History of Hecke polynomials of weight 2 newforms

   - - p Numbers:-  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-    '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 $K_f$.-    '17': x^2 - 6*x + 4-    '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 $K_f$.-  29.2.a.a:-    '2': x^2 + 2*x - 1-    '3': x^2 - 2*x - 1-    '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 $K_f$.-    '7': x^2 - 8-    '11': x^2 - 2*x - 1-    '13': x^2 + 2*x - 7-    '17': x^2 + 4*x - 4-    '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 $K_f$.-  31.2.a.a:-    '2': x^2 - x - 1-    '3': x^2 + 2*x - 4-    '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 $K_f$.-    '7': x^2 + 4*x - 1-    '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 $K_f$.-    '13': x^2 + 2*x - 4-    '17': x^2 - 6*x + 4-    '19': x^2 - 5-  35.2.a.b:-    '2': x^2 + x - 4-    '3': x^2 + x - 4-    '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 $K_f$.-    '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 $K_f$.-    '11': x^2 - x - 4-    '13': x^2 - 5*x + 2-    '17': x^2 + 5*x + 2-    '19': x^2 + 6*x - 8-  39.2.a.b:-    '2': x^2 + 2*x - 1-    '3':-      number: x^2 - 2*x + 1-      comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{3}$-        does not generate the full coefficient field $K_f$.-    '5': x^2 - 8-    '7': x^2 - 8-    '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 $K_f$.-    '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 $K_f$.-    '17': x^2 - 4*x - 28-    '19': x^2 - 8-  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-    '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 $K_f$.-    '19': x^3 - 4*x^2 - 16*x - 10-  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-  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 - 16*x + 48-    '7': x^4 - 4*x^3 - 7*x^2 + 44*x - 43-    '11': x^4 + 6*x^3 - 4*x^2 - 56*x - 48-    '13': x^4 - 8*x^3 + 56*x + 48-    '17': x^4 - 6*x^3 - 21*x^2 + 74*x + 141-    '19': x^4 - 16*x^2 - 8*x + 16-  51.2.a.b:-    '2': x^2 + x - 4-    '3':-      number: x^2 + 2*x + 1-      comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{3}$-        does not generate the full coefficient field $K_f$.-    '5': x^2 - 3*x - 2-    '7':-      number: x^2-      comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{7}$-        does not generate the full coefficient field $K_f$.-    '11': x^2 + x - 4-    '13': x^2 - 5*x + 2-    '17':-      number: x^2 - 2*x + 1-      comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{17}$-        does not generate the full coefficient field $K_f$.-    '19': x^2 - 3*x - 36-  53.2.a.b:-    '2': x^3 + x^2 - 3*x - 1-    '3': x^3 - 3*x^2 - x + 1-    '5': x^3 + 2*x^2 - 4*x - 4-    '7': x^3 - 4*x^2 + 4-    '11': x^3 + 4*x^2 - 4*x - 20-    '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 $K_f$.-    '17': x^3 + 5*x^2 - 5*x - 17-    '19': x^3 - 11*x^2 + 37*x - 37-  55.2.a.b:-    '2': x^2 - 2*x - 1-    '3': x^2 - 8-    '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 $K_f$.-    '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 $K_f$.-    '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 $K_f$.-    '13': x^2 + 8*x + 8-    '17': x^2 - 8*x + 8-    '19':-      number: x^2-      comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{19}$-        does not generate the full coefficient field $K_f$.-  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-  61.2.a.b:-    '2': x^3 - x^2 - 3*x + 1-    '3': x^3 - 2*x^2 - 4*x + 4-    '5': x^3 + x^2 - 9*x - 13-    '7': x^3 + 3*x^2 - x - 1-    '11': x^3 - 13*x^2 + 53*x - 67-    '13': x^3 + 9*x^2 + 11*x - 37-    '17': x^3 + 2*x^2 - 8*x + 4-    '19': x^3 - 48*x - 20-  62.2.a.b:-    '2':-      number: x^2 + 2*x + 1-      comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{2}$-        does not generate the full coefficient field $K_f$.-    '3': x^2 - 2*x - 2-    '5': x^2 - 12-    '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 $K_f$.-    '11': x^2 + 6*x + 6-    '13': x^2 + 2*x - 26-    '17': x^2 - 12-    '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 $K_f$.-  63.2.a.b:-    '2': x^2 - 3-    '3':-      number: x^2-      comment: Here $p^2$ divides the level $N$, so $a_p=0$. The characteristic polynomial-        is reducible over $\mathbb{Q}$; $a_{3}$ does not generate the full coefficient-        field $K_f$.-    '5': x^2 - 12-    '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 $K_f$.-    '11': x^2 - 12-    '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 $K_f$.