#include <bits/stdc++.h>
using namespace std;
template <typename T> void read(T &t) {
    t=0; char ch=getchar(); int f=1;
    while (ch<'0'||ch>'9') { if (ch=='-') f=-1; ch=getchar(); }
    do { (t*=10)+=ch-'0'; ch=getchar(); } while ('0'<=ch&&ch<='9'); t*=f;
}
typedef long long ll;
const ll mod=(1e9)+7;
const int maxn=1000010;
int T,mx;
ll ans,n,tmp,f[maxn],l,r;
ll c(ll x) {
    if (x%2==0) return ((x/2)%mod)*((x+1)%mod)%mod;
    return (((x+1)/2)%mod)*(x%mod)%mod;
}
void update(ll &x,ll y) {
    x+=y%mod; if (x>=mod) x-=mod;
}
int main() {
    //freopen("1.txt","r",stdin);
    read(T);
    while (T--) {
        read(n);
        ans=0; mx=0;
        for (ll d=1;d*d<=n;d++) {
            tmp=n/d/d; f[d]=0; mx=d;
            for (ll x=1;x*x<=tmp;x++) {
                update(f[d],x);
                if (x*x==tmp) break;
                else {
                    l=x+1,r=tmp/x;
                    update(f[d],(ll)x%mod*((r-l+1)%mod)%mod);
                    update(f[d],(c(r)-c(l-1)+mod)%mod);
                }
            }
            f[d]=f[d]*d%mod;
            //printf("%lld %lld\n",d,f[d]);
        }
        for (int i=mx;i>=1;i--)
        for (int j=i+i;j<=mx;j+=i) update(f[i],mod-f[j]);
        printf("%lld\n",f[1]);
    }
    return 0;
}
/*
  0. Enough array size? Enough array size? Enough array size? Interger overflow?
  
  1. Think TWICE, Code ONCE!
  Are there any counterexamples to your algo?
    
  2. Be careful about the BOUNDARIES!
  N=1? P=1? Something about 0?
    
  3. Do not make STUPID MISTAKES!
  Time complexity? Memory usage? Precision error?
*/