[was@laptop 02-25-03]$ ping meccah connect: Network is unreachable [was@laptop 02-25-03]$ /sbin/route Kernel IP routing table Destination Gateway Genmask Flags Metric Ref Use Iface 140.247.240.0 * 255.255.252.0 U 0 0 0 wlan0 127.0.0.0 * 255.0.0.0 U 0 0 0 lo default sc-mr-1-gw-vl24 0.0.0.0 UG 0 0 0 wlan0 [was@laptop 02-25-03]$ ping abel.math.harvard.edu PING abel.math.harvard.edu (140.247.28.153) from 140.247.240.72 : 56(84) bytes of data. 64 bytes from abel (140.247.28.153): icmp_seq=1 ttl=254 time=2.36 ms 64 bytes from abel (140.247.28.153): icmp_seq=2 ttl=254 time=2.64 ms --- abel.math.harvard.edu ping statistics --- 2 packets transmitted, 2 received, 0% loss, time 1007ms rtt min/avg/max/mdev = 2.361/2.503/2.645/0.142 ms [was@laptop 02-25-03]$ meccah was@meccah.math.harvard.edu's password: Permission denied, please try again. was@meccah.math.harvard.edu's password: Last login: Tue Feb 25 15:39:50 2003 from roam240-72.fas.harvard.edu ********************************************************************** Welcome to MECCAH.MATH.HARVARD.EDU Mathematics Extreme Computation Cluster At Harvard 12 Athlon 2000 MP processors (2 are only 1900) master node has 3 GB memory and the other five have 2GB each openMosix 2.4.19 with RedHat Linux 7.3 and Kernel 2.4.19 Administrator: William Stein (was@math.harvard.edu) HINTS: * Type mosmon and mtop for CPU usage and multi-process top. * Type ulimit -S -v 2000000 etc to use about 2G memory per process, instead of the default 900MB. 09/29/02: Upgraded to Redhat 7.3, Kernel 2.4.19, openMosix 2.4.19. 09/29/02: Rebooted because of "slapper worm". 10/14/02: Rebooted because power off (due to construction). 10/23/02: I ran a bunch of HUGE memory jobs, which resulted in a mosix "VM memory overcommit" error message, and a reboot. 11/14/02: MECCAH3 is back from the shop, and works so far... 11/16/02: Changed gp back to 2.1.4 (from 2.2.alpha) 11/26/02: MECCAH1 crashed when we found a bug in openMosix. 01/19/03: MECCAH3 crashed. MECCAH1 was overloaded probably, since it responded to pings but not much else. 01/25/03: I installed Macaulay 2-0.9.2. 01/25/03: MECCAH3 has stopped working again. I'll fix it myself this time, so it will really get fixed. 02/07/03: Rebooted, since things were locked up because of meccah3. ********************************************************************** [was@meccah was]$ magma Magma V2.9-19 Tue Feb 25 2003 15:49:02 [Seed = 3951952720] Type ? for help. Type -D to quit. Loading startup file "/home/was/magma/local/init.m" > E := EllipticCurve([0,0,0,0,1]); > E; Elliptic Curve defined by y^2 = x^3 + 1 over Rational Field > time f := qEigenform(E,500); Time: 0.100 > time f := qEigenform(E,1000); Time: 0.120 > time f := qEigenform(E,5000); Time: 0.590 > f; q - 4*q^7 + 2*q^13 + 8*q^19 - 5*q^25 - 4*q^31 - 10*q^37 + 8*q^43 + 9*q^49 + 14*q^61 - 16*q^67 - 10*q^73 - 4*q^79 - 8*q^91 + 14*q^97 + 20*q^103 + 2*q^109 - 11*q^121 + 20*q^127 - 32*q^133 - 16*q^139 - 4*q^151 + 14*q^157 + 8*q^163 - 9*q^169 + 20*q^175 + 26*q^181 + 2*q^193 - 28*q^199 - 16*q^211 + 16*q^217 - 