Digital signature algorithm ( sage tool)

 
Question:
Use Sage to solve the following problems. 
For this questions assume that we are using dsa with domain parameters:
p = 7,877,914,592,603,328,881
q = 44449
g = 2,860,021,798,868,462,661
Use these domain parameters to determine if the signatures are valid in parts (a)-(c)

public key y = 3798043471854149631, hash value H = 59367, and signature (r,s) = (31019, 4047)
public key y = 1829820126190370021, hash value H = 77241, and signature (r,s) = (24646, 43556)
public key y = 4519088706115097514, hash value H = 48302, and signature (r,s) = (36283, 32514)

Perform a signing operation for the below parts (a)-(b)

private key x = 8146, hash value H = 22655
private key x = 1548, hash value H = 3278

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