diff --git a/singular_values.c b/singular_values.c
index 3907c0f..04d3068 100644
--- a/singular_values.c
+++ b/singular_values.c
@@ -6,7 +6,7 @@
 
 //#define MAX_ELEMENTS 2800000
 //#define MAX_ELEMENTS 720000
-#define MAX_ELEMENTS 14000
+#define MAX_ELEMENTS 3000
 //#define DRAW_PICTURE 1
 
 void continued_fraction_approximation(mpq_t out, double in, int level)
@@ -57,39 +57,99 @@ void quartic(mpq_t out, mpq_t in, int a, int b, int c, int d, int e)
 	mpq_clear(tmp);
 }
 
-void initialize_triangle_generators(mat_workspace *ws, mat *gen, mpq_t s, mpq_t t)
+void initialize_triangle_generators(mat_workspace *ws, mat *gen, mpq_t s, mpq_t q)
 {
-	mpq_set_ui(*mat_ref(gen[0], 0, 0), 0, 1);
-	mpq_set_ui(*mat_ref(gen[0], 0, 1), 0, 1);
-	mpq_set_ui(*mat_ref(gen[0], 0, 2), 1, 1);
-	mpq_set_ui(*mat_ref(gen[0], 1, 0), 1, 1);
-	mpq_set_ui(*mat_ref(gen[0], 1, 1), 0, 1);
-	mpq_set_ui(*mat_ref(gen[0], 1, 2), 0, 1);
-	mpq_set_ui(*mat_ref(gen[0], 2, 0), 0, 1);
-	mpq_set_ui(*mat_ref(gen[0], 2, 1), 1, 1);
-	mpq_set_ui(*mat_ref(gen[0], 2, 2), 0, 1);
+	mat r1,r2,r3;
+	mpq_t rho1, rho2, rho3;
+	mpq_t b1,c1,a2,c2,a3,b3;
+	mpq_t sinv;
 
-	mpq_set_ui(*mat_ref(gen[1], 0, 0), 1, 1);
-	mpq_set_ui(*mat_ref(gen[1], 1, 0), 0, 1);
-	mpq_set_ui(*mat_ref(gen[1], 2, 0), 0, 1);
-	quartic(*mat_ref(gen[1], 0, 1), t, 0, 0, 1, -1, 2);
-	quartic(*mat_ref(gen[1], 1, 1), t, 0, 0, -1, 2, -2);
-	quartic(*mat_ref(gen[1], 2, 1), t, 0, 0, 1, -3, 3);
-	quartic(*mat_ref(gen[1], 0, 2), t, 0, 0, 1, 0, 3);
-	quartic(*mat_ref(gen[1], 1, 2), t, 0, 0, -1, 1, -1);
-	quartic(*mat_ref(gen[1], 2, 2), t, 0, 0, 1, -2, 1);
+	mpq_inits(sinv,rho1,rho2,rho3,b1,c1,a2,c2,a3,b3,NULL);
+	mat_init(r1, 3);
+	mat_init(r2, 3);
+	mat_init(r3, 3);
 
