  We give explicit expressions for the finite frequency greybody factor,
quasinormal modes and Love numbers of Kerr black holes by computing the exact
connection coefficients of the radial and angular parts of the Teukolsky
equation. This is obtained by solving the connection problem of the confluent
Heun equation in terms of the explicit expression of irregular Virasoro
conformal blocks as sums over partitions via the AGT correspondence. In the
relevant approximation limits our results are in agreement with existing
literature. The method we use can be extended to solve the linearized Einstein
equation in other interesting gravitational backgrounds.
