******* Eigenvalues for the 3+1 transverse lattice  *******
Couplings:  m^2, G^2 N, t/a^2, la_1/a^2, la_2/a^2
             0     1       2      3         4    
           la_3/a^2, la_4/a^2, la_5/a^2, tau     
             5        6         7         8      
Use chi^2 fit with 39 criteria and tolerance 0.01.
Overall scale from minimizing chi^2.
Parity doublets (multi,o,state) with fractional error
  ( 5, 1,0) and ( 6, 1,0), error 0.5
  ( 5,-1,0) and ( 6,-1,0), error 0.5
  ( 7, 1,0) and ( 4,-1,0), error 0.5
Spectrum for P_perp a = (0,0), ( 0.25 0)
  using (# states, multiplet, o, c^2 error for each) =
  (4,  9 &  8,  1 & -1, 0.25 2 2 2)
  (4,  8 &  9,  1 & -1, 0.25 2 2 2)
  (4,  7 & 10,  1 & -1, 0.25 2 2 2)
  (4, 10 &  7,  1 & -1, 0.25 2 2 2)
Spectrum for P_perp a = (0,0), ( 0.25 0.25)
  using (# states, multiplet, o, c^2 error for each) =
  (4, 11 & 12,  1 & -1, 0.25 2 2 2)
  (4, 12 & 11,  1 & -1, 0.25 2 2 2)
  (4, 14 & 13,  1 & -1, 0.25 2 2 2)
  (4, 13 & 14,  1 & -1, 0.25 2 2 2).
Ordinary spectra multiplets, 4 states, (o,multiplet) = ( 1,  3) 
  (-1,  3)  ( 1,  4)  (-1,  4)  ( 1,  5)  (-1,  5)  ( 1,  6) 
  (-1,  6)  ( 1,  7)  (-1,  7) .
All spectra extrapolated using (K,p) = (16/2,8)  (16/2,6) 
  (20/2,6)  (26/2,6) .
Winding potential using (n,K,p) = ( 2 0,20/2,4)  ( 2 0,20/2,6) 
  ( 2 0,24/2,4)  ( 2 0,32/2,4)  ( 3 0,19/2,5)  ( 3 0,19/2,7) 
  ( 3 0,25/2,5)  ( 3 0,33/2,5)  ( 4 0,18/2,6)  ( 4 0,18/2,8) 
  ( 4 0,24/2,6)  ( 4 0,32/2,6) .
Roundness of winding using n = (2,2) and (K,p) = (16/2,6) 
  (16/2,8)  (24/2,6)  (28/2,6) 
  with error 0.3 (in G^2 N^2 units).
Heavy potential determined using (n,K,p,K_max) = ( 0 0,-34/2,2,4) 
  ( 0 0,-34/2,4,4)  ( 0 0,-34/2,2,5)  ( 0 0,-40/2,2,4) 
  ( 0 0,-50/2,2,5)  ( 0 0,-60/2,2,4)  ( 0 0,-60/2,2,6) ,
  L = 3 4 6 (all in G^2 N^2 units); with relative error=0.25.
Roundness determined using (n,K,p,K_max) = ( 1 0,-17/2,3,4) 
  ( 1 0,-17/2,5,4)  ( 1 0,-17/2,3,5)  ( 1 0,-33/2,3,4) 
  ( 1 0,-33/2,3,5)  ( 1 0,-55/2,3,4)  ( 1 0,-55/2,3,6) ,
  L=3 and error 0.3
  ( 1 1,-30/2,2,4)  ( 1 1,-30/2,4,4)  ( 1 1,-30/2,2,5) 
  ( 1 1,-40/2,2,4)  ( 1 1,-50/2,2,5)  ( 1 1,-60/2,2,4) 
  ( 1 1,-60/2,2,6) ,
  with L=3 and error 0.3 (all in G^2 N^2 units).
p-extrapolation using n=( 1 0) and (K,p) = (13/2,3)  (35/2,3) 
  (13/2,5)  (29/2,5)  (13/2,7)  (17/2,7) .
Result format:
 fit info, # steps, chi^2, and p damping, scale g^2 N/(a^2 sigma);
 the 9 couplings  (G^2 N units) and which--if any--were fit;
 winding and longitudinal string tension fits;
 the n=(2,2) winding eigenvalue and
   the n=(1,0) (1,1) longitudinal eigenvalues (G^2 N units)
   showing measured value and derived value for each.
 In each direction, the spectra for each P_perp*a and c^2 values.
 Finally come the states for the ordinary spectra.

2 35 65.492544 -1.247804 8.337809
0.051777 1.000000 0.967683 0.011722 -0.094739 9.475637 0.259780 2.592820 -2.359694  2 3 4 5 6 7 8
0.189322 -1.097888 0.554713  0.183910 -1.223731 -0.734538
0.484865 0.486030  -0.744938 -0.513987  -0.196663 -0.254284
 3.010383 3.043036 0.824692
 19.386019 19.410869 0.627614
 23.015415 23.001774 -0.344528
 23.334150 23.428580 2.384989
 20.119060 20.132709 0.344723
 37.888459 37.919596 0.786400
 46.857795 46.883351 0.645449
 53.607200 53.591124 -0.406007
 20.119060 20.151399 0.816775
 27.343148 27.397024 1.360726
 37.888459 37.874330 -0.356843
 46.857795 46.887454 0.749072
 24.657092 24.679906 0.576215
 29.695502 29.684147 -0.286777
 44.792811 44.803947 0.281265
 46.568919 46.595396 0.668721
 3.010383 3.075719 0.825077
 19.386019 19.435367 0.623175
 23.334150 23.380718 0.588083
 24.657092 24.962026 3.850791
 20.119060 20.158382 0.496566
 37.888459 37.902164 0.173065
 46.857795 46.883435 0.323783
 52.276557 52.308981 0.409457
 20.119060 20.171790 0.665892
 27.343148 27.450845 1.360033
 37.888459 37.908802 0.256894
 46.857795 46.941255 1.053956
 23.015415 22.985255 -0.380867
 23.380441 23.658736 3.514386
 23.557074 23.732591 2.216474
 24.657092 24.569424 -1.107096
3.010383 19.386019 23.334150 29.754926 
62.338546 63.949659 83.580283 81.455583 
53.519587 87.334742 88.675396 91.407131 
27.343148 52.438606 64.657486 80.779900 
23.015415 23.380441 23.557074 39.817437 
53.607200 61.282702 81.017720 81.515644 
29.695502 68.934677 61.272402 105.718623 
52.276557 62.873335 77.365216 96.372432 
20.119060 37.888459 46.857795 65.945846 
24.657092 44.792811 46.568919 58.779247