-    '17': x^2 - 12-    '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 $K_f$.-  65.2.a.b:-    '2': x^2 + 2*x - 1-    '3': x^2 - 2-    '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 $K_f$.-    '7': x^2 - 4*x - 4-    '11': x^2 - 4*x + 2-    '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 $K_f$.-    '17': x^2 + 4*x - 4-    '19': x^2 - 4*x + 2-  65.2.a.c:-    '2': x^2 - 3-    '3': x^2 - 2*x - 2-    '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 $K_f$.-    '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 $K_f$.-    '11': x^2 + 6*x + 6-    '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 $K_f$.-    '17': x^2 - 12-    '19': x^2 + 2*x - 26-  67.2.a.b:-    '2': x^2 + 3*x + 1-    '3': x^2 + 3*x + 1-    '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 $K_f$.-    '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-  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-    '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 $K_f$.-    '13': x^2 + x - 1-    '17': x^2 - 6*x + 4-    '19': x^2 + 11*x + 29-  68.2.a.a:-    '2':-      number: x^2-      comment: Here $p^2$ divides the level $N$, so $a_p=0$. The characteristic polynomial-        is reducible over $\mathbb{Q}$; $a_{2}$ does not generate the full coefficient-        field $K_f$.-    '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-    '17':-      number: x^2 + 2*x + 1-      comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{17}$-        does not generate the full coefficient field $K_f$.-    '19': x^2 - 4*x - 8-  69.2.a.b:-    '2': x^2 - 5-    '3':-      number: x^2 + 2*x + 1-      comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{3}$-        does not generate the full coefficient field $K_f$.-    '5': x^2 + 2*x - 4-    '7': x^2 - 2*x - 4-    '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 $K_f$.-    '13': x^2 - 20-    '17': x^2 + 10*x + 20-    '19': x^2 - 10*x + 20-  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-  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-    '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 $K_f$.-    '17': x^3 - 2*x^2 - 16*x + 24-    '19': x^3 - 11*x^2 + 36*x - 35-  73.2.a.b:-    '2': x^2 + 3*x + 1-    '3': x^2 + 3*x + 1-    '5': x^2 + 3*x + 1-    '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 $K_f$.-    '11': x^2 + 3*x + 1-    '13': x^2 - x - 11-    '17': x^2 - 45-    '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 $K_f$.-  73.2.a.c:-    '2': x^2 - x - 3-    '3': x^2 - x - 3-    '5': x^2 + x - 3-    '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 $K_f$.-    '11': x^2 - 7*x + 9-    '13': x^2 + x - 3-    '17': x^2 + 4*x - 9-    '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 $K_f$.-  74.2.a.a:-    '2':-      number: x^2 + 2*x + 1-      comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{2}$-        does not generate the full coefficient field $K_f$.-    '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-    '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 $K_f$.-    '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 $K_f$.-  74.2.a.b:-    '2':-      number: x^2 - 2*x + 1-      comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{2}$-        does not generate the full coefficient field $K_f$.-    '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-  77.2.a.d:-    '2': x^2 - 5-    '3': x^2 - 2*x - 4-    '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 $K_f$.-    '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 $K_f$.-    '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 $K_f$.-    '13': x^2 - 2*x - 4-    '17': x^2 + 2*x - 4-    '19': x^2 - 4*x - 16-  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-  81.2.a.a:-    '2': x^2 - 3-    '3':-      number: x^2-      comment: Here $p^2$ divides the level $N$, so $a_p=0$. The characteristic polynomial-        is reducible over $\mathbb{Q}$; $a_{3}$ does not generate the full coefficient-        field $K_f$.-    '5': x^2 - 3-    '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 $K_f$.-    '11': x^2 - 12-    '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 $K_f$.-    '17': x^2 - 27-    '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 $K_f$.-  82.2.a.b:-    '2':-      number: x^2 - 2*x + 1-      comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{2}$-        does not generate the full coefficient field $K_f$.-    '3': x^2 - 2-    '5': x^2 - 8-    '7': x^2 + 4*x + 2-    '11': x^2 - 18-    '13':-      number: x^2-      comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{13}$-        does not generate the full coefficient field $K_f$.