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-Sum_{k=1..2*q-1} J(k,q)*J(-4,k)*k/4 as q runs through numbers == 3 (mod 4), where J(i,j) is the Jacobi symbol.
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%I #4 Mar 30 2012 16:50:01

%S 1,4,7,12,19,20,1,40,38,52,63,56,78,92,85,-8,123,116,6,168,129,156,

%T 206,172,28,228,197,244,278,248,270,320,279,12,381,292,8,444,364,420,

%U 467,364,-38,24,471,492,550,520,540,660,508,80,737,556,692,720,575,744,846,712,1

%N -Sum_{k=1..2*q-1} J(k,q)*J(-4,k)*k/4 as q runs through numbers == 3 (mod 4), where J(i,j) is the Jacobi symbol.

%C Suggested by a formula in Petersson.

%D H. Petersson, Modulfunktionen und Quadratische Formen, Springer-Verlag, 1982; p. 103.

%p with(numtheory); J:=jacobi; f:=proc(q) add( J(k,q)*J(-4,k)*k, k=1..2*q-1); (-1)*(%/4); end;

%Y Cf. A097537.

%K sign

%O 1,2

%A _N. J. A. Sloane_, Aug 27 2004