ECDSA x,y coordinate validity verification doesn’t seem to work

The ECDSA algorithm, secp256k1 for Bitcoin allegedly uses the equation

y ^ 2 = x ^ 3 + 7 mod P

to determine the validity of an alleged point upon the elliptical curve. Utilizing
http://web2.0calc.com/

When verifying public key 1 which has the following qualities:

x = 55066263022277343669578718895168534326250603453777594175500187360389116729240

y = 32670510020758816978083085130507043184471273380659243275938904335757337482424

I applied x ^ 3, then added 7, then mod P on that webpage. Then I square rooted it and got

180964706334543048141953325634608696715.426683454595872

Which is not y. How am I doing this wrong? My results suggests that this point is not a valid point on the curve, but everyone knows it is. Obviously I’m the one who’s wrong.

EDIT: I’d like to further clarify the question. My question is, how does one actually determine (as an example) the Y value while only having the X value. Bitcoin does it, the “Bitcoin Address Utility” also does it. When someone has a compressed key (which only contains the x coordinate) they are able to get the y coordinate as well. Utilizing the aforementioned webpage calculator does not work and others are saying its “modular root”. Anyone have Python 2.7.7 code which would do this or have a relatively simple way of explaining how to accomplish this whole thing? Thanks.

Negative Dogecoin Balances?

Through dogecoin-cli, I sent half the dogecoins I own to an external address. Now, when I call the listaccounts function, I get this:

[root@web ~]# ./dogecoin-cli listaccounts
{
    "" : -25001.00000000,
    "doge" : 48136.85072100
}

Notice how the “” has -25001.00000000. I am using a query from php to get the balance of “doge” and display it to users. That returns 48136.85072100, which is a problem, because I only have 23135.85072100 doge. How can I fix this problem? Thanks!

Do Miners get a reward for re-confirming blocks?

As far as I know, to ensure double-spending didn’t happened and also for other security reasons, there is minimum number of confirmations that a transaction should have to be accepted. That value is around 4-6 blocks I think, but merchants can put their own threshold.

My question is if with the sub-sequent confirmations after the first one, the miners get the mining reward, or a share of it.

Or maybe a transaction is included in different blocks per each confirmation? But how the mining fees are paid then?

If there is no reward for re-confirmations, I’m wondering what would happen after the Bitcoin limit is reached and the only reward for the miners will be the transaction fees. Will transaction get more than 1 confirmation then?

What is a thin client?

I’ve heard that if you don’t want do download gigabytes of data just to use bitcoin you gotta use a thin client. But what is a thin client?
What are the main advantages of a thin bitcoin client and what defines it as such?

Bitcoin transaction with dust output stuck

I made this transaction more than 24 hours ago, and it still has no confirmations at all.

What should I do? This transaction was created by the mobile Blockchain.info wallet. At the time, it didn’t warn me that transaction was problematic. However, I later noticed that one of the outputs of transaction is dust, using Blockchain.info’s block explorer.

Any suggestions how to solve this issue?