#include <bits/stdc++.h>
#define int long long
using namespace std;

long long gcd(long long a, long long b)
{
    if(!b)
        return a;
    return gcd(b, a % b);
}

long long lcm(long long a, long long b)
{
    long long z = gcd(a, b);
    a /= z;
    if(a > 1e18 / b)
        return -1;
    return a * b;
}
const int MOD = 1e9 + 7;
int inv(int x)
{
    int y = MOD - 2, r = 1;
    while(y)
    {
        if(y&1)
            r=1LL*r*x%MOD;
        y>>=1;
        x=1LL*x*x%MOD;
    }
    return r;
}
int32_t main()
{
    long long n;
    int t;
    cin >> t;
    while(t--)
    {
       cin >> n;
        long long q = 1, ans = 0;

        for(int i = 1; i <= 1000; ++i)
        {

            long long p = lcm(q, i);

            if(p == -1)
                break;
            else
                q = p;
            long long mul = (i + 1) / gcd(q, (i + 1));
            long long divI = n / q, t3 = divI / mul;
            long long pqr = divI - t3;
            long long qq = (1LL * pqr * (i + 1)) % MOD;
            ans = (ans + qq) % MOD;
        }
        cout << ans << '\n';

    }
}
