How can I tell if a string repeats itself in Python?

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I"m looking for a way to test whether or not a given string repeats itself for the entire string or not.

Examples:

[
    "0045662100456621004566210045662100456621",             # "00456621"
    "0072992700729927007299270072992700729927",             # "00729927"
    "001443001443001443001443001443001443001443",           # "001443"
    "037037037037037037037037037037037037037037037",        # "037"
    "047619047619047619047619047619047619047619",           # "047619"
    "002457002457002457002457002457002457002457",           # "002457"
    "001221001221001221001221001221001221001221",           # "001221"
    "001230012300123001230012300123001230012300123",        # "00123"
    "0013947001394700139470013947001394700139470013947",    # "0013947"
    "001001001001001001001001001001001001001001001001001",  # "001"
    "001406469760900140646976090014064697609",              # "0014064697609"
]

are strings which repeat themselves, and

[
    "004608294930875576036866359447",
    "00469483568075117370892018779342723",
    "004739336492890995260663507109",
    "001508295625942684766214177978883861236802413273",
    "007518796992481203",
    "0071942446043165467625899280575539568345323741",
    "0434782608695652173913",
    "0344827586206896551724137931",
    "002481389578163771712158808933",
    "002932551319648093841642228739",
    "0035587188612099644128113879",
    "003484320557491289198606271777",
    "00115074798619102416570771",
]

are examples of ones that do not.

The repeating sections of the strings I"m given can be quite long, and the strings themselves can be 500 or more characters, so looping through each character trying to build a pattern then checking the pattern vs the rest of the string seems awful slow. Multiply that by potentially hundreds of strings and I can"t see any intuitive solution.

I"ve looked into regexes a bit and they seem good for when you know what you"re looking for, or at least the length of the pattern you"re looking for. Unfortunately, I know neither.

How can I tell if a string is repeating itself and if it is, what the shortest repeating subsequence is?

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