#include<iostream>

#include<cstdio>

#include<cmath>

#include<cstdlib>

#include<cstring>

#include<algorithm>

using namespace std;

#define ll long long

#define P 1000000007

#define N 100

char getc(){char c=getchar();while ((c<'A'||c>'Z')&&(c<'a'||c>'z')&&(c<''||c>'')) c=getchar();return c;}

int gcd(int n,int m){return m==?n:gcd(m,n%m);}

int read()

{

    int x=,f=;char c=getchar();

    while (c<''||c>'') {if (c=='-') f=-;c=getchar();}

    while (c>=''&&c<='') x=(x<<)+(x<<)+(c^),c=getchar();

    return x*f;

}

int m,T,prime[N],cnt[N],p[N][N],t,ans;

int ksm(int a,int k)

{

    int s=;

    for (;k;k>>=,a=1ll*a*a%P) if (k&) s=1ll*s*a%P;

    return s;

}

void dfs(int k,int s,int phi)

{

    if (k>t) {ans=(ans+1ll*ksm(m,s-)*phi)%P;return;}

    for (int i=;i<cnt[k];i++) dfs(k+,1ll*s*p[k][i]%P,1ll*phi*(prime[k]-)%P*p[k][cnt[k]-i-]%P);

    dfs(k+,1ll*s*p[k][cnt[k]]%P,phi);

}

int main()

{

#ifndef ONLINE_JUDGE

    freopen("a.in","r",stdin);

    freopen("a.out","w",stdout);

    const char LL[]="%I64d\n";

#else

    const char LL[]="%lld\n";

#endif

    T=read();

    while (T--)

    {

        int n=read();m=n,t=;

        for (int i=;i*i<=n;i++)

        if (n%i==)

        {

            prime[++t]=i,cnt[t]=;n/=i;

            while (n%i==) cnt[t]++,n/=i;

        }

        if (n>) prime[++t]=n,cnt[t]=;

        for (int i=;i<=t;i++)

        {

            p[i][]=;

            for (int j=;j<=cnt[i];j++) p[i][j]=1ll*p[i][j-]*prime[i]%P;

        }

        ans=;dfs(,,);

        printf("%d\n",ans);

    }

    return ;

}