Battery instead of 9v crown battery

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Hello, I have a question! There is a device powered by a 9V battery of the "Krona" type. Basically (and this is 98-99% of the operating time of the device), it consumes a current equal to 1.1 mA. Sometimes (1-2% of the operating time of the device) there are current surges up to 50 mA. The minimum battery voltage (salt) with which my device worked is 7.15V. I decided to buy batteries, but I am not sure about the choice. I have a choice between two batteries (hereinafter referred to as battery). The first battery (Li-polymer) charges up to 9.5V. Tests have shown that at a load of 100mA at the output of the battery, the voltage is 9.5V and after 3 hours the battery is discharged i.e. its capacity is 300mA / h. During these 3 hours, the voltage at the output of the battery is stable at 9.5V (only hundredths of the value change). The second battery (Li-ion) is charged up to 8.4V. tests have shown that at a load of 130mA, the voltage gradually decreases to 7.3-7.2V in 4 hours 30 minutes, and then drops sharply, i.e. its capacity is 585mA / h. Question! What batteries should I buy so that the device works as long as possible on a single battery charge?

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