28*q^223 - 22*q^229 + 14*q^241 + 16*q^247 + 40*q^259 - 28*q^271 + 26*q^277 + 32*q^283 - 17*q^289 - 32*q^301 - 16*q^307 - 22*q^313 - 10*q^325 + 32*q^331 - 34*q^337 - 8*q^343 + 14*q^349 + 45*q^361 - 4*q^367 + 38*q^373 + 8*q^379 - 34*q^397 - 8*q^403 + 38*q^409 - 22*q^421 - 56*q^427 + 2*q^433 - 28*q^439 - 10*q^457 + 20*q^463 + 64*q^469 - 40*q^475 - 20*q^481 + 44*q^487 + 32*q^499 + 40*q^511 + 8*q^523 - 23*q^529 - 46*q^541 - 40*q^547 + 16*q^553 + 16*q^559 - 16*q^571 - 46*q^577 - 32*q^589 + 26*q^601 + 20*q^607 - 10*q^613 + 32*q^619 + 25*q^625 + 44*q^631 + 18*q^637 - 40*q^643 + 38*q^661 + 50*q^673 - 56*q^679 + 8*q^691 - 80*q^703 - 22*q^709 - 80*q^721 + 44*q^727 + 50*q^733 - 16*q^739 - 52*q^751 + 26*q^757 - 8*q^763 + 2*q^769 + 20*q^775 + 56*q^787 + 28*q^793 + 56*q^811 + 64*q^817 - 52*q^823 - 46*q^829 - 29*q^841 + 44*q^847 - 58*q^853 + 56*q^859 - 32*q^871 - 34*q^877 + 8*q^883 - 80*q^889 - 40*q^907 - 52*q^919 + 50*q^925 + 72*q^931 + 26*q^937 - 20*q^949 - 15*q^961 + 20*q^967 + 64*q^973 + 44*q^991 - 10*q^997 + 62*q^1009 + 14*q^1021 - 8*q^1027 - 58*q^1033 - 52*q^1039 - 64*q^1051 + 16*q^1057 - 28*q^1063 + 62*q^1069 - 40*q^1075 - 4*q^1087 - 22*q^1093 - 56*q^1099 - 46*q^1117 + 32*q^1123 + 38*q^1129 - 32*q^1141 + 40*q^1147 + 62*q^1153 + 112*q^1159 - 64*q^1171 + 36*q^1183 + 2*q^1201 + 50*q^1213 - 45*q^1225 + 68*q^1231 - 70*q^1237 + 14*q^1249 + 28*q^1261 - 104*q^1267 - 128*q^1273 - 28*q^1279 + 56*q^1291 - 46*q^1297 + 68*q^1303 - 22*q^1321 - 4*q^1327 - 32*q^1333 + 40*q^1339 - 8*q^1351 + 63*q^1369 + 74*q^1381 - 80*q^1387 + 112*q^1393 + 68*q^1399 + 4*q^1417 + 20*q^1423 - 58*q^1429 - 76*q^1447 + 2*q^1453 + 56*q^1459 - 76*q^1471 + 64*q^1477 - 40*q^1483 - 34*q^1489 - 32*q^1501 - 36*q^1519 - 70*q^1525 - 64*q^1531 - 52*q^1543 + 62*q^1549 + 112*q^1561 + 44*q^1567 - 22*q^1573 + 32*q^1579 - 80*q^1591 + 50*q^1597 + 88*q^1603 - 58*q^1609 + 26*q^1621 + 80*q^1627 + 40*q^1651 - 70*q^1657 + 68*q^1663 + 74*q^1669 + 80*q^1675 - 41*q^1681 - 56*q^1687 - 82*q^1693 - 64*q^1699 - 40*q^1723 - 64*q^1729 - 34*q^1741 + 80*q^1747 - 10*q^1753 - 52*q^1759 + 14*q^1777 - 28*q^1783 - 82*q^1789 + 74*q^1801 - 32*q^1807 - 90*q^1813 + 50*q^1825 + 68*q^1831 + 112*q^1843 + 21*q^1849 + 86*q^1861 + 56*q^1867 - 82*q^1873 - 4*q^1879 - 56*q^1891 + 112*q^1897 + 62*q^1933 - 104*q^1939 - 76*q^1951 + 160*q^1957 - 8*q^1963 + 20*q^1975 - 128*q^1981 - 40*q^1987 - 70*q^1993 - 52*q^1999 - 88*q^2011 - 34*q^2017 + 68*q^2023 + 2*q^2029 + 28*q^2041 - 10*q^2053 + 16*q^2071 + 64*q^2077 - 88*q^2083 + 38*q^2089 + 72*q^2107 - 82*q^2113 + 16*q^2119 + 32*q^2131 + 74*q^2137 + 92*q^2143 + 64*q^2149 + 62*q^2161 - 88*q^2179 + 88*q^2191 - 44*q^2197 + 8*q^2203 - 47*q^2209 - 94*q^2221 + 68*q^2239 - 16*q^2251 - 140*q^2257 + 40*q^2263 - 82*q^2269 + 40*q^2275 + 86*q^2281 + 20*q^2287 - 58*q^2293 - 88*q^2299 - 76*q^2311 - 128*q^2317 + 74*q^2341 - 64*q^2347 + 52*q^2353 + 136*q^2359 + 56*q^2371 - 10*q^2377 - 28*q^2383 + 38*q^2389 - 31*q^2401 + 160*q^2413 - 70*q^2425 + 86*q^2437 - 56*q^2443 + 16*q^2449 + 80*q^2467 - 22*q^2473 + 160*q^2479 - 100*q^2503 + 4*q^2509 + 26*q^2521 - 180*q^2527 + 8*q^2539 - 52*q^2551 - 46*q^2557 + 16*q^2569 - 100*q^2575 - 56*q^2587 + 98*q^2593 - 152*q^2611 + 86*q^2617 + 112*q^2623 - 128*q^2641 - 100*q^2647 - 32*q^2653 + 56*q^2659 + 44*q^2671 - 70*q^2677 + 80*q^2683 + 62*q^2689 + 100*q^2701 + 104*q^2707 + 38*q^2713 - 28*q^2719 - 10*q^2725 + 104*q^2731 - 32*q^2743 + 14*q^2749 - 76*q^2767 + 136*q^2779 + 92*q^2791 - 94*q^2797 - 88*q^2803 - 53*q^2809 + 32*q^2821 + 98*q^2833 + 104*q^2851 - 106*q^2857 - 152*q^2863 - 32*q^2869 - 128*q^2881 - 4*q^2887 - 56*q^2899 - 106*q^2917 + 40*q^2923 + 88*q^2947 - 70*q^2953 + 56*q^2971 - 44*q^2977 + 112*q^2983 + 126*q^2989 - 106*q^3001 - 56*q^3007 - 88*q^3019 + 55*q^3025 - 8*q^3031 + 110*q^3037 + 86*q^3049 + 38*q^3061 + 104*q^3067 + 112*q^3073 - 28*q^3079 + 64*q^3097 - 106*q^3109 + 14*q^3121 + 28*q^3133 - 80*q^3139 - 112*q^3163 + 98*q^3169 - 100*q^3175 - 94*q^3181 + 80*q^3187 - 80*q^3193 + 40*q^3199 - 72*q^3211 + 110*q^3217 - 46*q^3229 - 80*q^3241 - 70*q^3253 - 88*q^3259 - 4*q^3271 - 144*q^3283 + 86*q^3301 + 56*q^3307 + 62*q^3313 - 76*q^3319 + 160*q^3325 - 16*q^3331 + 68*q^3343 - 34*q^3361 + 80*q^3367 + 98*q^3373 - 8*q^3379 + 116*q^3391 - 32*q^3397 - 176*q^3409 + 38*q^3433 + 208*q^3439 + 110*q^3457 - 28*q^3463 + 2*q^3469 + 80*q^3475 - 59*q^3481 - 128*q^3493 - 112*q^3499 + 116*q^3511 + 14*q^3517 - 56*q^3523 - 118*q^3529 - 58*q^3541 - 64*q^3547 - 52*q^3559 + 104*q^3571 - 90*q^3577 - 100*q^3583 - 140*q^3589 + 52*q^3601 + 116*q^3607 + 110*q^3613 - 76*q^3631 + 26*q^3637 - 112*q^3643 - 32*q^3661 + 16*q^3667 - 118*q^3673 + 64*q^3679 + 8*q^3691 + 50*q^3697 + 92*q^3703 - 82*q^3709 + 135*q^3721 + 116*q^3727 + 122*q^3733 - 16*q^3739 + 44*q^3751 - 34*q^3757 + 122*q^3769 + 20*q^3775 - 224*q^3781 + 184*q^3787 + 110*q^3793 - 200*q^3811 - 100*q^3823 + 160*q^3829 - 124*q^3847 + 98*q^3853 - 36*q^3871 + 86*q^3877 + 2*q^3889 - 64*q^3907 - 64*q^3913 - 124*q^3919 - 70*q^3925 + 32*q^3931 - 80*q^3937 - 52*q^3943 - 76*q^3967 - 32*q^3991 + 64*q^3997 - 112*q^4003 - 128*q^4009 + 122*q^4021 + 104*q^4027 - 20*q^4033 + 184*q^4039 + 56*q^4051 + 26*q^4057 - 44*q^4069 - 40*q^4075 - 224*q^4087 + 50*q^4093 + 128*q^4099 - 4*q^4111 + 128*q^4123 + 98*q^4129 + 122*q^4153 + 44*q^4159 + 112*q^4171 - 34*q^4177 + 86*q^4201 - 104*q^4207 - 112*q^4219 + 45*q^4225 + 116*q^4231 - 224*q^4237 + 128*q^4243 - 80*q^4249 - 106*q^4261 - 130*q^4273 + 40*q^4291 - 70*q^4297 + 64*q^4303 + 64*q^4309 - 76*q^4327 - 128*q^4333 + 128*q^4339 - 176*q^4351 - 10*q^4357 + 32*q^4363 - 100*q^4375 - 68*q^4381 - 176*q^4417 + 68*q^4423 + 160*q^4429 + 74*q^4441 + 116*q^4447 - 140*q^4453 - 16*q^4459 + 110*q^4477 + 80*q^4483 + 189*q^4489 + 160*q^4501 - 40*q^4507 + 50*q^4513 - 124*q^4519 - 130*q^4525 + 28*q^4537 + 86*q^4549 - 94*q^4561 - 4*q^4567 + 112*q^4579 + 44*q^4591 + 134*q^4597 + 128*q^4603 - 34*q^4621 - 152*q^4627 + 92*q^4639 - 136*q^4651 - 130*q^4657 + 20*q^4663 + 16*q^4681 + 16*q^4687 + 90*q^4693 - 200*q^4699 - 200*q^4711 - 112*q^4723 - 58*q^4729 + 126*q^4753 - 28*q^4759 - 8*q^4771 - 52*q^4783 + 134*q^4789 + 2*q^4801 - 130*q^4813 - 56*q^4819 - 10*q^4825 + 68*q^4831 - 32*q^4837 + 76*q^4849 - 46*q^4861 - 56*q^4867 + 160*q^4891 + 140*q^4903 - 94*q^4909 + 320*q^4921 + 16*q^4927 - 118*q^4933 + 116*q^4951 + 50*q^4957 + 88*q^4963 + 26*q^4969 + 140*q^4975 - 136*q^4987 - 130*q^4993 + 92*q^4999 + O(q^5000) > time f := qEigenform(E,5000); Time: 0.600 > v := Eltseq(f); > v; [ 1, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -9, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, -17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, 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0, 0, 0, 0, 0, 0, -112, 0, 0, 0, 0, 0, -58, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 126, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -52, 0, 0, 0, 0, 0, 134, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -130, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 68, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 76, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -46, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 140, 0, 0, 0, 0, 0, -94, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 320, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, -118, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 116, 0, 0, 0, 0, 0, 50, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 140, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -136, 0, 0, 0, 0, 0, -130, 0, 0, 0, 0, 0, 92 ] > Max(v); 320 4921 > EllipticCurve; Intrinsic 'EllipticCurve' Signatures: ( S) -> CrvEll The elliptic curve defined by the coefficients of S. S must be of length 2 or 5 ( j) -> CrvEll Creates an elliptic curve with j-invariant j ( D, N, I, J) -> CrvEll The J-th elliptic curve in the I-th isogeny class of conductor N found in the elliptic curve database D ( D, S) -> SeqEnum An elliptic curve with label S (e.g. "101A" or "101A1") in the elliptic curve database D. ( D, N, S, J) -> SeqEnum The J-th elliptic curve of conductor N and label S (e.g. "A") in the elliptic curve database D. ( C) -> CrvEll, MapIsoSch, MapIsoSch ( C) -> CrvEll, MapIsoSch, MapIsoSch The elliptic curve E specified by the genus one curve C, assuming that the equation of C is in odd degree Weierstrass form, followed by the isomorphism C -> E and its inverse E -> C. ( C, P) -> CrvEll, Map, Map ( C, P) -> CrvEll, Map, Map The elliptic curve E specified by the genus one curve C and the point P, followed by the birational map C -> E, and the morphism E -> C. ( f) -> CrvEll An elliptic curve with associated modular form f. ( M) -> SeqEnum [ StartPrec, Database ] An elliptic curve over the rational numbers that lies in the isogeny class of elliptic curves associated to M. > > EllipticCurve([0,0,0,0,1]); Elliptic Curve defined by y^2 = x^3 + 1 over Rational Field > EllipticCurve(CremonaDatabase(),"36A"); Elliptic Curve defined by y^2 = x^3 + 1 over Rational Field > EllipticCurve(CremonaDatabase(),"389A"); Elliptic Curve defined by y^2 + y = x^3 + x^2 - 2*x over Rational Field > E := $1; > E; Elliptic Curve defined by y^2 + y = x^3 + x^2 - 2*x over Rational Field > Rank(E); 2 > G := MordellWeilGroup(E); > G; Abelian Group isomorphic to Z + Z Defined on 2 generators (free) > MordellWeilGroup; Intrinsic 'MordellWeilGroup' Signatures: ( E) -> GrpAb, Map [ Bound: RngIntElt, HeightBound: RngElt ] ( E) -> GrpAb, Map [ Bound: RngIntElt, HeightBound: RngElt ] The Mordell-Weil group of E; E must be defined over Q > G, f := MordellWeilGroup(E); > G; Abelian Group isomorphic to Z + Z Defined on 2 generators (free) > f; Mapping from: GrpAb: G to Set of points of E with coordinates in Rational Field > G.1; G.1 > f(G.1); (0 : 0 : 1) > E; Elliptic Curve defined by y^2 + y = x^3 + x^2 - 2*x over Rational Field > f(G.2); (1 : 0 : 1) > P := f(G.1); > Q := f(G.2); > P; (0 : 0 : 1) > Q; (1 : 0 : 1) > 34*P + 12*Q; (477805705976878844505325262579609087084560365031069416679779976991183584846064074\ 1655275118179395961642579224383510268218757483839597387699729342841726020221215259\ 3326716306117329512565350384973360875656551510599953/65645305037757344015388219947\ 1871441784022195260747999018579964643379211493927952037961682811909894573928083808\ 2395668515553521992636212456524952385227368010460251974250346453480093820825456377\ 260034039776943614096 : -112213737169145243192677077816538659019333835095353462257\ 7025895020638765997556081805990592432611528666293572405111006547163997951392611918\ 6863968081218873258483551799978674902353403755785782884693437059175253315172446091\ 2788199724629286285279979364588787733805053716913445569894210482234994751251836199\ 69456181380405657599/5318700139093965100962700365038452008738328529808365237791133\ 7796637202891028870886948515247235608889365743524993847683750225438696363042826970\ 7666997920057075877516222107286771236166779710454755866188823396726407109664018710\ 5956252376135235120062323456736947690390733714603949349499006705661324030862397149\ 75225861822144 : 1) > 100*P; (113399050355811077175874979317351573863157877248631711633953453511478043738734351\ 2434665668950341476867302112163895352466434150875126112526613710930434733425925572\ 0680538591233929364023058296172234872428661532976446380732408906983571626069933705\ 3655164040320910097770865447980740355811493798676072890464049195270612569278920542\ 2471394515904930545397555159942071330852527672749194203967856289009597693892558584\ 4846663862491757100199491107270632763878451175619641506971683985605728124341989618\ 2623875419336510007995059221306187335425701339920796051173838240026791715698672995\ 0616508953392467354207185236133374655850644959006373352642810001961061061456635153\ 0528051882702644799011843710524421945182134654964025066343815959198043854241471218\ 6364807204103386440955365595342542997725051342139292026070162250289879707422560077\ 4875320763039614794607007975451534691601867508378617348410953397537783547524268626\ 4141637883325075166580780326898767873589158040858601505326618054722926054781867872\ 6873515699211078096005206620492295134639105361026245024958016012405503591701059235\ 1687135293082015581290089039676055930824832626791724907717902839859727099120713346\ 9552203060825533943874840837964461388653064867444147790358871882691012096476883683\ 