-	mat_pseudoinverse(ws, gen[3], gen[0]); // p^{-1}
-	mat_pseudoinverse(ws, gen[4], gen[1]); // q^{-1}
-	mat_multiply(ws, gen[2], gen[4], gen[3]); // r = q^{-1}p^{-1}
+	mpq_set_ui(sinv, 1, 1);
+	mpq_div(sinv, sinv, s);
+
+	quartic(rho1, s, 0, 0, 1, -1, 1);
+	quartic(rho2, s, 0, 0, 1, -1, 1);
+	quartic(rho3, s, 0, 0, 1,  0, 1);
+
+	mpq_mul(c1, rho2, q);
+	mpq_mul(a2, rho3, q);
+	mpq_mul(b3, rho1, q);
+	mpq_set_ui(b1, 1, 1);
+	mpq_set_ui(c2, 1, 1);
+	mpq_set_ui(a3, 1, 1);
+	mpq_div(b1, b1, q);
+	mpq_div(c2, c2, q);
+	mpq_div(a3, a3, q);
+
+	// actually, we want minus everything
+	mat_zero(r1);
+	mat_zero(r2);
+	mat_zero(r3);
+	mpq_set_si(*mat_ref(r1, 0, 0), -1, 1);
+	mpq_set_si(*mat_ref(r1, 1, 1), 1, 1);
+	mpq_set_si(*mat_ref(r1, 2, 2), 1, 1);
+	mpq_set_si(*mat_ref(r2, 0, 0), 1, 1);
+	mpq_set_si(*mat_ref(r2, 1, 1), -1, 1);
+	mpq_set_si(*mat_ref(r2, 2, 2), 1, 1);
+	mpq_set_si(*mat_ref(r3, 0, 0), 1, 1);
+	mpq_set_si(*mat_ref(r3, 1, 1), 1, 1);
+	mpq_set_si(*mat_ref(r3, 2, 2), -1, 1);
+
+	mpq_set(*mat_ref(r1, 1, 0), b1);
+	mpq_set(*mat_ref(r1, 2, 0), c1);
+	mpq_set(*mat_ref(r2, 0, 1), a2);
+	mpq_set(*mat_ref(r2, 2, 1), c2);
+	mpq_set(*mat_ref(r3, 0, 2), a3);
+	mpq_set(*mat_ref(r3, 1, 2), b3);
+
+	mat_zero(gen[0]);
+	mat_zero(gen[1]);
+	mat_zero(gen[2]);
+
+	mpq_set_ui(*mat_ref(gen[0], 0, 0), 1, 1);
+	mat_set(gen[0], 1, 1, sinv);
+	mat_set(gen[0], 2, 2, s);
+
+	mat_set(gen[1], 0, 0, s);
+	mpq_set_ui(*mat_ref(gen[1], 1, 1), 1, 1);
+	mat_set(gen[1], 2, 2, sinv);
+
+	mat_set(gen[2], 0, 0, sinv);
+	mat_set(gen[2], 1, 1, s);
+	mpq_set_ui(*mat_ref(gen[2], 2, 2), 1, 1);
+
+	mat_multiply(ws, gen[0], r2, gen[0]);
+	mat_multiply(ws, gen[0], gen[0], r3);
+	mat_multiply(ws, gen[1], r3, gen[1]);
+	mat_multiply(ws, gen[1], gen[1], r1);
+	mat_multiply(ws, gen[2], r1, gen[2]);
+	mat_multiply(ws, gen[2], gen[2], r2);
+
+	mat_pseudoinverse(ws, gen[3], gen[0]);
+	mat_pseudoinverse(ws, gen[4], gen[1]);
 	mat_pseudoinverse(ws, gen[5], gen[2]);
 
-//	mat_print(gen[0]);
-//	mat_print(gen[1]);
-//	mat_print(gen[2]);
-//	mat_print(gen[3]);
-//	mat_print(gen[4]);
-//	mat_print(gen[5]);
+	/*
+	mat_print(r1);
+	mat_print(r2);
+	mat_print(r3);
+	mat_print(gen[0]);
+	mat_print(gen[1]);
+	mat_print(gen[2]);
+	mat_print(gen[3]);
+	mat_print(gen[4]);
+	mat_print(gen[5]);
+	*/
+
+	mpq_clears(sinv,rho1,rho2,rho3,b1,c1,a2,c2,a3,b3,NULL);
+	mat_clear(r1);
+	mat_clear(r2);
+	mat_clear(r3);
 }
 
 char *print_word(groupelement_t *g, char *str)
@@ -154,7 +214,7 @@ void enumerate(groupelement_t *group, mat *matrices, mpq_t s, mpq_t t)
 	mat_workspace_clear(ws);
 }
 
-void output_invariants(groupelement_t *group, mat *matrices, mpq_t s, mpq_t t)
+void output_invariants(groupelement_t *group, mat *matrices, mpq_t s, mpq_t q)
 {
 	mpq_t tr, trinv;
 	char buf[100];
@@ -206,35 +266,46 @@ double max_slope(groupelement_t *group, mat *matrices, mpq_t s, mpq_t t, int *in
 
 int main(int argc, char *argv[])
 {
-	mpq_t s, t, tmp;
-	mpz_t accuracy;
-	double t_;
+	mpq_t s, q, t, tmp;
+	double sapprox, tapprox, qapprox, tqfactor;
 	mat *matrices;
 	groupelement_t *group;
 	int index;
 
-	mpq_inits(s, t, tmp, NULL);
-	mpz_init(accuracy);
+	mpq_inits(s, q, t, tmp, NULL);
 	group = malloc(MAX_ELEMENTS*sizeof(groupelement_t));
 	matrices = malloc(MAX_ELEMENTS*sizeof(mat));
 	for(int i = 0; i < MAX_ELEMENTS; i++)
 		mat_init(matrices[i], 3);
 
