;ò [Ó@c@s(dkZdkZd„Zd„ZdS(NcCs¥t|tƒp td‚t|tƒp td‚ti|ƒp td‚|ddjp td‚tti|dƒti |ddƒt ||ƒƒSdS(sê Returns the conjectural valuation at p of the index of the Hecke algebra T_k(Gamma_0(p)) in its normalization. INPUTS: p -- a prime integer k -- an even integer >= 2. OUTPUT: an integer sArgument 1 must be an int.sArgument 1 must be prime.iisArgument 2 must be even.i N( s isinstancespsintsAssertionErrorsksarithsis_primesmathsfloorsbinomsa(spsk((sdisc.pysconjs cCsût|tƒp td‚t|tƒp td‚ti|ƒp td‚|d}|djodSn‹|djo+dtitt i |dƒƒd ƒSnS|d jo+d titt i |d ƒƒd ƒSnt d|ƒt d |ƒSd S( sÊ Function a(p,k) involved in the conjectural formula returned by the conj function. INPUTS: p -- a prime integer k -- an even integer >= 2. OUTPUT: an integer sArgument 1 must be an int.sArgument 1 must be prime.i iiiif6.0iif4.0N( s isinstancespsintsAssertionErrorsksarithsis_primespmodsbinomsmathsceilsa(spskspmod((sdisc.pysas    + +(sarithsmathsconjsa(sasconjsarithsmath((sdisc.pys?s