******* 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 1 (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=1.
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 1
  ( 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 1 (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 44 16.206431 -1.345474 8.604610
0.032492 1.000000 0.638347 -0.025629 -0.154774 8.437317 0.136438 1.342864 -1.617216  2 3 4 5 6 7 8
0.215659 -0.819607 0.417663  0.198827 -0.781424 -0.415661
1.735911 0.957873  -0.124505 0.128870  0.363387 0.425702
 12.280000 12.325470 1.350032
 20.992341 21.021091 0.853586
 21.648158 21.676219 0.833152
 30.761872 30.791291 0.873492
 25.076104 25.097961 0.648957
 48.177696 48.208766 0.922470
 54.353991 54.385094 0.923475
 60.570835 60.567807 -0.089877
 25.076104 25.100991 0.738934
 33.924197 33.953882 0.881370
 48.177696 48.189607 0.353642
 54.353991 54.367386 0.397717
 30.761872 30.788702 0.796624
 36.328218 36.314265 -0.414253
 54.133414 54.161273 0.827169
 54.623824 54.631185 0.218539
 12.280000 12.370979 1.350614
 21.648158 21.702760 0.810585
 30.761872 30.805821 0.652441
 33.044564 33.089444 0.666245
 25.076104 25.115689 0.587663
 48.177696 48.213044 0.524746
 54.353991 54.386082 0.476402
 64.608129 64.612108 0.059071
 25.076104 25.130050 0.800857
 33.924197 33.983582 0.881593
 48.177696 48.228172 0.749325
 54.353991 54.410626 0.840763
 20.992341 21.051376 0.876380
 30.761872 30.776459 0.216556
 32.620061 32.593885 -0.388594
 34.718926 34.789965 1.054597
12.280000 21.648158 33.264093 33.044564 
70.475131 72.589290 91.973726 91.900652 
62.912850 89.115268 91.077505 114.153488 
33.924197 61.628312 72.476443 100.735204 
20.992341 34.718926 32.620061 48.702932 
60.570835 70.372139 89.814726 92.195255 
36.328218 77.621560 75.106902 106.415749 
64.608129 79.329037 91.719956 86.230958 
25.076104 48.177696 54.353991 71.277810 
30.761872 54.133414 54.623824 65.678710 

2 18 17.158721 -1.240409 8.523168
0.051777 1.000000 0.756663 -0.078985 -0.140706 8.847381 0.168940 1.799150 -4.158906  2 3 4 5 6 7 8
0.236178 -0.798412 0.240545  0.208737 -3.729105 -0.998047
1.917674 1.121082  -3.168680 -2.856685  -2.025746 -2.506982
 12.280000 12.321467 1.335567
 21.061067 21.084609 0.758248
 21.426183 21.451766 0.823971
 30.236193 30.263113 0.867041
 26.163503 26.182493 0.611615
 49.533021 49.562408 0.946458
 55.851974 55.880557 0.920599
 62.420829 62.415934 -0.157650
 26.163503 26.189572 0.839628
 36.989849 37.022486 1.051135
 49.533021 49.540419 0.238270
 55.851974 55.867141 0.488507
 31.392996 31.419383 0.849887
 36.878916 36.863678 -0.490793
 54.691388 54.699964 0.276199
 55.293707 55.319413 0.827930
 12.280000 12.362975 1.336214
 21.426183 21.476395 0.808610
 30.236193 30.222942 -0.213394
 31.392996 31.464834 1.156874
 26.163503 26.199104 0.573309
 49.533021 49.563957 0.498186
 55.851974 55.880617 0.461272
 65.875410 65.888157 0.205272
 26.163503 26.218056 0.878516
 36.989849 37.055137 1.051378
 49.533021 49.575550 0.684869
 55.851974 55.910434 0.941442
 21.061067 21.109135 0.774093
 30.388945 30.387167 -0.028636
 31.392996 31.380654 -0.198746
 34.420005 34.563349 2.308405
12.280000 21.426183 30.236193 35.648713 
72.066966 74.148083 93.824858 93.932922 
63.019408 95.382017 94.101811 115.719112 
36.989849 62.987038 77.991674 103.300025 
21.061067 34.420005 30.388945 49.495708 
62.420829 71.645684 92.187820 94.233927 
36.878916 82.059444 76.480685 109.752931 
65.875410 76.405530 89.918055 103.056984 
26.163503 49.533021 55.851974 72.681657 
31.392996 55.293707 54.691388 68.364838 

