Probably irrelevant but I see a lot of NaN32 when initializing the Complex{Float32} part:
julia> ω,χR,χI,χRC,χIC,γᵢ,a,ωᵣ=provideData(Float32)
(Float32[2150.0, 2150.001, 2150.0017, 2150.0027, 2150.0037, 2150.0044, 2150.0054, 2150.0063, 2150.007, 2150.008 … 2439.9917, 2439.9927, 2439.9934, 2439.9944, 2439.9954, 2439.996, 2439.997, 2439.998, 2439.9988, 2439.9998], Float32[-1.1871652f23, 5.076202, 1.0814404f17, 5.0762024, -9.829634f10, 5.0762024, 89128.96, 5.076203, -0.0806, 5.076203 … 0.0, 2213.8955, 0.0, 2213.8965, 0.0, 2213.8972, 0.0, 2213.8982, 0.0, 2213.8992], Float32[2216.3552, 0.0, 2216.3562, 0.0, 2216.357, 0.0, 2216.358, 0.0, 2216.359, 0.0 … 0.0, 2361.3516, 0.0, 2361.3523, 0.0, 2361.3533, 0.0, 2361.3542, 0.0, 2361.355], Float32[2363.8113, 0.0, 2363.812, 0.0, 2363.813, 0.0, 2363.814, 0.0, 2363.8147, 0.0 … 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], Float32[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 … 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], Float32[0.014695484, 0.014325275, 0.014013623, 0.013746131, 0.0135149835, 0.013314734, 0.013141038, 0.012990155, 0.012858742, 0.012743745 … 0.012123074, 0.0120550655, 0.0119848205, 0.0126423575, 0.01247028, 0.0123243695, 0.012189823, 0.0120550655, 0.011911526, 0.0117533235], Float32[2.7667483f-21, 2.3668141f-21, 6.532759f-21, 4.1158403f-21, 9.841103f-21, 5.679168f-21, 1.2776748f-20, 7.044395f-21, 1.5287225f-20, 8.182855f-21 … 1.0287981f-21, 2.0359744f-21, 1.0021638f-21, 4.8442865f-22, 5.1569915f-22, 5.3303904f-22, 5.3718166f-22, 5.293419f-22, 5.111076f-22, 4.843169f-22], Float32[2317.9744, 2309.9817, 2301.955, 2293.8948, 2285.801, 2277.674, 2269.514, 2261.3213, 2253.0964, 2244.8394 … 2424.3635, 2431.351, 2438.2974, 2344.6335, 2358.9841, 2373.1768, 2387.2092, 2401.0793, 2414.7847, 2428.323])
julia> ω,χR,χI,χRC,χIC,γᵢ,a,ωᵣ=provideData(ComplexF32)
(ComplexF32[2150.0f0 + 0.0f0im, 2150.001f0 + 0.0f0im, 2150.0017f0 + 0.0f0im, 2150.0027f0 + 0.0f0im, 2150.0037f0 + 0.0f0im, 2150.0044f0 + 0.0f0im, 2150.0054f0 + 0.0f0im, 2150.0063f0 + 0.0f0im, 2150.007f0 + 0.0f0im, 2150.008f0 + 0.0f0im … 2439.9917f0 + 0.0f0im, 2439.9927f0 + 0.0f0im, 2439.9934f0 + 0.0f0im, 2439.9944f0 + 0.0f0im, 2439.9954f0 + 0.0f0im, 2439.996f0 + 0.0f0im, 2439.997f0 + 0.0f0im, 2439.998f0 + 0.0f0im, 2439.9988f0 + 0.0f0im, 2439.9998f0 + 0.0f0im], ComplexF32[0.0f0 + NaN32*im, 1.4587136f-37 + 3.4438f-41im, 1.1f-44 + 0.0f0im, 1.4594831f-37 + 3.4438f-41im, 1.1f-44 + 0.0f0im, 0.0f0 + NaN32*im, 1.4576266f-37 + 3.4438f-41im, 1.1f-44 + 0.0f0im, 1.4578634f-37 + 3.4438f-41im, 1.1f-44 + 0.0f0im … 0.0f0 + 6.0955567f-22im, 0.0f0 + 6.105026f-22im, 0.0f0 + 6.112172f-22im, 0.0f0 + 6.1217555f-22im, 0.0f0 + 6.1314076f-22im, 0.0f0 + 6.138689f-22im, 0.0f0 + 6.1484536f-22im, 0.0f0 + 6.1582865f-22im, -0.0f0 + NaN32*im, 0.0f0 + 6.17565f-22im], ComplexF32[-0.0f0 + NaN32*im, -0.0f0 + NaN32*im, -0.0f0 + NaN32*im, -0.0f0 + NaN32*im, -0.0f0 + NaN32*im, -0.0f0 + NaN32*im, 0.0f0 + 1.3562106f-21im, 0.0f0 + 1.3507185f-21im, -0.0f0 + NaN32*im, -0.0f0 + NaN32*im … NaN32 + 6.0955567f-22im, NaN32 + 6.105026f-22im, NaN32 + 6.112172f-22im, NaN32 + 6.1217555f-22im, NaN32 + 6.1314076f-22im, NaN32 + 6.138689f-22im, NaN32 + 6.1484536f-22im, -1.2332106f-19 + 6.1582865f-22im, -1.2327342f-19 + NaN32*im, -1.232376f-19 + 6.17565f-22im], ComplexF32[NaN32 + NaN32*im, NaN32 + NaN32*im, NaN32 + NaN32*im, NaN32 + NaN32*im, NaN32 + NaN32*im, NaN32 + NaN32*im, -1.9681535f-19 + 1.3562106f-21im, -1.967118f-19 + 1.3507185f-21im, -1.9660859f-19 + NaN32*im, -1.9653147f-19 + NaN32*im … 0.0f0 + 0.0f0im, 0.0f0 + 0.0f0im, 0.0f0 + 0.0f0im, 0.0f0 + 0.0f0im, 0.0f0 + 0.0f0im, 0.0f0 + 0.0f0im, 0.0f0 + 0.0f0im, 0.0f0 + 0.0f0im, 0.0f0 + 0.0f0im, 0.0f0 + 0.0f0im], ComplexF32[0.0f0 + 0.0f0im, 0.0f0 + 0.0f0im, 0.0f0 + 0.0f0im, 0.0f0 + 0.0f0im, 0.0f0 + 0.0f0im, 0.0f0 + 0.0f0im, 0.0f0 + 0.0f0im, 0.0f0 + 0.0f0im, 0.0f0 + 0.0f0im, 0.0f0 + 0.0f0im … -1.2362867f-19 + 6.0955567f-22im, -1.2358155f-19 + 6.105026f-22im, -1.2354626f-19 + 6.112172f-22im, -1.2349893f-19 + 6.1217555f-22im, -1.2345167f-19 + 6.1314076f-22im, -1.2341607f-19 + 6.138689f-22im, -1.2336857f-19 + 6.1484536f-22im, -1.2332106f-19 + 6.1582865f-22im, -1.2327341f-19 + 6.168184f-22im, -1.232376f-19 + 6.17565f-22im], ComplexF32[0.014695484f0 + 0.0f0im, 0.014325275f0 + 0.0f0im, 0.014013623f0 + 0.0f0im, 0.013746131f0 + 0.0f0im, 0.0135149835f0 + 0.0f0im, 0.013314734f0 + 0.0f0im, 0.013141038f0 + 0.0f0im, 0.012990155f0 + 0.0f0im, 0.012858742f0 + 0.0f0im, 0.012743745f0 + 0.0f0im … 0.012123074f0 + 0.0f0im, 0.0120550655f0 + 0.0f0im, 0.0119848205f0 + 0.0f0im, 0.0126423575f0 + 0.0f0im, 0.01247028f0 + 0.0f0im, 0.0123243695f0 + 0.0f0im, 0.012189823f0 + 0.0f0im, 0.0120550655f0 + 0.0f0im, 0.011911526f0 + 0.0f0im, 0.0117533235f0 + 0.0f0im], ComplexF32[2.7667483f-21 + 0.0f0im, 2.3668141f-21 + 0.0f0im, 6.532759f-21 + 0.0f0im, 4.1158403f-21 + 0.0f0im, 9.841103f-21 + 0.0f0im, 5.679168f-21 + 0.0f0im, 1.2776748f-20 + 0.0f0im, 7.044395f-21 + 0.0f0im, 1.5287225f-20 + 0.0f0im, 8.182855f-21 + 0.0f0im … 1.0287981f-21 + 0.0f0im, 2.0359744f-21 + 0.0f0im, 1.0021638f-21 + 0.0f0im, 4.8442865f-22 + 0.0f0im, 5.1569915f-22 + 0.0f0im, 5.3303904f-22 + 0.0f0im, 5.3718166f-22 + 0.0f0im, 5.293419f-22 + 0.0f0im, 5.111076f-22 + 0.0f0im, 4.843169f-22 + 0.0f0im], ComplexF32[2317.9744f0 + 0.0f0im, 2309.9817f0 + 0.0f0im, 2301.955f0 + 0.0f0im, 2293.8948f0 + 0.0f0im, 2285.801f0 + 0.0f0im, 2277.674f0 + 0.0f0im, 2269.514f0 + 0.0f0im, 2261.3213f0 + 0.0f0im, 2253.0964f0 + 0.0f0im, 2244.8394f0 + 0.0f0im … 2424.3635f0 + 0.0f0im, 2431.351f0 + 0.0f0im, 2438.2974f0 + 0.0f0im, 2344.6335f0 + 0.0f0im, 2358.9841f0 + 0.0f0im, 2373.1768f0 + 0.0f0im, 2387.2092f0 + 0.0f0im, 2401.0793f0 + 0.0f0im, 2414.7847f0 + 0.0f0im, 2428.323f0 + 0.0f0im])