S_10,2:

Highest Precision:  1600
Number Field: Q
Eigenvalues:

[2, -6168]
[3, 1653624]
[4, -96585152]
[5, 1886723580]
[7, -96525844688]
[9, -4891929398991]
[11, 114598830623784]
[13, -471278635866836]


S_14,2:

Highest Precision:  1600
Number Field:  Q
Eigenvalues:

[2, -19200]
[3, 2251800]
[4, 35454976]
[5, -311252100]
[7, 159125638000]
[9, -4797957991599]
[11, -77471324747256]
[13, 1419674440557100]


S_16,2:

Highest Precision:  1600
Number Field:  K.<a> = NumberField(x^2 + 58752*x + 858931200)
Eigenvalues:

[2, (a)]
[3, (-3348*a - 111893400)]
[4, (825984*a + 23442866176)]
[5, (-35242000*a - 981077386500)]
[7, (7956692856*a + 229643057971600)]
[9, (-213056735184*a - 6561857408269599)]
[11, (3694145174500*a + 118059102422392824)]
[13, (26617626492912*a + 883271709053051500)]

[8, (-49542332416*a - 1469390782464000)]


S_18,2:

Highest Precision:  1600
Number Field:  K.<a> = NumberField(x^2 + 28032*x - 291594240)
Eigenvalues:

[2, (a)]
[3, (-5058*a - 213147720)]
[4, (1348224*a - 7430119424)]
[5, (-43319800*a - 356840151300)]
[7, (-1992651444*a + 558313980802480)]
[9, (1987636888296*a - 847521349014159)]
[11, (-94131074781590*a - 2950704862164348696)]
[13, (1680800712436872*a + 33891881194121037100)]


S_20,2 (1):

Highest Precision:  
Number Field:
Eigenvalues:

S_20,2 (2):

Highest Precision:  
Number Field:
Eigenvalues: