Exceptional Slopes

As pointed out in "Where the Slopes Are", most of the slopes we computed were integers less than (k-1)/(p+1). The known (to me) exceptions to this are as follows:

Slopes larger than (k-1)/(p+1)

Prime p	Weights k
59	16, 46, 76, 106, 136, 166, 196, 226, 256, 286, 316, 346, 376, 406, 436, 466, 496, 826, 886
79	38, 44, 118, 124, 198, 204, 278, 284, 358, 364, 438, 444
2411	12
15271	16
187441	16
3371	20
64709	20
27310421	26

In each case, there is one exceptional slope, and it is (of course) the largest slope in that slope sequence. The slopes for p = 59 and k up to 500 were confirmed independently by Kevin Buzzard. I checked every weight up to 500, then looked at k = 826 and 886 to make sure the pattern continued "farther out." Weights k such that 500 < k < 826 or 826 < k < 886 were not checked. For the forms of weight 12, 16, 20, see my paper "Non-ordinary forms: a story" (Experimental Mathematics, 6 (1997), 195--205). You can get it online from the journal's web site. The computation for weight 26 was done by Oliver Atkin (private communication).

Slopes that are non-integral

In each case, the pattern is one of the following:

A weight whose slope sequence contains a larger-than expected slope equal to 2 is preceded by a weight whose sequence contains two slopes equal to 1/2. (For p = 59, weights 74 and 76, then 104 and 106; for p=79, weights 116 and 118, then 122 and 124.)
A weight whose slope sequece contains a larger-than expected slope equal to 3 is preceded by a weight whose sequence contains two slopes equal to 3/2, and that one is preceded by a sequence containing two slopes equal to 1/2. (E.g., for p=59 and weights 132, 134, 136, 162, 164, 166.)
A weight containing larger-than-expected slope equal to 4 is preceded by three weights for which there are fractional slopes, the fractions first being 1/2, then 3/2, then 5/2.
And so on.

Here is a complete table of known exceptional and non-integral weights for p=59:

k	Slope sequence
16	1
46	0, 0, 1
74	1/2, 1/2, 1, 1, 1
76	0, 1, 1, 1, 1, 2
104	0, 0, 1/2, 1/2, 1, 1, 1, 1
106	0, 0, 0, 0, 1, 1, 1, 2
132	1/2, 1/2, 1, 1, 1, 2, 2, 2, 2, 2, 2
134	0, 1, 1, 1, 1, 3/2, 3/2, 2, 2, 2
136	0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3
162	0, 0, 1/2, 1/2, 1, 1, 1, 1, 2, 2, 2, 2, 2
164	0, 0, 0, 0, 1, 1, 1, 3/2, 3/2, 2, 2, 2, 2
166	0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3
190	1/2, 1/2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3
192	0, 1, 1, 1, 1, 3/2, 3/2, 2, 2, 2, 3, 3, 3, 3, 3, 3
194	0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 5/2, 5/2, 3, 3, 3
196	0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4
220	0, 0, 1/2, 1/2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3
222	0, 0, 0, 0, 1, 1, 1, 3/2, 3/2, 2, 2, 2, 2, 3, 3, 3, 3, 3
224	0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 5/2, 5/2, 3, 3, 3, 3
226	0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4
248	1/2, 1/2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4
250	0, 1, 1, 1, 1, 3/2, 3/2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4
252	0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 5/2, 5/2, 3, 3, 3, 4, 4, 4, 4, 4, 4
254	0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 7/2, 7/2, 4, 4, 4
256	0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5
278	0, 0, 1/2, 1/2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4
280	0, 0, 0, 0, 1, 1, 1, 3/2, 3/2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4
282	0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 5/2, 5/2, 3, 3, 3, 3, 4, 4, 4, 4, 4
284	0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 7/2, 7/2, 4, 4, 4, 4
286	0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 5
306	1/2, 1/2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5
308	0, 1, 1, 1, 1, 3/2, 3/2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5
310	0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 5/2, 5/2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5
312	0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 7/2, 7/2, 4, 4, 4, 5, 5, 5, 5, 5, 5
314	0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 9/2, 9/2, 5, 5, 5
316	0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6
336	0, 0, 1/2, 1/2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5
338	0, 0, 0, 0, 1, 1, 1, 3/2, 3/2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5
340	0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 5/2, 5/2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5
342	0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 7/2, 7/2, 4, 4, 4, 4, 5, 5, 5, 5, 5
344	0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 9/2, 9/2, 5, 5, 5, 5
346	0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 6
364	1/2, 1/2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6
366	0, 1, 1, 1, 1, 3/2, 3/2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6
368	0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 5/2, 5/2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6
370	0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 7/2, 7/2, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6
372	0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 9/2, 9/2, 5, 5, 5, 6, 6, 6, 6, 6, 6
374	0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 11/2, 11/2, 6, 6, 6
376	0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7
394	0, 0, 1/2, 1/2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6
396	0, 0, 0, 0, 1, 1, 1, 3/2, 3/2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6
398	0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 5/2, 5/2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6
400	0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 7/2, 7/2, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6
402	0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 9/2, 9/2, 5, 5, 5, 5, 6, 6, 6, 6, 6
404	0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 11/2, 11/2, 6, 6, 6, 6
406	0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7
422	1/2, 1/2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7
424	0, 1, 1, 1, 1, 3/2, 3/2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7
426	0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 5/2, 5/2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7
428	0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 7/2, 7/2, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7
430	0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 9/2, 9/2, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7
432	0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 11/2, 11/2, 6, 6, 6, 7, 7, 7, 7, 7, 7
434	0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 13/2, 13/2, 7, 7, 7
436	0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 8
452	0, 0, 1/2, 1/2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7
454	0, 0, 0, 0, 1, 1, 1, 3/2, 3/2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7
456	0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 5/2, 5/2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7
458	0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 7/2, 7/2, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7
460	0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 9/2, 9/2, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7
462	0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 11/2, 11/2, 6, 6, 6, 6, 7, 7, 7, 7, 7
464	0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 13/2, 13/2, 7, 7, 7, 7
466	0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 8
480	1/2, 1/2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7
482	0, 1, 1, 1, 1, 3/2, 3/2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8
484	0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 5/2, 5/2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8
486	0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 7/2, 7/2, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8
488	0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 9/2, 9/2, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8
490	0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 11/2, 11/2, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8
492	0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 13/2, 13/2, 7, 7, 7, 8, 8, 8, 8, 8, 8
494	0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 15/2, 15/2, 8, 8, 8
496	0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9
826	1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 13, 13, 13, 14
886	1/2, 1/2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 15

