History of Hecke polynomials of weight 2 newforms

   - - label   - - 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: '13'+  number: x^2 - 6*x + 9+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_13$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 23.2.a.a+    p: '17'+  number: x^2 - 6*x + 4+- params:+    label: 23.2.a.a+    p: '19'+  number: x^2 + 4*x + 4+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_19$ does+    not generate the full coefficient field $K_f$.+- 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: '5'+  number: x^2 + 2*x + 1+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_5$ does+    not generate the full coefficient field $K_f$.+- 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: '19'+  number: x^2 - 12*x + 36+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_19$ does+    not generate the full coefficient field $K_f$.+- 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: '5'+  number: x^2 - 2*x + 1+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_5$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 31.2.a.a+    p: '7'+  number: x^2 + 4*x - 1+- params:+    label: 31.2.a.a+    p: '11'+  number: x^2 - 4*x + 4+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_11$ does+    not generate the full coefficient field $K_f$.+- 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: 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: '5'+  number: x^2 - 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_5$ does not generate the full coefficient field $K_f$.+- params:+    label: 35.2.a.b+    p: '7'+  number: x^2 + 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_7$ does not generate the full coefficient field $K_f$.+- 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: 39.2.a.b+    p: '2'+  number: x^2 + 2*x - 1+- params:+    label: 39.2.a.b+    p: '3'+  number: x^2 - 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_3$ does not generate the full coefficient field $K_f$.+- 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: '11'+  number: x^2 + 4*x + 4+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_11$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 39.2.a.b+    p: '13'+  number: x^2 + 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_13$ does not generate the full coefficient field $K_f$.+- 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: 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: '17'+  number: x^3 + 6*x^2 + 12*x + 8+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_17$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 41.2.a.a+    p: '19'+  number: x^3 - 4*x^2 - 16*x - 10+- 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: 47.2.a.a+    p: '2'+  number: x^4 - x^3 - 5*x^2 + 5*x - 1+- params:+    label: 47.2.a.a+    p: '3'+  number: x^4 - 7*x^2 + 4*x + 1+- params:+    label: 47.2.a.a+    p: '5'+  number: x^4 + 2*x^3 - 16*x^2 - 16*x + 48+- params:+    label: 47.2.a.a+    p: '7'+  number: x^4 - 4*x^3 - 7*x^2 + 44*x - 43+- params:+    label: 47.2.a.a+    p: '11'+  number: x^4 + 6*x^3 - 4*x^2 - 56*x - 48+- params:+    label: 47.2.a.a+    p: '13'+  number: x^4 - 8*x^3 + 56*x + 48+- params:+    label: 47.2.a.a+    p: '17'+  number: x^4 - 6*x^3 - 21*x^2 + 74*x + 141+- params:+    label: 47.2.a.a+    p: '19'+  number: x^4 - 16*x^2 - 8*x + 16+- params:+    label: 51.2.a.b+    p: '2'+  number: x^2 + x - 4+- params:+    label: 51.2.a.b+    p: '3'+  number: x^2 + 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_3$ does not generate the full coefficient field $K_f$.+- params:+    label: 51.2.a.b+    p: '5'+  number: x^2 - 3*x - 2+- params:+    label: 51.2.a.b+    p: '7'+  number: x^2+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_7$ does+    not generate the full coefficient field $K_f$.+- 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: '17'+  number: x^2 - 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_17$ does not generate the full coefficient field $K_f$.