What is the thermopile - Hayward H Series Millivolt 250,000 Btu Pool Heater H2501

https://heatinghelp.com/systems-help-center/thermocouple-testing-procedure/

thermopile should show 600mv clean thermopile . clean pilot so its strong and blue . see how that goes, may need new thermopile .

pilot flame to small
over temp safety thermostat trip
dirty connection points
thermocouple fail not the same as thermopile fail
thermopile drives the gas valve.700MV
thermocouple drives the pilot light safety system.30MV
gas valve magnet fail
check the above for any faults

That doesn't sound out of line for a cold thermopile. Check it hot - hold a candle flame against it. The voltage should rise.

You could have a weak pilot or thermopile. If the thermopile is not heated correctly by the pilot, it cannot generate enough millivolts to open the gas valve. The same is true if the thermopile is faulty. Thermopiles consist of several junctions of which only some may go bad causing low millivolt output. Millivolt output with the thermostat off and pilot lit should be around 600 millivolt, you can check with a DC multimeter set on MV across the two wires coming from the thermopile. Remember, the thermopile has to be heated by the pilot thoroughly before you will get the full millivolt reading and the thermostat must be off. Cleaning the pilot assembly is often helpful, thermopiles are inexpensive and relatively easy to change. Of course, other problems can cause this issue as well, but the above are most common.

Check if the the gas pressure is sufficient (as stated on unit's nameplate). Check if the hi limit device is good. Check also if the thermopile (cylindrical metal with two wires standing behind the pilot hood) is receiving enough heat from the pilot flame. The voltage generated by thermopile should be 500millivolts in order to open pilot and main valve. If there is 500millivolt on gas valve thermopile and the pilot flame does not stay lit, you have to replace the gas valve. If the thermopile is glowing red and the voltage generated does not reach 500 millivots, you have to replace the thermopile.

replace the thermocouple pretty easy looks like bare copper wire

Most thermopile/therocouple units are generic.  Remove the old one and go to a large hardware store.  The correct one will be easily found among the several available.

if you changed the thermopile and still have the same problem make sure that the sensing bulb is directly over the flame. If it is and the thermopile is installed correctly the next thing would be the gas valve.

Hope this helps

The thermopile for the 35cd,35cs,pit40sn,sg185 are the same thermopile the part number is P5047541. The only other thermopile in use for pitco products is the one for the solstice series it is part number 60125501