Append(~systems_of_eigenvalues, <"7803", [ <1, [ ], x + 1, [ -1, 0, -4, 2, 3, -5, 0, 2, 8, 0, -10, 11 ]>, <2, [ ], x - 1, [ 1, 0, 4, 2, -3, -5, 0, 2, -8, 0, -10, 11 ]>, <3, [ ], x, [ 0, 0, 0, -5, 0, -7, 0, 8, 0, 0, 7, 10 ]>, <4, [ ], x - 2, [ 2, 0, -2, 1, 0, 1, 0, -4, 4, 6, 1, 10 ]>, <5, [ ], x + 2, [ -2, 0, 2, 1, 0, 1, 0, -4, -4, -6, 1, 10 ]>, <6, [ ], x - 2, [ 2, 0, 2, -4, -3, 7, 0, -4, -1, 9, 2, 8 ]>, <7, [ ], x + 2, [ -2, 0, -2, -4, 3, 7, 0, -4, 1, -9, 2, 8 ]>, <8, [ ], x + 1, [ -1, 0, -1, 2, 0, -5, 0, -1, -1, 9, 8, 2 ]>, <9, [ ], x - 1, [ 1, 0, 1, 2, 0, -5, 0, -1, 1, -9, 8, 2 ]>, <10, [ ], x, [ 0, 0, 0, 4, 0, 2, 0, -1, 0, 0, -11, 1 ]>, <11, [ ], x^2 + 6*x - 8, [ 0, 0, -1/2*x, 0, -a - 3, 3/2*a + 5, 0, -3/2*a - 2, 1/2*a + 9, a + 9, 0, 0 ]>, <12, [ ], x^2 + 6*x - 8, [ 0, 0, 1/2*x, 0, a + 3, 3/2*a + 5, 0, -3/2*a - 2, -1/2*a - 9, -a - 9, 0, 0 ]>, <13, [ ], x, [ 0, 0, 0, -4, 0, 2, 0, -1, 0, 0, 11, -1 ]>, <14, [ ], x + 2, [ -2, 0, 4, -1, -6, 1, 0, -7, 4, 6, 8, -1 ]>, <15, [ ], x - 2, [ 2, 0, -4, -1, 6, 1, 0, -7, -4, -6, 8, -1 ]>, <16, [ ], x, [ 0, 0, -3, -2, 3, 2, 0, 5, 0, 3, -8, -8 ]>, <17, [ ], x, [ 0, 0, 3, -2, -3, 2, 0, 5, 0, -3, -8, -8 ]>, <18, [ ], x + 2, [ -2, 0, -2, -1, 0, 1, 0, -4, 4, 6, -1, -10 ]>, <19, [ ], x - 2, [ 2, 0, 2, -1, 0, 1, 0, -4, -4, -6, -1, -10 ]>, <20, [ ], x, [ 0, 0, 0, 5, 0, -7, 0, 8, 0, 0, -7, -10 ]>, <21, [ ], x - 1, [ 1, 0, -4, -2, 3, -5, 0, 2, 8, 0, 10, -11 ]>, <22, [ ], x + 1, [ -1, 0, 4, -2, -3, -5, 0, 2, -8, 0, 10, -11 ]>, <23, [ ], x, [ 0, 0, 0, 1, 0, 5, 0, -7, 0, 0, 4, -11 ]>, <24, [ ], x^2 - x - 1, [ x, 0, a + 1, 3*a, -2*a + 5, 2*a, 0, 3, -5*a + 4, 2*a + 5, -2*a - 1, -4*a + 6 ]>, <25, [ ], x^2 + x - 1, [ x, 0, a - 1, -3*a, -2*a - 5, -2*a, 0, 3, -5*a - 4, 2*a - 5, 2*a - 1, 4*a + 6 ]>, <26, [ ], x^2 - 2, [ x, 0, 4, 2*a, -5, 1, 0, 6, 1, 7, a, -8*a ]>, <27, [ ], x^2 - 2, [ x, 0, -4, -2*a, 5, 1, 0, 6, -1, -7, -a, 8*a ]>, <28, [ ], x^2 + x - 3, [ x, 0, a + 3, -a - 2, 3, -2*a - 4, 0, -1, a, 3, 2*a + 1, -4*a - 2 ]>, <29, [ ], x^2 - x - 3, [ x, 0, a - 3, a - 2, -3, 2*a - 4, 0, -1, a, -3, -2*a + 1, 4*a - 2 ]>, <30, [ ], x^6 - 11*x^4 + 31*x^2 - 18, [ x, 0, -1/3*a^5 + 8/3*a^3 - 10/3*a, a^2 - 3, 1/3*a^5 - 8/3*a^3 + 13/3*a, -a^4 + 7*a^2 - 7, 0, 1, 1/3*a^5 - 11/3*a^3 + 28/3*a, -1/3*a^5 + 14/3*a^3 - 43/3*a, -a^4 + 9*a^2 - 12, -a^4 + 9*a^2 - 9 ]>, <31, [ ], x^6 - 10*x^4 + 22*x^2 - 4, [ x, 0, 1/2*a^5 - 5*a^3 + 10*a, -1/2*a^4 + 3*a^2 - 2, 1/2*a^5 - 4*a^3 + 5*a, 1/2*a^4 - 4*a^2 + 6, 0, -1/2*a^4 + 3*a^2 + 1, 1/2*a^5 - 5*a^3 + 13*a, 3/2*a^5 - 13*a^3 + 22*a, -2*a^2 + 7, -1/2*a^4 + 5*a^2 - 7 ]>, <32, [ ], x^3 - 84*x + 296, [ 0, 0, 0, -1/2*x, 0, 11/4*a^2 + 29/2*a - 154, 0, 9/4*a^2 + 25/2*a - 126, 0, 0, -2*a^2 - 23/2*a + 112, 1/2*a^2 + 3/2*a - 28 ]>, <33, [ ], x^3 - 21*x - 37, [ 0, 0, 0, -x, 0, 11*a^2 - 29*a - 154, 0, 9*a^2 - 25*a - 126, 0, 0, 8*a^2 - 23*a - 112, -2*a^2 + 3*a + 28 ]>, <34, [ ], x^6 - 10*x^4 + 22*x^2 - 4, [ x, 0, -1/2*a^5 + 5*a^3 - 10*a, 1/2*a^4 - 3*a^2 + 2, -1/2*a^5 + 4*a^3 - 5*a, 1/2*a^4 - 4*a^2 + 6, 0, -1/2*a^4 + 3*a^2 + 1, -1/2*a^5 + 5*a^3 - 13*a, -3/2*a^5 + 13*a^3 - 22*a, 2*a^2 - 7, 1/2*a^4 - 5*a^2 + 7 ]>, <35, [ ], x^3 - x^2 - 7*x + 9, [ x, 0, a^2 - 6, -a^2 - 2*a + 7, 2*a^2 + 2*a - 12, -2*a^2 - 2*a + 11, 0, a^2 + 2*a - 4, -2*a^2 + 9, -a^2 + 6, -2*a^2 + 10, -a^2 + 1 ]>, <36, [ ], x^3 + x^2 - 7*x - 9, [ x, 0, -a^2 + 6, -a^2 + 2*a + 7, -2*a^2 + 2*a + 12, -2*a^2 + 2*a + 11, 0, a^2 - 2*a - 4, 2*a^2 - 9, a^2 - 6, -2*a^2 + 10, -a^2 + 1 ]>, <37, [ ], x^6 - 11*x^4 + 31*x^2 - 18, [ x, 0, 1/3*a^5 - 8/3*a^3 + 10/3*a, -a^2 + 3, -1/3*a^5 + 8/3*a^3 - 13/3*a, -a^4 + 7*a^2 - 7, 0, 1, -1/3*a^5 + 11/3*a^3 - 28/3*a, 1/3*a^5 - 14/3*a^3 + 43/3*a, a^4 - 9*a^2 + 12, a^4 - 9*a^2 + 9 ]>, <38, [ ], x^4 - 8*x^2 + 13, [ x, 0, -a^2 + 4, -a^3 + 5*a, -2, 2*a^2 - 9, 0, 3*a^2 - 14, -2*a^2 + 13, a^2 - 4, -4*a, 3*a^3 - 13*a ]>, <39, [ ], x^4 - 8*x^2 + 13, [ x, 0, a^2 - 4, a^3 - 5*a, 2, 2*a^2 - 9, 0, 3*a^2 - 14, 2*a^2 - 13, -a^2 + 4, 4*a, -3*a^3 + 13*a ]>, <40, [ ], x^5 + 3*x^4 - 5*x^3 - 19*x^2 - 6*x + 9, [ x, 0, a^4 + a^3 - 7*a^2 - 5*a + 6, -2*a^4 - 3*a^3 + 14*a^2 + 16*a - 10, 2*a^4 + 3*a^3 - 15*a^2 - 16*a + 12, a^4 + a^3 - 8*a^2 - 7*a + 8, 0, -a^4 - a^3 + 7*a^2 + 4*a - 7, 3*a^4 + 4*a^3 - 20*a^2 - 22*a + 9, a^3 - 4*a + 3, -4*a^4 - 6*a^3 + 28*a^2 + 31*a - 22, -a^4 - a^3 + 7*a^2 + 5*a - 4 ]>, <41, [ ], x^5 - 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5*a + 4 ]>, <44, [ ], x^12 - 18*x^10 + 115*x^8 - 318*x^6 + 395*x^4 - 208*x^2 + 34, [ x, 0, -17/33*a^11 + 290/33*a^9 - 1684/33*a^7 + 3856/33*a^5 - 298/3*a^3 + 808/33*a, 16/33*a^10 - 271/33*a^8 + 1550/33*a^6 - 3404/33*a^4 + 230/3*a^2 - 413/33, -2/33*a^11 + 38/33*a^9 - 268/33*a^7 + 871/33*a^5 - 118/3*a^3 + 625/33*a, 1/11*a^10 - 19/11*a^8 + 123/11*a^6 - 309/11*a^4 + 23*a^2 - 43/11, 0, 4/11*a^10 - 65/11*a^8 + 349/11*a^6 - 675/11*a^4 + 30*a^2 + 37/11, 1/33*a^11 - 19/33*a^9 + 134/33*a^7 - 452/33*a^5 + 74/3*a^3 - 626/33*a, 1/33*a^11 - 19/33*a^9 + 134/33*a^7 - 452/33*a^5 + 71/3*a^3 - 461/33*a, 32/33*a^10 - 542/33*a^8 + 3100/33*a^6 - 6841/33*a^4 + 475/3*a^2 - 826/33, -49/33*a^10 + 832/33*a^8 - 4784/33*a^6 + 10730/33*a^4 - 797/3*a^2 + 1931/33 ]>, <45, [ ], x^12 - 15*x^10 + 81*x^8 - 190*x^6 + 189*x^4 - 72*x^2 + 9, [ x, 0, -1/3*a^11 + 5*a^9 - 27*a^7 + 190/3*a^5 - 62*a^3 + 19*a, -a^2 + 2, -8/3*a^11 + 39*a^9 - 202*a^7 + 1310/3*a^5 - 356*a^3 + 74*a, -1/3*a^10 + 5*a^8 - 26*a^6 + 163/3*a^4 - 41*a^2 + 8, 0, a^10 - 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