******* 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 fitting lowest state to lattice value.
Parity doublets (o,multi,state) with error for difference
  over average.
  ( 1, 5,0) and ( 1, 6,0), error 0.5
  (-1, 5,0) and (-1, 6,0), error 0.5
  ( 1, 7,0) and (-1, 4,0), 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 18 33.794500 -1.259736 6.329520
0.145309 1.000000 1.260070 0.176242 -0.220548 10.799089 0.262786 1.781729 -2.451335  2 3 4 5 6 7 8
0.287419 -0.708955 -0.663491  0.187547 -0.945905 -0.583851
1.828725 1.507462  -0.358564 -0.225346  0.244698 0.012351
 12.280000 12.329308 1.435226
 29.056974 29.069415 0.362114
 29.206610 29.244454 1.101538
 29.442783 29.449773 0.203467
 20.751532 20.761786 0.298472
 40.538831 40.556569 0.516320
 52.114937 52.109750 -0.150960
 55.282047 55.282269 0.006468
 20.751532 20.776402 0.723918
 32.742530 32.781132 1.123615
 40.538831 40.543386 0.132590
 52.114937 52.111336 -0.104804
 34.648460 34.670558 0.643218
 39.073035 39.061757 -0.328273
 47.936023 47.954339 0.533151
 53.272108 53.274865 0.080232
 12.280000 12.378672 1.436051
 29.056974 29.066819 0.143279
 30.125888 30.147016 0.307500
 34.648460 34.640540 -0.115269
 20.751532 20.776948 0.369898
 40.538831 40.560187 0.310805
 52.114937 52.105546 -0.136674
 54.431708 54.446045 0.208670
 20.751532 20.796373 0.652612
 32.742530 32.819735 1.123619
 40.538831 40.562106 0.338740
 52.114937 52.106928 -0.116559
 29.206610 29.281943 1.096384
 29.442783 29.471909 0.423892
 34.648460 34.640372 -0.117715
 37.836374 37.833227 -0.045811
12.280000 30.125888 29.056974 37.687670 
64.190055 65.002409 79.330766 76.660750 
59.006038 75.952296 94.985349 109.054536 
32.742530 55.982123 69.107028 76.387008 
29.206610 29.442783 37.836374 52.756159 
55.282047 63.628407 75.525978 77.425416 
39.073035 65.842842 76.471594 69.994596 
54.431708 70.471506 75.501611 68.253890 
20.751532 40.538831 55.485641 52.114937 
34.648460 47.936023 53.272108 61.126808 


2 11 81.221481 -0.854603 4.645677
0.192168 1.000000 0.772506 -0.224938 -0.278557 19.142169 -0.103180 4.767502 -1.513213  2 3 4 5 6 7 8
0.446440 -0.483542 -0.734060  0.206078 -0.409503 -0.376994
4.662684 2.996223  0.399500 0.392773  0.937930 0.615307
 12.280000 12.327633 1.580651
 21.885415 21.910683 0.838498
 28.114467 28.129498 0.498792
 28.294675 28.248186 -1.542706
 22.016637 22.028027 0.377980
 41.914476 41.927020 0.416265
 48.850471 48.857184 0.222781
 48.995493 48.971142 -0.808069
 22.016637 22.028047 0.378664
 33.359342 33.370629 0.374545
 41.914476 41.933858 0.643186
 48.850471 48.852325 0.061538
 30.404438 30.419433 0.497625
 34.310837 34.301481 -0.310482
 43.969285 43.986937 0.585746
 49.447734 49.431711 -0.531706
 12.280000 12.375242 1.580263
 28.114467 28.143197 0.476692
 28.294675 28.201483 -1.546264
 30.404438 30.429850 0.421646
 22.016637 22.041976 0.420431
 41.914476 41.947945 0.555324
 48.850471 48.859278 0.146137
 48.995493 48.987749 -0.128480
 22.016637 22.036894 0.336113
 33.359342 33.381920 0.374612
 41.914476 41.944879 0.504448
 48.850471 48.858823 0.138582
 21.885415 21.935987 0.839090
 28.488806 28.524452 0.591450
 30.404438 30.382073 -0.371073
 32.524059 32.541783 0.294077
12.280000 28.294675 28.114467 32.533736 
57.039226 60.958772 68.569161 72.178175 
52.200181 73.121865 71.286770 91.958791 
33.359342 51.760928 64.090495 69.593510 
21.885415 28.488806 32.524059 44.471467 
49.268791 59.880684 67.843828 70.809075 
34.310837 62.667741 66.788986 66.696917 
54.336888 67.528776 66.573608 69.762929 
22.016637 41.914476 48.850471 48.995493 
30.404438 43.969285 49.447734 54.974073 


2 18 46.646797 -1.405269 5.073936
0.250000 1.000000 1.748421 0.405609 -0.269656 7.037470 0.447642 1.013783 -1.291602  2 3 4 5 6 7 8
0.306327 -0.431433 -1.815354  0.221218 -0.237087 -0.078228
1.847818 1.792268  0.670886 0.652926  1.185631 0.848245
 12.280000 12.332550 1.306855
 21.836274 21.882660 1.153542
 23.557737 23.553702 -0.100351
 28.536499 28.549399 0.320824
 17.288376 17.294879 0.161737
 33.500393 33.512612 0.303871
 43.883751 43.893046 0.231166
 46.248574 46.253272 0.116839
 17.288376 17.307842 0.484109
 30.266462 30.305157 0.962294
 33.500393 33.505034 0.115413
 43.883751 43.890813 0.175632
 33.796257 33.814526 0.454337
 37.519373 37.509679 -0.241083
 41.564520 41.577856 0.331644
 47.310426 47.316088 0.140811
 12.280000 12.385049 1.306214
 23.557737 23.549514 -0.102256
 28.536499 28.561775 0.314298
 33.796257 33.911916 1.438143
 17.288376 17.304473 0.200161
 33.500393 33.515930 0.193187
 43.883751 43.889503 0.071522
 45.754972 45.757374 0.029869
 17.288376 17.324234 0.445867
 30.266462 30.343837 0.962103
 33.500393 33.518604 0.226437
 43.883751 43.910508 0.332711
 21.836274 21.928726 1.149571
 28.764225 28.783852 0.244046
 33.796257 33.916444 1.494445
 38.668299 38.641913 -0.328097
12.280000 23.557737 28.536499 38.628610 
55.387431 56.474868 65.039826 63.125695 
52.739807 74.359270 71.515506 72.688702 
30.266462 49.361680 58.086653 70.991278 
21.836274 28.764225 38.668299 39.679469 
48.238619 54.781905 62.471929 63.266369 
37.519373 53.257952 65.479631 73.180223 
45.754972 56.882790 66.107006 68.694011 
17.288376 33.500393 46.248574 43.883751 
33.796257 41.564520 47.310426 54.443862