# 2 chunks cover panels 0..335 with no gap
# midpoint to 24 places, then the TRUE radius from .rad();
# do not read a radius off a str(arb) of the midpoint -- it is inflated
k   f_k^odd (midpoint)           rad
 1  0.915268802906779164889696  3.19690e-79
 2  0.619685094441076291526850  2.46196e-87
 3  0.546010010883498718419890  2.16936e-87
 4  0.519581644854443117050576  2.06436e-87
 5  0.508737351382963523892143  2.02128e-87
 6  0.503999025478145230694958  2.00242e-87
 7  0.501858639680367139329935  1.99392e-87
 8  0.500872865463573130798137  1.99000e-87
 9  0.500413158880434032499280  1.98817e-87
10  0.500196850842369667282974  1.98731e-87
11  0.500094339957666716105769  1.98691e-87
12  0.500045456101039185541754  1.98671e-87
13  0.500022012229556067260575  1.98663e-87
14  0.500010709024821883981350  1.98674e-87
15  0.500005232107209760888966  1.98950e-87
16  0.500002566009318876562981  2.03487e-87
17  0.500001262703731485785818  2.73274e-87
18  0.500000623179686569696863  1.28687e-86
19  0.500000308324517669826051  1.52332e-85
20  0.500000152866821626460887  1.97527e-84
21  0.500000075922957590732953  2.46681e-83
22  0.500000037761631479342041  2.94313e-82
23  0.500000018803048708110511  3.35899e-81
24  0.500000009371436225194403  3.67389e-80
25  0.500000004674139978808749  3.85759e-79
26  0.500000002332637378893008  3.89468e-78
27  0.500000001164629865737219  3.78649e-77
28  0.500000000581674415260812  3.54984e-76
29  0.500000000290595321787287  3.21321e-75
30  0.500000000145206685128665  2.81156e-74
31  0.500000000072569256789422  2.38076e-73
32  0.500000000036271903840269  1.95297e-72
33  0.500000000018131218036102  1.55350e-71
34  0.500000000009063853617435  1.19939e-70
35  0.500000000004531277888662  8.99542e-70
36  0.500000000002265399761331  6.55916e-69
37  0.500000000001132611966894  4.65346e-68
38  0.500000000000566273755682  3.21456e-67
39  0.500000000000283125093497  2.16365e-66
40  0.500000000000141558248075  1.41989e-65
41  0.500000000000070777559573  9.09078e-65
42  0.500000000000035388211661  5.68174e-64
43  0.500000000000017693899951  3.46850e-63
44  0.500000000000008846875517  2.06928e-62
45  0.500000000000004423410882  1.20708e-61
46  0.500000000000002211695757  6.88822e-61
47  0.500000000000001105844395  3.84714e-60
48  0.500000000000000552920947  2.10391e-59
49  0.500000000000000276460025  1.12709e-58
50  0.500000000000000138229852  5.91724e-58
51  0.500000000000000069114869  3.04564e-57
52  0.500000000000000034557414  1.53746e-56
53  0.500000000000000017278700  7.61478e-56
54  0.500000000000000008639347  3.70163e-55
55  0.500000000000000004319673  1.76669e-54
56  0.500000000000000002159836  8.28135e-54
57  0.500000000000000001079918  3.81378e-53
58  0.500000000000000000539959  1.72606e-52
59  0.500000000000000000269979  7.67952e-52
60  0.500000000000000000134990  3.35979e-51
61  0.500000000000000000067495  1.44581e-50
62  0.500000000000000000033747  6.12138e-50
63  0.500000000000000000016874  2.55057e-49
64  0.500000000000000000008437  1.04613e-48
65  0.500000000000000000004218  4.22477e-48
66  0.500000000000000000002109  1.68031e-47
67  0.500000000000000000001055  6.58329e-47
68  0.500000000000000000000527  2.54134e-46
69  0.500000000000000000000264  9.66816e-46
70  0.500000000000000000000132  3.62556e-45
71  0.500000000000000000000066  1.34044e-44
72  0.500000000000000000000033  4.88700e-44
73  0.500000000000000000000016  1.75731e-43
74  0.500000000000000000000008  6.23371e-43
75  0.500000000000000000000004  2.18180e-42

f_k^odd strictly decreasing on [1,74]: True
  tightest pair k=74: difference >= 4.11956e-24 against radius 6.23371e-43 (ratio 6.61e+18)
f_k^odd strictly increasing on [1,74]: False