diff --git a/singular_values.c b/singular_values.c
index e63a15f..58013ad 100644
--- a/singular_values.c
+++ b/singular_values.c
@@ -9,6 +9,9 @@
 //#define DEBUG(msg, ...) fprintf(stderr, msg, ##__VA_ARGS__)
 #define DEBUG(msg, ...)
 
+#define OUTPUT_POINTS
+//#define OUTPUT_POINTS
+
 struct result {
 	mpq_t tr;
 	mpq_t trinv;
@@ -23,7 +26,7 @@ static int compare_result(const void *a_, const void *b_)
 
 	d = mpq_cmp((*a)->tr,(*b)->tr);
 	if(d == 0)
-		mpq_cmp((*a)->trinv, (*b)->trinv);
+		d = mpq_cmp((*a)->trinv, (*b)->trinv);
 
 	return d;
 }
@@ -356,11 +359,12 @@ int main(int argc, char *argv[])
 	int index;
 	mps_context *solver;
 	int acc = 100;
-	int n;
+	int n, nuniq, nmax;
 	int retval;
 	double evs[3];
 	double max_slope;
-	int nmax;
+	char buf[100];
+	char buf2[100];
 
 	struct result *invariants;
 	struct result **distinct_invariants;
@@ -413,15 +417,18 @@ int main(int argc, char *argv[])
 
 	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);
+#ifdef OUTPUT_POINTS
+	gmp_fprintf(stdout, "\"s = %Qd = %.3f, q = %Qd, t = %.3f\"\n", s, mpq_get_d(s), q, mpq_get_d(q)*tqfactor);
+#endif
 
 	// group
 	DEBUG("Generate group\n");
-	group = coxeter_init_triangle(3, 3, 4, nmax);
+	group = coxeter_init_triangle(4, 3, 3, nmax);
 
 	DEBUG("Compute matrices\n");
 	enumerate(group, matrices, s, q);
 
+	n = 0;
 	DEBUG("Compute traces\n");
 	for(int i = 0; i < nmax; i++) {
 		if(group->elements[i].length % 2 != 0 || !group->elements[i].inverse)
@@ -429,21 +436,25 @@ int main(int argc, char *argv[])
 
 		mat_trace(invariants[i].tr, matrices[i]);
 		mat_trace(invariants[i].trinv, matrices[group->elements[i].inverse->id]);
+
+		distinct_invariants[n++] = &invariants[i];
 	}
 
 	DEBUG("Get unique traces\n");
-	qsort(distinct_invariants, nmax, sizeof(struct result*), compare_result);
 
-	n = 0;
-	for(int i = 0; i < nmax; i++) {
-		if(i == 0 || compare_result(&distinct_invariants[i], &distinct_invariants[n-1]) != 0)
-			distinct_invariants[n++] = distinct_invariants[i];
+	qsort(distinct_invariants, n, sizeof(struct result*), compare_result);
+
+	nuniq = 0;
+	for(int i = 0; i < n; i++) {
+		if(i == 0 || compare_result(&distinct_invariants[i], &distinct_invariants[nuniq-1]) != 0)
+			distinct_invariants[nuniq++] = distinct_invariants[i];
 	}
 
 	max_slope = 0;
+	int max_slope_index;
 
 	DEBUG("Solve characteristic polynomials\n");
-	for(int i = 0; i < n; i++) {
+	for(int i = 0; i < nuniq; i++) {
 		retval = solve_characteristic_polynomial(solver, distinct_invariants[i]->tr, distinct_invariants[i]->trinv, evs);
 		if(retval == 1) {
 			fprintf(stderr, "Error! Could not solve polynomial.\n");
@@ -459,16 +470,22 @@ int main(int argc, char *argv[])
 		if(fabs(evs[0]) < fabs(evs[1]))
 			SWAP(double, evs[0], evs[1]);
 
-		double x = log(evs[0]);
-		double y = -log(evs[2]);
+		double x = log(fabs(evs[0]));
+		double y = -log(fabs(evs[2]));
 
-		if(y/x > max_slope && (x > 0.1 || y > 0.1))
+		if(y/x > max_slope && (x > 0.1 || y > 0.1)) {
+			max_slope_index = distinct_invariants[i] - invariants;
 			max_slope = y/x;
+		}
 
-		gmp_printf("%Qd %Qd %f %f %f\n", distinct_invariants[i]->tr, distinct_invariants[i]->trinv, x, y, y/x);
+#ifdef OUTPUT_POINTS
+		gmp_printf("%Qd %Qd %f %f %f %d\n", distinct_invariants[i]->tr, distinct_invariants[i]->trinv, x, y, y/x);
+#endif
 	}
 
-//	printf("%.3f %.3f %f\n", mpq_get_d(s), mpq_get_d(q)*tqfactor, max_slope);
+#ifdef OUTPUT_SUMMARY
+	fprintf(stdout, "%.3f %.3f %f %s\n", mpq_get_d(s), mpq_get_d(q)*tqfactor, max_slope, print_word(&group->elements[max_slope_index], buf));
+#endif
 
 //	output_invariants(group, matrices, s, q, solver);
 
diff --git a/singular_values.plt b/singular_values.plt
index af86668..f85674c 100644
--- a/singular_values.plt
+++ b/singular_values.plt
@@ -1,7 +1,8 @@
 if(!exists("logt")) logt = log(1.78)
 if(!exists("logs")) logs = log(0.5)
 
-file = sprintf("< ./singular_values 1000 %f %f", exp(logs), exp(logt))
+#file = sprintf("< ./singular_values 713698 %f %f", exp(logs), exp(logt))
+file = sprintf("< ./singular_values 1621 %f %f", exp(logs), exp(logt))
 
 set zeroaxis
 set samples 1000