After two years of waiting, three waves of tickets sales, tens of thousands of individual purchasers and about 250,000 actual seats, “Hamilton” has made its mark on Washington.

Most of the tickets to the blockbuster musical about Alexander Hamilton have been sold, but the Kennedy Center’s handling of sales has been marked by confusion and complaints, with many patrons struggling to buy tickets to the 14-week run, which opens June 12.

Many standing in line outside the Kennedy Center for the March 26 general sale — the final round, after subscribers and members — grumbled about the way tickets were being distributed. Many members who hadn’t been able to get tickets at the early-access sale in February came back for a second try. Other members complained that the arts center manipulated them into buying premium seats — which topped out at more than $700 each if purchased online — because they thought it was their only opportunity. But a month later, many $99-to-$199 tickets were still available.

Others, like Carol Burnett of Arlington, rose before dawn March 26, expecting most tickets to have been sold. They hadn’t been.

“The Kennedy Center handled the whole thing just horribly,” said Burnett, who left the arts center after seven hours in line with four tickets and loads of criticism. “The demand is going to be there. It wasn’t a show you needed to convince us to come and see. Why all the manipulation?”

The biggest complaint was that the Kennedy Center encouraged buying a membership to get tickets, but then there weren’t enough tickets to satisfy them.

“We were told to become a member and get first crack at the tickets until they sold out — not until they cut them off arbitrarily,” Burnett said.

Kennedy Center officials declined repeated requests for comment about the sales. They would not disclose how many members were eligible for priority pre-sale and how many tickets had been set aside for them.

“Membership, a philanthropic contribution, is never advertised as a guarantee to those tickets,” Kennedy Center spokesman Brendan Padgett said in an email. “We are always open to new members joining, as membership is not tied to any particular piece of programming.”

Many patrons — even those who ended up getting tickets — were unhappy that the Kennedy Center hadn’t provided better information about the two sales.

“Why the secrecy? Did they sell 200,000 tickets to members? How much chance do we really have?” Burnett asked. “We wanted to make personal assessments.”

Selling tickets to massively popular shows such as “Hamilton” is difficult, experts say. Although the top ticket price is steep, many seats were made available at a below-market price, said Eric Budish, a professor of economics at the University of Chicago’s Booth School of Business. There are many reasons to do that — including wanting to make the show more accessible to more people — but the consequence is that the demand for those tickets will be much higher than the supply.

The resale market is another issue. The Kennedy Center used tools to block brokers — including limiting the number of tickets to four per household and not offering instant e-tickets. Still, many tickets have been listed for upward of $2,500 on multiple resale websites.

Some of those tickets were probably purchased by brokers who bought $60 memberships, which would be a low-cost investment for the possibility of snagging four tickets sold below market value.

“I think what the Kennedy Center was trying to do with the members sale was find a way to allocate the . . . tickets in a way that was thoughtful and fair,” Budish said.

Other members were caught up in the hype of the pre-sale. One member who bought premium seats in February called the box office after noticing how many less expensive seats were still available.

“They were offering [priority sale] as a benefit,” said the member, who asked not to be identified because he felt tricked into buying the premium tickets. “But if I’m purchasing tickets that are undesirable, how is having early access to them helpful?”

Kennedy Center officials say that some “limited-view” tickets can still be purchased in person or by phone and that $625 premium seats are available for many shows. But that price is out of reach for many, including Nora Carroll of Silver Spring. Carroll received a Kennedy Center membership for Christmas, but after spending two days tied to her iPad trying to get tickets, she came away empty-handed. Both times, she said, only premium tickets were available.

“I assumed the members would wipe them out,” she said of the first sale. “More transparency would have been a nice thing.”

But Carroll said the blockbuster probably pushed the arts center to its limits. “There were some problems, for sure,” she said, “but I’m sympathetic.”