The `ValueError` with the message `unconverted data remains` usually arises when you are utilizing a date or time parsing function (such as strptime in Python's datetime module) to convert a string into a date or time object. In this scenario, there is extra data within the string that could not be parsed successfully [5].
Here's when the error occurs and potential resolution methods:

When the error occurs:
1. Parsing Dates or Times: The error often occurs when you are parsing a date or time string using functions like `strptime`, and the string contains extra characters or data that the parsing function cannot interpret.
2. Input Data Mismatch: It can also occur when the format of the input string doesn't match the format expected by the parsing function.

Resolution Methods:
1. Check Input Data: Examine the input string that you are trying to parse. Make sure it adheres to the expected format for the parsing function. For example, if you are trying to parse a date in the format `YYYY-MM-DD`, ensure that the input string follows that format.
2. Use Try-Except: Wrap the parsing code in a try-except block to catch the ValueError and handle it gracefully. You can print an error message or take other appropriate action when parsing fails [2].

    from datetime import datetime

    date_string = "2023-09-11.582677"

    try:
        # Use the correct format to parse the date and time (including milliseconds)
        parsed_date = datetime.strptime(date_string, "%Y-%m-%d.%f")

        # Do something with the parsed_date
        print("Successfully parsed date:", parsed_date)

    except ValueError as e:
        # Handle the parsing error gracefully
        print(f"Error parsing date: {e}")
        # You can add additional error handling logic here if needed

3. Clean Input Data: If the input data frequently contains extra information that is not needed for parsing (e.g., milliseconds), you can clean the input string to remove such extra data before parsing.
4. Custom Parsing: If the input format varies or is complex, consider implementing a custom parsing function that can handle the specific format you are working with.
5. Using the Wrong Function: If you are using a library or function other than `datetime.strptime`, ensure that you are using the correct function for parsing date and time values.

The precise solution will vary depending on the particular context of your code and the format of the input data. The crucial aspect is to guarantee that the input data aligns with the anticipated format for the parsing function and to manage any exceptions that might arise during the parsing procedure.