\begin{table}%t2
%\centering
\par
\caption {\label{mtfvt1} Detected transitions of the first torsionally excited state of HCOOCH$_3$ in W51~e2.}
\begin{tabular}{lcrrrrrrl}
\hline\hline
& Transition$^a$ &  $S{\mu}^2$ & ${E_{\rm l}}$ & Frequency  & Obs. Freq. $^b$ &
$\int {T_{\rm mb}}\Delta v^c$ & $T{\rm _{mb}}$  & Comment$^d$\\
&                &  (D$^2$)       & (cm$^{-1}$)       & (MHz)        & (MHz)               &  (K~km~s$^{-1}$)     &  (mK)                               &        \\
\hline
1(8) 		& 7(4, 4)--6(4, 3) A     	& 12.5  	& 146.86	&  85~327.104 	&  85~326.864 	& 1.22	& 87 	& 	\\
2(5)		& 7(4, 3)--6(4, 2) A     	& 12.5  	& 146.86 	&  85~360.669 	&  85~359.685 	& 0.40	& 81 	&  	\\
3 		& 7(3, 5)--6(3, 4) A     	& 15.1  	& 143.62 	&  85~371.762 	&  85~371.871 	& 0.67 	& 102 	&   	\\
4 		& 7(6, 2)--6(6, 1) E     	& 4.94  	& 155.53 	&  85~456.630 	&  85~456.067 	& 14.33	& 1133 	& CH$_3$CCH	 \\
5(2)		& 7(4, 3)--6(4, 2) E     	& 12.6  	& 146.60 	&  85~506.175 	&  85~506.053 	& 0.57 	& 84 	&  	\\
6 		& 7(5, 3)--6(5, 2) E    		& 9.12  	& 150.40 	&  85~553.365 	&  85~553.361 	& 0.54 	& 78 	&  	\\
7 		& 10(2, 9)--10(1, 10) A   	& 1.40  	& 151.83 	&  85~664.038 	&  85~664.621 	& 1.06 	& 61  	& C$_2$H$_3$CN \\
8(1) 		& 7(4, 4)--6(4, 3) E     	& 12.5  	& 146.22 	&  85~743.967 	&  85~743.915 	& 0.79 	& 102 	&  	\\
9(10)		& 7(2, 5)--6(2, 4) A   		& 17.0 	& 141.50 	&  88~998.368 	&  88~997.692 	& 0.77 	& 83  	&	\\
10(9) 	& 7(2, 5)--6(2, 4) E 		& 17.1  	& 141.01 	&  89~140.383 	&  89~140.161 	& 1.20 	& 120  	&	\\
11 		& 25(5, 20)--25(4, 21) A 	& 8.29  	& 274.84 	& 107~021.644 	& 107~021.862 	& 1.99	& 186   	&	\\
12 		& 9(2, 8)--8(2, 7) E     	& 22.6  	& 146.68 	& 107~022.162 	& 	--	 	&    --	&  --	 	& 	\\
13 		& 10(1, 9)--9(2, 8) A    	& 2.14  	& 150.76 	& 107~472.351 	& 107~472.400 	&  0.27 	&  45  	& 	\\
14 		& 9(3, 7)--8(3, 6) E     	& 20.8  	& 149.16 	& 111~005.617 	& 111~005.832 	&  2.67	&  261  	&	\\
15 		& 9(1, 8)--8(1, 7) E     	& 23.2  	& 146.08 	& 111~094.105 	& 111~094.010 	&  2.27	&  244  	& 	\\
16(17) 	& 12(0, 12)--11(0, 11) A 	& 31.4  	& 155.85 	& 131~536.624 	& 131~536.949 	&  3.53	&  407 	&  	\\
17(16)	& 12(0, 12)--11(0, 11) E 	& 31.6  	& 155.29 	& 131~612.344 	& 131~612.094 	&  3.97	&  410 	&   	\\
18 		& 12(1, 12)--11(0, 11) A 	& 4.87  	& 155.85 	& 131~764.316 	& 131~765.100  	& 1.70	&  100  	& S$^{18}$O	\\
19 		& 11(5, 7)--10(5, 6) A   	& 23.1  	& 164.85 	& 134~531.846 	& 134~531.411 	&  3.44	&  478 	& SO$_2$ $\upsilon_2=1$\\
