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Display properties: number-header: $\Psi_{p,k}(x)$-Numbers: []+Numbers:+- params:+ p: '5'+ k: '2'+ number: x^2 + x - 1+ comment: '$p^*=5$; roots $\frac{-1\pm\sqrt{5}}{2}$, in HREF{Algebraic_numbers_of_degree_2#1,1,-1,1}[Algebraic+ numbers of degree 2]; $f=2$: the roots are $2\cos(2\pi a/5)$, $1\leq a\leq 2$'+- params:+ p: '7'+ k: '2'+ number: x^2 + x + 2+ comment: $p^*=-7$; roots $\frac{-1\pm\sqrt{-7}}{2}$, in HREF{Algebraic_numbers_of_degree_2#1,1,2,1}[Algebraic+ numbers of degree 2]+- params:+ p: '7'+ k: '3'+ number: x^3 + x^2 - 2*x - 1+ comment: '$4p=L^2+27M^2$ with $L=1$, $M=1$; $f=2$: the roots are $2\cos(2\pi a/7)$,+ $1\leq a\leq 3$'+- params:+ p: '11'+ k: '2'+ number: x^2 + x + 3+ comment: $p^*=-11$; roots $\frac{-1\pm\sqrt{-11}}{2}$, in HREF{Algebraic_numbers_of_degree_2#1,1,3,1}[Algebraic+ numbers of degree 2]+- params:+ p: '11'+ k: '5'+ number: x^5 + x^4 - 4*x^3 - 3*x^2 + 3*x + 1+ comment: '$f=2$: the roots are $2\cos(2\pi a/11)$, $1\leq a\leq 5$'+- params:+ p: '13'+ k: '2'+ number: x^2 + x - 3+ comment: $p^*=13$; roots $\frac{-1\pm\sqrt{13}}{2}$, in HREF{Algebraic_numbers_of_degree_2#1,1,-3,1}[Algebraic+ numbers of degree 2]+- params:+ p: '13'+ k: '3'+ number: x^3 + x^2 - 4*x + 1+ comment: $4p=L^2+27M^2$ with $L=-5$, $M=1$+- params:+ p: '13'+ k: '4'+ number: x^4 + x^3 + 2*x^2 - 4*x + 3+- params:+ p: '13'+ k: '6'+ number: x^6 + x^5 - 5*x^4 - 4*x^3 + 6*x^2 + 3*x - 1+ comment: '$f=2$: the roots are $2\cos(2\pi a/13)$, $1\leq a\leq 6$'+- params:+ p: '17'+ k: '2'+ number: x^2 + x - 4+ comment: $p^*=17$; roots $\frac{-1\pm\sqrt{17}}{2}$, in HREF{Algebraic_numbers_of_degree_2#1,1,-4,1}[Algebraic+ numbers of degree 2]; a period equation of Gauss's construction of the regular+ 17-gon+- params:+ p: '17'+ k: '4'+ number: x^4 + x^3 - 6*x^2 - x + 1+ comment: a period equation of Gauss's construction of the regular 17-gon+- params:+ p: '17'+ k: '8'+ number: x^8 + x^7 - 7*x^6 - 6*x^5 + 15*x^4 + 10*x^3 - 10*x^2 - 4*x + 1+ comment: '$f=2$: the roots are $2\cos(2\pi a/17)$, $1\leq a\leq 8$; a period equation+ of Gauss''s construction of the regular 17-gon'+- params:+ p: '19'+ k: '2'+ number: x^2 + x + 5+ comment: $p^*=-19$; roots $\frac{-1\pm\sqrt{-19}}{2}$, in HREF{Algebraic_numbers_of_degree_2#1,1,5,1}[Algebraic+ numbers of degree 2]+- params:+ p: '19'+ k: '3'+ number: x^3 + x^2 - 6*x - 7+ comment: $4p=L^2+27M^2$ with $L=7$, $M=1$+- params:+ p: '19'+ k: '6'+ number: x^6 + x^5 + 2*x^4 - 8*x^3 - x^2 + 5*x + 7+- params:+ p: '19'+ k: '9'+ number: x^9 + x^8 - 8*x^7 - 7*x^6 + 21*x^5 + 15*x^4 - 20*x^3 - 10*x^2 + 5*x + 1+ comment: '$f=2$: the roots are $2\cos(2\pi a/19)$, $1\leq a\leq 9$'+- params:+ p: '23'+ k: '2'+ number: x^2 + x + 6+ comment: $p^*=-23$; roots $\frac{-1\pm\sqrt{-23}}{2}$+- params:+ p: '23'+ k: '11'+ number: x^11 + x^10 - 10*x^9 - 9*x^8 + 36*x^7 + 28*x^6 - 56*x^5 - 35*x^4 + 35*x^3+ + 15*x^2 - 6*x - 1+ comment: '$f=2$: the roots are $2\cos(2\pi a/23)$, $1\leq a\leq 11$'+- params:+ p: '29'+ k: '2'+ number: x^2 + x - 7+ comment: $p^*=29$; roots $\frac{-1\pm\sqrt{29}}{2}$+- params:+ p: '29'+ k: '4'+ number: x^4 + x^3 + 4*x^2 + 20*x + 23+- params:+ p: '29'+ k: '7'+ number: x^7 + x^6 - 12*x^5 - 7*x^4 + 28*x^3 + 14*x^2 - 9*x + 1+- params:+ p: '31'+ k: '2'+ number: x^2 + x + 8+ comment: $p^*=-31$; roots $\frac{-1\pm\sqrt{-31}}{2}$+- params:+ p: '31'+ k: '3'+ number: x^3 + x^2 - 10*x - 8+ comment: $4p=L^2+27M^2$ with $L=4$, $M=2$+- params:+ p: '31'+ k: '5'+ number: x^5 + x^4 - 12*x^3 - 21*x^2 + x + 5+- params:+ p: '31'+ k: '6'+ number: x^6 + x^5 + 3*x^4 + 11*x^3 + 44*x^2 + 36*x + 32+- params:+ p: '31'+ k: '10'+ number: x^10 + x^9 + 2*x^8 - 16*x^7 - 9*x^6 - 11*x^5 + 43*x^4 + 6*x^3 + 63*x^2 ++ 20*x + 25+- params:+ p: '37'+ k: '2'+ number: x^2 + x - 9+ comment: $p^*=37$; roots $\frac{-1\pm\sqrt{37}}{2}$+- params:+ p: '37'+ k: '3'+ number: x^3 + x^2 - 12*x + 11+ comment: $4p=L^2+27M^2$ with $L=-11$, $M=1$+- params:+ p: '37'+ k: '4'+ number: x^4 + x^3 + 5*x^2 + 7*x + 49+- params:+ p: '37'+ k: '6'+ number: x^6 + x^5 - 15*x^4 - 28*x^3 + 15*x^2 + 38*x - 1+- params:+ p: '37'+ k: '9'+ number: x^9 + x^8 - 16*x^7 - 11*x^6 + 66*x^5 + 32*x^4 - 73*x^3 - 7*x^2 + 7*x + 1+- params:+ p: '37'+ k: '12'+ number: x^12 + x^11 + 2*x^10 - 20*x^9 - 13*x^8 - 19*x^7 + 85*x^6 + 51*x^5 + 94*x^4+ - 2*x^3 - 13*x^2 - 77*x + 47+- params:+ p: '41'+ k: '2'+ number: x^2 + x - 10+ comment: $p^*=41$; roots $\frac{-1\pm\sqrt{41}}{2}$+- params:+ p: '41'+ k: '4'+ number: x^4 + x^3 - 15*x^2 + 18*x - 4+- params:+ p: '41'+ k: '5'+ number: x^5 + x^4 - 16*x^3 + 5*x^2 + 21*x - 9+- params:+ p: '41'+ k: '8'+ number: x^8 + x^7 + 3*x^6 + 11*x^5 + 44*x^4 - 53*x^3 + 153*x^2 - 160*x + 59+- params:+ p: '41'+ k: '10'+ number: x^10 + x^9 - 18*x^8 - 13*x^7 + 91*x^6 + 47*x^5 - 143*x^4 - 7*x^3 + 72*x^2+ - 23*x + 1+- params:+ p: '43'+ k: '2'+ number: x^2 + x + 11+ comment: $p^*=-43$; roots $\frac{-1\pm\sqrt{-43}}{2}$+- params:+ p: '43'+ k: '3'+ number: x^3 + x^2 - 14*x + 8+ comment: $4p=L^2+27M^2$ with $L=-8$, $M=2$+- params:+ p: '43'+ k: '6'+ number: x^6 + x^5 + 4*x^4 - 23*x^3 + 67*x^2 - 50*x + 44+- params:+ p: '43'+ k: '7'+ number: x^7 + x^6 - 18*x^5 - 35*x^4 + 38*x^3 + 104*x^2 + 7*x - 49+- params:+ p: '47'+ k: '2'+ number: x^2 + x + 12+ comment: $p^*=-47$; roots $\frac{-1\pm\sqrt{-47}}{2}$+- params:+ p: '53'+ k: '2'+ number: x^2 + x - 13+ comment: $p^*=53$; roots $\frac{-1\pm\sqrt{53}}{2}$+- params:+ p: '53'+ k: '4'+ number: x^4 + x^3 + 7*x^2 - 43*x + 47+- params:+ p: '59'+ k: '2'+ number: x^2 + x + 15+ comment: $p^*=-59$; roots $\frac{-1\pm\sqrt{-59}}{2}$+- params:+ p: '61'+ k: '2'+ number: x^2 + x - 15+ comment: $p^*=61$; roots $\frac{-1\pm\sqrt{61}}{2}$+- params:+ p: '61'+ k: '3'+ number: x^3 + x^2 - 20*x - 9+ comment: $4p=L^2+27M^2$ with $L=1$, $M=3$+- params:+ p: '61'+ k: '4'+ number: x^4 + x^3 + 8*x^2 + 42*x + 117+- params:+ p: '61'+ k: '5'+ number: x^5 + x^4 - 24*x^3 - 17*x^2 + 41*x - 13+- params:+ p: '61'+ k: '6'+ number: x^6 + x^5 - 25*x^4 + 8*x^3 + 123*x^2 - 126*x + 27+- params:+ p: '61'+ k: '10'+ number: x^10 + x^9 - 27*x^8 - 56*x^7 + 161*x^6 + 500*x^5 + x^4 - 1023*x^3 - 916*x^2+ - 202*x - 13+- params:+ p: '61'+ k: '12'+ number: x^12 + x^11 + 3*x^10 + 11*x^9 - 17*x^8 - 169*x^7 + 325*x^6 + 167*x^5 - 804*x^4+ + 160*x^3 + 1102*x^2 - 780*x + 1179+- params:+ p: '67'+ k: '2'+ number: x^2 + x + 17+ comment: $p^*=-67$; roots $\frac{-1\pm\sqrt{-67}}{2}$+- params:+ p: '67'+ k: '3'+ number: x^3 + x^2 - 22*x + 5+ comment: $4p=L^2+27M^2$ with $L=-5$, $M=3$+- params:+ p: '67'+ k: '6'+ number: x^6 + x^5 + 6*x^4 + 46*x^3 + 123*x^2 + 169*x + 617+- params:+ p: '67'+ k: '11'+ number: x^11 + x^10 - 30*x^9 - 63*x^8 + 220*x^7 + 698*x^6 - 101*x^5 - 1960*x^4 -+ 1758*x^3 - 35*x^2 + 243*x - 29+- params:+ p: '71'+ k: '2'+ number: x^2 + x + 18+ comment: $p^*=-71$; roots $\frac{-1\pm\sqrt{-71}}{2}$+- params:+ p: '71'+ k: '5'+ number: x^5 + x^4 - 28*x^3 + 37*x^2 + 25*x + 1+- params:+ p: '71'+ k: '7'+ number: x^7 + x^6 - 30*x^5 + 3*x^4 + 254*x^3 - 246*x^2 - 245*x + 137+- params:+ p: '71'+ k: '10'+ number: x^10 + x^9 + 4*x^8 + 20*x^7 - 103*x^6 + 141*x^5 + 207*x^4 - 1254*x^3 + 2635*x^2+ - 4020*x + 3737+- params:+ p: '73'+ k: '2'+ number: x^2 + x - 18+ comment: $p^*=73$; roots $\frac{-1\pm\sqrt{73}}{2}$+- params:+ p: '73'+ k: '3'+ number: x^3 + x^2 - 24*x - 27+ comment: $4p=L^2+27M^2$ with $L=7$, $M=3$+- params:+ p: '73'+ k: '4'+ number: x^4 + x^3 - 27*x^2 - 41*x + 2+- params:+ p: '73'+ k: '6'+ number: x^6 + x^5 - 30*x^4 - 31*x^3 + 206*x^2 + 