^5+    + 5*x^4 - 4*x^3 + 2*x - 1+  comment: $h(D)=13$; fundamental discriminant of $\mathbb{Q}(\sqrt{-191})$+- params:+    D: '-199'+  number: x^9 - 5*x^8 + 3*x^7 - 3*x^6 - 3*x^3 - x - 1+  comment: $h(D)=9$; fundamental discriminant of $\mathbb{Q}(\sqrt{-199})$+- params:+    D: '-215'+  number: x^14 - 6*x^13 + 4*x^12 + 11*x^11 - 13*x^10 - 7*x^9 + 16*x^8 - 4*x^7 - 13*x^6+    + 8*x^5 + 3*x^4 - 6*x^3 + 2*x - 1+  comment: $h(D)=14$; fundamental discriminant of $\mathbb{Q}(\sqrt{-215})$+- params:+    D: '-223'+  number: x^7 - 5*x^6 + x^4 - 4*x^3 - x^2 - 1+  comment: $h(D)=7$; fundamental discriminant of $\mathbb{Q}(\sqrt{-223})$+- params:+    D: '-239'+  number: x^15 - 6*x^14 + 2*x^13 + 8*x^12 + 4*x^11 - 27*x^10 + 13*x^9 + 15*x^8 - 4*x^7+    - 20*x^6 + 13*x^5 + 5*x^4 - 4*x^3 - 4*x^2 + 4*x - 1+  comment: $h(D)=15$; fundamental discriminant of $\mathbb{Q}(\sqrt{-239})$+- params:+    D: '-247'+  number: x^6 - 4*x^5 - 7*x^4 - 7*x^3 - 6*x^2 - 3*x - 1+  comment: $h(D)=6$; fundamental discriminant of $\mathbb{Q}(\sqrt{-247})$+- params:+    D: '-263'+  number: x^13 - 8*x^12 + 16*x^11 - 27*x^10 + 38*x^9 - 36*x^8 + 22*x^7 - 12*x^6 ++    13*x^5 - 19*x^4 + 21*x^3 - 15*x^2 + 6*x - 1+  comment: $h(D)=13$; fundamental discriminant of $\mathbb{Q}(\sqrt{-263})$+- params:+    D: '-271'+  number: x^11 - 5*x^10 - 6*x^9 - 5*x^8 + 3*x^7 + 6*x^6 + 3*x^5 - 3*x^4 - x^3 - x^2+    - 1+  comment: $h(D)=11$; fundamental discriminant of $\mathbb{Q}(\sqrt{-271})$+- params:+    D: '-287'+  number: x^14 - 8*x^13 + 9*x^12 + 6*x^11 - 5*x^10 - 7*x^9 - 8*x^8 + 6*x^7 + 2*x^6+    - x^4 - x^3 + 3*x^2 + x + 1+  comment: $h(D)=14$; fundamental discriminant of $\mathbb{Q}(\sqrt{-287})$+- params:+    D: '-295'+  number: x^8 - 8*x^7 + 9*x^6 - x^5 - 7*x^4 + 10*x^3 - 7*x^2 + 3*x - 1+  comment: $h(D)=8$; fundamental discriminant of $\mathbb{Q}(\sqrt{-295})$+- params:+    D: '-311'+  number: x^19 - 4*x^18 - 16*x^17 - 37*x^16 - 42*x^15 - 38*x^14 - 4*x^13 + 10*x^12+    + 25*x^11 + 18*x^10 + 9*x^9 + x^8 - 10*x^7 - 13*x^6 - 14*x^5 - 8*x^4 - 5*x^3 -+    2*x^2 - x - 1+  comment: $h(D)=19$; fundamental discriminant of $\mathbb{Q}(\sqrt{-311})$+- params:+    D: '-319'+  number: x^10 - 6*x^9 - 9*x^8 - 5*x^7 - x^6 - 2*x^5 - 10*x^4 - 14*x^3 - 11*x^2 -+    5*x - 1+  comment: $h(D)=10$; fundamental discriminant of $\mathbb{Q}(\sqrt{-319})$+- params:+    D: '-335'+  number: x^18 - 4*x^17 - 20*x^16 - 55*x^15 - 106*x^14 - 144*x^13 - 163*x^12 - 174*x^11+    - 179*x^10 - 171*x^9 - 144*x^8 - 102*x^7 - 64*x^6 - 42*x^5 - 33*x^4 - 25*x^3 -+    14*x^2 - 5*x - 1+  comment: $h(D)=18$; fundamental discriminant of $\mathbb{Q}(\sqrt{-335})$+- params:+    D: '-343'+  number: x^7 - 7*x^6 - 7*x^5 - 7*x^4 - 1+  comment: $h(D)=7$; order of conductor $7$ in $\mathbb{Q}(\sqrt{-7})$+- params:+    D: '-359'+  number: x^19 - 14*x^18 + 59*x^17 - 113*x^16 + 91*x^15 + 19*x^14 - 90*x^13 + 51*x^12+    + 2*x^11 - 5*x^10 + 9*x^9 - 30*x^8 + 22*x^7 + 7*x^6 - 14*x^5 + 3*x^4 + 2*x^3 -+    2*x^2 + 2*x - 1+  comment: $h(D)=19$; fundamental discriminant of $\mathbb{Q}(\sqrt{-359})$+- params:+    D: '-367'+  number: x^9 - 9*x^8 + 3*x^7 - 2*x^6 + 2*x^4 - 6*x^3 + x^2 + 2*x - 1+  comment: $h(D)=9$; fundamental discriminant of $\mathbb{Q}(\sqrt{-367})$+- params:+    D: '-383'+  number: x^17 - 6*x^16 - 24*x^15 - 42*x^14 - 31*x^13 - 23*x^12 - 7*x^11 - x^10 -+    4*x^9 - 11*x^8 - 7*x^7 - 13*x^6 - x^5 + x^3 + x^2 + x - 1+  comment: $h(D)=17$; fundamental discriminant of $\mathbb{Q}(\sqrt{-383})$+- params:+    D: '-391'+  number: x^14 - 8*x^13 - 12*x^12 - 12*x^11 + 4*x^9 - 3*x^8 - 8*x^7 + 6*x^6 + 15*x^5+    + 7*x^4 - 5*x^3 - 5*x^2 + 1+  comment: $h(D)=14$; fundamental discriminant of $\mathbb{Q}(\sqrt{-391})$+- params:+    D: '-407'+  number: x^16 - 10*x^15 + 4*x^14 - 33*x^13 + 17*x^12 - 19*x^11 - 4*x^10 - 12*x^8+    - 15*x^6 + 2*x^5 - 9*x^4 - x^3 - 2*x^2 - x - 1+  comment: $h(D)=16$; fundamental discriminant of $\mathbb{Q}(\sqrt{-407})$+- params:+    D: '-415'+  number: x^10 - 10*x^9 - x^8 - 7*x^7 - 11*x^6 + 2*x^5 - 14*x^4 + 2*x^3 - 6*x^2 -+    1+  comment: $h(D)=10$; fundamental discriminant of $\mathbb{Q}(\sqrt{-415})$+- params:+    D: '-431'+  number: x^21 - 12*x^20 + 15*x^19 - 16*x^18 + 40*x^17 - 21*x^16 - 10*x^15 - 44*x^14+    - 83*x^13 - 41*x^12 - 66*x^11 + 2*x^10 + 14*x^9 + 30*x^8 + 36*x^7 + 10*x^6 + 4*x^5+    - 9*x^4 - 9*x^3 - 6*x^2 - 3*x - 1+  comment: $h(D)=21$; fundamental discriminant of $\mathbb{Q}(\sqrt{-431})$+- params:+    D: '-439'+  number: x^15 - 13*x^14 + 23*x^13 - 7*x^12 - 24*x^11 + 20*x^10 + 13*x^9 - 38*x^8+    + 29*x^7 + x^6 - 17*x^5 + 7*x^4 + 9*x^3 - 11*x^2 + 5*x - 1+  comment: $h(D)=15$; fundamental discriminant of $\mathbb{Q}(\sqrt{-439})$+- params:+    D: '-455'+  number: x^20 - 6*x^19 - 50*x^18 - 142*x^17 - 200*x^16 - 129*x^15 + 38*x^14 + 191*x^13+    + 246*x^12 + 194*x^11 + 76*x^10 - 30*x^9 - 73*x^8 - 57*x^7 - 15*x^6 + 16*x^5 ++    26*x^4 + 23*x^3 + 15*x^2 + 6*x + 1+  comment: $h(D)=20$; fundamental discriminant of $\mathbb{Q}(\sqrt{-455})$+- params:+    D: '-463'+  number: x^7 - 11*x^6 - 9*x^5 - 8*x^4 - 7*x^3 - 7*x^2 - 3*x - 1+  comment: $h(D)=7$; fundamental discriminant of $\mathbb{Q}(\sqrt{-463})$+- params:+    D: '-479'+  number: x^25 - 10*x^24 - 23*x^23 - 76*x^22 - 104*x^21 - 126*x^20 - 109*x^19 - 144*x^18+    - 205*x^17 - 317*x^16 - 336*x^15 - 280*x^14 - 138*x^13 - 11*x^12 + 76*x^11 + 82*x^10+    + 48*x^9 - 6*x^8 - 47*x^7 - 66*x^6 - 60*x^5 - 41*x^4 - 22*x^3 - 9*x^2 - 3*x -+    1+  comment: $h(D)=25$; fundamental discriminant of $\mathbb{Q}(\sqrt{-479})$+- params:+    D: '-487'+  number: x^7 - 13*x^6 + 4*x^5 - 4*x^4 + 7*x^3 - 4*x^2 + x - 1+  comment: $h(D)=7$; fundamental discriminant of $\mathbb{Q}(\sqrt{-487})$+- params:+    D: '-503'+  number: x^21 - 18*x^20 + 69*x^19 - 87*x^18 - 34*x^17 + 171*x^16 - 106*x^15 - 74*x^14+    + 92*x^13 + 19*x^12 - 27*x^11 - 30*x^10 + 23*x^9 + 10*x^8 - 12*x^7 + 3*x^6 - 7*x^4+    + 6*x^3 + x^2 - 1+  comment: $h(D)=21$; fundamental discriminant of $\mathbb{Q}(\sqrt{-503})$+- params:+    D: '-511'+  number: x^14 - 16*x^13 + 36*x^12 - 56*x^11 + 77*x^10 - 84*x^9 + 70*x^8 - 37*x^7+    + 16*x^6 - 21*x^5 + 35*x^4 - 35*x^3 + 21*x^2 - 7*x + 1+  comment: $h(D)=14$; fundamental discriminant of $\mathbb{Q}(\sqrt{-511})$+- params:+    D: '-527'+  number: x^18 - 12*x^17 - 31*x^16 - 24*x^15 + 45*x^14 + 15*x^13 + 12*x^12 + 20*x^11+    - 5*x^10 - 32*x^9 - 10*x^8 - x^7 - 7*x^6 - 4*x^5 + 8*x^4 + 5*x^3 + 2*x^2 + 1+  comment: $h(D)=18$; fundamental discriminant of $\mathbb{Q}(\sqrt{-527})$+- params:+    D: '-535'+  number: x^14 - 16*x^13 + 20*x^12 + 7*x^11 - 14*x^10 + 10*x^9 - 37*x^8 + 34*x^7 ++    3*x^6 - x^5 - 16*x^4 + 6*x^3 + 3*x^2 - 1+  comment: $h(D)=14$; fundamental discriminant of $\mathbb{Q}(\sqrt{-535})$+- params:+    D: '-551'+  number: x^26 - 10*x^25 - 62*x^24 - 237*x^23 - 618*x^22 - 1183*x^21 - 1773*x^20 -+    2121*x^19 - 2049*x^18 - 1625*x^17 - 1011*x^16 - 416*x^15 - 25*x^14 + 148*x^13+    + 111*x^12 - 95*x^11 - 323*x^10 - 469*x^9 - 504*x^8 - 437*x^7 - 316*x^6 - 198*x^5+    - 109*x^4 - 49*x^3 - 17*x^2 - 5*x - 1+  comment: $h(D)=26$; fundamental discriminant of $\mathbb{Q}(\sqrt{-551})$+- params:+    D: '-559'+  number: x^16 - 20*x^15 + 78*x^14 - 161*x^13 + 196*x^12 - 139*x^11 + 18*x^10 + 83*x^9+    - 123*x^8 + 98*x^7 - 51*x^6 + 14*x^5 - x^4 - 2*x^3 + x - 1+  comment: $h(D)=16$; fundamental discriminant of $\mathbb{Q}(\sqrt{-559})$+- params:+    D: '-575'+  number: x^18 - 20*x^17 + 64*x^16 - 64*x^15 + 25*x^12 - 60*x^11 - x^8 - 15*x^7 ++    6*x^6 + 4*x^5 + x^3 + 5*x^2 + 4*x + 1+  comment: $h(D)=18$; order of conductor $5$ in $\mathbb{Q}(\sqrt{-23})$+- params:+    D: '-583'+  number: x^8 - 16*x^7 - 12*x^6 + 11*x^5 + 12*x^4 + 5*x^3 - 3*x^2 - 4*x - 1+  comment: $h(D)=8$; fundamental discriminant of $\mathbb{Q}(\sqrt{-583})$+- params:+    D: '-599'+  number: x^25 - 16*x^24 - 25*x^23 + 3*x^22 + 82*x^21 - 92*x^20 - 63*x^19 - 28*x^18+    + 66*x^17 + 24*x^16 - 35*x^15 + 71*x^13 + 6*x^12 - 58*x^11 - 22*x^10 + 36*x^9+    + 13*x^8 - 32*x^7 + 5*x^6 + 17*x^5 - 6*x^4 - 8*x^3 + x^2 + 2*x - 1+  comment: $h(D)=25$; fundamental discriminant of $\mathbb{Q}(\sqrt{-599})$+- params:+    D: '-607'+  number: x^13 - 17*x^12 - 15*x^11 + 16*x^10 + 34*x^9 + 3*x^8 - 21*x^7 - 21*x^6 ++    9*x^5 + 7*x^4 + x^3 - 3*x^2 + 2*x - 1+  comment: $h(D)=13$; fundamental discriminant of $\mathbb{Q}(\sqrt{-607})$+- params:+    D: '-623'+  number: x^22 - 22*x^21 + 73*x^20 - 190*x^19 + 442*x^18 - 708*x^17 + 787*x^16 - 712*x^15+    + 546*x^14 - 303*x^13 + 129*x^12 - 74*x^11 + 39*x^10 + 3*x^9 - 38*x^8 + 61*x^7+    - 57*x^6 + 34*x^5 - 7*x^4 - 12*x^3 + 14*x^2 - 6*x + 1+  comment: $h(D)=22$; fundamental discriminant of $\mathbb{Q}(\sqrt{-623})$+- params:+    D: '-631'+  number: x^13 - 17*x^12 - 33*x^11 - 69*x^10 - 77*x^9 - 71*x^8 - 72*x^7 - 54*x^6 -+    46*x^5 - 37*x^4 - 21*x^3 - 12*x^2 - 4*x - 1+  comment: $h(D)=13$; fundamental discriminant of $\mathbb{Q}(\sqrt{-631})$+- params:+    D: '-647'+  number: x^23 - 20*x^22 + 3*x^21 + 37*x^20 + 46*x^19 - 2*x^18 - 151*x^17 - 384*x^16+    - 610*x^15 - 849*x^14 - 995*x^13 - 955*x^12 - 798*x^11 - 596*x^10 - 378*x^9 -+    202*x^8 - 75*x^7 + 21*x^5 + 19*x^4 + 13*x^3 + 3*x^2 - 2*x - 1+  comment: $h(D)=23$; fundamental discriminant of $\mathbb{Q}(\sqrt{-647})$+- params:+    D: '-655'+  number: x^12 - 18*x^11 - 41*x^10 - 47*x^9 - 55*x^8 - 43*x^7 - 32*x^6 - 19*x^5 -+    15*x^4 - 4*x^3 - 6*x^2 + x - 1+  comment: $h(D)=12$; fundamental