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comment-characteristic: The table stores the characteristic polynomial on $K_f$, not the minimal polynomial of $a_p$. Its degree is $[K_f:\mathbb{Q}]$, the dimension- of the newform orbit. For example, in the row $f=23.2.a.a$ and $p=13$, $a_{13}=3$- but $[K_f:\mathbb{Q}]=2$, so the entry is $(x-3)^2$.+ of the newform orbit. The two polynomials agree exactly when $a_p$ generates $K_f$,+ and those are the rows the table keeps.+ comment-omitted-rows: 'Rows where $a_p$ does not generate $K_f$ are omitted, because+ $\chi_{f,p}$ is then a proper power of the minimal polynomial of $a_p$ and carries+ nothing the generating primes do not already give. In the extreme $a_p\in\mathbb{Q}$+ and $\chi_{f,p}(x)=(x-a_p)^{[K_f:\mathbb{Q}]}$: at $f=23.2.a.a$ and $p=13$ the+ eigenvalue is $a_{13}=3$ and the characteristic polynomial is $(x-3)^2$, which+ is a small integer and the degree of a field rather than a number worth looking+ up.'+ comment-repeats: 'A polynomial can answer for more than one row. The $686$ entries+ hold $424$ distinct polynomials, of which $317$ occur once; the repetitions are+ small-height quadratics, $x^2-8$ and $x^2-12$ occurring $14$ times each. Some+ repeat within a single orbit, where two primes give conjugate eigenvalues: $a_5$+ and $a_7$ of $39.2.a.b$ are both roots of $x^2-8$.' comment-normalisation: 'The eigenvalues are the usual Fourier coefficients $a_p$, not the analytically normalised values $a_p/\sqrt{p}$. If $p\mid N$, $a_p$ is
complete: 'no' complete-note: it holds every weight $2$ newform orbit of trivial character and- level $N\leq100$ whose coefficient field has degree at least $2$, for primes $p<20$+ level $N\leq100$ whose coefficient field has degree at least $2$, for the primes+ $p\leq59$ at which $a_p$ generates that field rigour details: The generator enumerates Sage's `Newforms(N, 2)` CITE{SageNewforms} for $N\leq100$, uses the LMFDB label order CITE{LMFDBAPI1} CITE{LMFDBAPI2}, and keeps exactly the $50$ orbits whose coefficient field has degree at least $2$.- For each retained orbit and each prime $p<20$, it takes the exact Sage coefficient+ For each retained orbit and each prime $p\leq59$, it takes the exact Sage coefficient $a_p$, builds the multiplication matrix of $a_p$ on $K_f$, and computes $\det(xI-m_{a_p})$- by a permutation expansion over $\mathbb{Q}$. Before the draft was created, the- labels and degrees were compared with the LMFDB API data, including the LMFDB- page for 23.2.a.a CITE{LMFDB23}. For every level $N\leq100$ and every listed prime,- the product of the polynomials over all newform orbits, including dimension-one- orbits omitted from the table, was required to equal PARI/GP's `charpoly(mfheckemat(mfinit([N,2],0),p))`+ by a permutation expansion over $\mathbb{Q}$, keeping the row when that polynomial+ is irreducible, which is to say when $a_p$ generates $K_f$. Before the draft was+ created, the labels and degrees were compared with the LMFDB API data, including+ the LMFDB page for 23.2.a.a CITE{LMFDB23}. For every level $N\leq100$ and every+ prime $p\leq59$, the product of the polynomials over all newform orbits, including+ dimension-one orbits omitted from the table, was required to equal PARI/GP's `charpoly(mfheckemat(mfinit([N,2],0),p))` CITE{PARIHecke}. Display properties:
- - p Numbers:-- params:- label: 23.2.a.a- p: '2'- number: x^2 + x - 1-- params:- label: 23.2.a.a- p: '3'- number: x^2 - 5-- params:- label: 23.2.a.a- p: '5'- number: x^2 + 2*x - 4-- params:- label: 23.2.a.a- p: '7'- number: x^2 - 2*x - 4-- params:- label: 23.2.a.a- p: '11'- number: x^2 + 6*x + 4-- params:- label: 23.2.a.a- p: '17'- number: x^2 - 6*x + 4-- params:- label: 23.2.a.a- p: '31'- number: x^2 - 45-- params:- label: 23.2.a.a- p: '37'- number: x^2 - 2*x - 4-- params:- label: 23.2.a.a- p: '41'- number: x^2 - 2*x - 19-- params:- label: 23.2.a.a- p: '47'- number: x^2 - 5-- params:- label: 23.2.a.a- p: '53'- number: x^2 + 8*x - 4-- params:- label: 23.2.a.a- p: '59'- number: x^2 - 4*x - 16-- params:- label: 29.2.a.a- p: '2'- number: x^2 + 2*x - 1-- params:- label: 29.2.a.a- p: '3'- number: x^2 - 2*x - 1-- params:- label: 29.2.a.a- p: '7'- number: x^2 - 