CORRECTED INTERACTION OBSTRUCTION VERIFICATION
MOD=107
powers of 289 mod 840: [1, 289, 361, 169, 121, 529]

Weighted defect circulants:
k=0: vec=[0, 0, 0, 3, 0, 0], det=-729, det mod107=20, char=(X - 3)**3*(X + 3)**3
k=1: vec=[0, 0, 2, 1, 0, 0], det=63, det mod107=63, char=(X - 3)*(X - 1)*(X**2 + 3)*(X**2 + 4*X + 7)
k=2: vec=[0, 2, 0, 1, 0, 0], det=-81, det mod107=26, char=(X - 3)*(X + 3)*(X**2 + 3)**2
k=3: vec=[2, 0, 0, 1, 0, 0], det=27, det mod107=27, char=(X - 3)**3*(X - 1)**3
k=4: vec=[0, 0, 0, 1, 0, 2], det=-81, det mod107=26, char=(X - 3)*(X + 3)*(X**2 + 3)**2
k=5: vec=[0, 0, 0, 1, 2, 0], det=63, det mod107=63, char=(X - 3)*(X - 1)*(X**2 + 3)*(X**2 + 4*X + 7)

Champion prime support ladder:
R=27: a=2200849, factors=[(7, 1), (314407, 1)], targets=[26, 17], Gamma=[1, 4, 7, 10, 13, 16, 19, 22, 25], box=[1, 4, 7, 10, 13, 16, 19, 22, 25], states=['tau', 'tau']
R=43: a=2200853, factors=[(379, 1), (5807, 1)], targets=[42, 41], Gamma=[1, 2, 4, 8, 11, 16, 21, 22, 27, 32, 35, 39, 41, 42], box=[1, 2, 8, 16, 22, 27, 32, 35, 39], states=['0_Z', '0_Z']
R=107: a=2200869, factors=[(3, 2), (11, 2), (43, 1), (47, 1)], targets=[106, 86], Gamma=[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106], box=[1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 84, 85, 87, 88, 89, 91, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106], states=['2', '0_Z']
R=107 hits for -1: [(-2, 0, -1, -1), (2, 0, 1, 1)]

Eta/Fricke/Eisenstein critical-arm rows:
A8^3 n=744: (mod107,T9,I9,J9,Y9,f9)=(102, 0, 35, 35, 72, 89)
A5^4D4 n=744: (mod107,T6,F6,J6,Y6,f6)=(102, 34, 19, 16, 52, 67)
A8^3 n=747: (mod107,T9,I9,J9,Y9,f9)=(105, 0, 31, 31, 76, 45)
A5^4D4 n=747: (mod107,T6,F6,J6,Y6,f6)=(105, 83, 77, 1, 58, 48)
A8^3 n=750: (mod107,T9,I9,J9,Y9,f9)=(1, 0, 42, 42, 65, 52)
A5^4D4 n=750: (mod107,T6,F6,J6,Y6,f6)=(1, 101, 106, 2, 93, 21)

Resolvent determinants:
det M9=103
det M61=82
det M62=25

Transport matrices:
P1=[[32, 67, 44], [98, 72, 41], [51, 81, 71]]
P2=[[3, 28, 46], [106, 64, 81], [38, 47, 84]]
det P1=33, det P2=74
char P1=X**3 + 39*X**2 + 18*X - 33; factor=X**3 + 39*X**2 + 18*X - 33
char P2=X**3 - 44*X**2 - 28*X + 33; factor=(X + 17)*(X**2 + 46*X + 46)
