You don't owe anything because at that year the federal income tax rate was 0%.
You wouldn't be owing any federal income tax
The US government imposed the first income tax in 1861 and was at 3% for all incomes over $800 but this was cancelled and another was imposed in 1862. This second income tax was at 2% for all incomes over $4000. The Supreme court ruled the income tax unconstitutional.
In 1913, the federal income tax in the United States was made a permanent fixture.
This would imply that from 1863 to 1913, there was no federal income tax payments. Therefore, in 1962, nobody paid federal income taxes.