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

//入力が必ず-mod<=a<modの時.
template<const int mod> //mod<2^30.
struct modint{ //mod変更が不可能.
    public:
    long long v;
    static void setmod(int m){} //飾り.
    static constexpr long long getmod(){return mod;}
    modint():v(0){}
    template<typename T>
    modint(T a):v(a){if(v < 0) v += mod;}
    long long val()const{return v;}
 
    modint &operator=(const modint &b) = default;
    modint &operator+()const{return (*this);}
    modint operator-()const{return modint(0)-(*this);}
    modint operator+(const modint b)const{return modint(v)+=b;}
    modint operator-(const modint b)const{return modint(v)-=b;}
    modint operator*(const modint b)const{return modint(v)*=b;}
    modint operator/(const modint b)const{return modint(v)/=b;}
    modint &operator+=(const modint b){
        v += b.v; if(v >= mod) v -= mod;
        return *this;
    }
    modint &operator-=(const modint b){
        v -= b.v; if(v < 0) v += mod; 
        return *this;
    }   
    modint &operator*=(const modint b){v = v*b.v%mod; return *this;}
    modint &operator/=(modint b){ //b!=0 mod素数が必須.
        assert(b.v != 0);
        (*this) *= b.pow(mod-2);
        return *this;
    }
    modint pow(long long n)const{
        modint ret = 1,p = v;
        if(n < 0) p = p.inv(),n = -n;
        while(n){
            if(n&1) ret *= p;
            p *= p; n >>= 1;
        }
        return ret;
    }
    modint inv()const{return pow(mod-2);} //素数mod必須.
 
    modint &operator++(){*this += 1; return *this;}
    modint &operator--(){*this -= 1; return *this;}
    modint operator++(int){modint ret = *this; *this += 1; return ret;}
    modint operator--(int){modint ret = *this; *this -= 1; return ret;}
    friend bool operator==(const modint a,const modint b){return a.v==b.v;}
    friend bool operator!=(const modint a,const modint b){return a.v!=b.v;}
    friend bool operator<(const modint a,const modint b){return a.v<b.v;}
    friend bool operator<=(const modint a,const modint b){return a.v<=b.v;}
    friend bool operator>=(const modint a,const modint b){return a.v>=b.v;}
    friend bool operator>(const modint a,const modint b){return a.v>b.v;}
    friend ostream &operator<<(ostream &os,const modint a){return os<<a.v;}
    friend istream &operator>>(istream &is,modint &a){ //入力はmodをとってくれる.
        long long x; is >> x; x %= mod;
        a = modint(x); return is;
    }
};
using mint = modint<998244353>; const long long mod = 998244353;

vector<long long> LCM = {1,1,2,6,12,60,60,420,840,2520,2520,27720,27720,360360,360360,360360,720720,12252240,12252240,232792560,232792560,232792560,232792560,5354228880,5354228880,26771144400,26771144400,80313433200,80313433200,2329089562800,2329089562800,72201776446800,144403552893600,144403552893600,144403552893600,144403552893600,144403552893600,5342931457063200,5342931457063200,5342931457063200,5342931457063200,219060189739591200};

int solve(int L,int R){
    vector<int> V(R+1);
    for(int i=R; i>=L; i--){
        for(int k=i; k<=R; k+=i) if(V.at(k)+1 == k/i) V.at(k)++;
    }
    return *max_element(V.begin(),V.end());
}

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    int T; cin >> T;
    mint div2 = mint(1)/2;
    while(T--){
        long long N; cin >> N;
        mint answer = 0,n1 = N%mod,n2 = n1*n1;
        for(int i=1; ; i++){
            if(LCM.at(i) > N) break;
            long long l = LCM.at(i)/i,r = LCM.at(i),m = r/l;
            answer += n2;
            long long ok = N/m;
            ok = ok/l*l;
            answer -= (n1-ok%mod)*n1;
            answer += ok%mod;
            ok /= l;
            mint v = ok%mod;
            answer -= v*(v+1)*div2*(l%mod)*(r%mod);

        }
        cout << answer << "\n";
    }
}