20 		& 27(7, 20)--27(6, 21) A 	& 8.58  	& 304.51 	& 134~545.609 	& 134~546.431 	& 7.95	&  630  	& C$_3$H$_2$CN + $^{33}$SO$_2$\\
21 		& 11(7, 5)--10(7, 4) E   	& 17.4  	& 175.45 	& 134~545.615 	& 	--	 	&  --		&  --   	& -- \\
22 		& 35(8, 27)--35(7,28) A 	& 12.6  	& 416.62 	& 134~553.290 	& 134~553.647	&  0.71	&  991 	& $^{33}$SO$_2$ \\
23(25) 	& 11(5, 6)--10(5, 5) A  	& 23.1  	& 164.85 	& 134~585.070 	& 134~584.263 	&  4.68	&  382  	& C$_3$H$_2$CN$\upsilon_{\rm t}$, $\upsilon_{\rm b}=1$ and ?\\
24 		& 11(3, 9)--10(3, 8) E   	& 26.7  	& 156.97 	& 134~713.629 	& 134~713.062 	&  3.59 	&  456  	&  	\\
25(23) 	& 11(5, 6)--10(5, 5) E   	& 23.3  	& 164.70 	& 134~739.630 	& 134~739.110 	&  3.55	&  386  	&  	\\
\hline
26(28) 	& 12(2, 11)--11(2, 10) A 	& 30.6  	& 159.00 	& 140~020.525 	& 140~020.145 	&  2.96 	&  472  	&  	\\
27 		& 11(2, 9)--10(2, 8) A   	& 28.1  	& 155.98 	& 140~166.667 	& 140~166.502 	&  3.42 	&  528  	& 	\\
28(26) 	& 12(2, 11)--11(2, 10) E 	& 30.8  	& 158.50 	& 140~324.728 	& 140~324.321 	&  7.66	&  470 	&	\\
29 		& 13(1, 13)--12(1, 12) E 	& 34.2  	& 159.69 	& 142~032.334 	& 142~031.811 	&  4.52 	&  586  	&  	\\
30(31) 	& 13(0, 13)--12(0, 12) A 	& 34.0  	& 160.24 	& 142~052.800 	& 142~052.867 	&  5.95 	&  724  	&  	\\
31(30) 	& 13(0, 13)--12(0, 12) E 	& 34.2  	& 159.68 	& 142~125.416 	& 142~125.086 	&  4.01 	&  559  	&  	\\
32 		& 13(1, 13)--12(0, 12) A 	& 5.34  	& 160.24 	& 142~185.220 	& 142~184.202 	&  0.81	&  121  	&   	\\
33(35) 	& 15(0, 15)--14(1, 14) A 	& 6.27  	& 170.07 	& 163~042.398 	& 163~042.050 	&  2.32 	&  363  	& 	\\
34(38) 	& 15(1, 15)--14(1, 14) A 	& 39.3  	& 170.07 	& 163~086.032 	& 163~085.494 	&  6.39 	&  884  	& HCOOCH$_3$ $\upsilon_{\rm t}=0$\\
35(33) 	& 15(0, 15)--14(1, 14) E 	& 6.07  	& 169.52 	& 163~113.094 	& 163~113.656 	&  5.11 	&  549  	& SO$_2$\\
36(39) 	& 15(0, 15)--14(0, 14) A 	& 39.3  	& 169.52 	& 163~118.722 	& 163~118.285 	&  19.40	&   2184  	& SO$_2$\\
37 		& 14(1, 13)--13(1, 12) E 	& 36.2  	& 168.12 	& 163~142.587 	& 163~141.991 	&  7.69 	&  967  	& 	\\
38(34) 	& 15(1, 15)--14(1, 14) E 	& 39.6  	& 162.52 	& 163~154.325 	& 163~153.604 	&  8.99 	&  855  	&  	\\
39(36) 	& 15(0, 15)--14(0, 14) E 	& 39.6  	& 169.52 	& 163~185.864 	& 163~185.586 	&  5.15	&  679  	& 	\\
40 		& 15(1, 15)--14(0, 14) E 	& 6.07  	& 169.52 	& 163~227.097 	& 163~227.290 	& 4.23 	&  448  	&  	\\
41(44) 	& 16(0, 16)--15(1, 15) A 	& 6.73  	& 175.51 	& 173~616.616 	& 173~617.000   & 1.80  	&  177  	&  	\\
42(46) 	& 16(1, 16)--15(1, 15) A 	& 42.0  	& 175.51 	& 173~641.411 	& 173~636.978 	& 15.14 	&  1288  	& HCOOCH$_3$ $\upsilon_{\rm t}=0$ \\
