fn z_pow_p(index: u32) -> Self {
        // The constants written below are specifically for the BabyBear field.
        debug_assert_eq!(F::order(), BigUint::from(2013265921u32));
        if index == 0 {
            return Self::one();
        }
        if index == 1 {
            return SepticExtension([
                F::from_canonical_u32(954599710),
                F::from_canonical_u32(1359279693),
                F::from_canonical_u32(566669999),
                F::from_canonical_u32(1982781815),
                F::from_canonical_u32(1735718361),
                F::from_canonical_u32(1174868538),
                F::from_canonical_u32(1120871770),
            ]);
        }
        if index == 2 {
            return SepticExtension([
                F::from_canonical_u32(862825265),
                F::from_canonical_u32(597046311),
                F::from_canonical_u32(978840770),
                F::from_canonical_u32(1790138282),
                F::from_canonical_u32(1044777201),
                F::from_canonical_u32(835869808),
                F::from_canonical_u32(1342179023),
            ]);
        }
        if index == 3 {
            return SepticExtension([
                F::from_canonical_u32(596273169),
                F::from_canonical_u32(658837454),
                F::from_canonical_u32(1515468261),
                F::from_canonical_u32(367059247),
                F::from_canonical_u32(781278880),
                F::from_canonical_u32(1544222616),
                F::from_canonical_u32(155490465),
            ]);
        }
        if index == 4 {
            return SepticExtension([
                F::from_canonical_u32(557608863),
                F::from_canonical_u32(1173670028),
                F::from_canonical_u32(1749546888),
                F::from_canonical_u32(1086464137),
                F::from_canonical_u32(803900099),
                F::from_canonical_u32(1288818584),
                F::from_canonical_u32(1184677604),
            ]);
        }
        if index == 5 {
            return SepticExtension([
                F::from_canonical_u32(763416381),
                F::from_canonical_u32(1252567168),
                F::from_canonical_u32(628856225),
                F::from_canonical_u32(1771903394),
                F::from_canonical_u32(650712211),
                F::from_canonical_u32(19417363),
                F::from_canonical_u32(57990258),
            ]);
        }
        if index == 6 {
            return SepticExtension([
                F::from_canonical_u32(1734711039),
                F::from_canonical_u32(1749813853),
                F::from_canonical_u32(1227235221),
                F::from_canonical_u32(1707730636),
                F::from_canonical_u32(424560395),
                F::from_canonical_u32(1007029514),
                F::from_canonical_u32(498034669),
            ]);
        }
        unreachable!();
    }
Returns the value of z^{index * p} in the [`SepticExtension`] field.
crates/stark/src/septic_extension.rs