For everybody saying it can't be done:
010000000137c82cec0a27b399c3737c6c61f0f934deb33ff3cfb6ef1016e62d434a6204a3000000008b483045022100f8ecb38d7b9b2a1bdb8ea31af39466d88727ad863e82b3c52258011420c65715022039e0a55698347c8198385beb252814e08c48dab7b01f233d3f20e5deb054f2f7014104ed1df4aaa790f8118646976365a33de02dcbb4c78d92edf1271a85abe53c15a316d08c29b1069a52ae98e015a29aa52cbeb41c1fb77bf091d809d286adff8a73ffffffff01d02a0f00000000001976a914e432ffb6ef0bde696af29ca13dd37c0824a4082388ac00000000
You can use any online transaction decoder, like (for example)
https://live.blockcypher.com/btc/decodetx/ and verify that
1) the transaction has 0 fee
2) the transaction is signed
However, if you ever want this transaction to end up in a block, you'll need to find a mining node that:
1) still accepts 0 fee transactions
2) includes those transactions into the block the miner is trying to solve
I guess those miners should still exist, but i don't think they'll be easy to find tough...
BTW: if you're a pool operator, don't include this transaction as a favour, it's just spending an unspent output to fund exactly the same address, so it's a moot transaction