43(47) 	& 16(0, 16)--15(0, 15) A 	& 42.0  	& 175.51 	& 173~660.281 	& 173~659.384 	& 4.12  	&  380  	& 	\\
44(41) 	& 16(0, 16)--15(1, 15) E 	& 6.50  	& 175.51	& 173~683.479 	& 173~186.987	&  17.8	&  5300	&CH$_3$CHO \\ 
45 		& 24(3, 21)--24(2, 22) A 	& 4.32  	& 254.06 	& 173~704.470 	& 173~706.183 	&  9.03 	&  644  	& 	\\
46(42) 	& 16(1, 16)--15(1, 15) E 	& 42.2  	& 174.96 	& 173~706.683 	& 173~706.183 	&  --		&  -- 		& 	\\
47(43) 	& 16(0, 16)--15(0, 15) E 	& 42.2  	& 174.97	& 173~724.731 	& 173~724.558	&  2.02 	&  479 	& 	\\
48 		& 16(1, 16)--15(0, 15) E 	& 6.6  	& 174.97	& 173~747.990 	& 173~748.150	&  3.94 	&  264  	& 	\\
49(51) 	& 16(5, 11)--15(5, 10) E 	& 38.2 	& 191.37 	& 198~384.885 	& 198~384.516 	&   5.23	&  467  	& 	\\
50 		& 26(8,19)--26(7, 20) A 	& 6.92  	& 297.43 	& 198~429.332 	& 198~428.202 	&   1.67 	&  231  	&  c-C$_2$H$_4$ \\
51(49) 	& 16(5, 11)--15(5, 10) A 	& 38.3  	& 191.52 	& 198~539.350 	& 198~541.500 	&  19.44	&  1400  	&  HCOOCH$_3$ $\upsilon_{\rm t}=0$\\
52 		& 16(5, 12)--15(5, 11) E 	& 38.1  	& 191.05 	& 198~578.563 	& 198~577.928 	&   3.20	&  484 	& 	\\
53 		& 19(3, 16)--18(4, 15) A 	& 2.8   	& 208.13 	& 207~295.959 	& 207~296.361 	&   5.16	&   159  	&  CH$_3$CH$_2$CN\\
54 		& 17(12, 5)--16(12, 4) A 	& 21.2  	& 252.96 	& 207~354.058 	& 207~352.197 	&   5.57 	&  557  	& 	\\
55 		& 17(12, 6)--16(12, 5) A 	& 21.2  	& 252.96	& 	--		& --		 	&    	--	&   --	 	& 	\\
56	 	& 17(13, 5)--16(13, 4) E 	& 18.8  	& 264.55 	& 207~376.777 	& 207~378.506 	&   11.46	&   995 	&  CH$_2$NH\\
57 		& 17(9, 8)--16(9, 7) E   	& 32.5  	& 223.90 	& 207~397.312 	& 207~396.134 	&  8.62	&  758 	&  	\\
58 		& 17(11, 6)--16(11, 5) A 	& 26.2  	& 242.28 	& 207~404.993 	& 207~404.612 	&  5.67  	&  690  	& 	\\
59 		& 17(11, 7)--16(11, 6) A 	& 26.2 	& 242.28	&	--		& 	--	 	&  --		&  -- 		&  	\\
60 		& 17(10, 8)--16(10, 7) A 	& 29.5  	& 232.53 	& 207~500.297 	& 207~499.521 	&  4.8  	&  897 	&  	\\
61 		& 17(10, 7)--16(10, 6) A 	& 29.5  	& 232.53	& 	--		& 	--		&  -- 		&  -- 		&  	\\
62 		& 19(2, 18)--18(1, 17) A 	& 6.56  	& 199.21 	& 215~130.469 	& 215~130.828 	&  2.59  	&  394 	& CH$_3$CH$_2$CN\\
63(67) 	& 18(5, 13)--17(5, 12) A 	& 44.1  	& 205.21 	& 225~648.010 	& 225~647.974 	& 5.16   	& 1103 	& HCOOCH$_3$ $\upsilon_{\rm t}=0$\\
64 		& 19(2, 17)--18(2, 16) A 	& 48.7  	& 203.74 	& 225~702.569 	& 225~698.559   & 184  	& 1400   	& H$_2$CO  \\
65 		& 6(6, 1)--5(5, 0) A     	& 2.59  	& 148.59 	& 225~727.540 	& 225~726.732   &  2.55	& 372  	& CH$_2$DCN \\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
