c  =  299792458

Dia  =  0.0254

Len  =  0.0254

{W,  Q}  =  {1,  30}

{M,  Nn,  P}  =  {10,  3,  5}

$MachinePrecision

DP  =  6

BesselJRootsTM  =  
      Table[N[Union[
            Round[10^DP Select[
                    x  /. Table[
                        FindRoot[
                          BesselJ[m, x] == 0, {x,  
                            W (i  +  
                                  1/2)},   AccuracyGoal  ->  
                            AG],  {i, 0,  Q,  1}],  #  >  1  &]]/ 
              10^DP]],  {m,  0,  M, 1}]

BesselJRootsTM  =  
      Table[N[Union[
            Round[10^DP Select[
                    x  /. Table[
                        FindRoot[
                          BesselJ[m, x] == 0, {x,  
                            W (i  +  1/2)}],  {i, 0,  Q,  
                          1}],  #  >  1  &]]/ 10^DP]],  {m,  0,  M, 
          1}]

D[BesselJ[y, x], x]

BesselJRootsTE  = 
      Table[N[Union[
            Round[10^DP Select[
                    x  /. Table[
                        FindRoot[(BesselJ[m - 1, x]  -  
                                BesselJ[m + 1, x]) == 0, {x,  
                            W (i  +  
                                  1/2)},   AccuracyGoal  ->  
                            AG],  {i, 0,  Q,  1}],  #  >  1  &]]/ 
              10^DP]],  {m,  0,  M, 1}]

FrequencyTableGHz  =  {TableForm[
          Table[{ TextForm[{TM,  m, n + 1, p}],  
              NumberForm[
                c Sqrt[(BesselJRootsTM[[m  +  1, n  +  1]]/
                              Pi)^2  +  (p Dia / (2 Len))^2]/ (Dia 10^9),  10]}, {m, 0, M, 1}, {n, 0, Nn, 1}, {p, 0, P, 
              1}]], 
TableForm[
          Table[{ TextForm[{TE,  m, n + 1, p}],  
              NumberForm[
                c Sqrt[(BesselJRootsTE[[m  +  1, n  +  1]]/
                              Pi)^2  +  (p Dia / (2 Len))^2]/ (Dia 10^9),  10]}, {m, 0, M, 1}, {n, 0, Nn, 1}, {p, 0, P, 
              1}]]}