def mean_x(factor, values):
    return sum([cos(2*pi*v/factor) for v in values])/len(values)

def mean_y(factor, values):
    return sum([sin(2*pi*v/factor) for v in values])/len(values)

def calculatePeriodAppeal(factor, values):
    mx = mean_x(factor, values)
    my = mean_y(factor, values)
    appeal = sqrt(mx^2+my^2)
    return appeal

def calculateBestLinear(factor, values):
    mx = mean_x(factor, values).n()
    my = mean_y(factor, values).n()
    y0 = factor*atan2(my,mx)/(2*pi).n()
    err = 1-sqrt(mx^2+my^2).n()
    return [factor*x + y0, err]

def calculateGCDAppeal(factor, values):
    mx = mean_x(factor, values)
    my = mean_y(factor, values)
    appeal = 1 - sqrt((mx-1)^2+my^2)/2
    return appeal