66 		& 6(6, 0)--5(5, 1) A     	& 2.59  	& 148.59 	& 225~727.552 	&  	--	   	&  	--	& --	  	& -- \\
67(63) 	& 18(5, 13)--17(5, 12) E	& 43.4  	& 205.06 	& 225~756.154 	& 225~755.178	&  7.3	&  927  	& 	\\
68 		& 7(6, 1)--6(5, 2) A   		& 25.6  	& 229.84	& 237~899.08 	& 237~896.263 	& 15.91	& 1.667  	& NH$_2$CHO\\
69 		& 20(3, 18)--19(2, 17) A 	& 5.37  	& 211.27 	& 237~969.273 	& 237~969.938 	&  12.80	&  1.186   & unidentified species\\
70 		& 37(7, 31)--37(6, 32) A 	& 8.54  	& 434.55 	& 238~027.934 	& 238~026.742 	&  1.12	&  122 	&   	\\
71 		& 20(14, 7)--19(14, 6) E 	& 27.1  	& 299.15 	& 244~000.464 	& 243~999.803 	&  7.82	& 596 	&   	\\
72 		& 20(15, 6)--19(15, 5) A 	& 23.3  	& 312.58 	& 244~048.806 	& 244~048.230   & 90.33	&  10.84	& H$_2$CS \\
73 		& 20(15, 5)--19(15, 4) A 	& 23.3  	& 312.58 	& 	--		& 	--		& 	--	&    --		&	--	 \\
74 		& 19(4, 15)--18(4, 14) A 	& 18.4  	& 209.57 	& 244~066.113 	& 244~066.720 	&  5.49	&  730 	&   	\\
75 		& 20(14, 7)--19(14, 6) A 	& 14.2  	& 299.10 	& 244~073.956 	& 244~073.440 	&  3.54	&  314 	& unidentified species 	\\
76 		& 20(14, 6)--19(14, 5) A 	& 14.2  	& 299.10 	& 	--	 	& 	--	 	&  	--	&  --	 	&   	\\
77 		& 20(10, 10)--19(10, 9) E 	& 39.9  	& 254.74 	& 244~112.669 	& 244~112.254 	& 2.65 	&  677 	&   	\\
78(82) 	& 20(13, 8)--19(13, 7) A 	& 21.0  	& 286.55 	& 244~119.960 	& 244~119.708 	& 2.95 	& 886	&   	\\
79 		& 20(13, 7)--19(13, 6) A 	& 21.0  	& 286.55 	& 	--		&	--		& --	 	& --		&   	\\
80 		& 20(12, 8)--19(12, 7) A 	& 34.0  	& 274.94 	& 244~198.512 	& 244~198.232 	& 7.43 	& 1107  	&  	\\
81 		& 20(12, 9)--19(12,8) A 	& 34.0  	& 274.94 	& 	--		&	--		&   --	  	& --	 	&  	\\
82(78) 	& 20(13, 8)--19(13, 7) E 	& 30.7  	& 286.54 	& 244~207.619 	& 244~206.113 	& 7.33 	& 893 	& unidentified species  \\
\hline
\end{tabular}
\par
\smallskip
$^a$ The notation for the quantum numbers is the same as Table~\ref{mtfvt1lab} except that it does not contain information on the parity of the level, i.e. the signs present in Table~\ref{mtfvt1lab} (associated to $K_{\rm a}$ for the $E$~species and in a separate column for the A~species) have been suppressed;
 $^b$ observed frequencies for a systemic velocity of 
$V_{\rm lsr} = 55.3$~km~s$^{-1}$;
 $^c$ the line width is of the order of 7--8~km~s$^{-1}$;
 $^d$ this column indicates the molecules blended with the detected HCOOCH$_3$ $\upsilon_{\rm t}=1$ transitions.  
The dashes indicates that the value is the same as the one in the previous line.
\end{table}