discriminant of $\mathbb{Q}(\sqrt{-655})$+- params:+    D: '-671'+  number: x^30 - 18*x^29 - 58*x^28 - 101*x^27 - 12*x^26 - 37*x^25 + 80*x^24 - 151*x^23+    + 68*x^22 + 107*x^21 + 172*x^20 - 105*x^19 - 103*x^18 + 39*x^17 - 130*x^16 - 12*x^15+    - 7*x^14 + 123*x^13 - 9*x^12 + 30*x^11 + 4*x^10 - 31*x^9 - 33*x^8 - 6*x^7 + 13*x^6+    + 6*x^5 + x^4 + 7*x^3 - 4*x^2 - 1+  comment: $h(D)=30$; fundamental discriminant of $\mathbb{Q}(\sqrt{-671})$+- params:+    D: '-679'+  number: x^18 - 24*x^17 + 58*x^16 - 60*x^15 + 24*x^14 - 27*x^13 + 33*x^12 - 9*x^11+    - 8*x^10 - 3*x^9 + 13*x^8 + 6*x^7 + 12*x^6 - 9*x^5 + 12*x^4 + 7*x^2 + 1+  comment: $h(D)=18$; fundamental discriminant of $\mathbb{Q}(\sqrt{-679})$+- params:+    D: '-695'+  number: x^24 - 16*x^23 - 118*x^22 - 443*x^21 - 1125*x^20 - 1926*x^19 - 2175*x^18+    - 1631*x^17 - 1013*x^16 - 940*x^15 - 978*x^14 - 519*x^13 + 108*x^12 + 267*x^11+    + 96*x^10 + 96*x^9 + 231*x^8 + 190*x^7 + 18*x^6 - 59*x^5 - 29*x^4 - x^3 - x^2+    - 3*x - 1+  comment: $h(D)=24$; fundamental discriminant of $\mathbb{Q}(\sqrt{-695})$+- params:+    D: '-703'+  number: x^14 - 22*x^13 - 15*x^12 - 41*x^11 - 11*x^10 - 6*x^9 + 7*x^8 + 15*x^7 ++    2*x^6 + 4*x^5 - 9*x^4 - x^3 - x^2 - 3*x - 1+  comment: $h(D)=14$; fundamental discriminant of $\mathbb{Q}(\sqrt{-703})$+- params:+    D: '-719'+  number: x^31 - 26*x^30 + 53*x^29 + 68*x^28 - 168*x^27 - 176*x^26 + 161*x^25 + 172*x^24+    - 175*x^23 - 440*x^22 - 341*x^21 - 169*x^20 - 293*x^19 - 255*x^18 - 57*x^17 -+    9*x^16 - 114*x^15 - 157*x^14 - 21*x^13 + 68*x^12 + 59*x^11 + 20*x^10 + 37*x^9+    + 29*x^8 + 36*x^7 + 24*x^6 + 20*x^5 - x^4 - 11*x^3 - 11*x^2 - 4*x - 1+  comment: $h(D)=31$; fundamental discriminant of $\mathbb{Q}(\sqrt{-719})$+- params:+    D: '-727'+  number: x^13 - 25*x^12 + 23*x^11 - 41*x^10 + 15*x^9 - 30*x^8 - 8*x^7 - 4*x^6 - 6*x^4+    + 5*x^3 - 8*x^2 + 4*x - 1+  comment: $h(D)=13$; fundamental discriminant of $\mathbb{Q}(\sqrt{-727})$+- params:+    D: '-743'+  number: x^21 - 26*x^20 + 22*x^19 + 33*x^18 + 86*x^17 - 515*x^16 + 895*x^15 - 825*x^14+    + 509*x^13 - 451*x^12 + 701*x^11 - 897*x^10 + 832*x^9 - 642*x^8 + 491*x^7 - 387*x^6+    + 274*x^5 - 156*x^4 + 68*x^3 - 23*x^2 + 6*x - 1+  comment: $h(D)=21$; fundamental discriminant of $\mathbb{Q}(\sqrt{-743})$+- params:+    D: '-751'+  number: x^15 - 25*x^14 - 12*x^13 - 53*x^12 + 9*x^11 - 21*x^10 + 4*x^9 - 2*x^8 ++    29*x^7 - 17*x^6 + 12*x^5 - 7*x^4 + 6*x^3 - 9*x^2 + 5*x - 1+  comment: $h(D)=15$; fundamental discriminant of $\mathbb{Q}(\sqrt{-751})$+- params:+    D: '-767'+  number: x^22 - 24*x^21 - 60*x^20 - 187*x^19 - 260*x^18 - 74*x^17 - 20*x^16 - 136*x^15+    - 152*x^14 - 174*x^13 - 74*x^12 + 111*x^11 + 34*x^10 - 156*x^9 - 131*x^8 + 34*x^7+    + 81*x^6 - 3*x^5 - 39*x^4 - 5*x^3 + 9*x^2 + x - 1+  comment: $h(D)=22$; fundamental discriminant of $\mathbb{Q}(\sqrt{-767})$+- params:+    D: '-775'+  number: x^12 - 26*x^11 - 29*x^10 + 18*x^9 + 43*x^8 + 7*x^7 - 10*x^6 - 23*x^5 + x^4+    + 9*x^3 + 4*x^2 - 5*x + 1+  comment: $h(D)=12$; order of conductor $5$ in $\mathbb{Q}(\sqrt{-31})$+- params:+    D: '-791'+  number: x^32 - 30*x^31 + 55*x^30 - 34*x^29 + 171*x^28 - 186*x^27 - 278*x^26 - 726*x^25+    - 1095*x^24 - 1098*x^23 - 1235*x^22 - 704*x^21 - 203*x^20 + 722*x^19 + 1729*x^18+    + 2538*x^17 + 3118*x^16 + 3207*x^15 + 3052*x^14 + 2752*x^13 + 2381*x^12 + 1995*x^11+    + 1558*x^10 + 1121*x^9 + 760*x^8 + 489*x^7 + 327*x^6 + 212*x^5 + 132*x^4 + 67*x^3+    + 27*x^2 + 7*x + 1+  comment: $h(D)=32$; fundamental discriminant of $\mathbb{Q}(\sqrt{-791})$+- params:+    D: '-799'+  number: x^16 - 30*x^15 + 39*x^14 + 30*x^13 - 75*x^12 - 18*x^11 + 18*x^10 + 24*x^9+    + 52*x^8 - 6*x^7 - 39*x^6 - 21*x^5 - 6*x^4 + 9*x^3 + 9*x^2 + 3*x + 1+  comment: $h(D)=16$; fundamental discriminant of $\mathbb{Q}(\sqrt{-799})$+- params:+    D: '-815'+  number: x^30 - 22*x^29 - 198*x^28 - 813*x^27 - 2024*x^26 - 3585*x^25 - 4669*x^24+    - 4361*x^23 - 2694*x^22 - 466*x^21 + 936*x^20 + 1094*x^19 + 308*x^18 - 534*x^17+    - 966*x^16 - 1075*x^15 - 1137*x^14 - 1365*x^13 - 1528*x^12 - 1444*x^11 - 1075*x^10+    - 652*x^9 - 373*x^8 - 270*x^7 - 258*x^6 - 226*x^5 - 159*x^4 - 83*x^3 - 32*x^2+    - 8*x - 1+  comment: $h(D)=30$; fundamental discriminant of $\mathbb{Q}(\sqrt{-815})$+- params:+    D: '-823'+  number: x^9 - 29*x^8 - 36*x^7 - 30*x^6 - 33*x^5 - 30*x^4 - 12*x^3 - x - 1+  comment: $h(D)=9$; fundamental discriminant of $\mathbb{Q}(\sqrt{-823})$+- params:+    D: '-839'+  number: x^33 - 34*x^32 + 93*x^31 - 329*x^30 + 796*x^29 - 1415*x^28 + 1618*x^27 -+    1908*x^26 + 1977*x^25 - 1958*x^24 + 1127*x^23 - 979*x^22 + 372*x^21 - 71*x^20+    - 497*x^19 - 26*x^18 - 530*x^17 + 108*x^16 - 155*x^15 - 188*x^14 - 204*x^13 -+    267*x^12 - 3*x^11 - 104*x^10 - 26*x^9 - 126*x^8 - 52*x^7 - 41*x^6 - 9*x^5 - 12*x^4+    - 15*x^3 - 10*x^2 - 5*x - 1+  comment: $h(D)=33$; fundamental discriminant of $\mathbb{Q}(\sqrt{-839})$+- params:+    D: '-847'+  number: x^10 - 34*x^9 + 67*x^8 - 12*x^7 - 43*x^6 + 10*x^5 + 23*x^4 - 12*x^3 + x^2+    - x + 1+  comment: $h(D)=10$; order of conductor $11$ in $\mathbb{Q}(\sqrt{-7})$+- params:+    D: '-863'+  number: x^21 - 42*x^20 + 332*x^19 - 1316*x^18 + 3387*x^17 - 6531*x^16 + 10045*x^15+    - 12933*x^14 + 14339*x^13 - 14012*x^12 + 12265*x^11 - 9789*x^10 + 7233*x^9 - 5008*x^8+    + 3250*x^7 - 1946*x^6 + 1038*x^5 - 470*x^4 + 171*x^3 - 47*x^2 + 9*x - 1+  comment: $h(D)=21$; fundamental discriminant of $\mathbb{Q}(\sqrt{-863})$+- params:+    D: '-871'+  number: x^22 - 32*x^21 - 51*x^20 - 173*x^19 - 129*x^18 - 206*x^17 - 22*x^16 - 33*x^15+    + 37*x^14 + 31*x^13 - 30*x^12 + 22*x^11 - 69*x^10 - 8*x^9 - 40*x^8 + 6*x^7 - 2*x^6+    + x^5 - 9*x^4 - 11*x^3 - 9*x^2 - 2*x - 1+  comment: $h(D)=22$; fundamental discriminant of $\mathbb{Q}(\sqrt{-871})$+- params:+    D: '-887'+  number: x^29 - 32*x^28 - 98*x^27 - 95*x^26 + 265*x^25 + 6*x^24 - 13*x^23 - 247*x^22+    + 268*x^21 - 349*x^20 + 413*x^19 - 405*x^18 + 574*x^17 - 839*x^16 + 866*x^15 -+    953*x^14 + 951*x^13 - 820*x^12 + 758*x^11 - 628*x^10 + 447*x^9 - 336*x^8 + 217*x^7+    - 115*x^6 + 70*x^5 - 29*x^4 + 7*x^3 - 7*x^2 - x - 1+  comment: $h(D)=29$; fundamental discriminant of $\mathbb{Q}(\sqrt{-887})$+- params:+    D: '-895'+  number: x^16 - 36*x^15 + 17*x^14 + 