fn z_pow_p2(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(1013489358),
                F::from_canonical_u32(1619071628),
                F::from_canonical_u32(304593143),
                F::from_canonical_u32(1949397349),
                F::from_canonical_u32(1564307636),
                F::from_canonical_u32(327761151),
                F::from_canonical_u32(415430835),
            ]);
        }
        if index == 2 {
            return SepticExtension([
                F::from_canonical_u32(209824426),
                F::from_canonical_u32(1313900768),
                F::from_canonical_u32(38410482),
                F::from_canonical_u32(256593180),
                F::from_canonical_u32(1708830551),
                F::from_canonical_u32(1244995038),
                F::from_canonical_u32(1555324019),
            ]);
        }
        if index == 3 {
            return SepticExtension([
                F::from_canonical_u32(1475628651),
                F::from_canonical_u32(777565847),
                F::from_canonical_u32(704492386),
                F::from_canonical_u32(1218528120),
                F::from_canonical_u32(1245363405),
                F::from_canonical_u32(475884575),
                F::from_canonical_u32(649166061),
            ]);
        }
        if index == 4 {
            return SepticExtension([
                F::from_canonical_u32(550038364),
                F::from_canonical_u32(948935655),
                F::from_canonical_u32(68722023),
                F::from_canonical_u32(1251345762),
                F::from_canonical_u32(1692456177),
                F::from_canonical_u32(1177958698),
                F::from_canonical_u32(350232928),
            ]);
        }
        if index == 5 {
            return SepticExtension([
                F::from_canonical_u32(882720258),
                F::from_canonical_u32(821925756),
                F::from_canonical_u32(199955840),
                F::from_canonical_u32(812002876),
                F::from_canonical_u32(1484951277),
                F::from_canonical_u32(1063138035),
                F::from_canonical_u32(491712810),
            ]);
        }
        if index == 6 {
            return SepticExtension([
                F::from_canonical_u32(738287111),
                F::from_canonical_u32(1955364991),
                F::from_canonical_u32(552724293),
                F::from_canonical_u32(1175775744),
                F::from_canonical_u32(341623997),
                F::from_canonical_u32(1454022463),
                F::from_canonical_u32(408193320),
            ]);
        }
        unreachable!();
    }
Returns the value of z^{index * p^2} in the [`SepticExtension`] field.
crates/stark/src/septic_extension.rs