+- params:+    label: 51.2.a.b+    p: '19'+  number: x^2 - 3*x - 36+- 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: '13'+  number: x^3 - 3*x^2 + 3*x - 1+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_13$ does+    not generate the full coefficient field $K_f$.+- 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: 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: '5'+  number: x^2 + 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_5$ does not generate the full coefficient field $K_f$.+- params:+    label: 55.2.a.b+    p: '7'+  number: x^2 + 4*x + 4+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_7$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 55.2.a.b+    p: '11'+  number: x^2 - 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_11$ does not generate the full coefficient field $K_f$.+- 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: '19'+  number: x^2+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_19$ does+    not generate the full coefficient field $K_f$.+- 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 - 24*x^3 - 24*x^2 + 128*x - 64+- params:+    label: 59.2.a.a+    p: '13'+  number: x^5 - 8*x^4 + 88*x^2 - 48*x - 224+- params:+    label: 59.2.a.a+    p: '17'+  number: x^5 + x^4 - 45*x^3 - 81*x^2 + 224*x + 412+- params:+    label: 59.2.a.a+    p: '19'+  number: x^5 - 6*x^4 - 28*x^3 + 217*x^2 - 167*x - 469+- params:+    label: 61.2.a.b+    p: '2'+  number: x^3 - 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: 62.2.a.b+    p: '2'+  number: x^2 + 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_2$ does not generate the full coefficient field $K_f$.+- params:+    label: 62.2.a.b+    p: '3'+  number: x^2 - 2*x - 2+- params:+    label: 62.2.a.b+    p: '5'+  number: x^2 - 12+- params:+    label: 62.2.a.b+    p: '7'+  number: x^2 - 4*x + 4+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_7$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 62.2.a.b+    p: '11'+  number: x^2 + 6*x + 6+- params:+    label: 62.2.a.b+    p: '13'+  number: x^2 + 2*x - 26+- params:+    label: 62.2.a.b+    p: '17'+  number: x^2 - 12+- params:+    label: 62.2.a.b+    p: '19'+  number: x^2 + 8*x + 16+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_19$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 63.2.a.b+    p: '2'+  number: x^2 - 3+- params:+    label: 63.2.a.b+    p: '3'+  number: x^2+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_3$ does not generate the full coefficient field $K_f$.+- params:+    label: 63.2.a.b+    p: '5'+  number: x^2 - 12+- params:+    label: 63.2.a.b+    p: '7'+  number: x^2 - 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_7$ does not generate the full coefficient field $K_f$.+- params:+    label: 63.2.a.b+    p: '11'+  number: x^2 - 12+- params:+    label: 63.2.a.b+    p: '13'+  number: x^2 - 4*x + 4+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_13$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 63.2.a.b+    p: '17'+  number: x^2 - 12+- params:+    label: 63.2.a.b+    p: '19'+  number: x^2 + 8*x + 16+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_19$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 65.2.a.b+    p: '2'+  number: x^2 + 2*x - 1+- params:+    label: 65.2.a.b+    p: '3'+  number: x^2 - 2+- params:+    label: 65.2.a.b+    p: '5'+  number: x^2 - 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_5$ does not generate the full coefficient field $K_f$.+- params:+    label: 65.2.a.b+    p: '7'+  number: x^2 - 4*x - 4+- params:+    label: 65.2.a.b+    p: '11'+  number: x^2 - 4*x + 2+- params:+    label: 65.2.a.b+    p: '13'+  number: x^2 + 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_13$ does not generate the full coefficient field $K_f$.