31*x^13 - 95*x^12 + 24*x^11 - 8*x^10 + 29*x^9+    - 42*x^8 + 3*x^7 - 17*x^6 + 26*x^5 - 7*x^4 - 9*x^3 - x^2 + 4*x - 1+  comment: $h(D)=16$; fundamental discriminant of $\mathbb{Q}(\sqrt{-895})$+- params:+    D: '-911'+  number: x^31 - 38*x^30 + 54*x^29 - 324*x^28 + 682*x^27 - 1009*x^26 + 1574*x^25 -+    2183*x^24 + 2267*x^23 - 2041*x^22 + 2736*x^21 - 4322*x^20 + 4854*x^19 - 3806*x^18+    + 2937*x^17 - 3408*x^16 + 3938*x^15 - 3132*x^14 + 1783*x^13 - 1333*x^12 + 1700*x^11+    - 1778*x^10 + 1182*x^9 - 524*x^8 + 300*x^7 - 371*x^6 + 397*x^5 - 283*x^4 + 136*x^3+    - 44*x^2 + 9*x - 1+  comment: $h(D)=31$; fundamental discriminant of $\mathbb{Q}(\sqrt{-911})$+- params:+    D: '-919'+  number: x^19 - 37*x^18 - 17*x^17 + 77*x^16 + 15*x^15 - 183*x^14 - 147*x^13 + 63*x^12+    + 112*x^11 + 29*x^10 + 4*x^9 + 23*x^8 - 6*x^7 - 51*x^6 - 42*x^5 - 9*x^4 - 5*x^3+    - 10*x^2 - 5*x - 1+  comment: $h(D)=19$; fundamental discriminant of $\mathbb{Q}(\sqrt{-919})$+- params:+    D: '-935'+  number: x^28 - 44*x^27 + 212*x^26 - 270*x^25 - 298*x^24 + 952*x^23 - 1222*x^22 ++    772*x^21 + 517*x^20 - 1837*x^19 + 2371*x^18 - 1853*x^17 + 558*x^16 + 896*x^15+    - 1834*x^14 + 2075*x^13 - 1702*x^12 + 884*x^11 - 38*x^10 - 552*x^9 + 787*x^8 -+    707*x^7 + 508*x^6 - 307*x^5 + 155*x^4 - 67*x^3 + 22*x^2 - 5*x + 1+  comment: $h(D)=28$; fundamental discriminant of $\mathbb{Q}(\sqrt{-935})$+- params:+    D: '-943'+  number: x^16 - 38*x^15 - 55*x^14 + 32*x^13 + 66*x^12 - 46*x^11 - 59*x^10 + 28*x^9+    + 58*x^8 + 2*x^7 - 38*x^6 - 11*x^5 + x^3 + 8*x^2 + 5*x + 1+  comment: $h(D)=16$; fundamental discriminant of $\mathbb{Q}(\sqrt{-943})$+- params:+    D: '-959'+  number: x^36 - 40*x^35 - 35*x^34 + 194*x^33 + 515*x^32 - 1377*x^31 - 740*x^30 ++    2568*x^29 + 1518*x^28 - 2434*x^27 - 3070*x^26 + 488*x^25 + 4158*x^24 + 1024*x^23+    - 2989*x^22 - 970*x^21 + 778*x^20 + 726*x^19 + 198*x^18 - 954*x^17 - 35*x^16 ++    911*x^15 - 77*x^14 - 320*x^13 - 144*x^12 - 101*x^11 + 217*x^10 + 93*x^9 - 75*x^8+    - 3*x^7 - 11*x^6 - 3*x^5 + 7*x^4 - 7*x^3 + x^2 + 4*x + 1+  comment: $h(D)=36$; fundamental discriminant of $\mathbb{Q}(\sqrt{-959})$+- params:+    D: '-967'+  number: x^11 - 43*x^10 + 68*x^9 - 122*x^8 + 99*x^7 - 81*x^6 + 18*x^5 - 6*x^4 - 13*x^3+    + x^2 - 2*x - 1+  comment: $h(D)=11$; fundamental discriminant of $\mathbb{Q}(\sqrt{-967})$+- params:+    D: '-983'+  number: x^27 - 44*x^26 + 60*x^25 - 463*x^24 + 860*x^23 - 1678*x^22 + 2483*x^21 -+    2840*x^20 + 2620*x^19 - 1761*x^18 + 700*x^17 - 122*x^16 + 256*x^15 - 964*x^14+    + 1531*x^13 - 1556*x^12 + 1071*x^11 - 474*x^10 + 121*x^9 - 118*x^8 + 274*x^7 -+    380*x^6 + 347*x^5 - 234*x^4 + 116*x^3 - 41*x^2 + 9*x - 1+  comment: $h(D)=27$; fundamental discriminant of $\mathbb{Q}(\sqrt{-983})$+- params:+    D: '-991'+  number: x^17 - 43*x^16 - 23*x^15 - 64*x^14 + 36*x^13 + 7*x^12 - 121*x^11 - 54*x^10+    + 50*x^9 - 14*x^8 - 62*x^7 - 21*x^6 + 14*x^5 - 11*x^4 - 18*x^3 - 4*x^2 - x - 1+  comment: $h(D)=17$; fundamental discriminant of $\mathbb{Q}(\sqrt{-991})$+- params:+    D: '-1007'+  number: x^30 - 50*x^29 + 228*x^28 - 171*x^27 - 739*x^26 + 1063*x^25 + 642*x^24 -+    