GP/PARI CALCULATOR Version 2.3.1 (released) amd64 running linux (x86-64/GMP-4.2.1 kernel) 64-bit version compiled: Oct 7 2006, gcc-4.1.2 20060928 (prerelease) (Debian 4.1.1-15) (readline v5.2 enabled [was v5.1 in Configure], extended help available) Copyright (C) 2000-2006 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 64000000, primelimit = 500000 e=ellinit([1, -1, 1, 0, 0]); /* 53A */ wp=ellrootno(e,p); /* 1 */ mxl=qsetprime(53); Is=qidcl(mxl); /* # = 5 */ f=vector(8,i,ellap(e,prime(i))); /* [-1, -3, 0, -4, 0, -3, -3, -5] */ ef=get_ef(mxl,f,Is); /* [0, -1/2, 0, 1/2, 0]~ */ ht=hprod(ef,ef); /* 1/2 */ b0=qzero_modp(7); /* [0, 1, 1, 1], norm = 161 */ Qs=vector(#Is,i,qtheta_lp(Is[i],b0,-7,53)); ks=vector(#Qs,i,qfrep_lk(Qs[i]),1,1)); kf=sum(i=1,#ef,ef[i]*ks[i]); /* we are cheating, by adding up *half*, otherwise we get 0 for l < 0 */ kfs=sum(i=1,#kf\2,kf[i])+if(l>0,kf[p]); petnorm=2*e.area*deg; ll=elllseriestwist(e,l,1); if(!ll,return()); l1=petnorm/ht/ll/sqrt(abs(l)); /* [d, kfs[d], kf[d], L/Lformula or L+1] */ /* D = 2 (mod 53 ) [ 161, -1 ] [ 373, 1 ] [ 744, 0 ] [ 797, -3 ] [ 956, -2 ] [ 1009, 1 ] [ 1221, 3 ] [ 1433, 6 ] [ 1592, -8 ] [ 1645, 2 ] [ 1804, 2 ] [ 1857, -1 ] [ 2069, -1 ] [ 2281, -2 ] [ 2440, 0 ] [ 2652, -1 ] [ 2705, 4 ] [ 2917, -2 ] [ 3129, -3 ] [ 3288, 4 ] [ 3341, -4 ] [ 3553, -1 ] [ 3765, -6 ] [ 3977, 0 ] [ 4136, 6 ] [ 4189, -2 ] [ 4348, -1 ] [ 4613, 14 ] [ 4984, 0 ] [ 5037, 3 ] [ 5196, -1 ] [ 5249, 0 ] [ 5461, -1 ] [ 5673, 0 ] [ 5885, -10 ] [ 6044, 3 ] [ 6097, 0 ] [ 6521, 0 ] [ 6680, -2 ] [ 6733, 1 ] [ 6892, -1 ] [ 6945, 3 ] [ 7157, 10 ] [ 7369, 0 ] [ 7528, -2 ] [ 7793, -4 ] [ 8005, 3 ] [ 8376, -2 ] [ 8429, -3 ] [ 8588, 7 ] [ 8641, 4 ] [ 8853, -3 ] [ 9224, 14 ] [ 9277, 1 ] [ 9436, -4 ] [ 9489, -1 ] [ 9701, -10 ] [ 9913, 1 ] /* D = 3 (mod 53 ) [ 56, -2 ] [ 109, 0 ] [ 268, 0 ] [ 321, -1 ] [ 533, 4 ] [ 745, -1 ] [ 904, 1 ] [ 957, 1 ] [ 1169, -1 ] [ 1381, -1 ] [ 1752, -2 ] [ 