+- params:+    label: 65.2.a.b+    p: '17'+  number: x^2 + 4*x - 4+- params:+    label: 65.2.a.b+    p: '19'+  number: x^2 - 4*x + 2+- params:+    label: 65.2.a.c+    p: '2'+  number: x^2 - 3+- params:+    label: 65.2.a.c+    p: '3'+  number: x^2 - 2*x - 2+- params:+    label: 65.2.a.c+    p: '5'+  number: x^2 + 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_5$ does not generate the full coefficient field $K_f$.+- params:+    label: 65.2.a.c+    p: '7'+  number: x^2 - 4*x + 4+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_7$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 65.2.a.c+    p: '11'+  number: x^2 + 6*x + 6+- params:+    label: 65.2.a.c+    p: '13'+  number: x^2 - 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_13$ does not generate the full coefficient field $K_f$.+- params:+    label: 65.2.a.c+    p: '17'+  number: x^2 - 12+- params:+    label: 65.2.a.c+    p: '19'+  number: x^2 + 2*x - 26+- params:+    label: 67.2.a.b+    p: '2'+  number: x^2 + 3*x + 1+- params:+    label: 67.2.a.b+    p: '3'+  number: x^2 + 3*x + 1+- params:+    label: 67.2.a.b+    p: '5'+  number: x^2 + 6*x + 9+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_5$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 67.2.a.b+    p: '7'+  number: x^2 + x - 11+- params:+    label: 67.2.a.b+    p: '11'+  number: x^2 - 5+- params:+    label: 67.2.a.b+    p: '13'+  number: x^2 + 7*x + 1+- params:+    label: 67.2.a.b+    p: '17'+  number: x^2 + 6*x + 4+- params:+    label: 67.2.a.b+    p: '19'+  number: x^2 - x - 11+- params:+    label: 67.2.a.c+    p: '2'+  number: x^2 + x - 1+- params:+    label: 67.2.a.c+    p: '3'+  number: x^2 - x - 1+- params:+    label: 67.2.a.c+    p: '5'+  number: x^2 - 4*x - 1+- params:+    label: 67.2.a.c+    p: '7'+  number: x^2 - x - 1+- params:+    label: 67.2.a.c+    p: '11'+  number: x^2 - 2*x + 1+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_11$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 67.2.a.c+    p: '13'+  number: x^2 + x - 1+- params:+    label: 67.2.a.c+    p: '17'+  number: x^2 - 6*x + 4+- params:+    label: 67.2.a.c+    p: '19'+  number: x^2 + 11*x + 29+- params:+    label: 68.2.a.a+    p: '2'+  number: x^2+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_2$ does not generate the full coefficient field $K_f$.+- params:+    label: 68.2.a.a+    p: '3'+  number: x^2 - 2*x - 2+- params:+    label: 68.2.a.a+    p: '5'+  number: x^2 - 12+- params:+    label: 68.2.a.a+    p: '7'+  number: x^2 + 2*x - 2+- params:+    label: 68.2.a.a+    p: '11'+  number: x^2 + 6*x + 6+- params:+    label: 68.2.a.a+    p: '13'+  number: x^2 - 4*x - 8+- params:+    label: 68.2.a.a+    p: '17'+  number: x^2 + 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_17$ does not generate the full coefficient field $K_f$.+- params:+    label: 68.2.a.a+    p: '19'+  number: x^2 - 4*x - 8+- params:+    label: 69.2.a.b+    p: '2'+  number: x^2 - 5+- params:+    label: 69.2.a.b+    p: '3'+  number: x^2 + 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_3$ does not generate the full coefficient field $K_f$.+- params:+    label: 69.2.a.b+    p: '5'+  number: x^2 + 2*x - 4+- params:+    label: 69.2.a.b+    p: '7'+  number: x^2 - 2*x - 4+- params:+    label: 69.2.a.b+    p: '11'+  number: x^2 - 8*x + 16+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_11$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 69.2.a.b+    p: '13'+  number: x^2 - 20+- params:+    label: 69.2.a.b+    p: '17'+  number: x^2 + 10*x + 20+- params:+    label: 69.2.a.b+    p: '19'+  number: x^2 - 10*x + 20+- params:+    label: 71.2.a.a+    p: '2'+  number: x^3 + x^2 - 4*x - 3+- params:+    label: 71.2.a.a+    p: '3'+  number: x^3 - x^2 - 4*x + 3+- params:+    label: 71.2.a.a+    p: '5'+  number: x^3 - 5*x^2 - 2*x + 25+- params:+    label: 71.2.a.a+    p: '7'+  number: x^3 - 2*x^2 - 16*x + 24+- params:+    label: 71.2.a.a+    p: '11'+  number: x^3 - 20*x + 24+- params:+    label: 71.2.a.a+    p: '13'+  number: x^3 + 6*x^2 - 8*x - 56+- params:+    label: 71.2.a.a+    p: '17'+  number: x^3 + 2*x^2 - 32*x - 24+- params:+    label: 71.2.a.a+    p: '19'+  number: x^3 - x^2 - 20*x - 25+- params:+    label: 71.2.a.b+    p: '2'+  number: x^3 - 5*x + 3+- params:+    label: 71.2.a.b+    p: '3'+  number: x^3 + x^2 - 8*x - 3+- params:+    label: 71.2.a.b+    p: '5'+  number: x^3 + 3*x^2 - 2*x - 7+- params:+    label: 71.2.a.b+    p: '7'+  number: x^3 - 2*x^2 - 16*x + 24+- params:+    label: 71.2.a.b+    p: '11'+  number: x^3 + 2*x^2 - 16*x - 24+- params:+    label: 71.2.a.b+    p: '13'+  number: x^3 - 12*x^2 + 48*x - 64+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_13$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 71.2.a.b+    p: '17'+  number: x^3 - 2*x^2 - 16*x + 24+- params:+    label: 71.2.a.b+    p: '19'+  number: x^3 - 11*x^2 + 36*x - 35+- params:+    label: 73.2.a.b+    p: '2'+  number: x^2 + 3*x + 1+- params:+    label: 73.2.a.b+    p: '3'+  number: x^2 + 3*x + 1+- params:+    label: 73.2.a.b+    p: '5'+  number: x^2 + 3*x + 1+- params:+    label: 73.2.a.b+    p: '7'+  number: x^2 + 6*x + 9+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_7$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 73.2.a.b+    p: '11'+  number: x^2 + 3*x + 1+- params:+    label: 73.2.a.b+    p: '13'+  number: x^2 - x - 11+- params:+    label: 73.2.a.b+    p: '17'+  number: x^2 - 45+- params:+    label: 73.2.a.b+    p: '19'+  number: x^2 - 2*x + 1+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_19$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 73.2.a.c+    p: '2'+  number: x^2 - x - 3+- params:+    label: 73.2.a.c+    p: '3'+  number: x^2 - x - 3+- params:+    label: 73.2.a.c+    p: '5'+  number: x^2 + x - 3+- params:+    label: 73.2.a.c+    p: '7'+  number: x^2 + 2*x + 1+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_7$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 73.2.a.c+    p: '11'+  number: x^2 - 7*x + 9+- params:+    label: 73.2.a.c+    p: '13'+  number: x^2 + x - 3+- params:+    label: 73.2.a.c+    p: '17'+  number: x^2 + 4*x - 9+- params:+    label: 73.2.a.c+    p: '19'+  number: x^2 + 14*x + 49+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_19$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 74.2.a.a+    p: '2'+  number: x^2 + 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_2$ does not generate the full coefficient field $K_f$.+- params:+    label: 74.2.a.a+    p: '3'+  number: x^2 - 3*x - 1+- params:+    label: 74.2.a.a+    p: '5'+  number: x^2 + x - 3+- params:+    label: 74.2.a.a+    p: '7'+  number: x^2 - 2*x - 12+- params:+    label: 74.2.a.a+    p: '11'+  number: x^2 + x - 3+- params:+    label: 74.2.a.a+    p: '13'+  number: x^2 + x - 3+- params:+    label: 74.2.a.a+    p: '17'+  number: x^2 + 12*x + 36+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_17$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 74.2.a.a+    p: '19'+  number: x^2 - 4*x + 4+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_19$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 74.2.a.b+    p: '2'+  number: x^2 - 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_2$ does not generate the full coefficient field $K_f$.+- params:+    label: 74.2.a.b+    p: '3'+  number: x^2 + x - 1+- params:+    label: 74.2.a.b+    p: '5'+  number: x^2 - x - 11+- params:+    label: 74.2.a.b+    p: '7'+  number: x^2 + 2*x - 4+- params:+    label: 74.2.a.b+    p: '11'+  number: x^2 + 5*x + 5+- params:+    label: 74.2.a.b+    p: '13'+  number: x^2 - x - 11+- params:+    label: 74.2.a.b+    p: '17'+  number: x^2 - 20+- params:+    label: 74.2.a.b+    p: '19'+  number: x^2 - 20+- params:+    label: 77.2.a.d+    p: '2'+  number: x^2 - 5+- params:+    label: 77.2.a.d+    p: '3'+  number: x^2 - 2*x - 4+- params:+    label: 77.2.a.d+    p: '5'+  number: x^2 + 4*x + 4+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_5$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 77.2.a.d+    p: '7'+  number: x^2 - 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_7$ does not generate the full coefficient field $K_f$.