You are given an integer and a function such that
- the nonzero values of has period .
Consider the unique function such that
- when , then ;
- is differentiable everywhere.
- for a given complex number ;
- a complex number with a nonzero imaginary part such that .
You are further informed that
- The conditions of the function are equivalent to the conditions of being a primitive Dirichlet character.
- is the analytic continuation of the Dirichlet L-function onto the complex plane.
- Zeta functions can be analytically continued to any portion of the complex plane given by for real using the Euler-Maclaurin summation formula.
- If we let , and , and , then satisfies .
For the first question, the jury answer is precise to , and the magnitude of the difference between your answer and the jury answer should be less than .
For the second question, the checker is precise to , and the magnitude of of your answer should be less than .
The first line contains an integer, .
The next lines contain three nonnegative integers , , and each, representing respectively. The three integers correspond to .
The next line contains two real numbers, with at most digits after the decimal point, representing the real and imaginary parts of .
On the first line, output the real and imaginary parts for the first answer.
On the second line, output the real and imaginary parts for the second answer.
5 0 0 1 1 0 2 1 1 2 1 3 2 1 2 2 0.69 4.2069
1.5186663729999338699 -0.8641952653252008201 0.5000000000000000000 6.1835781954508539144
Explanation for Sample