******* 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 (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 10 33.359331 -0.938174 7.871422
0.032492 1.000000 0.595102 -0.069389 -0.207835 19.861147 0.098758 3.508270 -1.896179  2 3 4 5 6 7 8
0.190481 -0.894129 0.520560  0.195719 -1.146890 -0.607655
1.439887 0.694790  -0.543335 -0.387462  -0.043657 -0.135756
 6.571280 6.625102 1.291163
 12.054132 12.090861 0.881129
 13.680622 13.709686 0.697239
 24.812903 24.760119 -1.266267
 22.506417 22.536469 0.720938
 41.576759 41.605053 0.678751
 45.422594 45.459337 0.881450
 51.606104 51.611246 0.123339
 22.506417 22.529525 0.554352
 29.161394 29.189502 0.674301
 41.576759 41.597632 0.500734
 45.422594 45.431639 0.216966
 24.812903 24.843066 0.723601
 31.263697 31.251076 -0.302774
 46.212922 46.213641 0.017236
 46.272347 46.308114 0.858054
 6.571280 6.678950 1.291491
 13.680622 13.739107 0.701521
 24.812903 24.755180 -0.692379
 26.793414 26.748456 -0.539268
 22.506417 22.558569 0.625554
 41.576759 41.616822 0.480548
 45.422594 45.459392 0.441382
 57.683792 57.673834 -0.119440
 22.506417 22.560648 0.650495
 29.161394 29.217633 0.674568
 41.576759 41.634859 0.696900
 45.422594 45.477361 0.656916
 12.054132 12.127237 0.876890
 24.812903 24.825947 0.156462
 26.937131 26.885698 -0.616931
 36.287625 36.323158 0.426208
6.571280 13.680622 26.793414 32.791158 
61.699314 62.862291 81.059237 76.866555 
55.704989 75.951343 79.204596 94.894035 
29.161394 54.550933 60.373186 89.695047 
12.054132 26.937131 36.287625 40.329816 
51.606104 61.588124 78.815948 81.954550 
31.263697 64.924659 71.881677 87.428119 
57.683792 72.084723 80.136014 73.659141 
22.506417 41.576759 45.422594 64.377245 
24.812903 46.272347 46.212922 57.318879 

2 11 32.010233 -1.230918 8.191404
0.051777 1.000000 0.759751 -0.075265 -0.139860 8.559161 0.157577 1.847000 -3.702121  2 3 4 5 6 7 8
0.241775 -0.801668 0.230336  0.202789 -0.443086 -0.313546
1.901213 1.161325  0.272558 0.512936  0.712997 0.813732
 11.561644 11.600514 1.231729
 21.509342 21.529750 0.646682
 21.880119 21.901207 0.668249
 29.192075 29.199037 0.220601
 25.170016 25.186918 0.535572
 47.577938 47.605513 0.873771
 54.325187 54.351506 0.833968
 60.186923 60.180804 -0.193885
 25.170016 25.196001 0.823388
 35.321509 35.353146 1.002489
 47.577938 47.581238 0.104548
 54.325187 54.340429 0.482965
 30.300181 30.324367 0.766426
 35.359221 35.345032 -0.449616
 52.978280 53.000765 0.712513
 53.244437 53.253548 0.288718
 11.561644 11.639420 1.232269
 21.880119 21.921724 0.659182
 29.192075 29.181267 -0.171236
 30.300181 30.413363 1.793235
 25.170016 25.204170 0.541123
 47.577938 47.605064 0.429776
 54.325187 54.349918 0.391823
 63.079026 63.096213 0.272313
 25.170016 25.221662 0.818260
 35.321509 35.384795 1.002688
 47.577938 47.612502 0.547629
 54.325187 54.383167 0.918620
 21.509342 21.550661 0.654648
 29.249779 29.241415 -0.132516
 30.300181 30.293358 -0.108100
 32.001169 32.176034 2.770540
11.561644 21.880119 29.192075 34.282707 
69.816940 71.488439 90.734466 90.476604 
60.537576 91.804895 91.056670 110.189700 
35.321509 60.452627 74.722881 99.299644 
21.509342 32.001169 29.249779 47.936785 
60.186923 69.356741 88.699103 90.778056 
35.359221 78.612613 73.228798 105.352187 
63.079026 73.677287 85.832678 99.460612 
25.170016 47.577938 54.325187 69.898007 
30.300181 52.978280 53.244437 65.765799 