+- params:+    label: 77.2.a.d+    p: '11'+  number: x^2 + 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_11$ does not generate the full coefficient field $K_f$.+- params:+    label: 77.2.a.d+    p: '13'+  number: x^2 - 2*x - 4+- params:+    label: 77.2.a.d+    p: '17'+  number: x^2 + 2*x - 4+- params:+    label: 77.2.a.d+    p: '19'+  number: x^2 - 4*x - 16+- params:+    label: 79.2.a.b+    p: '2'+  number: x^5 - 6*x^3 + 8*x - 1+- params:+    label: 79.2.a.b+    p: '3'+  number: x^5 - x^4 - 12*x^3 + 8*x^2 + 24*x - 16+- params:+    label: 79.2.a.b+    p: '5'+  number: x^5 - 7*x^4 + 9*x^3 + 27*x^2 - 65*x + 31+- params:+    label: 79.2.a.b+    p: '7'+  number: x^5 + 5*x^4 - 6*x^3 - 52*x^2 - 56*x - 16+- params:+    label: 79.2.a.b+    p: '11'+  number: x^5 - 2*x^4 - 35*x^3 + 34*x^2 + 185*x + 106+- params:+    label: 79.2.a.b+    p: '13'+  number: x^5 + 3*x^4 - 23*x^3 - 123*x^2 - 197*x - 103+- params:+    label: 79.2.a.b+    p: '17'+  number: x^5 - 10*x^4 + 16*x^3 + 88*x^2 - 224*x + 32+- params:+    label: 79.2.a.b+    p: '19'+  number: x^5 + 4*x^4 - 47*x^3 - 124*x^2 + 541*x + 488+- params:+    label: 81.2.a.a+    p: '2'+  number: x^2 - 3+- params:+    label: 81.2.a.a+    p: '3'+  number: x^2+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_3$ does not generate the full coefficient field $K_f$.+- params:+    label: 81.2.a.a+    p: '5'+  number: x^2 - 3+- params:+    label: 81.2.a.a+    p: '7'+  number: x^2 - 4*x + 4+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_7$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 81.2.a.a+    p: '11'+  number: x^2 - 12+- params:+    label: 81.2.a.a+    p: '13'+  number: x^2 + 2*x + 1+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_13$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 81.2.a.a+    p: '17'+  number: x^2 - 27+- params:+    label: 81.2.a.a+    p: '19'+  number: x^2 - 4*x + 4+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_19$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 82.2.a.b+    p: '2'+  number: x^2 - 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_2$ does not generate the full coefficient field $K_f$.+- params:+    label: 82.2.a.b+    p: '3'+  number: x^2 - 2+- params:+    label: 82.2.a.b+    p: '5'+  number: x^2 - 8+- params:+    label: 82.2.a.b+    p: '7'+  number: x^2 + 4*x + 2+- params:+    label: 82.2.a.b+    p: '11'+  number: x^2 - 18+- params:+    label: 82.2.a.b+    p: '13'+  number: x^2+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_13$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 82.2.a.b+    p: '17'+  number: x^2 - 4*x - 28+- params:+    label: 82.2.a.b+    p: '19'+  number: x^2 + 8*x + 14+- params:+    label: 83.2.a.b+    p: '2'+  number: x^6 - x^5 - 9*x^4 + 7*x^3 + 20*x^2 - 12*x - 8+- params:+    label: 83.2.a.b+    p: '3'+  number: x^6 - x^5 - 10*x^4 + 5*x^3 + 30*x^2 - 4*x - 25+- params:+    label: 83.2.a.b+    p: '5'+  number: x^6 - 2*x^5 - 20*x^4 + 28*x^3 + 104*x^2 - 64*x - 160+- params:+    label: 83.2.a.b+    p: '7'+  number: x^6 - 3*x^5 - 22*x^4 + 55*x^3 + 154*x^2 - 228*x - 409+- params:+    label: 83.2.a.b+    p: '11'+  number: x^6 + 3*x^5 - 26*x^4 - 83*x^3 + 66*x^2 + 156*x - 113+- params:+    label: 83.2.a.b+    p: '13'+  number: x^6 - 14*x^5 + 44*x^4 + 108*x^3 - 488*x^2 - 288*x + 992+- params:+    label: 83.2.a.b+    p: '17'+  number: x^6 + 5*x^5 - 20*x^4 - 77*x^3 + 162*x^2 + 188*x - 275+- params:+    label: 83.2.a.b+    p: '19'+  number: x^6 + 4*x^5 - 68*x^4 - 300*x^3 + 976*x^2 + 5648*x + 6176+- params:+    label: 85.2.a.b+    p: '2'+  number: x^2 + 2*x - 1+- params:+    label: 85.2.a.b+    p: '3'+  number: x^2 + 4*x + 2+- params:+    label: 85.2.a.b+    p: '5'+  number: x^2 + 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_5$ does not generate the full coefficient field $K_f$.+- params:+    label: 85.2.a.b+    p: '7'+  number: x^2 + 4*x + 2+- params:+    label: 85.2.a.b+    p: '11'+  number: x^2 + 8*x + 14+- params:+    label: 85.2.a.b+    p: '13'+  number: x^2 - 8+- params:+    label: 85.2.a.b+    p: '17'+  number: x^2 + 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_17$ does not generate the full coefficient field $K_f$.+- params:+    label: 85.2.a.b+    p: '19'+  number: x^2 - 8+- params:+    label: 85.2.a.c+    p: '2'+  number: x^2 - 3+- params:+    label: 85.2.a.c+    p: '3'+  number: x^2 - 2*x - 2+- params:+    label: 85.2.a.c+    p: '5'+  number: x^2 - 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_5$ does not generate the full coefficient field $K_f$.+- params:+    label: 85.2.a.c+    p: '7'+  number: x^2 + 2*x - 2+- params:+    label: 85.2.a.c+    p: '11'+  number: x^2 - 6*x + 6+- params:+    label: 85.2.a.c+    p: '13'+  number: x^2 + 8*x + 16+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_13$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 85.2.a.c+    p: '17'+  number: x^2 + 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_17$ does not generate the full coefficient field $K_f$.+- params:+    label: 85.2.a.c+    p: '19'+  number: x^2 - 4*x - 8+- params:+    label: 86.2.a.a+    p: '2'+  number: x^2 + 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_2$ does not generate the full coefficient field $K_f$.+- params:+    label: 86.2.a.a+    p: '3'+  number: x^2 + x - 5+- params:+    label: 86.2.a.a+    p: '5'+  number: x^2 - 3*x - 3+- params:+    label: 86.2.a.a+    p: '7'+  number: x^2 - 4*x + 4+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_7$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 86.2.a.a+    p: '11'+  number: x^2+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_11$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 86.2.a.a+    p: '13'+  number: x^2 - 4*x + 4+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_13$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 86.2.a.a+    p: '17'+  number: x^2 + 9*x + 15+- params:+    label: 86.2.a.a+    p: '19'+  number: x^2 - x - 47+- params:+    label: 86.2.a.b+    p: '2'+  number: x^2 - 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_2$ does not generate the full coefficient field $K_f$.+- params:+    label: 86.2.a.b+    p: '3'+  number: x^2 - x - 1+- params:+    label: 86.2.a.b+    p: '5'+  number: x^2 + 3*x + 1+- params:+    label: 86.2.a.b+    p: '7'+  number: x^2 - 20+- params:+    label: 86.2.a.b+    p: '11'+  number: x^2 + 4*x - 16+- params:+    label: 86.2.a.b+    p: '13'+  number: x^2 - 20+- params:+    label: 86.2.a.b+    p: '17'+  number: x^2 + x - 1+- params:+    label: 86.2.a.b+    p: '19'+  number: x^2 - 11*x + 29+- params:+    label: 87.2.a.a+    p: '2'+  number: x^2 - x - 1+- params:+    label: 87.2.a.a+    p: '3'+  number: x^2 - 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_3$ does not generate the full coefficient field $K_f$.+- params:+    label: 87.2.a.a+    p: '5'+  number: x^2 - 2*x - 4+- params:+    label: 87.2.a.a+    p: '7'+  number: x^2 + 4*x - 1+- params:+    label: 87.2.a.a+    p: '11'+  number: x^2 - 4*x - 1+- params:+    label: 87.2.a.a+    p: '13'+  number: x^2 + 2*x - 19+- params:+    label: 87.2.a.a+    p: '17'+  number: x^2 - 6*x + 9+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_17$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 87.2.a.a+    p: '19'+  number: x^2 + 10*x + 20+- params:+    label: 87.2.a.b+    p: '2'+  number: x^3 - 2*x^2 - 4*x + 7+- params:+    label: 87.2.a.b+    p: '3'+  number: x^3 + 3*x^2 + 3*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_3$ does not generate the full coefficient field $K_f$.