Autocorrelation of Zadoff_chu sequence

Hi 
I have a query  with the Zadoff_chu sequence
I have the following matlab code
I  generated the zad_off chu sequence
then made a circular shift with factor of 6.
tried to correlate the shifted version with the original
as expected the peak has shifted but iam unable to get
the location of the peak mathematically
and what i dont understand is why is the peak shifting
based on the factor U which is the logical root sequence number
matlab reference,It will be helpful if somebody helps me in this 
regard


U = 140;
for n= 0:838
    
    conv_result(n+1) = exp((-j*pi*U*n*(n+1)/839));    
    shift_result(n+1)= conv_result(n+1)*exp((j*2*pi*6*n)/839);
end

[corr lag] = xcorr(shift_result,conv_result);
plot(lag,abs(corr));