I am trying to find eigenvalues using jacobian diagonalisation. Where am I going wrong?

Question

So I am trying to calculate the eigenvalues of a matrix using Jacobian diagonalisation. This is the math I am following:

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So I first calculate the tau, s, c and t values from the first function and then I find the maximum value of the upper triangle matrix A. using that I find what A'kk,A'kl,A'll should be. the formula i am using is given in the image I provided above.

import numpy as np

# finding tau,s,c,t
def t(A, k, l):
    arg = []
    phi = (-A[k, k] + A[l, l]) / (2 * A[k, l])
    if phi >= 0:
        t = 1 / (abs(phi) + ((phi**2 + 1)) ** 0.5)
    else:
        t = -1 / (abs(phi) + ((phi**2 + 1)) ** 0.5)
    c = 1 / (1 + t**2) ** 0.5
    s = t * c
    tau = s / (1 + c)
    arg.append(phi)
    arg.append(t)
    arg.append(c)
    arg.append(s)
    arg.append(tau)
    return arg


A = np.array(
    [[1, (2) ** 0.5, 2], [2**0.5, 3, 2**0.5], [2, 2**0.5, 1]], dtype=float
)
arg = []


while True:
    # finding the max value
    n = len(A)
    A1 = np.zeros((n, n))
    for i in range(n):
        for j in range(n):
            if j > i:
                A1[i, j] = A[j, i]
    max_value = np.max(np.abs(A1))
    max_row, max_col = np.unravel_index(np.argmax(np.abs(A1)), A1.shape)

    k = max_row
    l = max_col

    # finding A'kk, A'kl,A'lk

    if abs(A[k, l]) > 0.0011:
        arg = t(A, k, l)
        A[k, k] = A[k, k] - arg[1] * A[k, l]
        A[l, l] = A[l, l] + arg[1] * A[k, l]
        A[k, l] = A[l, k] = 0
        # finding the other elements
        for i in range(n):
            if i != k and i != l:
                A[k, i] = A[i, k] = A[k, i] - arg[3] * (A[l, i] + arg[4] * A[k, i])
                A[l, i] = A[i, l] = A[l, i] + arg[3] * (A[k, i] - arg[4] * A[l, i])
    else:
        break
print(A)