## How to calculate

The coefficients of Elliptic modular function.
The following program calculates j(tau) from z=-1 to 900.
``````
10   ' j(tau) : j_tau.ub
20   ' print=print+"\tmp\j_tau.txt"
30   word -36:point 2
40   L%=902:dim A(L%),B(L%),C(L%),P(L%),Q(24)
50   ' E4(q)
60   A(0)=1
70   for I%=1 to L%:S=0
80     for J%=1 to I%:if I%@J%>0 then 100
90       S=S+J%^3
100     next J%:S=S*240:A(I%)=S
110   next I%
120   ' E4(q)^3
130   for I%=0 to L%:C(I%)=0:next I%
140   '
150   for I%=0 to L%
160     for J%=0 to L%-I%
170       for K%=0 to L%-J%-I%
180         C(I%+J%+K%)=C(I%+J%+K%)+A(I%)*A(J%)*A(K%)
190       next K%
200     next J%
210   next I%
220   '
230   for I%=0 to L%:A(I%)=C(I%):next I%
240   '
250   ' delta(q)
260   for I%=0 to 24:Q(I%)=!(24)\!(I%)\!(24-I%)*(-1)^I%:next I%
270   '
280   for I%=0 to L%:B(I%)=0:next I%
290   C(0)=0:C(1)=1:for I%=2 to L%:C(I%)=0:next I%
300   '
310   for K%=1 to L%
320     for I%=0 to L%:P(I%)=0:next I%
330     for I%=0 to 24:if I%*K%>L% then cancel for:goto 370
340       P(I%*K%)=Q(I%)
350     next I%
360     '
370     for I%=0 to L%:if C(I%)=0 then 410
380       for J%=0 to L%-I%:if P(J%)=0 then 400
390         B(I%+J%)=B(I%+J%)+C(I%)*P(J%)
400       next J%
410     next I%
420     '
430     if K%=L% then cancel for:goto 470
440     for I%=0 to L%:C(I%)=B(I%):B(I%)=0:next I%
450   next K%
460   '
470   for I%=0 to L%:C(I%)=0:next I%
480   '
490   Cm%=1:print -1;Cm%
500   C(0)=A(1)-Cm%*B(2):print 0;C(0)
510   for I%=1 to L%-2
520     C(I%)=A(I%+1)-Cm%*B(I%+2)
530     for J%=0 to I%-1
540       C(I%)=C(I%)-C(J%)*B(I%+1-J%)
550     next J%
560     print I%;":";C(I%);"(";alen(C(I%));")"
570   next I%
``````

E-mail : kc2h-msm@asahi-net.or.jp
Hisanori Mishima