2904*x^23 + 468*x^22 + 3816*x^21 - 2916*x^20 - 2965*x^19 + 4638*x^18 + 738*x^17+    - 3948*x^16 + 1488*x^15 + 2069*x^14 - 1844*x^13 - 303*x^12 + 972*x^11 - 465*x^10+    - 198*x^9 + 349*x^8 - 122*x^7 - 111*x^6 + 110*x^5 + 13*x^4 - 34*x^3 + 3*x^2 ++    4*x - 1+  comment: $h(D)=30$; fundamental discriminant of $\mathbb{Q}(\sqrt{-1007})$+- params:+    D: '-1015'+  number: x^16 - 44*x^15 - 81*x^14 - 16*x^13 + 66*x^12 + 172*x^11 + 126*x^10 + 65*x^9+    - 50*x^8 - 97*x^7 - 69*x^6 - 32*x^5 + 12*x^4 + 11*x^3 + 12*x^2 + 4*x + 1+  comment: $h(D)=16$; fundamental discriminant of $\mathbb{Q}(\sqrt{-1015})$+- params:+    D: '-1031'+  number: x^35 - 46*x^34 - 60*x^33 - 79*x^32 + 427*x^31 - 949*x^30 + 2080*x^29 - 4134*x^28+    + 6081*x^27 - 6076*x^26 + 4296*x^25 - 2342*x^24 + 1071*x^23 - 509*x^22 + 832*x^21+    - 1863*x^20 + 1798*x^19 + 317*x^18 - 2117*x^17 + 1052*x^16 + 1732*x^15 - 2885*x^14+    + 1284*x^13 + 891*x^12 - 1317*x^11 + 133*x^10 + 944*x^9 - 865*x^8 + 101*x^7 ++    350*x^6 - 233*x^5 - 15*x^4 + 88*x^3 - 47*x^2 + 11*x - 1+  comment: $h(D)=35$; fundamental discriminant of $\mathbb{Q}(\sqrt{-1031})$+- params:+    D: '-1039'+  number: x^23 - 49*x^22 + 45*x^21 - 28*x^20 + 4*x^19 - 76*x^18 - 228*x^17 - 40*x^16+    + 34*x^15 + 17*x^14 + 24*x^13 - 19*x^12 + 19*x^11 + 62*x^10 + 48*x^9 - 31*x^8+    - 26*x^7 + 14*x^6 - 6*x^5 - 25*x^4 - 14*x^3 - 4*x^2 - 1+  comment: $h(D)=23$; fundamental discriminant of $\mathbb{Q}(\sqrt{-1039})$+- params:+    D: '-1055'+  number: x^36 - 44*x^35 - 258*x^34 - 1075*x^33 - 3055*x^32 - 5624*x^31 - 7937*x^30+    - 9923*x^29 - 10740*x^28 - 10326*x^27 - 10987*x^26 - 12930*x^25 - 15727*x^24 -+    19268*x^23 - 21853*x^22 - 21786*x^21 - 18965*x^20 - 13816*x^19 - 7586*x^18 - 1621*x^17+    + 2783*x^16 + 5133*x^15 + 5664*x^14 + 4813*x^13 + 3207*x^12 + 1596*x^11 + 298*x^10+    - 488*x^9 - 783*x^8 - 756*x^7 - 557*x^6 - 338*x^5 - 176*x^4 - 70*x^3 - 25*x^2+    - 5*x - 1+  comment: $h(D)=36$; fundamental discriminant of $\mathbb{Q}(\sqrt{-1055})$+- params:+    D: '-1063'+  number: x^19 - 51*x^18 + 27*x^17 + 7*x^16 - 88*x^15 - 15*x^14 + 63*x^13 - 55*x^12+    + 9*x^11 + 60*x^10 - 36*x^9 - 42*x^8 + 7*x^7 - 39*x^6 - 45*x^5 - 8*x^4 - 10*x^3+    - 9*x^2 - 1+  comment: $h(D)=19$; fundamental discriminant of $\mathbb{Q}(\sqrt{-1063})$+- params:+    D: '-1079'+  number: x^34 - 62*x^33 + 558*x^32 - 2311*x^31 + 5554*x^30 - 8827*x^29 + 9963*x^28+    - 8357*x^27 + 4465*x^26 + 47*x^25 - 3906*x^24 + 5450*x^23 - 4672*x^22 + 3217*x^21+    - 2784*x^20 + 2770*x^19 - 3078*x^18 + 3181*x^17 - 2630*x^16 + 1485*x^15 - 620*x^14+    + 207*x^13 - 283*x^12 + 465*x^11 - 501*x^10 + 274*x^9 - 17*x^8 - 152*x^7 + 182*x^6+    - 118*x^5 + 28*x^4 + 17*x^3 - 18*x^2 + 6*x - 1+  comment: $h(D)=34$; fundamental discriminant of $\mathbb{Q}(\sqrt{-1079})$+- params:+    D: '-1087'+  number: x^9 - 51*x^8 - 100*x^7 - 139*x^6 - 124*x^5 - 100*x^4 - 61*x^3 - 28*x^2 -+    8*x - 1+  comment: $h(D)=9$; fundamental discriminant of $\mathbb{Q}(\sqrt{-1087})$+- params:+    D: '-1103'+  number: x^23 - 50*x^22 - 244*x^21 - 524*x^20 - 89*x^19 - 129*x^18 + 28*x^17 - 515*x^16+    - 165*x^15 - 274*x^14 + 16*x^13 + 106*x^12 - 257*x^11 + 19*x^10 - 140*x^9 + 19*x^8+    + 34*x^7 - 53*x^6 + 14*x^5 - 33*x^4 + 17*x^3 - 5*x^2 - 1+  comment: $h(D)=23$; fundamental discriminant of $\mathbb{Q}(\sqrt{-1103})$+- params:+    D: '-1111'+  number: x^22 - 54*x^21 - 81*x^20 - 149*x^19 - 107*x^18 - 62*x^17 - 217*x^16 - 252*x^15+    + 85*x^14 - 237*x^13 - 192*x^12 + 40*x^11 - 128*x^10 - 68*x^9 - 70*x^8 + 45*x^7+    - 95*x^6 + 21*x^5 - 15*x^4 + x^3 - 8*x^2 + 4*x - 1+  comment: $h(D)=22$; fundamental discriminant of $\mathbb{Q}(\sqrt{-1111})$+- params:+    D: '-1127'+  number: x^24 - 56*x^23 - 64*x^22 - 512*x^21 + 14*x^20 + 448*x^19 + 896*x^18 - 217*x^16+    - 1064*x^15 + 35*x^13 + 448*x^12 + 56*x^11 - x^10 - 126*x^9 + 71*x^8 + 8*x^7 ++    21*x^6 - 28*x^5 - 21*x^4 - x^3 + 7*x^2 + x + 1+  comment: $h(D)=24$; order of conductor $7$ in $\mathbb{Q}(\sqrt{-23})$+- params:+    D: '-1135'+  number: x^18 - 54*x^17 - 235*x^16 - 439*x^15 - 512*x^14 - 354*x^13 - 64*x^12 + 199*x^11+    + 370*x^10 + 389*x^9 + 228*x^8 - x^7 - 144*x^6 - 131*x^5 - 43*x^4 + 9*x^3 + 8*x^2+    - x - 1+  comment: $h(D)=18$; fundamental discriminant of $\mathbb{Q}(\sqrt{-1135})$+- params:+    D: '-1151'+  number: x^41 - 64*x^40 + 242*x^39 - 128*x^38 + 67*x^37 - 1356*x^36 - 1996*x^35 ++    1602*x^34 + 1673*x^33 + 4366*x^32 - 273*x^31 - 6530*x^30 - 197*x^29 + 10*x^28+    + 1681*x^27 + 716*x^26 - 2057*x^25 + 885*x^24 + 2067*x^23 + 291*x^22 - 1309*x^21+    - 210*x^20 - 327*x^19 + 197*x^18 + 144*x^17 - 100*x^16 - 33*x^15 + 207*x^14 ++    33*x^13 - 229*x^12 + 128*x^11 - 26*x^10 + 49*x^9 + 32*x^8 - 50*x^7 - 59*x^6 ++    65*x^5 + 3*x^4 - 20*x^3 - 2*x^2 + 5*x - 1+  comment: $h(D)=41$; fundamental discriminant of $\mathbb{Q}(\sqrt{-1151})$+- params:+    D: '-1159'+  number: x^16 - 64*x^15 + 190*x^14 - 191*x^13 - 106*x^12 + 245*x^11 - 95*x^10 - 137*x^9+    + 114*x^8 + 34*x^7 - 106*x^6 + 32*x^5 + 22*x^4 - 23*x^3 - x^2 + 5*x - 1+  comment: $h(D)=16$; fundamental discriminant of $\mathbb{Q}(\sqrt{-1159})$+- params:+    D: '-1175'+  number: x^30 - 60*x^29 - 176*x^28 - 128*x^27 + 768*x^26 - 1024*x^25 + 130*x^24 ++    780*x^23 + 80*x^22 - x^20 - 185*x^19 - 789*x^18 - 612*x^17 + 32*x^16 + 66*x^15+    + 160*x^14 + 333*x^13 + 359*x^12 - 24*x^11 + 30*x^10 - 80*x^9 - 23*x^8 - 54*x^7+    - 21*x^6 + 9*x^5 + 15*x^4 - 11*x^3 + 2*x^2 + 3*x + 1+  comment: $h(D)=30$; order of conductor $5$ in $\mathbb{Q}(\sqrt{-47})$+- params:+    D: '-1183'+  number: x^14 - 64*x^13 + 13*x^12 + 52*x^10 + 78*x^8 + 78*x^6 + 52*x^4 + 13*x^2 ++    x + 1+  comment: $h(D)=14$; order of conductor $13$ in $\mathbb{Q}(\sqrt{-7})$+- params:+    D: '-1199'+  number: x^38 - 70*x^37 + 298*x^36 - 1333*x^35 + 4478*x^34 - 10837*x^33 + 18462*x^32+    - 24217*x^31 + 22355*x^30 - 10334*x^29 - 8896*x^28 + 27317*x^27 - 38888*x^26 ++    40346*x^25 - 32907*x^24 + 20669*x^23 - 6386*x^22 - 7422*x^21 + 16831*x^20 - 19069*x^19+    + 14744*x^18 - 6914*x^17 - 153*x^16 + 3408*x^15 - 3285*x^14 + 1854*x^13 - 601*x^12+    + 142*x^11 - 321*x^10 + 548*x^9 - 563*x^8 + 445*x^7 - 262*x^6 + 98*x^5 - 17*x^4+    - 2*x^3 + 3*x^2 - 1+  comment: $h(D)=38$; fundamental discriminant of $\mathbb{Q}(\sqrt{-1199})$