2553467495482301637420135435815935108151858990348064492429310390732887046480853684\ 5271303241195337966884832344342785745712356614244607420931868566172164639589484108\ 7149479213832333909687338305/38187567402054484019444416192720527422156218735111309\ 6512521892826164502892986636358885013914556559373769919547309366949480844594077496\ 9855549921250604667586362603032215345855060186471065779434326223513240135926213147\ 6421455781594942889586021328696376446315475527407054281596496926303277365698698969\ 9334535229366968821210445059580620435555464917546881618850208053463394472877727153\ 5034695818814311407408675386774232041515403364377246721842252239067554416219946825\ 4247913441158277484375902722462976501484371046712363364385090667111513653765630174\ 9638522595144227933081766803561920533734066354329386951810963811260586738975672165\ 9754545357450100391540706305394148411224680958282487407229547843876320339458608984\ 6905514140208238757317871221442720384395584180624601306137689519424186818179933563\ 0869584392995686976666364156707708370966450286740933320725987285283182780504634816\ 9218141951722418662698856163532143500274320866024331700373970045782507228684990376\ 0325147841200646163656511916842328773527312154083214243401156815551609108021890870\ 3160521094763529004152914691183223546064509094760526925581815591996806291778626951\ 6117699272201016467090629649627974019821856184161501871756460613536904559531183228\ 2683318557013630254727500534089657459876510349086672591462714397583408204237462234\ 1411381263390056315496807536538463060463213468606414878321892240793438409466015452\ 4272978455773472706178279659620622951154290290277265984 : 1159696900234235686214203254043058979406803469125910587004214349848723412340578742\ 2319221231550156712399296087510200837808427926421311484838314526254078135771666294\ 4011761828388185275564031638488292102068723679804914170870465352478719747257605636\ 0848225777440035472002990277184592964314908155544426763101849885962415138896801912\ 0580954606355639619682722798391897910439820864722640689900397003586615700380689587\ 8481163982030750059863852499043461273638978741696233043623644376592027130834541231\ 7517780975152187626465874928178443743599720830213039233705586996560903253956281645\ 8527684081588450767932105902504962258140175911958363693911460428944237555357171364\ 8694543491096780285440615346659117428261388011942404763278063307685578042088867709\ 3156135932488868740867623687349562167854691798517128690976886966899302509712751142\ 1152495451976931175409466084200368342861124744776429513714494843146640967645331130\ 2257740787183132458847391096858550046454697127347492610203134433819889032046694557\ 1145158185525221964560112420072979572292616189752716206934054324611740950306183119\ 4202198242623382458595035493090199124299335021694558352130625556661782063605882824\ 3792019099158041403295842046156994696410020272073001391107995073642610204618283603\ 8548806513088956680765980490113355720706053340364505843792686914588122609229147929\ 1527671996095787261452152854643864115200424405847945809287403124933429269969695345\ 