Magma V2.21-1 Wed Jan 8 2020 09:19:48 on sequoia [Seed = 2767153708] Type ? for help. Type -D to quit. We check assertions in Theorem 3. Computing forms at level N1=I2*I3*I7... Done ! We first perform standard elimination at level N1 = I2*I3*I7 using primes q = 13, 29 and 41 : Performing standard elimination for 5 form(s) with set of auxiliary primes [ 13, 29, 41 ] Checking form no 1 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 1 is eliminated ************************************************************* Checking form no 2 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 2 is eliminated ************************************************************* Checking form no 3 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Dealing with q = 41 Form no 3 with coefficient field : Number Field with defining polynomial x^3 - 3*x^2 - 10*x - 1 over the Rational Field is not eliminated for prime(s) : { 5, 13 } ************************************************************* Checking form no 4 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Dealing with q = 41 Form no 4 with coefficient field : Number Field with defining polynomial x^3 - x^2 - 30*x - 27 over the Rational Field is not eliminated for prime(s) : { 11 } ************************************************************* Checking form no 5 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Dealing with q = 41 Form no 5 is eliminated ************************************************************* ************************************************************* The prime p = 11 survives for the form no 4 ; we discard it using refined elimination with q = 5 : Performing refined elimination with set of auxiliary primes [ 5 ] Dealing with q = 5 This form can be eliminated for large enough p ! The form with coefficient field : Number Field with defining polynomial x^3 - x^2 - 30*x - 27 over the Rational Field is not eliminated for 6 prime ideal(s) above : { 13, 67, 125, 205379 } ************************************************************* ************************************************************* The primes p = 5, 13 survive for the form no 3 ; we discard p = 5 using refined elimination with q = 29 : Performing refined elimination with set of auxiliary primes [ 29 ] Dealing with q = 29 This form can be eliminated for large enough p ! The form with coefficient field : Number Field with defining polynomial x^3 - 3*x^2 - 10*x - 1 over the Rational Field is not eliminated for 2 prime ideal(s) above : { 13, 24389 } ************************************************************* ************************************************************* For each form f at level N1, we compute Norm(a_Q(f)-(Norm(Q)+1)) mod 13 for any of the three prime ideals Q above 29 in K : Form no 1 : Norm(a_Q(f)-(Norm(Q)+1)) mod 13 = 7 Form no 2 : Norm(a_Q(f)-(Norm(Q)+1)) mod 13 = 12 Form no 3 : Norm(a_Q(f)-(Norm(Q)+1)) mod 13 = 0 Form no 4 : Norm(a_Q(f)-(Norm(Q)+1)) mod 13 = 8 Form no 5 : Norm(a_Q(f)-(Norm(Q)+1)) mod 13 = 12 Hence form no 3 is the unique form with reducible mod 13 representation whose existence is predicted by Martin's result. It has exactly 1 prime ideal above 13 in its coefficient field. ************************************************************* Computing forms at level N2=I2^3*I3*I7... Done ! ************************************************************* We first perform standard elimination at level N2 = I2^3*I3*I7 using primes q = 13, 29, 41 and 43 : Performing standard elimination for 121 form(s) with set of auxiliary primes [ 13, 29, 41, 43 ] Checking form no 1 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 1 is eliminated ************************************************************* Checking form no 2 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Dealing with q = 41 Form no 2 is eliminated ************************************************************* Checking form no 3 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 3 is eliminated ************************************************************* Checking form no 4 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 4 is eliminated ************************************************************* Checking form no 5 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 5 is eliminated ************************************************************* Checking form no 6 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 6 is eliminated ************************************************************* Checking form no 7 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 7 is eliminated ************************************************************* Checking form no 8 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 8 is eliminated ************************************************************* Checking form no 9 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 9 is eliminated ************************************************************* Checking form no 10 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 10 is eliminated ************************************************************* Checking form no 11 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 11 is eliminated ************************************************************* Checking form no 12 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 12 is eliminated ************************************************************* Checking form no 13 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 13 is eliminated ************************************************************* Checking form no 14 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 14 is eliminated ************************************************************* Checking form no 15 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Dealing with q = 41 Form no 15 is eliminated ************************************************************* Checking form no 16 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 16 is eliminated ************************************************************* Checking form no 17 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 17 is eliminated ************************************************************* Checking form no 18 Dealing with q = 13 Dealing with q = 29 Dealing with q = 41 This form can be eliminated for large enough p ! Dealing with q = 43 Form no 18 is eliminated ************************************************************* Checking form no 19 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 19 is eliminated ************************************************************* Checking form no 20 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 20 is eliminated ************************************************************* Checking form no 21 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 21 is eliminated ************************************************************* Checking form no 22 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Dealing with q = 41 Form no 22 is eliminated ************************************************************* Checking form no 23 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 23 is eliminated ************************************************************* Checking form no 24 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 24 is eliminated ************************************************************* Checking form no 25 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 25 is eliminated ************************************************************* Checking form no 26 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 26 is eliminated ************************************************************* Checking form no 27 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 27 is eliminated ************************************************************* Checking form no 28 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 28 is eliminated ************************************************************* Checking form no 29 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 29 is eliminated ************************************************************* Checking form no 30 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 30 is eliminated ************************************************************* Checking form no 31 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 31 is eliminated ************************************************************* Checking form no 32 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 32 is eliminated ************************************************************* Checking