8-- params:- label: 29.2.a.a- p: '11'- number: x^2 - 2*x - 1-- params:- label: 29.2.a.a- p: '13'- number: x^2 + 2*x - 7-- params:- label: 29.2.a.a- p: '17'- number: x^2 + 4*x - 4-- params:- label: 29.2.a.a- p: '23'- number: x^2 + 4*x - 28-- params:- label: 29.2.a.a- p: '31'- number: x^2 - 6*x - 41-- params:- label: 29.2.a.a- p: '41'- number: x^2 - 8*x - 56-- params:- label: 29.2.a.a- p: '43'- number: x^2 - 10*x + 23-- params:- label: 29.2.a.a- p: '47'- number: x^2 - 2*x - 17-- params:- label: 29.2.a.a- p: '53'- number: x^2 - 2*x - 71-- params:- label: 29.2.a.a- p: '59'- number: x^2 - 4*x - 28-- params:- label: 31.2.a.a- p: '2'- number: x^2 - x - 1-- params:- label: 31.2.a.a- p: '3'- number: x^2 + 2*x - 4-- params:- label: 31.2.a.a- p: '7'- number: x^2 + 4*x - 1-- params:- label: 31.2.a.a- p: '13'- number: x^2 + 2*x - 4-- params:- label: 31.2.a.a- p: '17'- number: x^2 - 6*x + 4-- params:- label: 31.2.a.a- p: '19'- number: x^2 - 5-- params:- label: 31.2.a.a- p: '23'- number: x^2 + 2*x - 44-- params:- label: 31.2.a.a- p: '29'- number: x^2 - 10*x + 20-- params:- label: 31.2.a.a- p: '43'- number: x^2 + 2*x - 4-- params:- label: 31.2.a.a- p: '47'- number: x^2 + 4*x - 16-- params:- label: 31.2.a.a- p: '53'- number: x^2 + 12*x + 16-- params:- label: 31.2.a.a- p: '59'- number: x^2 - 5-- params:- label: 35.2.a.b- p: '2'- number: x^2 + x - 4-- params:- label: 35.2.a.b- p: '3'- number: x^2 + x - 4-- params:- label: 35.2.a.b- p: '11'- number: x^2 - x - 4-- params:- label: 35.2.a.b- p: '13'- number: x^2 - 5*x + 2-- params:- label: 35.2.a.b- p: '17'- number: x^2 + 5*x + 2-- params:- label: 35.2.a.b- p: '19'- number: x^2 + 6*x - 8-- params:- label: 35.2.a.b- p: '23'- number: x^2 + 2*x - 16-- params:- label: 35.2.a.b- p: '29'- number: x^2 - x - 38-- params:- label: 35.2.a.b- p: '41'- number: x^2 - 2*x - 16-- params:- label: 35.2.a.b- p: '43'- number: x^2 - 10*x + 8-- params:- label: 35.2.a.b- p: '47'- number: x^2 + 5*x - 32-- params:- label: 35.2.a.b- p: '53'- number: x^2 + 2*x - 16-- params:- label: 39.2.a.b- p: '2'- number: x^2 + 2*x - 1-- params:- label: 39.2.a.b- p: '5'- number: x^2 - 8-- params:- label: 39.2.a.b- p: '7'- number: x^2 - 8-- params:- label: 39.2.a.b- p: '17'- number: x^2 - 4*x - 28-- params:- label: 39.2.a.b- p: '19'- number: x^2 - 8-- params:- label: 39.2.a.b- p: '31'- number: x^2 + 8*x + 8-- params:- label: 39.2.a.b- p: '37'- number: x^2 + 4*x - 28-- params:- label: 39.2.a.b- p: '41'- number: x^2 - 16*x + 56-- params:- label: 39.2.a.b- p: '43'- number: x^2 - 8*x - 16-- params:- label: 39.2.a.b- p: '47'- number: x^2 + 12*x + 4-- params:- label: 39.2.a.b- p: '59'- number: x^2 - 4*x - 28-- params:- label: 41.2.a.a- p: '2'- number: x^3 + x^2 - 5*x - 1-- params:- label: 41.2.a.a- p: '3'- number: x^3 - 4*x + 2-- params:- label: 41.2.a.a- p: '5'- number: x^3 + 2*x^2 - 4*x - 4-- params:- label: 41.2.a.a- p: '7'- number: x^3 - 6*x^2 + 8*x - 2-- params:- label: 41.2.a.a- p: '11'- number: x^3 - 2*x^2 - 20*x + 50-- params:- label: 41.2.a.a- p: '13'- number: x^3 + 2*x^2 - 12*x - 8-- params:- label: 41.2.a.a- p: '19'- number: x^3 - 4*x^2 - 16*x - 10-- params:- label: 41.2.a.a- p: '23'- number: x^3 - 4*x^2 - 32*x - 32-- params:- label: 41.2.a.a- p: '29'- number: x^3 + 6*x^2 - 4*x - 40-- params:- label: 41.2.a.a- p: '31'- number: x^3 - 16*x^2 + 64*x - 32-- params:- label: 41.2.a.a- p: '37'- number: x^3 + 6*x^2 - 36*x - 108-- params:- label: 41.2.a.a- p: '43'- number: x^3 + 4*x^2 - 8*x - 16-- params:- label: 41.2.a.a- p: '47'- number: x^3 - 120*x - 502-- params:- label: 41.2.a.a- p: '53'- number: x^3 - 6*x^2 - 4*x + 8-- params:- label: 41.2.a.a- p: '59'- number: x^3 + 8*x^2 - 16*x - 160-- params:- label: 43.2.a.b- p: '2'- number: x^2 - 2-- params:- label: 43.2.a.b- p: '3'- number: x^2 - 2-- params:- label: 43.2.a.b- p: '5'- number: x^2 - 4*x + 2-- params:- label: 43.2.a.b- p: '7'- number: x^2 + 4*x + 2-- params:- label: 43.2.a.b- p: '11'- number: x^2 + 2*x - 7-- params:- label: 43.2.a.b- p: '13'- number: x^2 - 2*x - 7-- params:- label: 43.2.a.b- p: '17'- number: x^2 - 10*x + 17-- params:- label: 43.2.a.b- p: '19'- number: x^2 + 4*x - 4-- params:- label: 43.2.a.b- p: '23'- number: x^2 - 2*x - 31-- params:- label: 43.2.a.b- p: '29'- number: x^2 - 18-- params:- label: 