8707618449476630742026679582902964885003729544849626459832117960268112118274036711\ 3762857394994002603369639515197791715597122212486794307750375255666230143867040919\ 9921473987667060707568297229754153823751752453542183109770044417249012147102418408\ 4470857503253163726437423318034048600041302642014170471342554133824579182576603177\ 9147476881105530249110775952261602039607208369225992111987070610903712326996935409\ 9956276177925369816906434757842450479948387051836115177055499894941185974725683550\ 9813178450487005746756679373264016511733842212412479239126424561751718801604369227\ 6599745674272976217390252386638229559860421966455060088961856288152998171722817419\ 816292601487786838423280199763203719453797482854242221668604669308225969745529855/\ 2359842352341867801459790168216912946258521044680623929872106283578506290132444695\ 7438604231674629534972826698767108622335566515445961221495291661616896231519390392\ 8511502884788658520489873300239050437712965476025964687008146849667720317394556245\ 7615816380004595931319296860875357704239224989166703565569246782991562031791558630\ 9904716548818626271078714894603810530507423107000821365060346821888112516744210591\ 6786299422180777901174715596804886490441819742209731242177477196941270831827982512\ 3320326247000975009081518766219914006252373203720862585390133940925125203410818739\ 7686291041452905507589059897443288654009329411434948881930824364734756655765176914\ 0036201184707092302233056156956011674878583730990000975010171610229145488337416040\ 2837907639944307094590820619856933258857149116997508669935477014082417283202156278\ 2465048701616792132334268955228285791975712506961833038765434241958541175986425887\ 9319382181759552481392951436066129546044596329653042744999660578418897310907532736\ 2410929166430037684718073159801543686079949398305518688364472527959647200101922614\ 1530616652209210739412404753913822218628064148889551076085377346970579556998815536\ 0717276532917209865887065877792391523107946581952166762450841168865794324935561485\ 5521117044244149777122413184959533452021150554514100662585300408969765189558443759\ 4820977428610793266788114471058706625473047179076640068227184695312177751698046600\ 2067796149849894739897275475338007722893896135840090402622631974183225465714696284\ 9907534339097563663836606716757976241003959559323334109269656036655065642802843597\ 6311770835465385474761171677681460653907044340865944448555875129068427312340667635\ 8857391697683974108799116381717651826980750109686978706829859627729772431832035475\ 7816512392172570127423365411644113340881404300210878985520701958600630127319381646\ 9109184297303842156512429258068797918643610748204850128666492650545588832871433983\ 1223538520815030994996555970270365974760615714302955553860111447953506813937467157\ 8138863777280586445250632631223278578144536234344190587105825441889259282996639176\ 87837423174345058134364268031580794971263950695187638331292525207387674106459648 : 1) > P; (0 : 0 : 1) > 2*P; (3 : 5 : 1) > 4*P; (114/121 : -267/1331 : 1) > 8*P; (1169154495/76860289 : -41440508823358/673834153663 : 1) >