+- params:+    label: 87.2.a.b+    p: '5'+  number: x^3 - 16*x + 8+- params:+    label: 87.2.a.b+    p: '7'+  number: x^3 - 4*x^2 - x + 8+- params:+    label: 87.2.a.b+    p: '11'+  number: x^3 + 8*x^2 + 15*x + 4+- params:+    label: 87.2.a.b+    p: '13'+  number: x^3 - 4*x^2 - 7*x + 26+- params:+    label: 87.2.a.b+    p: '17'+  number: x^3 - 4*x^2 - 27*x + 94+- params:+    label: 87.2.a.b+    p: '19'+  number: x^3 + 2*x^2 - 20*x + 16+- params:+    label: 88.2.a.b+    p: '2'+  number: x^2+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_2$ does not generate the full coefficient field $K_f$.+- params:+    label: 88.2.a.b+    p: '3'+  number: x^2 - x - 4+- params:+    label: 88.2.a.b+    p: '5'+  number: x^2 - 3*x - 2+- params:+    label: 88.2.a.b+    p: '7'+  number: x^2 + 2*x - 16+- params:+    label: 88.2.a.b+    p: '11'+  number: x^2 + 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_11$ does not generate the full coefficient field $K_f$.+- params:+    label: 88.2.a.b+    p: '13'+  number: x^2 + 2*x - 16+- params:+    label: 88.2.a.b+    p: '17'+  number: x^2 - 4*x + 4+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_17$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 88.2.a.b+    p: '19'+  number: x^2 + 8*x + 16+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_19$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 89.2.a.c+    p: '2'+  number: x^5 + x^4 - 10*x^3 - 10*x^2 + 21*x + 17+- params:+    label: 89.2.a.c+    p: '3'+  number: x^5 + 3*x^4 - 4*x^3 - 16*x^2 - 9*x - 1+- params:+    label: 89.2.a.c+    p: '5'+  number: x^5 + x^4 - 14*x^3 - 14*x^2 + 29*x + 13+- params:+    label: 89.2.a.c+    p: '7'+  number: x^5 - 8*x^4 + 10*x^3 + 36*x^2 - 68*x + 28+- params:+    label: 89.2.a.c+    p: '11'+  number: x^5 - 6*x^4 - 20*x^3 + 112*x^2 + 80*x - 112+- params:+    label: 89.2.a.c+    p: '13'+  number: x^5 - 28*x^3 - 56*x^2 + 16+- params:+    label: 89.2.a.c+    p: '17'+  number: x^5 + 13*x^4 + 34*x^3 - 154*x^2 - 791*x - 883+- params:+    label: 89.2.a.c+    p: '19'+  number: x^5 - 13*x^4 + 42*x^3 + 42*x^2 - 297*x + 199+- params:+    label: 91.2.a.c+    p: '2'+  number: x^2 - 2+- params:+    label: 91.2.a.c+    p: '3'+  number: x^2 - 2+- params:+    label: 91.2.a.c+    p: '5'+  number: x^2 - 6*x + 7+- params:+    label: 91.2.a.c+    p: '7'+  number: x^2 - 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_7$ does not generate the full coefficient field $K_f$.+- params:+    label: 91.2.a.c+    p: '11'+  number: x^2 - 18+- params:+    label: 91.2.a.c+    p: '13'+  number: x^2 + 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_13$ does not generate the full coefficient field $K_f$.+- params:+    label: 91.2.a.c+    p: '17'+  number: x^2 - 2+- params:+    label: 91.2.a.c+    p: '19'+  number: x^2 + 6*x - 9+- params:+    label: 91.2.a.d+    p: '2'+  number: x^3 - x^2 - 4*x + 2+- params:+    label: 91.2.a.d+    p: '3'+  number: x^3 + 2*x^2 - 6*x - 8+- params:+    label: 91.2.a.d+    p: '5'+  number: x^3 - 2*x^2 - 3*x + 2+- params:+    label: 91.2.a.d+    p: '7'+  number: x^3 + 3*x^2 + 3*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_7$ does not generate the full coefficient field $K_f$.+- params:+    label: 91.2.a.d+    p: '11'+  number: x^3 - 2*x^2 - 6*x + 8+- params:+    label: 91.2.a.d+    p: '13'+  number: x^3 - 3*x^2 + 3*x - 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_13$ does not generate the full coefficient field $K_f$.+- params:+    label: 91.2.a.d+    p: '17'+  number: x^3 - 4*x^2 - 10*x - 4+- params:+    label: 91.2.a.d+    p: '19'+  number: x^3 + 4*x^2 + x - 4+- params:+    label: 93.2.a.a+    p: '2'+  number: x^2 + 3*x + 1+- params:+    label: 93.2.a.a+    p: '3'+  number: x^2 + 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_3$ does not generate the full coefficient field $K_f$.