1964, 1 ] [ 2017, 1 ] [ 2229, -3 ] [ 2441, -1 ] [ 2653, 1 ] [ 2812, -1 ] [ 2865, 1 ] [ 3077, 6 ] [ 3289, 1 ] [ 3448, 0 ] [ 3660, -8 ] [ 3713, 6 ] [ 4137, 4 ] [ 4296, 9 ] [ 4349, -6 ] [ 4561, 0 ] [ 4773, 3 ] [ 4985, 3 ] [ 5144, 2 ] [ 5197, 2 ] [ 5356, -1 ] [ 5621, 6 ] [ 5833, 0 ] [ 5992, 2 ] [ 6045, -4 ] [ 6204, -2 ] [ 6257, -2 ] [ 6469, -1 ] [ 6681, -5 ] [ 6893, -1 ] [ 7052, 2 ] [ 7529, -4 ] [ 7741, -4 ] [ 7953, 1 ] [ 8165, -3 ] [ 8377, 1 ] [ 8536, 4 ] [ 8589, 3 ] [ 8801, -2 ] [ 9013, 1 ] [ 9384, 1 ] [ 9437, 2 ] [ 9596, -1 ] [ 9649, -1 ] [ 9861, -4 ] /* D = 5 (mod 53 ) [ 5, -1 ] [ 217, 0 ] [ 376, 2 ] [ 429, 1 ] [ 641, 2 ] [ 853, 2 ] [ 1065, -1 ] [ 1277, -1 ] [ 1436, -3 ] [ 1489, 0 ] [ 1913, 1 ] [ 2072, -4 ] [ 2284, 0 ] [ 2337, 0 ] [ 2549, 0 ] [ 2761, -2 ] [ 2920, -2 ] [ 2973, 1 ] [ 3397, 3 ] [ 3768, -2 ] [ 3821, 10 ] [ 3980, -2 ] [ 4033, 0 ] [ 4245, -5 ] [ 4457, 4 ] [ 4616, 6 ] [ 4669, -1 ] [ 4828, 3 ] [ 4881, 2 ] [ 5093, 1 ] [ 5305, -3 ] [ 5464, 0 ] [ 5676, -6 ] [ 5729, -7 ] [ 5941, -2 ] [ 6153, -2 ] [ 6312, 0 ] [ 6365, 10 ] [ 6524, 6 ] [ 6577, -1 ] [ 6789, 0 ] [ 7001, -4 ] [ 7160, -4 ] [ 7213, -4 ] [ 7372, -1 ] [ 7637, -9 ] [ 7849, 0 ] [ 8008, -2 ] [ 8061, -1 ] [ 8220, 4 ] [ 8273, 13 ] [ 8485, -1 ] [ 8697, -3 ] [ 8909, -2 ] [ 9068, 1 ] [ 9121, 2 ] [ 9545, -3 ] [ 9704, 9 ] [ 9757, 3 ] [ 9916, 0 ] [ 9969, -3 ] /* D = 8 (mod 53 ) [ 8, 1 ] [ 61, -1 ] [ 220, 0 ] [ 273, -1 ] [ 485, -3 ] [ 697, 0 ] [ 856, -2 ] [ 1068, -2 ] [ 1121, 2 ] [ 1333, -2 ] [ 1545, 3 ] [ 1704, -3 ] [ 1757, 4 ] [ 1916, 1 ] [ 1969, 1 ] [ 2181, 2 ] [ 2393, -6 ] [ 2552, 2 ] [ 2605, 1 ] [ 2764, 1 ] [ 3029, -8 ] [ 3241, 1 ] [ 3453, -3 ] [ 3612, 4 ] [ 3665, 0 ] [ 3877, 0 ] [ 4089, 2 ] [ 4301, 3 ] [ 4460, 4 ] [ 4513, -1 ] [ 4937, -1 ] [ 5149, 2 ] [ 5308, 0 ] [ 5361, 0 ] [ 5573, 0 ] [ 5785, 4 ] [ 5944, 0 ] [ 5997, 4 ] [ 6209, 7 ] [ 6421, -1 ] [ 6792, -3 ] [ 7004, -3 ] [ 7057, 0 ] [ 7269, 3 ] [ 7481, 3 ] [ 7640, -10 ] [ 7852, 1 ] [ 7905, 