-	// mpq_set_str(t, argv[1], 10);
-	mpz_set_ui(accuracy, 100);
-	for(int i = 0; ; i++) {
-		mpq_set(t, tmp);
-		continued_fraction_approximation(tmp, atof(argv[1]), i);
-		if(mpz_cmp(mpq_numref(tmp),accuracy) > 0 && mpz_cmp(mpq_denref(tmp),accuracy) > 0)
-			break;
-	}
-	mpq_canonicalize(t);
-	gmp_fprintf(stdout, "\"t = %Qd = %.3f\"\n", mpq_get_d(t), t);
+	int acc = 100;
 
-	if(argc > 2 && strcmp(argv[2],"p") == 0) {
-		gmp_fprintf(stdout, "%Qd\n", t);
-		return 0;
+	sapprox = atof(argv[1]);
+	tapprox = atof(argv[2]);
+	tqfactor = pow((sapprox*sapprox-sapprox+1)*(sapprox*sapprox-sapprox+1)*(sapprox*sapprox+1), 1/6.0);
+	qapprox = tapprox/tqfactor;
+
+	for(int i = 0; ; i++) {
+		continued_fraction_approximation(tmp, sapprox, i);
+//		gmp_fprintf(stdout, "%Qd\n", tmp);
+		if(fabs(mpq_get_d(t)-sapprox) < 1e-10 || (mpz_cmpabs_ui(mpq_numref(tmp),acc) > 0 && mpz_cmpabs_ui(mpq_denref(tmp),acc) > 0))
+			break;
+		mpq_set(s, tmp);
 	}
+	mpq_canonicalize(s);
+
+	for(int i = 0; ; i++) {
+		continued_fraction_approximation(tmp, qapprox, i);
+//		gmp_fprintf(stdout, "%Qd\n", tmp);
+		if(fabs(mpq_get_d(t)-qapprox) < 1e-10 || (mpz_cmpabs_ui(mpq_numref(tmp),acc) > 0 && mpz_cmpabs_ui(mpq_denref(tmp),acc) > 0))
+			break;
+		mpq_set(q, tmp);
+	}
+	mpq_canonicalize(q);
+
+	tqfactor = pow((mpq_get_d(s)*mpq_get_d(s)-mpq_get_d(s)+1)*(mpq_get_d(s)*mpq_get_d(s)-mpq_get_d(s)+1)*(mpq_get_d(s)*mpq_get_d(s)+1), 1/6.0);
+
+	gmp_fprintf(stdout, "\"s = %Qd = %.3f, q = %Qd, t = %.3f\"\n", s, mpq_get_d(s), q, mpq_get_d(q)*tqfactor);
 
 	generate_triangle_group(group, MAX_ELEMENTS, 3, 3, 4);
 
@@ -242,15 +313,14 @@ int main(int argc, char *argv[])
 //		mpq_set_ui(t,100+i,100);
 //		mpq_canonicalize(t);
 
-		enumerate(group, matrices, s, t);
+		enumerate(group, matrices, s, q);
 		//printf("%f %f\n", mpq_get_d(t), max_slope(group, matrices, s, t, &index));
-		output_invariants(group, matrices, s, t);
+		output_invariants(group, matrices, s, q);
 //	}
 
 	for(int i = 0; i < MAX_ELEMENTS; i++)
 		mat_clear(matrices[i]);
 	free(matrices);
 	free(group);
-	mpq_clears(s, t, tmp, NULL);
-	mpz_clear(accuracy);
+	mpq_clears(s, q, t, tmp, NULL);
 }
diff --git a/singular_values.plt b/singular_values.plt
index cd4894e..03613ce 100644
--- a/singular_values.plt
+++ b/singular_values.plt
@@ -1,10 +1,7 @@
-if(!exists("logt")) logt = log(7)
-if(!exists("logs")) logs = log(1.0)
+if(!exists("logt")) logt = log(1.78)
+if(!exists("logs")) logs = log(0.5)
 
-file = sprintf("< ./singular_values %f", exp(logt))
-#title = sprintf("s = %f, t = %f", exp(logs), exp(logt))
-title = sprintf("t = %.3f", exp(logt))
-# print title
+file = sprintf("< ./singular_values %f %f", exp(logs), exp(logt))
 
 set zeroaxis
 set samples 1000