-    '17': x^2 - 4*x - 28-    '19': x^2 + 8*x + 14-  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-  85.2.a.b:-    '2': x^2 + 2*x - 1-    '3': x^2 + 4*x + 2-    '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 $K_f$.-    '7': x^2 + 4*x + 2-    '11': x^2 + 8*x + 14-    '13': x^2 - 8-    '17':-      number: x^2 + 2*x + 1-      comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{17}$-        does not generate the full coefficient field $K_f$.-    '19': x^2 - 8-  85.2.a.c:-    '2': x^2 - 3-    '3': x^2 - 2*x - 2-    '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 $K_f$.-    '7': x^2 + 2*x - 2-    '11': x^2 - 6*x + 6-    '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 $K_f$.-    '17':-      number: x^2 + 2*x + 1-      comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{17}$-        does not generate the full coefficient field $K_f$.-    '19': x^2 - 4*x - 8-  86.2.a.a:-    '2':-      number: x^2 + 2*x + 1-      comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{2}$-        does not generate the full coefficient field $K_f$.-    '3': x^2 + x - 5-    '5': x^2 - 3*x - 3-    '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 $K_f$.-    '11':-      number: x^2-      comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{11}$-        does not generate the full coefficient field $K_f$.-    '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 $K_f$.-    '17': x^2 + 9*x + 15-    '19': x^2 - x - 47-  86.2.a.b:-    '2':-      number: x^2 - 2*x + 1-      comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{2}$-        does not generate the full coefficient field $K_f$.-    '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-  87.2.a.a:-    '2': x^2 - x - 1-    '3':-      number: x^2 - 2*x + 1-      comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{3}$-        does not generate the full coefficient field $K_f$.-    '5': x^2 - 2*x - 4-    '7': x^2 + 4*x - 1-    '11': x^2 - 4*x - 1-    '13': x^2 + 2*x - 19-    '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 $K_f$.-    '19': x^2 + 10*x + 20-  87.2.a.b:-    '2': x^3 - 2*x^2 - 4*x + 7-    '3':-      number: x^3 + 3*x^2 + 3*x + 1-      comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{3}$-        does not generate the full coefficient field $K_f$.-    '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-  88.2.a.b:-    '2':-      number: x^2-      comment: Here $p^2$ divides the level $N$, so $a_p=0$. The characteristic polynomial-        is reducible over $\mathbb{Q}$; $a_{2}$ does not generate the full coefficient-        field $K_f$.-    '3': x^2 - x - 4-    '5': x^2 - 3*x - 2-    '7': x^2 + 2*x - 16-    '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 $K_f$.-    '13': x^2 + 2*x - 16-    '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 $K_f$.-    '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 $K_f$.-  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-  91.2.a.c:-    '2': x^2 - 2-    '3': x^2 - 2-    '5': x^2 - 6*x + 7-    '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 $K_f$.-    '11': x^2 - 18-    '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 $K_f$.-    '17': x^2 - 2-    '19': x^2 + 6*x - 9-  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-    '7':-      number: x^3 + 3*x^2 + 3*x + 1-      comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{7}$-        does not generate the full coefficient field $K_f$.-    '11': x^3 - 2*x^2 - 6*x + 8-    '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 $K_f$.-    '17': x^3 - 4*x^2 - 10*x - 4-    '19': x^3 + 4*x^2 + x - 4-  93.2.a.a:-    '2': x^2 + 3*x + 1-    '3':-      number: x^2 + 2*x + 1-      comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{3}$-        does not generate the full coefficient field $K_f$.-    '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-  93.2.a.b:-    '2': x^3 - 4*x + 1-    '3':-      number: x^3 - 3*x^2 + 3*x - 1-      comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{3}$-        does not generate the full coefficient field $K_f$.-    '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-  94.2.a.b:-    '2':-      number: x^2 + 2*x + 1-      comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{2}$-        does not generate the full coefficient field $K_f$.-    '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-    '17':-      number: x^2-      comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{17}$-        does not generate the full coefficient field $K_f$.