2 10 36.343728 -1.088230 6.658185
0.076429 1.000000 0.720115 -0.036097 -0.119606 15.214119 0.024745 4.329032 -2.893481  2 3 4 5 6 7 8
0.321139 -0.729583 -0.026882  0.195386 -1.904887 -0.833129
2.582390 1.836166  -1.341260 -1.135873  -0.608073 -0.844922
 12.280000 12.323372 1.483815
 28.192259 28.229401 1.270679
 29.747903 29.693202 -1.871399
 31.248274 31.286134 1.295232
 23.623153 23.634867 0.400745
 44.879693 44.899109 0.664226
 54.679188 54.688257 0.310259
 56.343472 56.349401 0.202829
 23.623153 23.646066 0.783856
 32.656905 32.678689 0.745256
 44.879693 44.883495 0.130068
 54.679188 54.649660 -1.010196
 32.110824 32.127552 0.572267
 35.609133 35.599250 -0.338120
 48.858255 48.880834 0.772457
 55.164854 55.135617 -1.000244
 12.280000 12.366734 1.483643
 29.747903 29.637454 -1.889301
 32.110824 32.291592 3.092133
 33.662484 33.651990 -0.179506
 23.623153 23.655749 0.557571
 44.879693 44.905587 0.442927
 54.679188 54.659991 -0.328391
 58.642008 58.739431 1.666479
 23.623153 23.659787 0.626648
 32.656905 32.700479 0.745360
 44.879693 44.900307 0.352612
 54.679188 54.658742 -0.349753
 28.192259 28.265657 1.255510
 31.248274 31.326738 1.342177
 32.110824 32.048500 -1.066103
 33.430004 33.504656 1.276965
12.280000 29.747903 33.780726 33.662484 
66.202715 68.827342 84.576848 82.994849 
58.230922 87.494680 88.148985 88.596571 
32.656905 56.792039 70.792095 82.038383 
28.192259 31.248274 33.430004 48.540009 
56.343472 67.824849 79.357639 83.356448 
35.609133 70.785341 69.399779 93.327087 
58.642008 74.102002 73.081490 92.392502 
23.623153 44.879693 54.679188 60.852259 
32.110824 48.858255 55.164854 61.723420 

2 10 31.115120 -1.068661 5.974807
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
0.335848 -0.677620 -0.322523  0.190705 -1.069428 -0.689675
2.774333 1.968850  -0.481027 -0.346271  0.113953 -0.094367
 12.280000 12.325380 1.456980
 27.109811 27.139389 0.949622
 29.232250 29.227664 -0.147232
 29.786585 29.800975 0.461997
 22.168516 22.179841 0.363584
 42.448498 42.465501 0.545919
 52.550642 52.577116 0.849984
 53.538489 53.548846 0.332512
 22.168516 22.189930 0.687501
 32.468585 32.491366 0.731417
 42.448498 42.456157 0.245919
 52.550642 52.544992 -0.181389
 31.784475 31.802978 0.594084
 35.628320 35.617832 -0.336712
 46.799645 46.821837 0.712509
 52.312754 52.295973 -0.538776
 12.280000 12.370758 1.456934
 29.232250 29.220462 -0.189235
 30.330289 30.288529 -0.670377
 31.784475 31.853546 1.108814
 22.168516 22.197252 0.461293
 42.448498 42.474297 0.414157
 52.550642 52.553636 0.048073
 54.916338 54.913152 -0.051147
 22.168516 22.205244 0.589588
 32.468585 32.514156 0.731554
 42.448498 42.472069 0.378393
 52.550642 52.589931 0.630718
 27.109811 27.169075 0.951365
 29.786585 29.818149 0.506688
 31.784475 31.742941 -0.666741
 33.410986 33.450647 0.636666
12.280000 30.330289 29.232250 33.536149 
62.439615 64.771424 78.771410 77.164542 
56.041948 76.383953 94.978025 86.566871 
32.468585 54.500616 68.405490 68.931401 
27.109811 29.786585 33.410986 45.724797 
53.538489 63.676958 74.589000 77.843338 
35.628320 66.639322 69.350295 81.393787 
55.579159 71.340282 71.240224 85.885979 
22.168516 42.448498 52.550642 54.916338 
31.784475 46.799645 52.312754 58.968517