## j(tau) n=285, 300, 331, 345, 346, 349

```    Subject: More j(tau) results
Date: Mon, 26 Oct 1998 10:07:00 +0000
From: Allan MacLeod <MACL-MS0@wpmail.paisley.ac.uk>
To: kc2h-msm@asahi-net.or.jp

Hello,

I think the following results finish off 200-300 range.

Allan MacLeod

Coefficient 285 of j(tau)

Input number is
2237452925410419348910627393062415019805506690256577497463452156961415620951924669 (82 digits)

Using B1=5000000, B2=500000000, polynomial x^60, sigma=494226297
Step 1 took 1030989ms for 65296230 muls, 3 gcdexts
Step 2 took 561538ms for 29218969 muls, 82414 gcdexts

********** Factor found in step 2: 2427447979556602323033481193363333

Found probable prime factor of 34 digits: 2427447979556602323033481193363333

Probable prime cofactor 921730535217942148039509786712299978835723595993 has 48 digits

Coefficient 300 of j(tau)

Input number is
259985215055891366064120936899980923258404348427970495168380269179540735245181 (78 digits)

Using B1=5000000, B2=500000000, polynomial x^60, sigma=1123278769
Step 1 took 987582ms for 65296230 muls, 3 gcdexts
Step 2 took 530275ms for 29218969 muls, 82414 gcdexts

********** Factor found in step 2: 710361625469843147666379507748661

Found probable prime factor of 33 digits: 710361625469843147666379507748661

Probable prime cofactor 365989948969911622725735008181385928547425321 has 45 digits

Coefficient 331 of j(tau)

Input number is
64398186943838696926118107110422263745044119126207085759541732498077711135982070497 (83 digits)

Using B1=3000000, B2=300000000, polynomial x^30, sigma=1226659993
Step 1 took 605329ms for 39102834 muls, 3 gcdexts
Step 2 took 290605ms for 16480797 muls, 29004 gcdexts

********** Factor found in step 2: 8693452261326468659659012141

Found probable prime factor of 28 digits: 8693452261326468659659012141

Probable prime cofactor 7407665563463123074071951860884352516020331709546650117 has 55 digits

Coefficient 345 of j(tau)

Input number is
19704947702301480156788545865907510957278094780043974459177702197276014571 (74 digits)

Using B1=3000000, B2=300000000, polynomial x^30, sigma=154379992
Step 1 took 519120ms for 39102834 muls, 3 gcdexts

********** Factor found in step 1: 304803675294273723193

Found probable prime factor of 21 digits: 304803675294273723193

Probable prime cofactor 64647999021918855760617262131437008723710694405396547 has 53 digits

Coefficient 346 of j(tau)

Input number is
151099338248100510206053009881640832856949574190084727267028528495977 (69 digits)

Using B1=3000000, B2=300000000, polynomial x^30, sigma=627519982
Step 1 took 519725ms for 39102834 muls, 3 gcdexts
Step 2 took 247582ms for 16480797 muls, 29004 gcdexts

********** Factor found in step 2: 12179839496518904938174403753

Found probable prime factor of 29 digits: 12179839496518904938174403753

Probable prime cofactor 12405692069364781334536281238069294537409 has 41 digits

Coefficient 349 of j(tau)

Input number is
34043132239779853845381903445363432040294230234173906370540582368042537695351 (77 digits)

Using B1=3000000, B2=300000000, polynomial x^30, sigma=94618370
Step 1 took 518681ms for 39102834 muls, 3 gcdexts
Step 2 took 125000ms for 7552905 muls, 23177 gcdexts

********** Factor found in step 2: 533429651882079132346371311806849

Found probable prime factor of 33 digits: 533429651882079132346371311806849

Probable prime cofactor 63819347349114905704338012874071051295927799 has 44 digits
```

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