-    '19': x^2 + 8*x - 2-  95.2.a.a:-    '2': x^3 - x^2 - 3*x + 1-    '3': x^3 - 2*x^2 - 4*x + 4-    '5':-      number: x^3 - 3*x^2 + 3*x - 1-      comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{5}$-        does not generate the full coefficient field $K_f$.-    '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-    '19':-      number: x^3 + 3*x^2 + 3*x + 1-      comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{19}$-        does not generate the full coefficient field $K_f$.-  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-    '5':-      number: x^4 + 4*x^3 + 6*x^2 + 4*x + 1-      comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{5}$-        does not generate the full coefficient field $K_f$.-    '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-    '19':-      number: x^4 - 4*x^3 + 6*x^2 - 4*x + 1-      comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{19}$-        does not generate the full coefficient field $K_f$.-  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-  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-  98.2.a.b:-    '2':-      number: x^2 - 2*x + 1-      comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{2}$-        does not generate the full coefficient field $K_f$.-    '3': x^2 - 2-    '5': x^2 - 8-    '7':-      number: x^2-      comment: Here $p^2$ divides the level $N$, so $a_p=0$. The characteristic polynomial-        is reducible over $\mathbb{Q}$; $a_{7}$ does not generate the full coefficient-        field $K_f$.-    '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 $K_f$.-    '13':-      number: x^2-      comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{13}$-        does not generate the full coefficient field $K_f$.-    '17': x^2 - 2-    '19': x^2 - 50+- 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+- 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: '13'+  number: x^2 - 6*x + 9+- params:+    label: 23.2.a.a+    p: '17'+  number: x^2 - 6*x + 4+- comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{19}$+    does not generate the full coefficient field $K_f$.+  params:+    label: 23.2.a.a+    p: '19'+  number: x^2 + 4*x + 4+- 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+- 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: '5'+  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+- 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: '19'+  number: x^2 - 12*x + 36+- 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+- 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: '5'+  number: x^2 - 2*x + 1+- params:+    label: 31.2.a.a+    p: '7'+  number: x^2 + 4*x - 1+- 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: '11'+  number: x^2 - 4*x + 4+- 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+- comment: 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: '5'+  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: 35.2.a.b+    p: '7'+  number: x^2 + 2*x + 1+- 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+- comment: 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: '3'+  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+- 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: '11'+  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: 39.2.a.b+    p: '13'+  number: x^2 + 2*x + 1+- 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+- 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: '17'+  number: x^3 + 6*x^2 + 12*x + 8+- 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+- comment: 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: '3'+  number: x^2 + 2*x + 1+- params:+    label: 51.2.a.b+    p: '5'+  number: x^2 - 3*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: '7'+  number: 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+- comment: 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: '17'+  number: x^2 - 2*x + 1+- 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+- 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: '13'+  number: x^3 - 3*x^2 + 3*x - 1+- 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+- comment: 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: '5'+  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: 55.2.a.b+    p: '7'+  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: 55.2.a.b+    p: '11'+  number: x^2 - 2*x + 1+- 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+- comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{19}$+    does not generate the full coefficient field $K_f$.