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

const int mod=1e9+7;

ll K(ll x,ll y=mod-2){
    ll t=1;
    for (;y;y>>=1,x=x*x%mod)
        if (y&1) t=t*x%mod;
    return t;
}

const int N=2e6;
bool np[N+5];
int pri[N/10], tot;
vector<int>HH[N/10];

void init(){
    for (int i=2;i<=N;++i){
        if (!np[i]){
            pri[++tot]=i;
            for (int j=i+i;j<=N;j+=i)
                np[j]=1;
        }
    }
    for (int pos=1;pos<=tot;++pos){
        ll p=pri[pos], en=1e12;
        vector<ll>F, G; int sz=0;
        {
            ll t=1;
            while (t<=en/p) t*=p, ++sz;
        }
        if (sz<2) continue;
        F.resize(sz+1);
        G.resize(sz+1);
        for (int i=0;i<=sz;++i){
            F[i]= i? (F[i-1]+K(p,i))%mod: 1;
            G[i]= i? (K(p,i)+1)%mod: 1;
        }
        swap(F,G);
        for (int i=0;i<=sz;++i){
            ll h=F[i];
            HH[pos].push_back(h);
            for (int j=0;i+j<=sz;++j)
                F[i+j]=(F[i+j]-G[j]*h%mod+mod)%mod;
        }
    }
}

ll T, n, ans;

ll Si(ll x){
    x%=mod; return x*(x+1)/2%mod;
}
unordered_map<ll,ll>sh;
ll shit(ll n){
    if (sh.count(n)) return sh[n];
    ll res=0, pre=0;
    for (ll i=1;i<=n;++i){
        ll nex=n/(n/i), p2=Si(nex);
        res+=(n/i%mod)*(p2-pre+mod)%mod;
        i=nex; pre=p2;
    }
    return sh[n]=res%mod;
}

ll ooooo=0;
void dfs(ll now,ll H,int pos,int fl){
    ++ooooo;
    if (fl){
        //cerr<<' '<<now<<' '<<H<<' '<<pos<<endl;
        ans=(ans+shit(n/now)*H)%mod;
    }
    ll p=pri[pos];
    if (p*p>n/now) return;
    ll en=n/now;

    ll now2=now;
    for (int i=1;now2<=n/p;++i){
        now2*=p;
        ll h=HH[pos][i];
        if (i>=2){
            dfs(now2,H*h%mod,pos+1,1);
        }
    }
    dfs(now,H,pos+1,0);
}

ll fuck(){
    ans=0;
    dfs(1,1,1,1);
    return ans;
}

int main(){
    init();
    for (cin>>T;T--;){
        cin>>n;
        cout<<fuck()<<endl;
    }
    //cerr<<ooooo<<endl;
}