150*x - 81+- params:+ p: '73'+ k: '8'+ number: x^8 + x^7 + 5*x^6 - 17*x^5 - 46*x^4 - 136*x^3 + 320*x^2 + 512*x + 4096+- params:+ p: '73'+ k: '9'+ number: x^9 + x^8 - 32*x^7 - 11*x^6 + 278*x^5 - 34*x^4 - 427*x^3 + 150*x^2 - 8*x+ - 1+- params:+ p: '73'+ k: '12'+ number: x^12 + x^11 - 33*x^10 - 70*x^9 + 288*x^8 + 929*x^7 - 298*x^6 - 3421*x^5+ - 2921*x^4 + 1195*x^3 + 1718*x^2 - 162*x - 211+- params:+ p: '79'+ k: '2'+ number: x^2 + x + 20+ comment: $p^*=-79$; roots $\frac{-1\pm\sqrt{-79}}{2}$+- params:+ p: '79'+ k: '3'+ number: x^3 + x^2 - 26*x + 41+ comment: $4p=L^2+27M^2$ with $L=-17$, $M=1$+- params:+ p: '79'+ k: '6'+ number: x^6 + x^5 + 7*x^4 + 63*x^3 - 81*x^2 - 353*x + 541+- params:+ p: '83'+ k: '2'+ number: x^2 + x + 21+ comment: $p^*=-83$; roots $\frac{-1\pm\sqrt{-83}}{2}$+- params:+ p: '89'+ k: '2'+ number: x^2 + x - 22+ comment: $p^*=89$; roots $\frac{-1\pm\sqrt{89}}{2}$+- params:+ p: '89'+ k: '4'+ number: x^4 + x^3 - 33*x^2 + 39*x + 8+- params:+ p: '89'+ k: '8'+ number: x^8 + x^7 + 6*x^6 + 46*x^5 - 143*x^4 - 575*x^3 + 1160*x^2 + 16*x + 512+- params:+ p: '89'+ k: '11'+ number: x^11 + x^10 - 40*x^9 - 19*x^8 + 482*x^7 + 84*x^6 - 2185*x^5 + 102*x^4 ++ 3152*x^3 - 781*x^2 + 57*x - 1+- params:+ p: '97'+ k: '2'+ number: x^2 + x - 24+ comment: $p^*=97$; roots $\frac{-1\pm\sqrt{97}}{2}$+- params:+ p: '97'+ k: '3'+ number: x^3 + x^2 - 32*x - 79+ comment: $4p=L^2+27M^2$ with $L=19$, $M=1$+- params:+ p: '97'+ k: '4'+ number: x^4 + x^3 - 36*x^2 + 91*x - 61+- params:+ p: '97'+ k: '6'+ number: x^6 + x^5 - 40*x^4 + 45*x^3 + 236*x^2 - 230*x - 389+- params:+ p: '97'+ k: '8'+ number: x^8 + x^7 - 42*x^6 - 59*x^5 + 497*x^4 + 719*x^3 - 1792*x^2 - 2295*x + 193+- params:+ p: '97'+ k: '12'+ number: x^12 + x^11 - 44*x^10 - 23*x^9 + 608*x^8 + 288*x^7 - 3367*x^6 - 1647*x^5+ + 7459*x^4 + 2633*x^3 - 7037*x^2 - 1034*x + 2209+- params:+ p: '101'+ k: '2'+ number: x^2 + x - 25+ comment: $p^*=101$; roots $\frac{-1\pm\sqrt{101}}{2}$+- params:+ p: '101'+ k: '4'+ number: x^4 + x^3 + 13*x^2 + 19*x + 361+- params:+ p: '101'+ k: '5'+ number: x^5 + x^4 - 40*x^3 + 93*x^2 - 21*x - 17+- params:+ p: '101'+ k: '10'+ number: x^10 + x^9 - 45*x^8 - 12*x^7 + 614*x^6 - 399*x^5 - 2937*x^4 + 3927*x^3 ++ 3176*x^2 - 7776*x + 3433+- params:+ p: '103'+ k: '2'+ number: x^2 + x + 26+ comment: $p^*=-103$; roots $\frac{-1\pm\sqrt{-103}}{2}$+- params:+ p: '103'+ k: '3'+ number: x^3 + x^2 - 34*x - 61+ comment: $4p=L^2+27M^2$ with $L=13$, $M=3$+- params:+ p: '103'+ k: '6'+ number: x^6 + x^5 + 9*x^4 - 