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Sage thinks the unknot complement is simply-connected?

See title. When I run the following:

for K in KnotInfo: if K.num_components() == 1 and K.crossing_number() <= 5: print(K.name + ": " + str(K.link().fundamental_group()))

I get as output:

K0_1: Finitely presented group < | > K3_1: Finitely presented group < x0, x1, x2 | x0x2x1^-1x2^-1, x1x0x2^-1x0^-1, x2x1x0^-1x1^-1 > K4_1: Finitely presented group < x0, x1, x2, x3 | x1x0x2^-1x0^-1, x3x2x0^-1x2^-1, x2x1^-1x3^-1x1, x0x3^-1x1^-1x3 > K5_1: Finitely presented group < x0, x1, x2, x3, x4 | x1x4x2^-1x4^-1, x2x0x3^-1x0^-1, x3x1x4^-1x1^-1, x4x2x0^-1x2^-1, x0x3x1^-1x3^-1 > K5_2: Finitely presented group < x0, x1, x2, x3, x4 | x0x2x1^-1x2^-1, x1x4x2^-1x4^-1, x2x0x3^-1x0^-1, x3x1x4^-1x1^-1, x4x3x0^-1*x3^-1 >

Sage thinks the unknot complement is simply-connected?

See title. When I run the following:

for K in KnotInfo: if K.num_components() == 1 and K.crossing_number() <= 5: print(K.name + ": " + str(K.link().fundamental_group()))str(K.link().fundamental_group()))

I get as output:

K0_1: Finitely presented group < | > K3_1: Finitely presented group < x0, x1, x2 | x0x2x1^-1x2^-1, x1x0x2^-1x0^-1, x2x1x0^-1x1^-1 x0*x2*x1^-1*x2^-1, x1*x0*x2^-1*x0^-1, x2*x1*x0^-1*x1^-1 > K4_1: Finitely presented group < x0, x1, x2, x3 | x1x0x2^-1x0^-1, x3x2x0^-1x2^-1, x2x1^-1x3^-1x1, x0x3^-1x1^-1x3 x1*x0*x2^-1*x0^-1, x3*x2*x0^-1*x2^-1, x2*x1^-1*x3^-1*x1, x0*x3^-1*x1^-1*x3 > K5_1: Finitely presented group < x0, x1, x2, x3, x4 | x1x4x2^-1x4^-1, x2x0x3^-1x0^-1, x3x1x4^-1x1^-1, x4x2x0^-1x2^-1, x0x3x1^-1x3^-1 x1*x4*x2^-1*x4^-1, x2*x0*x3^-1*x0^-1, x3*x1*x4^-1*x1^-1, x4*x2*x0^-1*x2^-1, x0*x3*x1^-1*x3^-1 > K5_2: Finitely presented group < x0, x1, x2, x3, x4 | x0x2x1^-1x2^-1, x1x4x2^-1x4^-1, x2x0x3^-1x0^-1, x3x1x4^-1x1^-1, x4x3x0^-1*x3^-1 >x0*x2*x1^-1*x2^-1, x1*x4*x2^-1*x4^-1, x2*x0*x3^-1*x0^-1, x3*x1*x4^-1*x1^-1, x4*x3*x0^-1*x3^-1 >