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How to guess the coordinate system of point data from a Canadian survey

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Hi, there

I have these point values (from Canadian Election Study 2011: http://ces-eec.org/pagesE/surveys.html) and I am trying to create the shapefiles from these values using Make XY Event Layer. However, I am not sure whether the coordinate system of these points is. The longitude values range from 52687153 to 132305176, and latitude values are from 42014609 to 58071269. It seems to me that they were not measured in degrees (using geographic coordinate systems) since the numbers are larger than 180. I guess they were measured in meters using other projected coordinate systems. As the dataset is Canada-wide, it is unlikely that they were measured in UTM or State Plane coordinate system which involves specific zones. I have tried projecting them using Canada Lambert Conformal Conic, but they didn't align with the country boundary (using the same projected coordinate system).

Does anyone can help me figure out which units of these coordinates are and which coordinate system of the data is? Or any suggestion for guessing an unknown coordinate system? Thank you very much.

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