form no 33 Dealing with q = 13 Dealing with q = 29 This form can be eliminated for large enough p ! Dealing with q = 41 Form no 33 is eliminated ************************************************************* Checking form no 34 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 34 is eliminated ************************************************************* Checking form no 35 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 35 is eliminated ************************************************************* Checking form no 36 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 36 is eliminated ************************************************************* Checking form no 37 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Dealing with q = 41 Form no 37 is eliminated ************************************************************* Checking form no 38 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Dealing with q = 41 Form no 38 is eliminated ************************************************************* Checking form no 39 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 39 is eliminated ************************************************************* Checking form no 40 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 40 is eliminated ************************************************************* Checking form no 41 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 41 is eliminated ************************************************************* Checking form no 42 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 42 is eliminated ************************************************************* Checking form no 43 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 43 is eliminated ************************************************************* Checking form no 44 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 44 is eliminated ************************************************************* Checking form no 45 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 45 is eliminated ************************************************************* Checking form no 46 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 46 is eliminated ************************************************************* Checking form no 47 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 47 is eliminated ************************************************************* Checking form no 48 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 48 is eliminated ************************************************************* Checking form no 49 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 49 is eliminated ************************************************************* Checking form no 50 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 50 is eliminated ************************************************************* Checking form no 51 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 51 is eliminated ************************************************************* Checking form no 52 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 52 is eliminated ************************************************************* Checking form no 53 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 53 is eliminated ************************************************************* Checking form no 54 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 54 is eliminated ************************************************************* Checking form no 55 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 55 is eliminated ************************************************************* Checking form no 56 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Dealing with q = 41 Dealing with q = 43 Form no 56 with coefficient field : Rational Field is not eliminated for prime(s) : { 5 } ************************************************************* Checking form no 57 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 57 is eliminated ************************************************************* Checking form no 58 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 58 is eliminated ************************************************************* Checking form no 59 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 59 is eliminated ************************************************************* Checking form no 60 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 60 is eliminated ************************************************************* Checking form no 61 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 61 is eliminated ************************************************************* Checking form no 62 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 62 is eliminated ************************************************************* Checking form no 63 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 63 is eliminated ************************************************************* Checking form no 64 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 64 is eliminated ************************************************************* Checking form no 65 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 65 is eliminated ************************************************************* Checking form no 66 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 66 is eliminated ************************************************************* Checking form no 67 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 67 is eliminated ************************************************************* Checking form no 68 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 68 is eliminated ************************************************************* Checking form no 69 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 69 is eliminated ************************************************************* Checking form no 70 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 70 is eliminated ************************************************************* Checking form no 71 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 71 is eliminated ************************************************************* Checking form no 72 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 72 is eliminated ************************************************************* Checking form no 73 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 73 is eliminated ************************************************************* Checking form no 74 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 74 is eliminated ************************************************************* Checking form no 75 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 75 is eliminated ************************************************************* Checking form no 76 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 76 is eliminated ************************************************************* Checking form no 77 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 77 is eliminated ************************************************************* Checking form no 78 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 78 is eliminated ************************************************************* Checking form no 79 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 79 is eliminated ************************************************************* Checking form no 80 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 80 is eliminated ************************************************************* Checking form no 81 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 81 is eliminated ************************************************************* Checking form no 82 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 82 is eliminated ************************************************************* Checking form no 83 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 83 is eliminated ************************************************************* Checking form no 84 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Dealing with q = 41 Dealing with q = 43 Form no 84 with coefficient field : Number Field with defining polynomial x^11 - 3*x^10 - 62*x^9 + 53*x^8 + 1431*x^7 + 1540*x^6 - 10083*x^5 - 27056*x^4 - 20844*x^3 - 3040*x^2 + 784*x - 32 over the Rational Field is not eliminated for prime(s) : { 5 } ************************************************************* Checking form no 85 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 85 is eliminated ************************************************************* Checking