from sys import argv
from math import pi
from math import e

function_formulas = [
    # 1. Square wave
    {
        'an': lambda n: 3 if n == 0 else 0,
        'bn': lambda n: 0 if n % 2 == 0 else 2 / (pi * n),
        'cn': lambda n: 3 if n == 0 else (0 if n % 2 == 0 else 1j / (pi * n))
    },
    # 2. Even func
    {
        'an': lambda n: 0 if n == 0 else (0 if n % 2 == 0 else 8 / (pi ** 2 * n ** 2)),
        'bn': lambda n: 0,
        'cn': lambda n: 0 if n == 0 else (0 if n % 2 == 0 else 4 / (pi ** 2 * n ** 2))
    },
    # 3. Odd func
    {
        'an': lambda n: 0,
        'bn': lambda n: 0 if n == 0 else 2 * (-1) ** (n + 1) / (pi * n),
        'cn': lambda n: 0 if n == 0 else (-1) ** n / (pi * n) if n > 0 else (-1) ** (n + 1) / (pi * n)
    },
    # 4. Not odd and not even func
    {
        'an': lambda n: -2/3 if n == 0 else (8 / (pi ** 2 * n ** 2) if n % 2 == 0 else 0),
        'bn': lambda n: 0 if n % 2 == 0 else -48 / (pi ** 3 * n ** 3),
        'cn': lambda n: -1/3 if n == 0 else (
            (4 / (pi ** 2 * n ** 2) if n % 2 == 0 else 24j / (pi ** 3 * n ** 3))
            if n > 0 else
            (4 / (pi ** 2 * n ** 2) if n % 2 == 0 else -24j / (pi ** 3 * n ** 3))
        )
    },
    # 5. Complex func
    {
        'an': lambda n: 0,
        'bn': lambda n: 0,
        'cn': lambda n: 0 if n == 0 else (
            complex(-pi * n / 4, -1 - pi * n / 4) * e ** (1j * pi * n / 4)
            + (1j + 1) * e ** (-1j * pi * n / 4)
            + (1j - 1) * e ** (-3j * pi * n / 4)
            + (-1j - 1) * e ** (-5j * pi * n / 4)
            + complex(1 + pi * n / 4, pi * n / 4) * e ** (-7j * pi * n / 4)
        ) / (pi ** 2 * n ** 2 / 2)
    }
]

index, nn = int(argv[1]), int(argv[2])

formulas = function_formulas[index - 1]
coefficients = {'an': [], 'bn': [], 'cn': []}

for coefficient in coefficients:
    for n in range(0, nn + 1):
        calc = formulas[coefficient](n)
        coefficients[coefficient].append(f'{n}: {calc:.5g}')
        if coefficient == 'cn' and n != 0:
            calc = formulas[coefficient](-n)
            coefficients[coefficient].insert(0, f'{-n}: {calc:.5g}')

for coefficient in coefficients:
    print(f'{coefficient} values: ', coefficients[coefficient])