******* 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 11 44.327224 -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 1.483814
 28.192259 28.229401 1.270679
 29.747903 29.693202 -1.871398
 31.248274 31.286134 1.295233
 23.623153 23.634867 0.400746
 44.879693 44.899109 0.664226
 54.679188 54.688257 0.310259
 56.343472 56.349401 0.202829
 23.623153 23.646065 0.783856
 32.656905 32.678689 0.745258
 44.879693 44.883495 0.130069
 54.679188 54.649660 -1.010196
 32.110824 32.127552 0.572267
 35.609133 35.599250 -0.338121
 48.858255 48.880834 0.772458
 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 0.557570
 44.879693 44.905587 0.442927
 54.679188 54.659991 -0.328391
 58.642008 58.739431 1.666480
 23.623153 23.659787 0.626648
 32.656905 32.700479 0.745361
 44.879693 44.900307 0.352612
 54.679188 54.658742 -0.349753
 28.192259 28.265657 1.255511
 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 68.827341 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 19 37.827549 -1.074629 5.967376
0.107240 1.000000 0.871783 -0.037729 -0.166609 14.465067 0.065997 3.243182 -1.433255  2 3 4 5 6 7 8
0.336187 -0.675008 -0.329615  0.204953 -0.423185 -0.323427
2.774472 1.973283  0.340404 0.444763  0.813895 0.696811
 12.280000 12.324155 1.417306
 27.000648 27.031737 0.997939
 29.251458 29.247219 -0.136086
 29.627350 29.642892 0.498878
 22.117410 22.128431 0.353754
 42.327740 42.344702 0.544462
 52.421235 52.447258 0.835308
 53.413075 53.422252 0.294554
 22.117410 22.138857 0.688433
 32.445286 32.468150 0.733908
 42.327740 42.334572 0.219299
 52.421235 52.416630 -0.147818
 31.587557 31.605770 0.584614
 35.373635 35.363153 -0.336449
 46.634479 46.656281 0.699792
 52.061526 52.045185 -0.524519
 12.280000 12.368308 1.417270
 29.251458 29.238427 -0.209146
 30.125239 30.087190 -0.610653
 31.587557 31.654233 1.070090
 22.117410 22.145648 0.453204
 42.327740 42.352704 0.400660
 52.421235 52.424214 0.047809
 54.789167 54.785561 -0.057872
 22.117410 22.154096 0.588776
 32.445286 32.491023 0.734043
 42.327740 42.350411 0.363859
 52.421235 52.461731 0.649920
 27.000648 27.062811 0.997669
 29.627350 29.663091 0.573618
 31.587557 31.542378 -0.725098
 33.006703 33.050654 0.705387
12.280000 30.125239 29.251458 33.123531 
62.331720 64.467469 78.599806 76.886833 
55.697108 75.983249 94.823636 86.157629 
32.445286 54.269167 68.265599 68.852452 
27.000648 29.627350 33.006703 45.541502 
53.413075 63.429147 74.431850 77.634056 
35.373635 66.454258 69.220727 80.900845 
55.353469 71.111917 71.007321 85.725078 
22.117410 42.327740 52.421235 54.789167 
31.587557 46.634479 52.061526 58.771733 

2 43 44.719036 -1.266780 7.897615
0.032492 1.000000 0.556728 -0.051954 -0.216152 8.945256 0.105503 2.410712 -1.199355  2 3 4 5 6 7 8
0.204511 -0.783563 0.424074  0.206207 -0.493783 -0.249175
2.005820 0.905538  0.255270 0.414612  0.702318 0.675201
 12.280000 12.329086 1.268503
 14.960137 15.005907 1.182805
 16.184778 16.220308 0.918188
 28.532305 28.478770 -1.383483
 23.891093 23.920191 0.751942
 45.927530 45.956607 0.751439
 48.874540 48.909664 0.907687
 55.556548 55.561559 0.129518
 23.891093 23.909382 0.472629
 32.595391 32.617627 0.574632
 45.927530 45.953030 0.658984
 48.874540 48.881302 0.174735
 28.532305 28.558310 0.672018
 34.718189 34.706113 -0.312061
 49.481768 49.487415 0.145931
 51.206132 51.234305 0.728077
 12.280000 12.378124 1.267887
 16.184778 16.254080 0.895461
 28.532305 28.464685 -0.873735
 31.611877 31.574990 -0.476628
 23.891093 23.934347 0.558887
 45.927530 45.968501 0.529404
 48.874540 48.914494 0.516246
 62.246628 62.224137 -0.290607
 23.891093 23.942669 0.666417
 32.595391 32.639884 0.574904
 45.927530 45.995502 0.878285
 48.874540 48.918364 0.566261
 14.960137 15.053168 1.202065
 28.532305 28.544884 0.162539
 29.474416 29.713248 3.086001
 31.052941 31.010725 -0.545476
12.280000 16.184778 31.611877 32.288869 
64.716380 67.007155 84.260064 83.680272 
59.634518 82.026969 85.224234 100.667160 
32.595391 58.424774 67.955355 93.312406 
14.960137 29.474416 31.052941 44.833212 
55.556548 64.947697 83.063442 85.822728 
34.718189 72.278552 75.272065 93.556097 
62.246628 77.916395 81.867833 80.140186 
23.891093 45.927530 48.874540 66.072367 
28.532305 51.206132 49.481768 61.119305 

2 27 34.221087 -1.230851 8.698366
0.051777 1.000000 0.753180 -0.075180 -0.129180 8.740709 0.162566 1.901035 -1.315469  2 3 4 5 6 7 8
0.241526 -0.802072 0.230809  0.202366 -0.453367 -0.322308
1.898684 1.158987  0.257585 0.541770  0.699920 0.864638
 12.280000 12.321418 1.392237
 22.841100 22.862720 0.726742
 23.239283 23.261824 0.757692
 31.044772 31.054537 0.328267
 26.718198 26.736207 0.605358
 50.516707 50.546002 0.984744
 57.675242 57.703262 0.941853
 63.911607 63.905196 -0.215517
 26.718198 26.745792 0.927532
 37.498117 37.531746 1.130399
 50.516707 50.520360 0.122810
 57.675242 57.691395 0.542965
 32.193056 32.218822 0.866094
 37.577563 37.562478 -0.507068
 56.268851 56.292833 0.806155
 56.552303 56.561950 0.324292
 12.280000 12.362873 1.392850
 23.239283 23.283742 0.747224
 31.044772 31.033435 -0.190529
 32.193056 32.325320 2.222963
 26.718198 26.754530 0.610634
 50.516707 50.545641 0.486291
 57.675242 57.701596 0.442935
 66.989751 67.007894 0.304938
 26.718198 26.773100 0.922736
 37.498117 37.565388 1.130623
 50.516707 50.553609 0.620224
 57.675242 57.736801 1.034624
 22.841100 22.884908 0.736284
 31.112682 31.104402 -0.139151
 32.193056 32.185010 -0.135223
 34.106038 34.288992 3.074915
12.280000 23.239283 31.044772 36.420272 
74.137924 75.911798 96.349594 96.073556 
64.318805 97.501872 96.771598 116.915882 
37.498117 64.208719 79.354384 105.448221 
22.841100 34.106038 31.112682 50.901102 
63.911607 73.648919 94.187124 96.390642 
37.577563 83.483389 77.753653 111.926440 
66.989751 78.236455 91.147555 105.625026 
26.718198 50.516707 57.675242 74.219349 
32.193056 56.268851 56.552303 69.835673