+  params:+    label: 55.2.a.b+    p: '19'+  number: x^2+- 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+- comment: 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: '2'+  number: x^2 + 2*x + 1+- 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+- 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: '7'+  number: x^2 - 4*x + 4+- 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+- comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{19}$+    does not generate the full coefficient field $K_f$.+  params:+    label: 62.2.a.b+    p: '19'+  number: x^2 + 8*x + 16+- params:+    label: 63.2.a.b+    p: '2'+  number: x^2 - 3+- comment: Here $p^2$ divides the level $N$, so $a_p=0$. 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: '3'+  number: x^2+- params:+    label: 63.2.a.b+    p: '5'+  number: x^2 - 12+- comment: 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: '7'+  number: x^2 - 2*x + 1+- params:+    label: 63.2.a.b+    p: '11'+  number: x^2 - 12+- 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: '13'+  number: x^2 - 4*x + 4+- params:+    label: 63.2.a.b+    p: '17'+  number: x^2 - 12+- 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: '19'+  number: x^2 + 8*x + 16+- 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+- comment: 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: '5'+  number: x^2 - 2*x + 1+- 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+- comment: 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: '13'+  number: x^2 + 2*x + 1+- 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+- comment: 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: '5'+  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: 65.2.a.c+    p: '7'+  number: x^2 - 4*x + 4+- params:+    label: 65.2.a.c+    p: '11'+  number: x^2 + 6*x + 6+- comment: 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: '13'+  number: x^2 - 2*x + 1+- 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+- 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: '5'+  number: x^2 + 6*x + 9+- 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+- 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: '11'+  number: x^2 - 2*x + 1+- 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+- comment: Here $p^2$ divides the level $N$, so $a_p=0$. 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: '2'+  number: x^2+- 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+- comment: 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: '17'+  number: x^2 + 2*x + 1+- 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+- comment: 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: '3'+  number: x^2 + 2*x + 1+- 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+- 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: '11'+  number: x^2 - 8*x + 16+- 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+- 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: '13'+  number: x^3 - 12*x^2 + 48*x - 64+- 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+- 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: '7'+  number: x^2 + 6*x + 9+- 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+- 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.b+    p: '19'+  number: x^2 - 2*x + 1+- 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+- 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: '7'+  number: x^2 + 2*x + 1+- 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+- 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: '19'+  number: x^2 + 14*x + 49+- comment: 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: '2'+  number: x^2 + 2*x + 1+- 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+- 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: '17'+  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: 74.2.a.a+    p: '19'+  number: x^2 - 4*x + 4+- comment: 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: '2'+  number: x^2 - 2*x + 1+- 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+- 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: '5'+  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: 77.2.a.d+    p: '7'+  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: 77.2.a.d+    p: '11'+  number: x^2 + 2*x + 1+- 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+- comment: Here $p^2$ divides the level $N$, so $a_p=0$. 