form no 86 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 86 is eliminated ************************************************************* Checking form no 87 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 87 is eliminated ************************************************************* Checking form no 88 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 88 is eliminated ************************************************************* Checking form no 89 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 89 is eliminated ************************************************************* Checking form no 90 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Dealing with q = 41 Dealing with q = 43 Form no 90 is eliminated ************************************************************* Checking form no 91 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 91 is eliminated ************************************************************* Checking form no 92 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 92 is eliminated ************************************************************* Checking form no 93 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 93 is eliminated ************************************************************* Checking form no 94 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 94 is eliminated ************************************************************* Checking form no 95 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 95 is eliminated ************************************************************* Checking form no 96 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Dealing with q = 41 Dealing with q = 43 Form no 96 is eliminated ************************************************************* Checking form no 97 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Dealing with q = 41 Dealing with q = 43 Form no 97 is eliminated ************************************************************* Checking form no 98 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Dealing with q = 41 Form no 98 is eliminated ************************************************************* Checking form no 99 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 99 is eliminated ************************************************************* Checking form no 100 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Dealing with q = 41 Form no 100 is eliminated ************************************************************* Checking form no 101 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 101 is eliminated ************************************************************* Checking form no 102 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 102 is eliminated ************************************************************* Checking form no 103 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 103 is eliminated ************************************************************* Checking form no 104 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 104 is eliminated ************************************************************* Checking form no 105 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 105 is eliminated ************************************************************* Checking form no 106 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Dealing with q = 41 Form no 106 is eliminated ************************************************************* Checking form no 107 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 107 is eliminated ************************************************************* Checking form no 108 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Dealing with q = 41 Form no 108 is eliminated ************************************************************* Checking form no 109 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 109 is eliminated ************************************************************* Checking form no 110 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Dealing with q = 41 Form no 110 is eliminated ************************************************************* Checking form no 111 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Dealing with q = 41 Form no 111 is eliminated ************************************************************* Checking form no 112 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Dealing with q = 41 Form no 112 is eliminated ************************************************************* Checking form no 113 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 113 is eliminated ************************************************************* Checking form no 114 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 114 is eliminated ************************************************************* Checking form no 115 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 115 is eliminated ************************************************************* Checking form no 116 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 116 is eliminated ************************************************************* Checking form no 117 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 117 is eliminated ************************************************************* Checking form no 118 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 118 is eliminated ************************************************************* Checking form no 119 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Form no 119 is eliminated ************************************************************* Checking form no 120 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Dealing with q = 41 Dealing with q = 43 Form no 120 with coefficient field : Number Field with defining polynomial x^18 + 6*x^17 - 129*x^16 - 792*x^15 + 6299*x^14 + 39175*x^13 - 151912*x^12 - 923664*x^11 + 2090978*x^10 + 11261011*x^9 - 17937590*x^8 - 71376648*x^7 + 91261904*x^6 + 219795072*x^5 - 221354112*x^4 - 308115584*x^3 + 219618048*x^2 + 138201344*x - 84347392 over the Rational Field is not eliminated for prime(s) : { 5 } ************************************************************* Checking form no 121 Dealing with q = 13 This form can be eliminated for large enough p ! Dealing with q = 29 Dealing with q = 41 Dealing with q = 43 Form no 121 with coefficient field : Number Field with defining polynomial x^18 - 149*x^16 + 66*x^15 + 8789*x^14 - 7971*x^13 - 261084*x^12 + 353462*x^11 + 4091944*x^10 - 7154721*x^9 - 32293194*x^8 + 66417652*x^7 + 111002728*x^6 - 243935776*x^5 - 155653920*x^4 + 286956800*x^3 + 99560704*x^2 + 9035264*x + 157184 over the Rational Field is not eliminated for prime(s) : { 17 } ************************************************************* ************************************************************* The prime p = 17 survives for the form no 121 ; we discard it using refined elimination with q = 5 : Performing refined elimination with set of auxiliary primes [ 5 ] Dealing with q = 5 This form can be eliminated for large enough p ! The form with coefficient field : Number Field with defining polynomial x^18 - 149*x^16 + 66*x^15 + 8789*x^14 - 7971*x^13 - 261084*x^12 + 353462*x^11 + 4091944*x^10 - 7154721*x^9 - 32293194*x^8 + 66417652*x^7 + 111002728*x^6 - 243935776*x^5 - 155653920*x^4 + 286956800*x^3 + 99560704*x^2 + 9035264*x + 157184 over the Rational Field is not eliminated for 18 prime ideal(s) above : { 67, 125, 127, 148877, 51895117, 1058089859, 39547260143, 840430616453, 6814692748079 } ************************************************************* ************************************************************* The prime p = 5 survives for three forms no 56, 84 and 120 ; we discard it using refined elimination with q = 29, 41, 83 : Performing refined elimination with set of auxiliary primes [ 29, 41, 83 ] Dealing with q = 29 This form can be eliminated for large enough p ! Dealing with q = 41 Dealing with q = 83 The form is eliminated ************************************************************* Performing refined elimination with set of auxiliary primes [ 29, 41, 83 ] Dealing with q = 29 This form can be eliminated for large enough p ! Dealing with q = 41 The form is eliminated ************************************************************* Performing refined elimination with set of auxiliary primes [ 29, 41, 83 ] Dealing with q = 29 This form can be eliminated for large enough p ! Dealing with q = 41 The form is eliminated ************************************************************* Total time: 22636.150 seconds, Total memory usage: 24059.66MB