C++ ranged vs manual for loop

I am new to C++ and for practice I have been solving some problems on projecteuler.net. One of the questions involves analyzing a 1000 digit number, so I wrote a program that can read in the number and stores it in a vector. In order to test my code, i have printed out the vector to the console.
I am confused because if I use a manually specified indexed for loop, it prints out the correct values, but when I use ranged for with the auto& keyword it gets confused and prints out wrong values.

Here is my code:

#include <iostream>
#include <fstream>
#include <vector>
using namespace std;

vector<int8_t> reader(string datei)
{
    ifstream file;
    char inputChar;
    vector<int8_t> data;
    file.open(datei);
    while(file >> inputChar) 
    	data.push_back(inputChar);
    file.close();
    
    return data;
}

int main()
{
    string a;
    cout << "Select file to open:" << endl;
    cin >> a;
    vector<int8_t> numbers = reader(a);
    for(int i = 0; i < numbers.size(); i++)
	   cout << numbers[i];
    for(int i = 0; i < index.size(); i++)
	   cout << index[i];
}

This version prints out the correct 1000 digit number, but if i use

for(auto& i : numbers)
    	   cout << numbers[i];

The digits are wrong.
The correct number is

731671765313306249192251196744265747423553491949349698352031277450632623957831801698480186947885184385861560789112949495459501737958
331952853208805511125406987471585238630507156932909632952274430435576689664895044524452316173185640309871112172238311362229893423380
308135336276614282806444486645238749303589072962904915604407723907138105158593079608667017242712188399879790879227492190169972088809
377665727333001053367881220235421809751254540594752243525849077116705560136048395864467063244157221553975369781797784617406495514929
086256932197846862248283972241375657056057490261407972968652414535100474821663704844031998900088952434506585412275886668811642717147
992444292823086346567481391912316282458617866458359124566529476545682848912883142607690042242190226710556263211111093705442175069416
589604080719840385096245544436298123098787992724428490918884580156166097919133875499200524063689912560717606058861164671094050775410
0225698315520005593572972571636269561882670428252483600823257530420752963450

And the "shifted" one is

564354538646633990409984403599938595996886904090690302689364955983369396085264234302923423095228429628234833520449090908980834565082
664089286932238844498933025954828962363835483069030369089959963968853320339208399899989643456428393630254449459962644639990206996623
632468663953349929233999923398962590636820359039039048339935596035462438482806350332335345999549422600250503250995909403430059322230
655338595666334386635224993968994230584989893809589996898290355443538833463392608239935336999485994886058630524505529345933908849090
323983069405293239992926059994658385383385903934935059032389949868433959294336539299364002033322089969833828949958223332244399545495
009999909296323693835924604049643929982345233982680499833890953898329292049226499335303399999403993543883936944444306538999458330943
820339323540293628303998899963902496302525009599992903042229823483433305040466258900933899336320049833545333382234439354309383558943
3998302648893338806859059854363930834229353992989926333296985863993589036983

Could anyone explain to me what is going on?

With auto& i, i is the number, not the index to the number in the numbers array.

So you simply need cout << i;

for(auto& i : numbers)
    cout << i;

Is what you are looking for. auto& i : numbers makes it so that i takes the values inside the vector. Not the indexes!

You went half-way from a classic counting loop for indices to a for-range loop over elements:

Counting loop:

for (int i = 0; i < numbers.size(); i++)
   cout << numbers[i];

For-range loop:

for (auto& i : numbers)
    cout << i;

Your weird chimaera takes the head from one and the body from the other:

for (auto& i : numbers)
    cout << numbers[i];

Translating the latter to a classic counting loop:

for (int i = 0; i < numbers.size(); i++)
   cout << numbers[numbers[i]];

Now it should be obvious why the output is different.