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: '3'+  number: x^2+- params:+    label: 81.2.a.a+    p: '5'+  number: x^2 - 3+- 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: '7'+  number: x^2 - 4*x + 4+- params:+    label: 81.2.a.a+    p: '11'+  number: x^2 - 12+- 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: '13'+  number: x^2 + 2*x + 1+- params:+    label: 81.2.a.a+    p: '17'+  number: x^2 - 27+- comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{19}$+    does not generate the full coefficient field $K_f$.+  params:+    label: 81.2.a.a+    p: '19'+  number: x^2 - 4*x + 4+- comment: 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: '2'+  number: x^2 - 2*x + 1+- 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+- 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: '13'+  number: x^2+- 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+- comment: 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: '5'+  number: x^2 + 2*x + 1+- 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+- comment: 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: '17'+  number: x^2 + 2*x + 1+- 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+- comment: 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: '5'+  number: x^2 - 2*x + 1+- 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+- 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: '13'+  number: x^2 + 8*x + 16+- comment: 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: '17'+  number: x^2 + 2*x + 1+- params:+    label: 85.2.a.c+    p: '19'+  number: x^2 - 4*x - 8+- comment: 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: '2'+  number: x^2 + 2*x + 1+- 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+- 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: '7'+  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: 86.2.a.a+    p: '11'+  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: 86.2.a.a+    p: '13'+  number: x^2 - 4*x + 4+- 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+- comment: 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: '2'+  number: x^2 - 2*x + 1+- 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+- comment: 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: '3'+  number: x^2 - 2*x + 1+- 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+- 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: '17'+  number: x^2 - 6*x + 9+- 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+- comment: 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: '3'+  number: x^3 + 3*x^2 + 3*x + 1+- 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+- comment: Here $p^2$ divides the level $N$, so $a_p=0$. 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: '2'+  number: x^2+- 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+- comment: 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: '11'+  number: x^2 + 2*x + 1+- params:+    label: 88.2.a.b+    p: '13'+  number: x^2 + 2*x - 16+- 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: '17'+  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: 88.2.a.b+    p: '19'+  number: x^2 + 8*x + 16+- 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+- comment: 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: '7'+  number: x^2 - 2*x + 1+- params:+    label: 91.2.a.c+    p: '11'+  number: x^2 - 18+- comment: 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: '13'+  number: x^2 + 2*x + 1+- 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+- comment: 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: '7'+  number: x^3 + 3*x^2 + 3*x + 1+- params:+    label: 91.2.a.d+    p: '11'+  number: x^3 - 2*x^2 - 6*x + 8+- comment: 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: '13'+  number: x^3 - 3*x^2 + 3*x - 1+- 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+- comment: 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: '3'+  number: x^2 + 2*x + 1+- 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+- comment: 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: '3'+  number: x^3 - 3*x^2 + 3*x - 1+- 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+- comment: 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: '2'+  number: x^2 + 2*x + 1+- 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+- 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: '17'+  number: x^2+- 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+- comment: 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: '5'+  number: x^3 - 3*x^2 + 3*x - 1+- 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+- comment: The characteristic polynomial is reducible over $\mathbb{Q}$; $a_{19}$+    does not generate the full coefficient field $K_f$.