Here is the analogous table for p = 79. Here the weights for which exceptional slopes occur are close enough that their patterns of fractional slopes superimposed without affecting each other (see weights 356, 434, 436).

k	Slope sequence
38	0, 1
44	0, 0, 1
116	0, 1/2, 1/2, 1, 1, 1, 1, 1, 1
118	0, 0, 0, 1, 1, 1, 1, 1, 2
122	0, 0, 1/2, 1/2, 1, 1, 1, 1, 1
124	0, 0, 0, 1, 1, 1, 1, 1, 1, 2
194	0, 1/2, 1/2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2
196	0, 0, 0, 1, 1, 1, 1, 1, 3/2, 3/2, 2, 2, 2, 2, 2, 2
198	0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3
200	0, 0, 1/2, 1/2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2
202	0, 0, 0, 1, 1, 1, 1, 1, 1, 3/2, 3/2, 2, 2, 2, 2, 2
204	0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3
272	0, 1/2, 1/2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3
274	0, 0, 0, 1, 1, 1, 1, 1, 3/2, 3/2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3
276	0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 5/2, 5/2, 3, 3, 3, 3, 3, 3
278	0, 0, 1/2, 1/2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4
280	0, 0, 0, 1, 1, 1, 1, 1, 1, 3/2, 3/2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3
282	0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 5/2, 5/2, 3, 3, 3, 3, 3
284	0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4
350	0, 1/2, 1/2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4
352	0, 0, 0, 1, 1, 1, 1, 1, 3/2, 3/2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4
354	0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 5/2, 5/2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4
356	0, 0, 1/2, 1/2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 7/2, 7/2, 4, 4, 4, 4, 4, 4
358	0, 0, 0, 1, 1, 1, 1, 1, 1, 3/2, 3/2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5
360	0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 5/2, 5/2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4
362	0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 7/2, 7/2, 4, 4, 4, 4, 4
364	0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5
428	0, 1/2, 1/2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5
430	0, 0, 0, 1, 1, 1, 1, 1, 3/2, 3/2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5
432	0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 5/2, 5/2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5
434	0, 0, 1/2, 1/2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 7/2, 7/2, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5
436	0, 0, 0, 1, 1, 1, 1, 1, 1, 3/2, 3/2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 9/2, 9/2, 5, 5, 5, 5, 5, 5
438	0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 5/2, 5/2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6
440	0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 7/2, 7/2, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5
442	0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 9/2, 9/2, 5, 5, 5, 5, 5
444	0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6

Fernando Q. Gouvêa ---- fqgouvea@colby.edu

Last modified: Thu Aug 31 10:36:13 -0500 2000