2 43 33.575551 -0.851791 5.983799
0.076429 1.000000 0.763352 0.046134 -0.273601 13.576367 0.041128 3.880680 -2.207218  2 3 4 5 6 7 8
0.257283 -0.906843 0.164779  0.186163 -1.105626 -0.770765
1.677293 1.172018  -0.567389 -0.491768  -0.072690 -0.277899
 6.546851 6.604407 1.417756
 20.755073 20.794201 0.963813
 22.496586 22.480147 -0.404923
 25.491021 25.558353 1.658548
 19.239753 19.258299 0.456832
 36.165939 36.184705 0.462248
 43.947229 43.966500 0.474700
 46.647825 46.660136 0.303251
 19.239753 19.262202 0.552977
 25.846201 25.872215 0.640792
 36.165939 36.182058 0.397033
 43.947229 43.937091 -0.249726
 27.083877 27.107381 0.578953
 32.048392 32.041030 -0.181346
 40.847174 40.873874 0.657681
 46.502672 46.491383 -0.278072
 6.546851 6.661935 1.417412
 22.496586 22.463341 -0.409449
 27.083877 27.119775 0.442120
 27.962688 27.982695 0.246410
 19.239753 19.280795 0.505487
 36.165939 36.201280 0.435268
 43.947229 43.950762 0.043521
 49.816043 49.906794 1.117710
 19.239753 19.280701 0.504329
 25.846201 25.898239 0.640912
 36.165939 36.200399 0.424408
 43.947229 43.962213 0.184554
 20.755073 20.833287 0.963299
 25.491021 25.624421 1.642979
 27.083877 27.071356 -0.154213
 31.610238 31.608180 -0.025351
6.546851 22.496586 27.962688 31.773676 
55.539448 57.930487 72.165017 70.069316 
52.290959 75.414531 75.781365 82.859150 
25.846201 49.231168 58.440302 71.563543 
20.755073 25.491021 31.610238 39.233156 
46.647825 57.150505 67.273206 71.037307 
32.048392 60.267003 55.938587 86.224450 
49.816043 59.507203 62.427886 82.403006 
19.239753 36.165939 43.947229 52.813787 
27.083877 40.847174 46.502672 52.747555 

2 11 38.447352 -1.046314 5.886881
0.107240 1.000000 0.865872 -0.032739 -0.173140 14.019979 0.060765 2.964501 -2.302870  2 3 4 5 6 7 8
0.333494 -0.690544 -0.313412  0.190052 -1.067395 -0.699798
2.702667 1.938233  -0.484864 -0.360041  0.102935 -0.113862
 11.618425 11.663584 1.418542
 26.559824 26.588250 0.892920
 28.718134 28.715616 -0.079073
 29.164014 29.178602 0.458245
 21.712733 21.723996 0.353777
 41.424619 41.441483 0.529731
 51.441401 51.466729 0.795589
 52.421105 52.432845 0.368792
 21.712733 21.734219 0.674896
 31.683107 31.706040 0.720355
 41.424619 41.432064 0.233862
 51.441401 51.434985 -0.201556
 31.033422 31.051827 0.578143
 34.839159 34.828836 -0.324271
 45.714983 45.737111 0.695083
 51.246876 51.229524 -0.545078
 11.618425 11.708739 1.418472
 28.718134 28.710250 -0.123819
 29.626634 29.576164 -0.792672
 31.033422 31.107660 1.165974
 21.712733 21.741619 0.453682
 41.424619 41.450055 0.399498
 51.441401 51.442242 0.013203
 54.006391 54.003813 -0.040484
 21.712733 21.749330 0.574780
 31.683107 31.728981 0.720486
 41.424619 41.447846 0.364813
 51.441401 51.479126 0.592508
 26.559824 26.616819 0.895158
 29.164014 29.195862 0.500197
 31.033422 30.990205 -0.678759
 32.631539 32.673820 0.664062
11.618425 29.626634 28.718134 32.764718 
61.116651 63.611287 77.251224 75.744737 
54.920895 74.819897 93.239908 84.939040 
31.683107 53.383779 67.016558 67.266580 
26.559824 29.164014 32.631539 44.690833 
52.421105 62.451553 73.122298 76.379185 
34.839159 65.269028 67.711030 80.113105 
54.366522 69.903825 69.650609 84.610072 
21.712733 41.424619 51.441401 54.006391 
31.033422 45.714983 51.246876 57.846593