Please check your bill again and post a new, separate question.
Series letters on 1957 $1 bills only went up to B. The only $1 bills with an H series letter were dated 1935.
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a mint condition silver certificate is worth $5-$6.
All silver certificates printed from 1928 to 1957 had blue seals. Please see the question "What is the value of a 1957 A US 1 dollar silver certificate?" for more information.
Except for certain wartime bills, all silver certificates issued from 1928 to 1957 had blue seals. Please see the question "What is the value of a 1957 B US 1 dollar silver certificate?" for more information.
Please take a closer look. The date is 1957.
Please check your bill again. As the banner across the top indicates, it's a silver certificate, not gold. All gold certificates were withdrawn in 1933. There's more information at the question "What is the value of a 1957 US 1 dollar silver certificate?"