+- params:+    label: 93.2.a.a+    p: '5'+  number: x^2 + 4*x - 1+- params:+    label: 93.2.a.a+    p: '7'+  number: x^2 + 4*x - 1+- params:+    label: 93.2.a.a+    p: '11'+  number: x^2 + 6*x + 4+- params:+    label: 93.2.a.a+    p: '13'+  number: x^2 + 2*x - 4+- params:+    label: 93.2.a.a+    p: '17'+  number: x^2 + 4*x - 16+- params:+    label: 93.2.a.a+    p: '19'+  number: x^2 + 8*x + 11+- params:+    label: 93.2.a.b+    p: '2'+  number: x^3 - 4*x + 1+- params:+    label: 93.2.a.b+    p: '3'+  number: x^3 - 3*x^2 + 3*x - 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_3$ does not generate the full coefficient field $K_f$.+- params:+    label: 93.2.a.b+    p: '5'+  number: x^3 + 2*x^2 - 5*x - 2+- params:+    label: 93.2.a.b+    p: '7'+  number: x^3 - 4*x^2 - x + 8+- params:+    label: 93.2.a.b+    p: '11'+  number: x^3 + 2*x^2 - 20*x + 16+- params:+    label: 93.2.a.b+    p: '13'+  number: x^3 - 4*x^2 - 16*x + 56+- params:+    label: 93.2.a.b+    p: '17'+  number: x^3 + 2*x^2 - 24*x - 32+- params:+    label: 93.2.a.b+    p: '19'+  number: x^3 - 4*x^2 - 45*x + 196+- params:+    label: 94.2.a.b+    p: '2'+  number: x^2 + 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_2$ does not generate the full coefficient field $K_f$.+- params:+    label: 94.2.a.b+    p: '3'+  number: x^2 - 8+- params:+    label: 94.2.a.b+    p: '5'+  number: x^2 - 4*x + 2+- params:+    label: 94.2.a.b+    p: '7'+  number: x^2 + 4*x - 4+- params:+    label: 94.2.a.b+    p: '11'+  number: x^2 - 8*x + 14+- params:+    label: 94.2.a.b+    p: '13'+  number: x^2 + 4*x + 2+- params:+    label: 94.2.a.b+    p: '17'+  number: x^2+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_17$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 94.2.a.b+    p: '19'+  number: x^2 + 8*x - 2+- params:+    label: 95.2.a.a+    p: '2'+  number: x^3 - x^2 - 3*x + 1+- params:+    label: 95.2.a.a+    p: '3'+  number: x^3 - 2*x^2 - 4*x + 4+- params:+    label: 95.2.a.a+    p: '5'+  number: x^3 - 3*x^2 + 3*x - 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_5$ does not generate the full coefficient field $K_f$.+- params:+    label: 95.2.a.a+    p: '7'+  number: x^3 - 16*x + 16+- params:+    label: 95.2.a.a+    p: '11'+  number: x^3 + 8*x^2 + 8*x - 16+- params:+    label: 95.2.a.a+    p: '13'+  number: x^3 - 8*x^2 + 12*x - 4+- params:+    label: 95.2.a.a+    p: '17'+  number: x^3 - 2*x^2 - 36*x + 104+- params:+    label: 95.2.a.a+    p: '19'+  number: x^3 + 3*x^2 + 3*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_19$ does not generate the full coefficient field $K_f$.+- params:+    label: 95.2.a.b+    p: '2'+  number: x^4 + 2*x^3 - 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: '5'+  number: x^4 + 4*x^3 + 6*x^2 + 4*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_5$ does not generate the full coefficient field $K_f$.+- 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: '19'+  number: x^4 - 4*x^3 + 6*x^2 - 4*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_19$ does not generate the full coefficient field $K_f$.+- 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.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: 98.2.a.b+    p: '2'+  number: x^2 - 2*x + 1+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_2$ does not generate the full coefficient field $K_f$.+- 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: '7'+  number: x^2+  comment: Here $p$ divides the level $N$; the polynomial records the usual Atkin-Lehner+    coefficient $a_p$ on $K_f$. The characteristic polynomial is reducible over $\mathbb{Q}$;+    $a_7$ does not generate the full coefficient field $K_f$.+- params:+    label: 98.2.a.b+    p: '11'+  number: x^2 + 4*x + 4+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_11$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 98.2.a.b+    p: '13'+  number: x^2+  comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_13$ does+    not generate the full coefficient field $K_f$.+- params:+    label: 98.2.a.b+    p: '17'+  number: x^2 - 2+- params:+    label: 98.2.a.b+    p: '19'+  number: x^2 - 50