+  params:+    label: 95.2.a.a+    p: '19'+  number: x^3 + 3*x^2 + 3*x + 1+- 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+- comment: 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: '5'+  number: x^4 + 4*x^3 + 6*x^2 + 4*x + 1+- 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+- comment: 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: '19'+  number: x^4 - 4*x^3 + 6*x^2 - 4*x + 1+- 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+- comment: 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: '2'+  number: x^2 - 2*x + 1+- params:+    label: 98.2.a.b+    p: '3'+  number: x^2 - 2+- params:+    label: 98.2.a.b+    p: '5'+  number: x^2 - 8+- comment: Here $p^2$ divides the level $N$, so $a_p=0$. 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: '7'+  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: 98.2.a.b+    p: '11'+  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: 98.2.a.b+    p: '13'+  number: x^2+- 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: 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: '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: '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: '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: '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: '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: '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 - 72+- params:+    label: 43.2.a.b+    p: '41'+  number: x^2 + 2*x - 7+- params:+    label: 43.2.a.b+    p: '53'+  number: x^2 - 22*x + 113+- params:+    label: 43.2.a.b+    p: '59'+  number: x^2 + 4*x - 4+- params:+    label: 47.2.a.a+    p: '23'+  number: x^4 + 6*x^3 - 20*x^2 - 40*x - 16+- params:+    label: 47.2.a.a+    p: '29'+  number: x^4 + 10*x^3 + 20*x^2 - 8*x - 16+- params:+    label: 47.2.a.a+    p: '31'+  number: x^4 + 8*x^3 - 56*x + 48+- params:+    label: 47.2.a.a+    p: '37'+  number: x^4 - 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: '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: '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: '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: '23'+  number: x^5 + 8*x^4 - 88*x^2 - 112*x - 32+- params:+    label: 59.2.a.a+    p: '29'+  number: x^5 - 14*x^4 + 10*x^3 + 389*x^2 - 485*x - 1757+- params:+    label: 59.2.a.a+    p: '31'+  number: x^5 - 116*x^3 + 56*x^2 + 1280*x + 256+- params:+    label: 59.2.a.a+    p: '37'+  number: x^5 - 18*x^4 + 80*x^3 + 64*x^2 - 592*x + 32+- params:+    label: 59.2.a.a+    p: '41'+  number: x^5 + 10*x^4 - 70*x^3 - 693*x^2 - 93*x + 217+- params:+    label: 59.2.a.a+    p: '43'+  number: x^5 + 4*x^4 - 28*x^3 - 56*x^2 + 256*x - 128+- params:+    label: 59.2.a.a+    p: '47'+  number: x^5 + 20*x^4 + 124*x^3 + 192*x^2 - 320*x - 256+- params:+    label: 59.2.a.a+    p: '53'+  number: x^5 + 10*x^4 - 22*x^3 - 77*x^2 + 91*x + 73+- 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 - 12*x - 8+- params:+    label: 61.2.a.b+    p: '59'+  number: x^3 - 29*x^2 + 231*x - 325+- params:+    label: 62.2.a.b+    p: '29'+  number: x^2 + 6*x - 18+- params:+    label: 62.2.a.b+    p: '37'+  number: x^2 - 10*x - 2+- params:+    label: 62.2.a.b+    p: '41'+  number: x^2 - 12*x + 24+- params:+    label: 62.2.a.b+    p: '43'+  number: x^2 + 2*x - 26+- params:+    label: 62.2.a.b+    p: '53'+  number: x^2 - 6*x + 6+- params:+    label: 62.2.a.b+    p: '59'+  number: x^2 + 12*x + 24+- params:+    label: 63.2.a.b+    p: '23'+  number: x^2 - 12+- params:+    label: 63.2.a.b+    p: '41'+  number: x^2 - 108+- params:+    label: 63.2.a.b+    p: '47'+  number: x^2 - 48+- params:+    label: 63.2.a.b+    p: '53'+  number: x^2 - 48+- params:+    label: 63.2.a.b+    p: '59'+  number: x^2 - 48+- params:+    label: 65.2.a.b+    p: '23'+  number: x^2 - 2+- params:+    label: 65.2.a.b+    p: '29'+  number: x^2 - 32+- params:+    label: 65.2.a.b+    p: '31'+  number: x^2 - 12*x + 18+- params:+    label: 65.2.a.b+    p: '37'+  number: x^2 - 72+- params:+    label: 65.2.a.b+    p: '41'+  number: x^2 + 12*x + 28+- params:+    label: 65.2.a.b+    p: '43'+  number: x^2 + 8*x - 34+- params:+    label: 65.2.a.b+    p: '47'+  number: x^2 + 4*x - 4+- params:+    label: 65.2.a.b+    p: '53'+  number: x^2 + 12*x - 36+- params:+    label: 65.2.a.b+    p: '59'+  number: x^2 - 12*x + 18+- params:+    label: 65.2.a.c+    p: '23'+  number: x^2 - 6*x + 6+- params:+    label: 65.2.a.c+    p: '29'+  number: x^2 + 12*x + 24+- params:+    label: 65.2.a.c+    p: '31'+  number: x^2 - 10*x - 2+- params:+    label: 65.2.a.c+    p: '41'+  number: x^2 - 12+- params:+    