101*x^3 + 129*x^2 + 91*x + 1373+- params:+ p: '107'+ k: '2'+ number: x^2 + x + 27+ comment: $p^*=-107$; roots $\frac{-1\pm\sqrt{-107}}{2}$+- params:+ p: '109'+ k: '2'+ number: x^2 + x - 27+ comment: $p^*=109$; roots $\frac{-1\pm\sqrt{109}}{2}$+- params:+ p: '109'+ k: '3'+ number: x^3 + x^2 - 36*x - 4+ comment: $4p=L^2+27M^2$ with $L=-2$, $M=4$+- params:+ p: '109'+ k: '4'+ number: x^4 + x^3 + 14*x^2 - 34*x + 393+- params:+ p: '109'+ k: '6'+ number: x^6 + x^5 - 45*x^4 - 10*x^3 + 135*x^2 + 9*x - 27+- params:+ p: '109'+ k: '9'+ number: x^9 + x^8 - 48*x^7 - 73*x^6 + 660*x^5 + 1454*x^4 - 2149*x^3 - 8350*x^2 -+ 7432*x - 2008+- params:+ p: '109'+ k: '12'+ number: x^12 + x^11 + 5*x^10 - 41*x^9 + 149*x^8 - 794*x^7 + 2669*x^6 + 759*x^5 ++ 3238*x^4 + 2526*x^3 + 13868*x^2 + 6509*x + 2503+- params:+ p: '113'+ k: '2'+ number: x^2 + x - 28+ comment: $p^*=113$; roots $\frac{-1\pm\sqrt{113}}{2}$+- params:+ p: '113'+ k: '4'+ number: x^4 + x^3 - 42*x^2 - 120*x - 64+- params:+ p: '113'+ k: '7'+ number: x^7 + x^6 - 48*x^5 + 37*x^4 + 312*x^3 - 12*x^2 - 49*x - 1+- params:+ p: '113'+ k: '8'+ number: x^8 + x^7 - 49*x^6 + 16*x^5 + 511*x^4 - 367*x^3 - 1499*x^2 + 798*x + 1372+- params:+ p: '127'+ k: '2'+ number: x^2 + x + 32+ comment: $p^*=-127$; roots $\frac{-1\pm\sqrt{-127}}{2}$+- params:+ p: '127'+ k: '3'+ number: x^3 + x^2 - 42*x + 80+ comment: $4p=L^2+27M^2$ with $L=-20$, $M=2$+- params:+ p: '127'+ k: '6'+ number: x^6 + x^5 + 11*x^4 - 181*x^3 + 660*x^2 - 972*x + 608+- params:+ p: '127'+ k: '7'+ number: x^7 + x^6 - 54*x^5 - 31*x^4 + 558*x^3 - 32*x^2 - 1713*x + 1121+- params:+ p: '127'+ k: '9'+ number: x^9 + x^8 - 56*x^7 - 118*x^6 + 573*x^5 + 1249*x^4 - 1582*x^3 - 2700*x^2+ + 1576*x + 32+- params:+ p: '131'+ k: '2'+ number: x^2 + x + 33+ comment: $p^*=-131$; roots $\frac{-1\pm\sqrt{-131}}{2}$+- params:+ p: '131'+ k: '5'+ number: x^5 + x^4 - 52*x^3 - 89*x^2 + 109*x + 193+- params:+ p: '131'+ k: '10'+ number: x^10 + x^9 + 7*x^8 + 63*x^7 + 237*x^6 + 783*x^5 + 7565*x^4 + 21935*x^3 ++ 39574*x^2 + 36034*x + 18289+- params:+ p: '137'+ k: '2'+ number: x^2 + x - 34+ comment: $p^*=137$; roots $\frac{-1\pm\sqrt{137}}{2}$+- params:+ p: '137'+ k: '4'+ number: x^4 + x^3 - 51*x^2 - 214*x - 236+- params:+ p: '137'+ k: '8'+ number: x^8 + x^7 + 9*x^6 + 105*x^5 + 954*x^4 + 3767*x^3 + 9149*x^2 + 12828*x ++ 7607+- params:+ p: '139'+ k: '2'+ number: x^2 + x + 35+ comment: $p^*=-139$; roots $\frac{-1\pm\sqrt{-139}}{2}$+- params:+ p: '139'+ k: '3'+ number: x^3 + x^2 - 46*x + 103+ comment: $4p=L^2+27M^2$ with $L=-23$, $M=1$+- params:+ p: '139'+ k: '6'+ number: x^6 + x^5 + 12*x^4 + 188*x^3 - 46*x^2 - 1356*x + 1723+- params:+ p: '149'+ k: '2'+ number: x^2 + x - 37+ comment: $p^*=149$; roots $\frac{-1\pm\sqrt{149}}{2}$+- params:+ p: '149'+ k: '4'+ number: x^4 + x^3 + 19*x^2 - 121*x + 635+- params:+ p: '151'+ k: '2'+ number: x^2 + x + 38+ comment: $p^*=-151$; roots $\frac{-1\pm\sqrt{-151}}{2}$+- params:+ p: '151'+ k: '3'+ number: x^3 + x^2 - 50*x - 123+ comment: $4p=L^2+27M^2$ with $L=19$, $M=3$+- params:+ p: '151'+ k: '5'+ number: x^5 + x^4 - 60*x^3 - 12*x^2 + 784*x + 128+- params:+ p: '151'+ k: '6'+ number: x^6 + x^5 + 13*x^4 - 81*x^3 - 331*x^2 + 1347*x + 6543+- params:+ p: '151'+ k: '10'+ number: x^10 + x^9 + 8*x^8 - 18*x^7 + 397*x^6 - 351*x^5 + 4010*x^4 - 720*x^3 + 4352*x^2+ + 11264*x + 292352+- params:+ p: '157'+ k: '2'+ number: x^2 + x - 39+ comment: $p^*=157$; roots $\frac{-1\pm\sqrt{157}}{2}$+- params:+ p: '157'+ k: '3'+ number: x^3 + x^2 - 52*x + 64+ comment: $4p=L^2+27M^2$ with $L=-14$, $M=4$+- params:+ p: '157'+ k: '4'+ number: x^4 + x^3 + 20*x^2 - 206*x + 517+- params:+ p: '157'+ k: '6'+ number: x^6 + x^5 - 65*x^4 + 160*x^3 + 20*x^2 - 208*x + 64+- params:+ p: '157'+ k: '12'+ number: x^12 + x^11 + 7*x^10 + 63*x^9 - 312*x^8 - 701*x^7 + 7047*x^6 - 33689*x^5+ + 64030*x^4 - 41071*x^3 + 14685*x^2 + 86965*x + 53381+- params:+ p: '163'+ k: '2'+ number: x^2 + x + 41+ comment: $p^*=-163$; roots $\frac{-1\pm\sqrt{-163}}{2}$+- params:+ p: '163'+ k: '3'+ number: x^3 + x^2 - 54*x - 169+ comment: $4p=L^2+27M^2$ with $L=25$, $M=1$+- params:+ p: '163'+ k: '6'+ number: x^6 + x^5 + 14*x^4 - 178*x^3 - 552*x^2 + 1854*x + 5023+- params:+ p: '163'+ k: '9'+ number: x^9 + x^8 - 72*x^7 - 73*x^6 + 1482*x^5 + 1034*x^4 - 9637*x^3 - 1173*x^2+ + 10087*x + 853+- params:+ p: '167'+ k: '2'+ number: x^2 + x + 42+ comment: $p^*=-167$; roots $\frac{-1\pm\sqrt{-167}}{2}$+- params:+ p: '173'+ k: '2'+ number: x^2 + x - 43+ comment: $p^*=173$; roots $\frac{-1\pm\sqrt{173}}{2}$+- params:+ p: '173'+ k: '4'+ number: x^4 + x^3 + 22*x^2 + 292*x + 667+- params:+ p: '179'+ k: '2'+ number: x^2 + x + 45+ comment: $p^*=-179$; roots $\frac{-1\pm\sqrt{-179}}{2}$+- params:+ p: '181'+ k: '2'+ number: x^2 + x - 45+ comment: $p^*=181$; roots $\frac{-1\pm\sqrt{181}}{2}$+- params:+ p: '181'+ k: '3'+ number: x^3 + x^2 - 60*x - 67+ comment: $4p=L^2+27M^2$ with $L=7$, $M=5$+- params:+ p: '181'+ k: '4'+ number: x^4 + x^3 + 23*x^2 + 215*x + 975+- params:+ p: '181'+ k: '5'+ number: x^5 + x^4 - 72*x^3 - 123*x^2 + 223*x - 49+- params:+ p: '181'+ k: '6'+ number: x^6 + x^5 - 75*x^4 + 104*x^3 + 918*x^2 - 2509*x + 1685+- params:+ p: '181'+ k: '9'+ number: x^9 + x^8 - 80*x^7 + 53*x^6 + 1668*x^5 - 3314*x^4 - 4261*x^3 + 10795*x^2+ - 2933*x - 1949+- params:+ p: '181'+ k: '10'+ number: x^10 + x^9 - 81*x^8 - 94*x^7 + 2418*x^6 + 3121*x^5 - 31973*x^4 - 43245*x^3+ + 170860*x^2 + 209252*x - 201337+- params:+ p: '181'+ k: '12'+ number: x^12 + x^11 + 8*x^10 - 38*x^9 + 830*x^8 - 2182*x^7 + 8320*x^6 + 5533*x^5+ - 11441*x^4 + 7976*x^3 + 385657*x^2 - 675065*x + 358525+- params:+ p: '191'+ k: '2'+ number: x^2 + x + 48+ comment: $p^*=-191$; roots $\frac{-1\pm\sqrt{-191}}{2}$+- params:+ p: '191'+ k: '5'+ number: x^5 + x^4 - 76*x^3 - 359*x^2 - 437*x - 155+- params:+ p: '191'+ k: '10'+ number: x^10 + x^9 + 10*x^8 - 252*x^7 - 216*x^6 + 3244*x^5 + 17715*x^4 + 24287*x^3+ + 16260*x^2 + 5200*x + 625+- params:+ p: '193'+ k: '2'+ number: x^2 + x - 48+ comment: $p^*=193$; roots $\frac{-1\pm\sqrt{193}}{2}$+- params:+ p: '193'+ k: '3'+ number: x^3 + x^2 - 64*x + 143+ comment: $4p=L^2+27M^2$ with $L=-23$, $M=3$+- params:+ p: '193'+ k: '4'+ number: x^4 + x^3 - 72*x^2 - 205*x - 49+- params:+ p: '193'+ k: '6'+ number: x^6 + x^5 - 80*x^4 - 125*x^3 + 1456*x^2 + 1744*x - 5184+- params:+ p: '193'+ k: '8'+ number: x^8 + x^7 - 84*x^6 - 21*x^5 + 1981*x^4 + 63*x^3 - 14652*x^2 - 799*x + 30961+- params:+ p: '193'+ k: '12'+ number: x^12 + x^11 - 88*x^10 - 3*x^9 + 2617*x^8 - 1105*x^7 - 31612*x^6 + 16656*x^5+ + 136836*x^4 - 25812*x^3 - 144990*x^2 - 40095*x + 6561+- params:+ p: '197'+ k: '2'+ number: x^2 + x - 49+ comment: $p^*=197$; roots $\frac{-1\pm\sqrt{197}}{2}$+- params:+ p: '197'+ k: '4'+ number: x^4 + x^3 + 25*x^2 + 37*x + 1369+- params:+ p: '197'+ k: '7'+ number: x^7 + x^6 - 84*x^5 - 217*x^4 + 1348*x^3 + 3988*x^2 - 1433*x - 1163+- params:+ p: '199'+ k: '2'+ number: x^2 + x + 50+ comment: $p^*=-199$; roots $\frac{-1\pm\sqrt{-199}}{2}$+- params:+ p: '199'+ k: '3'+ number: x^3 + x^2 - 66*x + 59+ comment: $4p=L^2+27M^2$ with $L=-11$, $M=5$+- params:+ p: '199'+ k: '6'+ number: x^6 + x^5 + 17*x^4 + 247*x^3 + 1001*x^2 + 1871*x + 14485+- params:+ p: '199'+ k: '9'+ number: x^9 + x^8 - 88*x^7 - 325*x^6 + 775*x^5 + 3447*x^4 - 1602*x^3 - 7354*x^2+ - 3333*x + 121+- params:+ p: '199'+ k: '11'+ number: x^11 + x^10 - 90*x^9 - 115*x^8 + 2349*x^7 + 943*x^6 - 26327*x^5 + 21284*x^4+ + 102168*x^3 - 217794*x^2 + 148930*x - 30647
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