43.2.a.b- p: '37'- number: x^2 - 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10*x^3 + 15*x^2 + 34*x + 9-- params:- label: 47.2.a.a- p: '41'- number: x^4 - 6*x^3 - 8*x^2 + 32*x - 16-- params:- label: 47.2.a.a- p: '43'- number: x^4 - 2*x^3 - 80*x^2 - 112*x + 432-- params:- label: 47.2.a.a- p: '53'- number: x^4 + 6*x^3 - 101*x^2 - 314*x + 2429-- params:- label: 47.2.a.a- p: '59'- number: x^4 - 4*x^3 - 115*x^2 + 704*x - 519-- params:- label: 51.2.a.b- p: '2'- number: x^2 + x - 4-- params:- label: 51.2.a.b- p: '5'- number: x^2 - 3*x - 2-- params:- label: 51.2.a.b- p: '11'- number: x^2 + x - 4-- params:- label: 51.2.a.b- p: '13'- number: x^2 - 5*x + 2-- params:- label: 51.2.a.b- p: '19'- number: x^2 - 3*x - 36-- params:- label: 51.2.a.b- p: '23'- number: x^2 + 9*x + 16-- params:- label: 51.2.a.b- p: '29'- number: x^2 - 68-- params:- label: 51.2.a.b- p: '31'- number: x^2 + 2*x - 16-- params:- label: 51.2.a.b- p: '37'- number: x^2 + 2*x - 16-- params:- label: 51.2.a.b- p: '41'- number: x^2 + 3*x - 2-- params:- label: 51.2.a.b- p: '43'- number: x^2 + 3*x - 36-- params:- label: 51.2.a.b- p: '47'- number: x^2 + 14*x + 32-- params:- label: 51.2.a.b- p: '53'- number: x^2 - 8*x - 52-- params:- label: 51.2.a.b- p: '59'- number: x^2 - 6*x - 8-- params:- label: 53.2.a.b- p: '2'- number: x^3 + x^2 - 3*x - 1-- params:- label: 53.2.a.b- p: '3'- number: x^3 - 3*x^2 - x + 1-- params:- label: 53.2.a.b- p: '5'- number: x^3 + 2*x^2 - 4*x - 4-- params:- label: 53.2.a.b- p: '7'- number: x^3 - 4*x^2 + 4-- params:- label: 53.2.a.b- p: '11'- number: x^3 + 4*x^2 - 4*x - 20-- params:- label: 53.2.a.b- p: '17'- number: x^3 + 5*x^2 - 5*x - 17-- params:- label: 53.2.a.b- p: '19'- number: x^3 - 11*x^2 + 37*x - 37-- params:- label: 53.2.a.b- p: '23'- number: x^3 - 3*x^2 - 31*x - 29-- params:- label: 53.2.a.b- p: '29'- number: x^3 + 5*x^2 - 37*x - 61-- params:- label: 53.2.a.b- p: '31'- number: x^3 + 2*x^2 - 76*x + 116-- params:- label: 53.2.a.b- p: '37'- number: x^3 + 5*x^2 - 89*x - 353-- params:- label: 53.2.a.b- p: '41'- number: x^3 + 10*x^2 + 20*x - 8-- params:- label: 53.2.a.b- p: '43'- number: x^3 - 18*x^2 + 24*x + 556-- params:- label: 53.2.a.b- p: '47'- number: x^3 + 10*x^2 - 4*x - 8-- params:- label: 53.2.a.b- p: '59'- number: x^3 - 2*x^2 - 60*x + 200-- params:- label: 55.2.a.b- p: '2'- number: x^2 - 2*x - 1-- params:- label: 55.2.a.b- p: '3'- number: x^2 - 8-- params:- label: 55.2.a.b- p: '13'- number: x^2 + 8*x + 8-- params:- label: 55.2.a.b- p: '17'- number: x^2 - 8*x + 8-- params:- label: 55.2.a.b- p: '23'- number: x^2 - 8-- params:- label: 55.2.a.b- p: '29'- number: x^2 - 4*x - 28-- params:- label: 55.2.a.b- p: '37'- number: x^2 + 4*x - 28-- params:- label: 55.2.a.b- p: '47'- number: x^2 - 8-- params:- label: 55.2.a.b- p: '53'- number: x^2 - 12*x + 4-- params:- label: 55.2.a.b- p: '59'- number: x^2 + 8*x - 16-- params:- label: 59.2.a.a- p: '2'- number: x^5 - 9*x^3 + 2*x^2 + 16*x - 8-- params:- label: 59.2.a.a- p: '3'- number: x^5 + 2*x^4 - 8*x^3 - 11*x^2 + 13*x - 1-- params:- label: 59.2.a.a- p: '5'- number: x^5 - 2*x^4 - 14*x^3 + 23*x^2 + 19*x + 1-- params:- label: 59.2.a.a- p: '7'- number: x^5 - 2*x^4 - 16*x^3 + 43*x^2 + 13*x - 71-- params:- label: 59.2.a.a- p: '11'- number: x^5 + 2*x^4 - 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x^2 - 3*x + 1-- params:- label: 61.2.a.b- p: '3'- number: x^3 - 2*x^2 - 4*x + 4-- params:- label: 61.2.a.b- p: '5'- number: x^3 + x^2 - 9*x - 13-- params:- label: 61.2.a.b- p: '7'- number: x^3 + 3*x^2 - x - 1-- params:- label: 61.2.a.b- p: '11'- number: x^3 - 13*x^2 + 53*x - 67-- params:- label: 61.2.a.b- p: '13'- number: x^3 + 9*x^2 + 11*x - 37-- params:- label: 61.2.a.b- p: '17'- number: x^3 + 2*x^2 - 8*x + 4-- params:- label: 61.2.a.b- p: '19'- number: x^3 - 48*x - 20-- params:- label: 61.2.a.b- p: '23'- number: x^3 - 5*x^2 + 5*x + 1-- params:- label: 61.2.a.b- p: '29'- number: x^3 - 4*x^2 - 4*x + 20-- params:- label: 61.2.a.b- p: '31'- number: x^3 + 2*x^2 - 76*x + 116-- params:- label: 61.2.a.b- p: '37'- number: x^3 + 6*x^2 - 36*x - 108-- params:- label: 61.2.a.b- p: '41'- number: x^3 - 3*x^2 - 61*x + 191-- params:- label: 61.2.a.b- p: '43'- number: x^3 + 14*x^2 + 56*x + 68-- params:- label: 61.2.a.b- p: '47'- number: x^3 + 4*x^2 - 88*x + 16-- params:- label: 61.2.a.b- p: '53'- number: x^3 + 2*x^2 - 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6*x^2 - 8*x + 9-- params:- label: 95.2.a.b- p: '3'- number: x^4 - 2*x^3 - 8*x^2 + 16*x - 4-- params:- label: 95.2.a.b- p: '7'- number: x^4 - 4*x^3 - 16*x^2 + 48*x + 32-- params:- label: 95.2.a.b- p: '11'- number: x^4 - 4*x^3 - 16*x^2 + 32*x + 48-- params:- label: 95.2.a.b- p: '13'- number: x^4 - 2*x^3 - 24*x^2 + 32*x + 20-- params:- label: 95.2.a.b- p: '17'- number: x^4 - 4*x^3 - 32*x^2 + 16*x + 48-- params:- label: 95.2.a.b- p: '23'- number: x^4 + 8*x^3 - 24*x^2 - 176*x + 288-- params:- label: 95.2.a.b- p: '29'- number: x^4 - 4*x^3 - 32*x^2 + 16*x + 48-- params:- label: 95.2.a.b- p: '31'- number: x^4 - 4*x^3 - 80*x^2 + 512*x - 640-- params:- label: 95.2.a.b- p: '37'- number: x^4 + 6*x^3 - 24*x^2 - 40*x + 4-- params:- label: 95.2.a.b- p: '41'- number: x^4 - 16*x^3 + 56*x^2 + 32*x - 240-- params:- label: 95.2.a.b- p: '43'- number: x^4 - 4*x^3 - 16*x^2 + 48*x + 32-- params:- label: 95.2.a.b- p: '47'- number: x^4 + 12*x^3 - 64*x^2 - 656*x + 1056-- params:- label: 95.2.a.b- p: '53'- number: x^4 + 10*x^3 - 184*x - 348-- params:- label: 95.2.a.b- p: '59'- number: x^4 - 64*x^2 - 224*x - 192-- params:- label: 97.2.a.a- p: '2'- number: x^3 + 4*x^2 + 3*x - 1-- params:- label: 97.2.a.a- p: '3'- number: x^3 + 4*x^2 + 3*x - 1-- params:- label: 97.2.a.a- p: '5'- number: x^3 + 3*x^2 - 4*x + 1-- params:- label: 97.2.a.a- p: '7'- number: x^3 + 7*x^2 + 14*x + 7-- params:- label: 97.2.a.a- p: '11'- number: x^3 + 7*x^2 + 14*x + 7-- params:- label: 97.2.a.a- p: '13'- number: x^3 + 2*x^2 - x - 1-- params:- label: 97.2.a.a- p: '17'- number: x^3 + 3*x^2 - 4*x - 13-- params:- label: 97.2.a.a- p: '19'- number: x^3 - 5*x^2 - 57*x + 293-- params:- label: 97.2.a.a- p: '23'- number: x^3 + 12*x^2 + 27*x - 13-- params:- label: 97.2.a.a- p: '29'- number: x^3 - x^2 - 65*x + 169-- params:- label: 97.2.a.a- p: '31'- number: x^3 + 8*x^2 + 5*x - 43-- params:- label: 97.2.a.a- p: '37'- number: x^3 + 2*x^2 - 71*x + 97-- params:- label: 97.2.a.a- p: '41'- number: x^3 - 3*x^2 - 4*x - 1-- params:- label: 97.2.a.a- p: '43'- number: x^3 - x^2 - 16*x + 29-- params:- label: 97.2.a.a- p: '47'- number: x^3 + 17*x^2 + 59*x - 13-- params:- label: 97.2.a.a- p: '53'- number: x^3 - 2*x^2 - 155*x + 659-- params:- label: 97.2.a.a- p: '59'- number: x^3 - 19*x^2 + 104*x - 169-- params:- label: 97.2.a.b- p: '2'- number: x^4 - 3*x^3 - x^2 + 6*x - 1-- params:- label: 97.2.a.b- p: '3'- number: x^4 - 5*x^2 - x + 4-- params:- label: 97.2.a.b- p: '5'- number: x^4 - x^3 - 4*x^2 + x + 2-- params:- label: 97.2.a.b- p: '7'- number: x^4 - 3*x^3 - 6*x^2 + 23*x - 16-- params:- label: 97.2.a.b- p: '11'- number: x^4 - 5*x^3 - 14*x^2 + 47*x + 92-- params:- label: 97.2.a.b- p: '13'- number: x^4 + 6*x^3 - 29*x^2 - 167*x - 122-- params:- label: 97.2.a.b- p: '17'- number: x^4 - 3*x^3 - 20*x^2 + 15*x + 74-- params:- label: 97.2.a.b- p: '19'- number: x^4 + 3*x^3 - 5*x^2 - 11*x + 4-- params:- label: 97.2.a.b- p: '23'- number: x^4 - 22*x^3 + 151*x^2 - 265*x - 368-- params:- label: 97.2.a.b- p: '29'- number: x^4 - 7*x^3 - 27*x^2 + 199*x - 254-- params:- label: 97.2.a.b- p: '31'- number: x^4 + 4*x^3 - 67*x^2 - 79*x + 592-- params:- label: 97.2.a.b- p: '37'- number: x^4 + 6*x^3 - 27*x^2 - 81*x + 162-- params:- label: 97.2.a.b- p: '41'- number: x^4 - 3*x^3 - 158*x^2 + 131*x + 5506-- params:- label: 97.2.a.b- p: '43'- number: x^4 - 9*x^3 + 20*x^2 + 9*x - 44-- params:- label: 97.2.a.b- p: '47'- number: x^4 - 19*x^3 + 99*x^2 - 161*x + 16-- params:- label: 97.2.a.b- p: '53'- number: x^4 + 4*x^3 - 75*x^2 - 123*x + 1262-- params:- label: 97.2.a.b- p: '59'- number: x^4 - x^3 - 98*x^2 + 3*x + 772-- params:- label: 98.2.a.b- p: '3'- number: x^2 - 2-- params:- label: 98.2.a.b- p: '5'- number: x^2 - 8-- params:- label: 98.2.a.b- p: '17'- number: x^2 - 2-- params:- label: 98.2.a.b- p: '19'- number: x^2 - 50-- params:- label: 98.2.a.b- p: '31'- number: x^2 - 72-- params:- label: 98.2.a.b- p: '41'- number: x^2 - 98-- params:- label: 98.2.a.b- p: '47'- number: x^2 - 8-- params:- label: 98.2.a.b- p: '59'- number: x^2 - 2+ 23.2.a.a:+ '2': x^2 + x - 1+ '3': x^2 - 5+ '5': x^2 + 2*x - 4+ '7': x^2 - 2*x - 4+ '11': x^2 + 6*x + 4+ '17': x^2 - 6*x + 4+ '31': x^2 - 45+ '37': x^2 - 2*x - 4+ '41': x^2 - 2*x - 19+ '47': x^2 - 5+ '53': x^2 + 8*x - 4+ '59': x^2 - 4*x - 16+ 29.2.a.a:+ '2': x^2 + 2*x - 1+ '3': x^2 - 2*x - 1+ '7': x^2 - 8+ '11': x^2 - 2*x - 1+ '13': x^2 + 2*x - 7+ '17': x^2 + 4*x - 4+ '23': x^2 + 4*x - 28+ '31': x^2 - 6*x - 41+ '41': x^2 - 8*x - 56+ '43': x^2 - 10*x + 23+ '47': x^2 - 2*x - 17+ '53': x^2 - 2*x - 71+ '59': x^2 - 4*x - 28+ 31.2.a.a:+ '2': x^2 - x - 1+ '3': x^2 + 2*x - 4+ '7': x^2 + 4*x - 1+ '13': x^2 + 2*x - 4+ '17': x^2 - 6*x + 4+ '19': x^2 - 5+ '23': x^2 + 2*x - 44+ '29': x^2 - 10*x + 20+ '43': x^2 + 2*x - 4+ '47': x^2 + 4*x - 16+ '53': x^2 + 12*x + 16+ '59': x^2 - 5+ 35.2.a.b:+ '2': x^2 + x - 4+ '3': x^2 + x - 4+ '11': x^2 - x - 4+ '13': x^2 - 5*x + 2+ '17': x^2 + 5*x + 2+ '19': x^2 + 6*x - 8+ '23': x^2 + 2*x - 16+ '29': x^2 - x - 38+ '41': x^2 - 2*x - 16+ '43': x^2 - 10*x + 8+ '47': x^2 + 5*x - 32+ '53': x^2 + 2*x - 16+ 39.2.a.b:+ '2': x^2 + 2*x - 1+ '5': x^2 - 8+ '7': x^2 - 8+ '17': x^2 - 4*x - 28+ '19': x^2 - 8+ '31': x^2 + 8*x + 8+ '37': x^2 + 4*x - 28+ '41': x^2 - 16*x + 56+ '43': x^2 - 8*x - 16+ '47': x^2 + 12*x + 4+ '59': x^2 - 4*x - 28+ 41.2.a.a:+ '2': x^3 + x^2 - 5*x - 1+ '3': x^3 - 4*x + 2+ '5': x^3 + 2*x^2 - 4*x - 4+ '7': x^3 - 6*x^2 + 8*x - 2+ '11': x^3 - 2*x^2 - 20*x + 50+ '13': x^3 + 2*x^2 - 12*x - 8+ '19': x^3 - 4*x^2 - 16*x - 10+ '23': x^3 - 4*x^2 - 32*x - 32+ '29': x^3 + 6*x^2 - 4*x - 40+ '31': x^3 - 16*x^2 + 64*x - 32+ '37': x^3 + 6*x^2 - 36*x - 108+ '43': x^3 + 4*x^2 - 8*x - 16+ '47': x^3 - 120*x - 502+ '53': x^3 - 6*x^2 - 4*x + 8+ '59': x^3 + 8*x^2 - 16*x - 160+ 43.2.a.b:+ '2': x^2 - 2+ '3': x^2 - 2+ '5': x^2 - 4*x + 2+ '7': x^2 + 4*x + 2+ '11': x^2 + 2*x - 7+ '13': x^2 - 2*x - 7+ '17': x^2 - 10*x + 17+ '19': x^2 + 4*x - 4+ '23': x^2 - 2*x - 31+ '29': x^2 - 18+ '37': x^2 - 72+ '41': x^2 + 2*x - 7+ '53': x^2 - 22*x + 113+ '59': x^2 + 4*x - 4+ 47.2.a.a:+ '2': x^4 - x^3 - 5*x^2 + 5*x - 1+ '3': x^4 - 7*x^2 + 4*x + 1+ '5': x^4 + 2*x^3 - 16*x^2 - 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37+ '23': x^3 - 3*x^2 - 31*x - 29+ '29': x^3 + 5*x^2 - 37*x - 61+ '31': x^3 + 2*x^2 - 76*x + 116+ '37': x^3 + 5*x^2 - 89*x - 353+ '41': x^3 + 10*x^2 + 20*x - 8+ '43': x^3 - 18*x^2 + 24*x + 556+ '47': x^3 + 10*x^2 - 4*x - 8+ '59': x^3 - 2*x^2 - 60*x + 200+ 55.2.a.b:+ '2': x^2 - 2*x - 1+ '3': x^2 - 8+ '13': x^2 + 8*x + 8+ '17': x^2 - 8*x + 8+ '23': x^2 - 8+ '29': x^2 - 4*x - 28+ '37': x^2 + 4*x - 28+ '47': x^2 - 8+ '53': x^2 - 12*x + 4+ '59': x^2 + 8*x - 16+ 59.2.a.a:+ '2': x^5 - 9*x^3 + 2*x^2 + 16*x - 8+ '3': x^5 + 2*x^4 - 8*x^3 - 11*x^2 + 13*x - 1+ '5': x^5 - 2*x^4 - 14*x^3 + 23*x^2 + 19*x + 1+ '7': x^5 - 2*x^4 - 16*x^3 + 43*x^2 + 13*x - 71+ '11': x^5 + 2*x^4 - 24*x^3 - 24*x^2 + 128*x - 64+ '13': x^5 - 8*x^4 + 88*x^2 - 48*x - 224+ '17': x^5 + x^4 - 45*x^3 - 81*x^2 + 224*x + 412+ '19': x^5 - 6*x^4 - 28*x^3 + 217*x^2 - 167*x - 469+ '23': x^5 + 8*x^4 - 88*x^2 - 112*x - 32+ '29': x^5 - 14*x^4 + 10*x^3 + 389*x^2 - 485*x - 1757+ '31': x^5 - 116*x^3 + 56*x^2 + 1280*x + 256+ '37': x^5 - 18*x^4 + 80*x^3 + 64*x^2 - 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12+ '11': x^2 - 12+ '17': x^2 - 12+ '23': x^2 - 12+ '41': x^2 - 108+ '47': x^2 - 48+ '53': x^2 - 48+ '59': x^2 - 48+ 65.2.a.b:+ '2': x^2 + 2*x - 1+ '3': x^2 - 2+ '7': x^2 - 4*x - 4+ '11': x^2 - 4*x + 2+ '17': x^2 + 4*x - 4+ '19': x^2 - 4*x + 2+ '23': x^2 - 2+ '29': x^2 - 32+ '31': x^2 - 12*x + 18+ '37': x^2 - 72+ '41': x^2 + 12*x + 28+ '43': x^2 + 8*x - 34+ '47': x^2 + 4*x - 4+ '53': x^2 + 12*x - 36+ '59': x^2 - 12*x + 18+ 65.2.a.c:+ '2': x^2 - 3+ '3': x^2 - 2*x - 2+ '11': x^2 + 6*x + 6+ '17': x^2 - 12+ '19': x^2 + 2*x - 26+ '23': x^2 - 6*x + 6+ '29': x^2 + 12*x + 24+ '31': x^2 - 10*x - 2+ '41': x^2 - 12+ '43': x^2 - 10*x - 2+ '53': x^2 - 108+ '59': x^2 + 6*x - 138+ 67.2.a.b:+ '2': x^2 + 3*x + 1+ '3': x^2 + 3*x + 1+ '7': x^2 + x - 11+ '11': x^2 - 5+ '13': x^2 + 7*x + 1+ '17': x^2 + 6*x + 4+ '19': x^2 - x - 11+ '23': x^2 - 6*x - 11+ '29': x^2 + 6*x - 11+ '37': x^2 + x - 11+ '41': x^2 + 3*x + 1+ '43': x^2 - 3*x - 9+ '47': x^2 + 15*x + 55+ 67.2.a.c:+ '2': x^2 + x - 1+ '3': x^2 - x - 1+ '5': x^2 - 4*x - 1+ '7': x^2 - x - 1+ '13': x^2 + x - 1+ '17': x^2 - 6*x + 4+ '19': x^2 + 11*x + 29+ '23': x^2 + 2*x - 19+ '29': x^2 - 10*x + 5+ '31': x^2 - 45+ '37': x^2 - 3*x + 1+ '41': x^2 - 5*x - 25+ '43': x^2 + 9*x - 11+ '47': x^2 + 7*x + 11+ '53': x^2 - 45+ 68.2.a.a:+ '3': x^2 - 2*x - 2+ '5': x^2 - 12+ '7': x^2 + 2*x - 2+ '11': x^2 + 6*x + 6+ '13': x^2 - 4*x - 8+ '19': x^2 - 4*x - 8+ '23': x^2 + 6*x + 6+ '29': x^2 - 12+ '31': x^2 + 2*x - 26+ '37': x^2 - 16*x + 52+ '43': x^2 - 4*x - 104+ '47': x^2 - 48+ '53': x^2 - 12*x - 12+ '59': x^2 - 12*x + 24+ 69.2.a.b:+ '2': x^2 - 5+ '5': x^2 + 2*x - 4+ '7': x^2 - 2*x - 4+ '13': x^2 - 20+ '17': x^2 + 10*x + 20+ '19': x^2 - 10*x + 20+ '29': x^2 - 20+ '31': x^2 + 4*x - 16+ '37': x^2 - 20+ '41': x^2 + 4*x - 76+ '43': x^2 - 2*x - 44+ '53': x^2 + 6*x + 4+ '59': x^2 - 8*x - 64+ 71.2.a.a:+ '2': x^3 + x^2 - 4*x - 3+ '3': x^3 - x^2 - 4*x + 3+ '5': x^3 - 5*x^2 - 2*x + 25+ '7': x^3 - 2*x^2 - 16*x + 24+ '11': x^3 - 20*x + 24+ '13': x^3 + 6*x^2 - 8*x - 56+ '17': x^3 + 2*x^2 - 32*x - 24+ '19': x^3 - x^2 - 20*x - 25+ '29': x^3 - 11*x^2 + 14*x + 71+ '37': x^3 + 15*x^2 + 70*x + 97+ '41': x^3 + 2*x^2 - 68*x + 56+ '43': x^3 - 13*x^2 + 48*x - 45+ '47': x^3 - 4*x^2 - 28*x + 40+ '53': x^3 + 18*x^2 + 28*x - 456+ '59': x^3 + 4*x^2 - 36*x - 152+ 71.2.a.b:+ '2': x^3 - 5*x + 3+ '3': x^3 + x^2 - 8*x - 3+ '5': x^3 + 3*x^2 - 2*x - 7+ '7': x^3 - 2*x^2 - 16*x + 24+ '11': x^3 + 2*x^2 - 16*x - 24+ '17': x^3 - 2*x^2 - 16*x + 24+ '19': x^3 - 11*x^2 + 36*x - 35+ '23': x^3 - 8*x^2 - 12*x + 72+ '29': x^3 + 5*x^2 - 2*x - 25+ '31': x^3 + 6*x^2 - 8*x - 56+ '37': x^3 - 9*x^2 - 26*x + 37+ '41': x^3 - 14*x^2 + 48*x - 8+ '43': x^3 + 17*x^2 + 72*x + 81+ '47': x^3 + 10*x^2 - 72+ '53': x^3 - 20*x - 24+ '59': x^3 + 22*x^2 + 144*x + 280+ 73.2.a.b:+ '2': x^2 + 3*x + 1+ '3': x^2 + 3*x + 1+ '5': x^2 + 3*x + 1+ '11': x^2 + 3*x + 1+ '13': x^2 - x - 11+ '17': x^2 - 45+ '23': x^2 + 15*x + 55+ '29': x^2 - 6*x - 11+ '31': x^2 - 2*x - 44+ '37': x^2 + 4*x - 41+ '41': x^2 - 20+ '47': x^2 + 6*x - 11+ '53': x^2 - 6*x - 71+ '59': x^2 + 12*x + 16+ 73.2.a.c:+ '2': x^2 - x - 3+ '3': x^2 - x - 3+ '5': x^2 + x - 3+ '11': x^2 - 7*x + 9+ '13': x^2 + x - 3+ '17': x^2 + 4*x - 9+ '23': x^2 - 13*x + 39+ '29': x^2 - 2*x - 51+ '31': x^2 - 6*x - 4+ '37': x^2 - 8*x + 3+ '43': x^2 - 6*x - 43+ '53': x^2 + 2*x - 51+ 74.2.a.a:+ '3': x^2 - 3*x - 1+ '5': x^2 + x - 3+ '7': x^2 - 2*x - 12+ '11': x^2 + x - 3+ '13': x^2 + x - 3+ '23': x^2 + 3*x - 27+ '29': x^2 - 3*x - 27+ '31': x^2 - 3*x - 1+ '41': x^2 - 9*x - 9+ '43': x^2 + 6*x - 4+ '47': x^2 - 2*x - 12+ '59': x^2 - 14*x + 36+ 74.2.a.b:+ '3': x^2 + x - 1+ '5': x^2 - x - 11+ '7': x^2 + 2*x - 4+ '11': x^2 + 5*x + 5+ '13': x^2 - x - 11+ '17': x^2 - 20+ '19': x^2 - 20+ '23': x^2 + x - 11+ '29': x^2 + 3*x - 59+ '31': x^2 - 17*x + 71+ '41': x^2 - 17*x + 71+ '43': x^2 + 6*x + 4+ '47': x^2 - 2*x - 4+ '53': x^2 + 8*x - 4+ '59': x^2 + 14*x + 44+ 77.2.a.d:+ '2': x^2 - 5+ '3': x^2 - 2*x - 4+ '13': x^2 - 2*x - 4+ '17': x^2 + 2*x - 4+ '19': x^2 - 4*x - 16+ '23': x^2 + 4*x - 16+ '29': x^2 - 8*x - 4+ '31': x^2 + 10*x + 20+ '37': x^2 + 8*x - 4+ '41': x^2 + 18*x + 76+ '47': x^2 - 10*x + 20+ '53': x^2 - 8*x - 4+ '59': x^2 - 2*x - 4+ 79.2.a.b:+ '2': x^5 - 6*x^3 + 8*x - 1+ '3': x^5 - x^4 - 12*x^3 + 8*x^2 + 24*x - 16+ '5': x^5 - 7*x^4 + 9*x^3 + 27*x^2 - 65*x + 31+ '7': x^5 + 5*x^4 - 6*x^3 - 52*x^2 - 56*x - 16+ '11': x^5 - 2*x^4 - 35*x^3 + 34*x^2 + 185*x + 106+ '13': x^5 + 3*x^4 - 23*x^3 - 123*x^2 - 197*x - 103+ '17': x^5 - 10*x^4 + 16*x^3 + 88*x^2 - 224*x + 32+ '19': x^5 + 4*x^4 - 47*x^3 - 124*x^2 + 541*x + 488+ '23': x^5 - 2*x^4 - 43*x^3 + 106*x^2 + 177*x - 142+ '29': x^5 - 6*x^4 - 52*x^3 + 392*x^2 - 496*x - 32+ '31': x^5 - 2*x^4 - 63*x^3 + 6*x^2 + 397*x + 314+ '37': x^5 - 84*x^3 - 64*x^2 + 1264*x + 2272+ '41': x^5 - 30*x^4 + 336*x^3 - 1752*x^2 + 4256*x - 3872+ '43': x^5 + 14*x^4 + 44*x^3 - 120*x^2 - 688*x - 704+ '47': x^5 - 5*x^4 - 136*x^3 + 536*x^2 + 4176*x - 13456+ '53': x^5 - 2*x^4 - 136*x^3 - 240*x^2 + 3792*x + 12352+ '59': x^5 - 5*x^4 - 70*x^3 + 368*x^2 + 864*x - 4624+ 81.2.a.a:+ '2': x^2 - 3+ '5': x^2 - 3+ '11': x^2 - 12+ '17': x^2 - 27+ '23': x^2 - 12+ '29': x^2 - 3+ '41': x^2 - 48+ '47': x^2 - 48+ '59': x^2 - 192+ 82.2.a.b:+ '3': x^2 - 2+ '5': x^2 - 8+ '7': x^2 + 4*x + 2+ '11': x^2 - 18+ '17': x^2 - 4*x - 28+ '19': x^2 + 8*x + 14+ '23': x^2 - 8*x + 8+ '29': x^2 - 8*x - 16+ '31': x^2 + 8*x + 8+ '37': x^2 - 72+ '43': x^2 - 8*x - 16+ '47': x^2 + 4*x - 46+ '59': x^2 + 8*x + 8+ 83.2.a.b:+ '2': x^6 - x^5 - 9*x^4 + 7*x^3 + 20*x^2 - 12*x - 8+ '3': x^6 - x^5 - 10*x^4 + 5*x^3 + 30*x^2 - 4*x - 25+ '5': x^6 - 2*x^5 - 20*x^4 + 28*x^3 + 104*x^2 - 64*x - 160+ '7': x^6 - 3*x^5 - 22*x^4 + 55*x^3 + 154*x^2 - 228*x - 409+ '11': x^6 + 3*x^5 - 26*x^4 - 83*x^3 + 66*x^2 + 156*x - 113+ '13': x^6 - 14*x^5 + 44*x^4 + 108*x^3 - 488*x^2 - 288*x + 992+ '17': x^6 + 5*x^5 - 20*x^4 - 77*x^3 + 162*x^2 + 188*x - 275+ '19': x^6 + 4*x^5 - 68*x^4 - 300*x^3 + 976*x^2 + 5648*x + 6176+ '23': x^6 + 5*x^5 - 61*x^4 - 377*x^3 + 608*x^2 + 7024*x + 10912+ '29': x^6 + x^5 - 88*x^4 - 181*x^3 + 578*x^2 - 192*x - 55+ '31': x^6 - 3*x^5 - 66*x^4 - 93*x^3 + 390*x^2 + 608*x - 313+ '37': x^6 - 39*x^5 + 576*x^4 - 3785*x^3 + 7934*x^2 + 22268*x - 91499+ '41': x^6 + x^5 - 47*x^4 - x^3 + 482*x^2 - 516*x - 248+ '43': x^6 + 8*x^5 - 44*x^4 - 456*x^3 - 192*x^2 + 4224*x + 6400+ '47': x^6 + 12*x^5 - 96*x^4 - 1812*x^3 - 6648*x^2 + 992*x + 25952+ '53': x^6 - 14*x^5 - 64*x^4 + 1064*x^3 + 448*x^2 - 10048*x - 64+ '59': x^6 + 17*x^5 + 10*x^4 - 493*x^3 - 1018*x^2 + 1768*x + 3527+ 85.2.a.b:+ '2': x^2 + 2*x - 1+ '3': x^2 + 4*x + 2+ '7': x^2 + 4*x + 2+ '11': x^2 + 8*x + 14+ '13': x^2 - 8+ '19': x^2 - 8+ '23': x^2 + 4*x + 2+ '29': x^2 + 4*x - 4+ '31': x^2 - 18+ '37': x^2 + 4*x - 68+ '41': x^2 - 4*x - 68+ '43': x^2 - 4*x - 28+ '47': x^2 + 4*x - 4+ '53': x^2 - 12*x + 4+ '59': x^2 + 24*x + 136+ 85.2.a.c:+ '2': x^2 - 3+ '3': x^2 - 2*x - 2+ '7': x^2 + 2*x - 2+ '11': x^2 - 6*x + 6+ '19': x^2 - 4*x - 8+ '23': x^2 + 6*x - 18+ '29': x^2 - 12+ '31': x^2 - 10*x + 22+ '37': x^2 + 8*x + 4+ '41': x^2 - 12+ '43': x^2 + 8*x + 4+ '47': x^2 - 12*x - 12+ '59': x^2 - 12*x + 24+ 86.2.a.a:+ '3': x^2 + x - 5+ '5': x^2 - 3*x - 3+ '17': x^2 + 9*x + 15+ '19': x^2 - x - 47+ '23': x^2 + 9*x + 15+ '29': x^2 - 3*x - 3+ '31': x^2 - x - 47+ '37': x^2 - x - 47+ '41': x^2 - 3*x - 45+ '47': x^2 + 9*x - 27+ '53': x^2 - 6*x - 12+ 86.2.a.b:+ '3': x^2 - x - 1+ '5': x^2 + 3*x + 1+ '7': x^2 - 20+ '11': x^2 + 4*x - 16+ '13': x^2 - 20+ '17': x^2 + x - 1+ '19': x^2 - 11*x + 29+ '23': x^2 - 3*x - 9+ '29': x^2 + 7*x + 1+ '31': x^2 - 13*x + 41+ '37': x^2 + 5*x + 5+ '41': x^2 + 5*x - 5+ '47': x^2 - 3*x - 59+ '53': x^2 + 10*x + 20+ '59': x^2 - 16*x + 44+ 87.2.a.a:+ '2': x^2 - x - 1+ '5': x^2 - 2*x - 4+ '7': x^2 + 4*x - 1+ '11': x^2 - 4*x - 1+ '13': x^2 + 2*x - 19+ '19': x^2 + 10*x + 20+ '23': x^2 + 2*x - 44+ '31': x^2 + 6*x - 36+ '37': x^2 - 6*x + 4+ '47': x^2 + 4*x - 41+ '53': x^2 - 18*x + 76+ '59': x^2 - 20+ 87.2.a.b:+ '2': x^3 - 2*x^2 - 4*x + 7+ '5': x^3 - 16*x + 8+ '7': x^3 - 4*x^2 - x + 8+ '11': x^3 + 8*x^2 + 15*x + 4+ '13': x^3 - 4*x^2 - 7*x + 26+ '17': x^3 - 4*x^2 - 27*x + 94+ '19': x^3 + 2*x^2 - 20*x + 16+ '23': x^3 - 6*x^2 - 4*x + 32+ '31': x^3 - 6*x^2 - 4*x + 32+ '37': x^3 - 8*x^2 + 8+ '41': x^3 + 2*x^2 - 100*x + 56+ '43': x^3 + 4*x^2 - 96*x - 256+ '47': x^3 + 12*x^2 - 9*x - 216+ '53': x^3 - 8*x^2 - 104*x + 248+ '59': x^3 + 20*x^2 + 108*x + 112+ 88.2.a.b:+ '3': x^2 - x - 4+ '5': x^2 - 3*x - 2+ '7': x^2 + 2*x - 16+ '13': x^2 + 2*x - 16+ '23': x^2 - 9*x + 16+ '29': x^2 + 2*x - 16+ '31': x^2 + 7*x + 8+ '37': x^2 + 11*x + 26+ '41': x^2 - 6*x - 8+ '43': x^2 + 6*x - 8+ '53': x^2 - 8*x - 52+ '59': x^2 + 5*x - 100+ 89.2.a.c:+ '2': x^5 + x^4 - 10*x^3 - 10*x^2 + 21*x + 17+ '3': x^5 + 3*x^4 - 4*x^3 - 16*x^2 - 9*x - 1+ '5': x^5 + x^4 - 14*x^3 - 14*x^2 + 29*x + 13+ '7': x^5 - 8*x^4 + 10*x^3 + 36*x^2 - 68*x + 28+ '11': x^5 - 6*x^4 - 20*x^3 + 112*x^2 + 80*x - 112+ '13': x^5 - 28*x^3 - 56*x^2 + 16+ '17': x^5 + 13*x^4 + 34*x^3 - 154*x^2 - 791*x - 883+ '19': x^5 - 13*x^4 + 42*x^3 + 42*x^2 - 297*x + 199+ '23': x^5 - x^4 - 62*x^3 + 150*x^2 + 631*x - 1657+ '29': x^5 - 2*x^4 - 72*x^3 + 312*x^2 - 48*x - 784+ '31': x^5 - 19*x^4 + 102*x^3 - 114*x^2 + 13*x + 7+ '37': x^5 + 14*x^4 + 8*x^3 - 336*x^2 + 80*x + 1120+ '41': x^5 + 2*x^4 - 60*x^3 - 24*x^2 + 800*x - 1072+ '43': x^5 - x^4 - 68*x^3 - 56*x^2 + 877*x + 1573+ '47': x^5 + 4*x^4 - 44*x^3 + 32*x^2 + 112*x - 16+ '53': x^5 + 11*x^4 - 6*x^3 - 342*x^2 - 547*x + 1319+ '59': x^5 - 118*x^3 + 784*x^2 - 1900*x + 1580+ 91.2.a.c:+ '2': x^2 - 2+ '3': x^2 - 2+ '5': x^2 - 6*x + 7+ '11': x^2 - 18+ '17': x^2 - 2+ '19': x^2 + 6*x - 9+ '23': x^2 + 6*x + 1+ '29': x^2 - 6*x + 1+ '31': x^2 + 2*x - 17+ '37': x^2 + 4*x - 14+ '41': x^2 - 12*x + 28+ '47': x^2 - 6*x + 7+ '53': x^2 + 6*x + 1+ '59': x^2 - 12*x + 4+ 91.2.a.d:+ '2': x^3 - x^2 - 4*x + 2+ '3': x^3 + 2*x^2 - 6*x - 8+ '5': x^3 - 2*x^2 - 3*x + 2+ '11': x^3 - 2*x^2 - 6*x + 8+ '17': x^3 - 4*x^2 - 10*x - 4+ '19': x^3 + 4*x^2 + x - 4+ '23': x^3 - 10*x^2 + x + 136+ '29': x^3 - 24*x^2 + 185*x - 454+ '31': x^3 + 4*x^2 - 19*x + 16+ '37': x^3 - 58*x - 124+ '41': x^3 - 2*x^2 - 28*x - 8+ '43': x^3 - 10*x^2 - 71*x + 628+ '47': x^3 + 8*x^2 - 79*x - 544+ '53': x^3 - 8*x^2 - 35*x - 22+ '59': x^3 + 4*x^2 - 156*x - 688+ 93.2.a.a:+ '2': x^2 + 3*x + 1+ '5': x^2 + 4*x - 1+ '7': x^2 + 4*x - 1+ '11': x^2 + 6*x + 4+ '13': x^2 + 2*x - 4+ '17': x^2 + 4*x - 16+ '19': x^2 + 8*x + 11+ '23': x^2 - 2*x - 4+ '29': x^2 - 2*x - 4+ '37': x^2 - 2*x - 44+ '41': x^2 - 45+ '43': x^2 + 6*x - 36+ '47': x^2 - 4*x - 16+ '53': x^2 - 80+ 93.2.a.b:+ '2': x^3 - 4*x + 1+ '5': x^3 + 2*x^2 - 5*x - 2+ '7': x^3 - 4*x^2 - x + 8+ '11': x^3 + 2*x^2 - 20*x + 16+ '13': x^3 - 4*x^2 - 16*x + 56+ '17': x^3 + 2*x^2 - 24*x - 32+ '19': x^3 - 4*x^2 - 45*x + 196+ '23': x^3 + 6*x^2 - 4*x - 32+ '29': x^3 + 8*x^2 - 56*x - 392+ '37': x^3 - 16*x + 8+ '41': x^3 + 10*x^2 - 17*x - 262+ '43': x^3 - 14*x^2 + 4*x + 368+ '47': x^3 - 12*x^2 - 16*x + 256+ '53': x^3 + 10*x^2 - 16*x - 32+ '59': x^3 - 26*x^2 + 213*x - 556+ 94.2.a.b:+ '3': x^2 - 8+ '5': x^2 - 4*x + 2+ '7': x^2 + 4*x - 4+ '11': x^2 - 8*x + 14+ '13': x^2 + 4*x + 2+ '19': x^2 + 8*x - 2+ '23': x^2 - 8+ '29': x^2 - 12*x + 18+ '31': x^2 - 72+ '37': x^2 - 4*x - 68+ '41': x^2 + 12*x + 28+ '43': x^2 + 8*x - 2+ '53': x^2 - 4*x - 4+ '59': x^2 + 8*x - 16+ 95.2.a.a:+ '2': x^3 - x^2 - 3*x + 1+ '3': x^3 - 2*x^2 - 4*x + 4+ '7': x^3 - 16*x + 16+ '11': x^3 + 8*x^2 + 8*x - 16+ '13': x^3 - 8*x^2 + 12*x - 4+ '17': x^3 - 2*x^2 - 36*x + 104+ '23': x^3 + 4*x^2 - 8*x - 16+ '29': x^3 + 10*x^2 + 12*x - 40+ '31': x^3 - 4*x^2 - 48*x + 64+ '37': x^3 - 20*x^2 + 124*x - 244+ '41': x^3 + 2*x^2 - 36*x - 104+ '43': x^3 + 4*x^2 - 144*x - 592+ '47': x^3 - 16*x + 16+ '53': x^3 - 16*x^2 + 76*x - 92+ '59': x^3 + 20*x^2 + 112*x + 160+ 95.2.a.b:+ '2': x^4 + 2*x^3 - 6*x^2 - 8*x + 9+ '3': x^4 - 2*x^3 - 8*x^2 + 16*x - 4+ '7': x^4 - 4*x^3 - 16*x^2 + 48*x + 32+ '11': x^4 - 4*x^3 - 16*x^2 + 32*x + 48+ '13': x^4 - 2*x^3 - 24*x^2 + 32*x + 20+ '17': x^4 - 4*x^3 - 32*x^2 + 16*x + 48+ '23': x^4 + 8*x^3 - 24*x^2 - 176*x + 288+ '29': x^4 - 4*x^3 - 32*x^2 + 16*x + 48+ '31': x^4 - 4*x^3 - 80*x^2 + 512*x - 640+ '37': x^4 + 6*x^3 - 24*x^2 - 40*x + 4+ '41': x^4 - 16*x^3 + 56*x^2 + 32*x - 240+ '43': x^4 - 4*x^3 - 16*x^2 + 48*x + 32+ '47': x^4 + 12*x^3 - 64*x^2 - 656*x + 1056+ '53': x^4 + 10*x^3 - 184*x - 348+ '59': x^4 - 64*x^2 - 224*x - 192+ 97.2.a.a:+ '2': x^3 + 4*x^2 + 3*x - 1+ '3': x^3 + 4*x^2 + 3*x - 1+ '5': x^3 + 3*x^2 - 4*x + 1+ '7': x^3 + 7*x^2 + 14*x + 7+ '11': x^3 + 7*x^2 + 14*x + 7+ '13': x^3 + 2*x^2 - x - 1+ '17': x^3 + 3*x^2 - 4*x - 13+ '19': x^3 - 5*x^2 - 57*x + 293+ '23': x^3 + 12*x^2 + 27*x - 13+ '29': x^3 - x^2 - 65*x + 169+ '31': x^3 + 8*x^2 + 5*x - 43+ '37': x^3 + 2*x^2 - 71*x + 97+ '41': x^3 - 3*x^2 - 4*x - 1+ '43': x^3 - x^2 - 16*x + 29+ '47': x^3 + 17*x^2 + 59*x - 13+ '53': x^3 - 2*x^2 - 155*x + 659+ '59': x^3 - 19*x^2 + 104*x - 169+ 97.2.a.b:+ '2': x^4 - 3*x^3 - x^2 + 6*x - 1+ '3': x^4 - 5*x^2 - x + 4+ '5': x^4 - x^3 - 4*x^2 + x + 2+ '7': x^4 - 3*x^3 - 6*x^2 + 23*x - 16+ '11': x^4 - 5*x^3 - 14*x^2 + 47*x + 92+ '13': x^4 + 6*x^3 - 29*x^2 - 167*x - 122+ '17': x^4 - 3*x^3 - 20*x^2 + 15*x + 74+ '19': x^4 + 3*x^3 - 5*x^2 - 11*x + 4+ '23': x^4 - 22*x^3 + 151*x^2 - 265*x - 368+ '29': x^4 - 7*x^3 - 27*x^2 + 199*x - 254+ '31': x^4 + 4*x^3 - 67*x^2 - 79*x + 592+ '37': x^4 + 6*x^3 - 27*x^2 - 81*x + 162+ '41': x^4 - 3*x^3 - 158*x^2 + 131*x + 5506+ '43': x^4 - 9*x^3 + 20*x^2 + 9*x - 44+ '47': x^4 - 19*x^3 + 99*x^2 - 161*x + 16+ '53': x^4 + 4*x^3 - 75*x^2 - 123*x + 1262+ '59': x^4 - x^3 - 98*x^2 + 3*x + 772+ 98.2.a.b:+ '3': x^2 - 2+ '5': x^2 - 8+ '17': x^2 - 2+ '19': x^2 - 50+ '31': x^2 - 72+ '41': x^2 - 98+ '47': x^2 - 8+ '59': x^2 - 2
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