label: 65.2.a.c+    p: '43'+  number: x^2 - 10*x - 2+- params:+    label: 65.2.a.c+    p: '53'+  number: x^2 - 108+- params:+    label: 65.2.a.c+    p: '59'+  number: x^2 + 6*x - 138+- params:+    label: 67.2.a.b+    p: '23'+  number: x^2 - 6*x - 11+- params:+    label: 67.2.a.b+    p: '29'+  number: x^2 + 6*x - 11+- params:+    label: 67.2.a.b+    p: '37'+  number: x^2 + x - 11+- params:+    label: 67.2.a.b+    p: '41'+  number: x^2 + 3*x + 1+- params:+    label: 67.2.a.b+    p: '43'+  number: x^2 - 3*x - 9+- params:+    label: 67.2.a.b+    p: '47'+  number: x^2 + 15*x + 55+- params:+    label: 67.2.a.c+    p: '23'+  number: x^2 + 2*x - 19+- params:+    label: 67.2.a.c+    p: '29'+  number: x^2 - 10*x + 5+- params:+    label: 67.2.a.c+    p: '31'+  number: x^2 - 45+- params:+    label: 67.2.a.c+    p: '37'+  number: x^2 - 3*x + 1+- params:+    label: 67.2.a.c+    p: '41'+  number: x^2 - 5*x - 25+- params:+    label: 67.2.a.c+    p: '43'+  number: x^2 + 9*x - 11+- params:+    label: 67.2.a.c+    p: '47'+  number: x^2 + 7*x + 11+- params:+    label: 67.2.a.c+    p: '53'+  number: x^2 - 45+- params:+    label: 68.2.a.a+    p: '23'+  number: x^2 + 6*x + 6+- params:+    label: 68.2.a.a+    p: '29'+  number: x^2 - 12+- params:+    label: 68.2.a.a+    p: '31'+  number: x^2 + 2*x - 26+- params:+    label: 68.2.a.a+    p: '37'+  number: x^2 - 16*x + 52+- params:+    label: 68.2.a.a+    p: '43'+  number: x^2 - 4*x - 104+- params:+    label: 68.2.a.a+    p: '47'+  number: x^2 - 48+- params:+    label: 68.2.a.a+    p: '53'+  number: x^2 - 12*x - 12+- params:+    label: 68.2.a.a+    p: '59'+  number: x^2 - 12*x + 24+- params:+    label: 69.2.a.b+    p: '29'+  number: x^2 - 20+- params:+    label: 69.2.a.b+    p: '31'+  number: x^2 + 4*x - 16+- params:+    label: 69.2.a.b+    p: '37'+  number: x^2 - 20+- params:+    label: 69.2.a.b+    p: '41'+  number: x^2 + 4*x - 76+- params:+    label: 69.2.a.b+    p: '43'+  number: x^2 - 2*x - 44+- params:+    label: 69.2.a.b+    p: '53'+  number: x^2 + 6*x + 4+- params:+    label: 69.2.a.b+    p: '59'+  number: x^2 - 8*x - 64+- params:+    label: 71.2.a.a+    p: '29'+  number: x^3 - 11*x^2 + 14*x + 71+- params:+    label: 71.2.a.a+    p: '37'+  number: x^3 + 15*x^2 + 70*x + 97+- params:+    label: 71.2.a.a+    p: '41'+  number: x^3 + 2*x^2 - 68*x + 56+- params:+    label: 71.2.a.a+    p: '43'+  number: x^3 - 13*x^2 + 48*x - 45+- params:+    label: 71.2.a.a+    p: '47'+  number: x^3 - 4*x^2 - 28*x + 40+- params:+    label: 71.2.a.a+    p: '53'+  number: x^3 + 18*x^2 + 28*x - 456+- params:+    label: 71.2.a.a+    p: '59'+  number: x^3 + 4*x^2 - 36*x - 152+- params:+    label: 71.2.a.b+    p: '23'+  number: x^3 - 8*x^2 - 12*x + 72+- params:+    label: 71.2.a.b+    p: '29'+  number: x^3 + 5*x^2 - 2*x - 25+- params:+    label: 71.2.a.b+    p: '31'+  number: x^3 + 6*x^2 - 8*x - 56+- params:+    label: 71.2.a.b+    p: '37'+  number: x^3 - 9*x^2 - 26*x + 37+- params:+    label: 71.2.a.b+    p: '41'+  number: x^3 - 14*x^2 + 48*x - 8+- params:+    label: 71.2.a.b+    p: '43'+  number: x^3 + 17*x^2 + 72*x + 81+- params:+    label: 71.2.a.b+    p: '47'+  number: x^3 + 10*x^2 - 72+- params:+    label: 71.2.a.b+    p: '53'+  number: x^3 - 20*x - 24+- params:+    label: 71.2.a.b+    p: '59'+  number: x^3 + 22*x^2 + 144*x + 280+- params:+    label: 73.2.a.b+    p: '23'+  number: x^2 + 15*x + 55+- params:+    label: 73.2.a.b+    p: '29'+  number: x^2 - 6*x - 11+- params:+    label: 73.2.a.b+    p: '31'+  number: x^2 - 2*x - 44+- params:+    label: 73.2.a.b+    p: '37'+  number: x^2 + 4*x - 41+- params:+    label: 73.2.a.b+    p: '41'+  number: x^2 - 20+- params:+    label: 73.2.a.b+    p: '47'+  number: x^2 + 6*x - 11+- params:+    label: 73.2.a.b+    p: '53'+  number: x^2 - 6*x - 71+- params:+    label: 73.2.a.b+    p: '59'+  number: x^2 + 12*x + 16+- params:+    label: 73.2.a.c+    p: '23'+  number: x^2 - 13*x + 39+- params:+    label: 73.2.a.c+    p: '29'+  number: x^2 - 2*x - 51+- params:+    label: 73.2.a.c+    p: '31'+  number: x^2 - 6*x - 4+- params:+    label: 73.2.a.c+    p: '37'+  number: x^2 - 8*x + 3+- params:+    label: 73.2.a.c+    p: '43'+  number: x^2 - 6*x - 43+- params:+    label: 73.2.a.c+    p: '53'+  number: x^2 + 2*x - 51+- params:+    label: 74.2.a.a+    p: '23'+  number: x^2 + 3*x - 27+- params:+    label: 74.2.a.a+    p: '29'+  number: x^2 - 3*x - 27+- params:+    label: 74.2.a.a+    p: '31'+  number: x^2 - 3*x - 1+- params:+    label: 74.2.a.a+    p: '41'+  number: x^2 - 9*x - 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