0 ] [ 8117, -1 ] [ 8329, 0 ] [ 8488, -3 ] [ 8753, 6 ] [ 8965, 4 ] [ 9177, -3 ] [ 9336, 6 ] [ 9389, 0 ] [ 9548, 12 ] [ 9601, -2 ] [ 9813, -8 ] /* D = 12 (mod 53 ) [ 12, -1 ] [ 65, 1 ] [ 277, 0 ] [ 489, 1 ] [ 701, -1 ] [ 860, 8 ] [ 913, 1 ] [ 1337, -1 ] [ 1496, 8 ] [ 1549, 1 ] [ 1708, 0 ] [ 1761, -3 ] [ 1973, -8 ] [ 2185, -1 ] [ 2344, 2 ] [ 2397, 4 ] [ 2609, -1 ] [ 2821, -2 ] [ 3192, -6 ] [ 3245, 8 ] [ 3404, 7 ] [ 3457, -1 ] [ 3669, -4 ] [ 3881, -2 ] [ 4040, -4 ] [ 4093, 3 ] [ 4252, -3 ] [ 4305, 2 ] [ 4517, 8 ] [ 4729, -1 ] [ 4888, 2 ] [ 5153, 4 ] [ 5365, -1 ] [ 5736, 6 ] [ 5789, -7 ] [ 5948, -9 ] [ 6001, -1 ] [ 6213, 0 ] [ 6584, 4 ] [ 6637, 0 ] [ 6796, 3 ] [ 7061, -14 ] [ 7273, 0 ] [ 7432, -4 ] [ 7485, 1 ] [ 7697, -1 ] [ 7909, -2 ] [ 8121, -3 ] [ 8333, -8 ] [ 8492, 4 ] [ 8545, 3 ] [ 8969, 2 ] [ 9128, -8 ] [ 9181, 0 ] [ 9340, 2 ] [ 9393, 0 ] [ 9605, 1 ] [ 9817, 3 ] [ 9976, -2 ] /* D = 14 (mod 53 ) [ 120, 0 ] [ 173, -4 ] [ 332, 3 ] [ 385, 0 ] [ 597, 1 ] [ 809, 3 ] [ 1021, 2 ] [ 1180, 2 ] [ 1657, -1 ] [ 1816, -2 ] [ 1869, 2 ] [ 2081, -1 ] [ 2293, -1 ] [ 2505, -3 ] [ 2717, -3 ] [ 2876, -4 ] [ 2929, -3 ] [ 3353, -5 ] [ 3512, 12 ] [ 3565, 2 ] [ 3777, 0 ] [ 3989, -2 ] [ 4201, 0 ] [ 4360, 4 ] [ 4413, -4 ] [ 4837, 1 ] [ 5208, -4 ] [ 5261, 2 ] [ 5420, -2 ] [ 5473, -2 ] [ 5685, 1 ] [ 5897, 6 ] [ 6056, -1 ] [ 6109, 2 ] [ 6268, -3 ] [ 6533, 2 ] [ 6745, -1 ] [ 6904, -2 ] [ 7116, -5 ] [ 7169, 4 ] [ 7593, -4 ] [ 7752, -1 ] [ 7805, -2 ] [ 7964, -18 ] [ 8017, 2 ] [ 8229, 2 ] [ 8441, 7 ] [ 8653, -2 ] [ 8812, 1 ] [ 9077, -3 ] [ 9289, 2 ] [ 9448, -1 ] [ 9501, -2 ] [ 9660, 6 ] [ 9713, -4 ] /* D = 18 (mod 53 ) [ 124, 2 ] [ 177, 0 ] [ 389, -2 ] [ 601, -1 ] [ 760, 0 ] [ 813, 0 ] [ 1237, 3 ] [ 1608, -4 ] [ 1661, -5 ] [ 1820, 6 ] [ 1873, 0 ] [ 2085, 6 ] [ 2297, 0 ] [ 2456, 2 ] [ 2509, 1 ] [ 2668, -1 ] [ 2721, -1 ] [ 2933, 4 ] [ 3145, -1 ] [ 3304, 0 ] [ 3516, 2 ] [ 3569, -7 ] [ 3781, 1 ] [ 4152, 2 ] [ 4364, 3 ] [ 4417, 1 ] [ 4629, -3 ] [ 4841, 2 ] [ 5053, -4 ] [ 5212, 0 ] [ 5477, 10 ] [ 5689, -4 ] [ 5848, -4 ] [ 5901, 1 ] [ 6060, -4 ] [ 6113, 0 ] [ 6537, -2 ] [ 6749, 6 ] [ 6908, -8 ] [ 6961, -1 ] [ 7385, 8 ] [ 7544, 6 ] [ 7597, 1 ] [ 7756, 0 ] [ 7809, 3 ] [ 8021, -9 ] [ 8233, -1 ] [ 8392, 5 ] [ 8445, -3 ] [ 8657, 10 ] [ 9240, 4 ] [ 9293, 0 ] [ 9452, -4 ] [ 9505, 2 ] [ 9717, 6 ] [ 9929, -5 ] /* D = 19 (mod 53 ) [ 284, 3 ] [ 337, -1 ] [ 761, 3 ] [ 920, -6 ] [ 973, 0 ] [ 1132, -1 ] [ 1185, -1 ] [ 1397, 5 ] [ 1609, 0 ] [ 1768, 1 ] [ 1821, 0 ] [ 2033, 7 ] [ 2245, -1 ] [ 2616, 4 ] [ 2669, 3 ] [ 2828, 0 ] [ 2881, -2 ] [ 3093, 3 ] [ 3305, -5 ] [ 3464, 1 ] [ 3517, 3 ] [ 3676, 1 ] [ 3729, -5 ] [ 3941, -11 ] [ 4153, -1 ] [ 4524, 3 ] [ 4577, 1 ] [ 4789, 2 ] [ 5001, 0 ] [ 5160, 0 ] [ 5213, 2 ] [ 5372, -9 ] [ 5637, 1 ] [ 5849, 1 ] [ 6008, 2 ] [ 6061, 5 ] [ 6220, 2 ] [ 6485, -3 ] [ 6697, 2 ] [ 6856, 4 ] [ 7068, -4 ] [ 7121, -1 ] [ 7333, -2 ] [ 7545, 6 ] [ 7757, -1 ] [ 7916, 6 ] [ 7969, 2 ] [ 8393, 8 ] [ 8552, 5 ] [ 8605, 3 ] [ 8764, -2 ] [ 8817, 1 ] [ 9029, -12 ] [ 9241, -3 ] [ 9453, -7 ] [ 9665, -2 ] [ 9877, -1 ] /* D = 20 (mod 53 ) [ 73, 1 ] [ 232, -1 ] [ 285, 1 ] [ 444, -1 ] [ 497, -1 ] [ 709, 0 ] [ 921, 2 ] [ 1133, -9 ] [ 1292, 5 ] [ 1345, 1 ] [ 1769, -3 ] [ 1928, -5 ] [ 1981, -3 ] [ 2140, 0 ] [ 2193, 1 ] [ 2405, 1 ] [ 2617, -1 ] [ 2776, 0 ] [ 2829, -2 ] [ 3041, 1 ] [ 3253, 0 ] [ 3624, -3 ] [ 3677, 5 ] [ 3836, -6 ] [ 3889, 2 ] [ 4101, 2 ] [ 4313, -3 ] [ 4472, 6 ] [ 4684, -1 ] [ 4737, -2 ] [ 5161, 0 ] [ 5320, -2 ] [ 5532, -1 ] [ 5585, -5 ] [ 5797, -2 ] [ 6009, 1 ] [ 6168, -2 ] [ 6221, 2 ] [ 6380, 12 ] [ 6433, 1 ] [ 6645, 1 ] [ 6857, -1 ] [ 7016, 2 ] [ 7069, -2 ] [ 7228, -2 ] [ 7493, -8 ] [ 7705, 2 ] [ 7864, 0 ] [ 7917, -1 ] [ 8076, 0 ] [ 8129, 3 ] [ 8341, 2 ] [ 8553, 0 ] [ 8765, 1 ] [ 8924, -5 ] [ 8977, 0 ] [ 9401, 7 ] [ 9560, 12 ] [ 9613, 3 ] [ 9772, 2 ] /* D = 21 (mod 53 ) [ 21, 1 ] [ 233, 2 ] [ 445, 2 ] [ 604, 1 ] [ 869, -3 ] [ 1081, -2 ] [ 1240, 0 ] [ 1293, 1 ] [ 1505, 2 ] [ 1717, -1 ] [ 1929, -2 ] [ 2141, 2 ] [ 2353, 0 ] [ 2777, -1 ] [ 2936, -10 ] [ 3148, 0 ] [ 3201, 3 ] [ 3413, -3 ] [ 3784, -2 ] [ 3837, 1 ] [ 4049, 10 ] [ 4261, -2 ] [ 4632, 0 ] [ 4685, 1 ] [ 4844, -8 ] [ 4897, 0 ] [ 5109, 1 ] [ 5321, 5 ] [ 5480, 16 ] [ 5533, 4 ] [ 5692, 0 ] [ 5745, -6 ] [ 5957, -11 ] [ 6169, -2 ] [ 6328, 2 ] [ 6540, -4 ] [ 6593, -4 ] [ 6805, -2 ] [ 7017, 0 ] [ 7176, -1 ] [ 7229, 3 ] [ 7388, -1 ] [ 7441, -3 ] [ 7653, 1 ] [ 8024, 2 ] [ 8077, -4 ] [ 8236, 1 ] [ 8501, -1 ] [ 8713, 0 ] [ 8872, -1 ] [ 9084, 3 ] [ 9137, 1 ] [ 9349, -1 ] [ 9561, 1 ] [ 9773, -3 ] [ 9932, 1 ] [ 9985, 1 ] /* D = 22 (mod 53 ) [ 181, 0 ] [ 393, 1 ] [ 552, -1 ] [ 764, 3 ] [ 817, -1 ] [ 1241, -1 ] [ 1453, -1 ] [ 1612, 0 ] [ 1877, -3 ] [ 2089, 0 ] [ 2248, 1 ] [ 2301, 8 ] [ 2460, 2 ] [ 2513, -5 ] [ 2937, 0 ] [ 3149, 8 ] [ 3308, 3 ] [ 3361, 1 ] [ 3785, -1 ] [ 3944, -9 ] [ 3997, 2 ] [ 4156, -2 ] [ 4209, 1 ] [ 4421, -4 ] [ 4633, 0 ] [ 4792, 2 ] [ 4845, -3 ] [ 5057, -8 ] [ 5269, 3 ] [ 5640, 4 ] [ 5693, -5 ] [ 5852, 2 ] [ 5905, -1 ] [ 6117, 8 ] [ 6329, 5 ] [ 6488, 4 ] [ 6541, 2 ] [ 6753, -1 ] [ 6965, 6 ] [ 7177, -1 ] [ 7336, 0 ] [ 7548, -1 ] [ 7601, 7 ] [ 7813, -3 ] [ 8184, 4 ] [ 8237, 3 ] [ 8396, 10 ] [ 8449, -1 ] [ 8661, -2 ] [ 8873, 0 ] [ 9032, -7 ] [ 9085, -1 ] [ 9244, 0 ] [ 9509, -12 ] [ 9721, 2 ] [ 9880, 6 ] [ 9933, -4 ] /* D = 23 (mod 53 ) [ 76, -1 ] [ 129, -1 ] [ 341, 0 ] [ 553, -1 ] [ 712, 0 ] [ 924, -2 ] [ 977, 0 ] [ 1189, 0 ] [ 1401, 0 ] [ 1560, 2 ] [ 1613, -2 ] [ 1772, -5 ] [ 2037, -1 ] [ 2249, 0 ] [ 2408, -4 ] [ 2461, 1 ] [ 2620, 2 ] [ 2885, -4 ] [ 3097, -1 ] [ 3256, -2 ] [ 3309, -1 ] [ 3521, -2 ] [ 3733, 2 ] [ 3945, 2 ] [ 4157, 5 ] [ 4316, 5 ] [ 4369, -2 ] [ 4793, 6 ] [ 4952, -2 ] [ 5005, 0 ] [ 5164, 5 ] [ 5217, 0 ] [ 5429, -4 ] [ 5641, 2 ] [ 5853, 2 ] [ 6065, 1 ] [ 6277, 4 ] [ 6648, -4 ] [ 6701, 8 ] [ 6913, 2 ] [ 7337, -7 ] [ 7496, -3 ] [ 7549, 0 ] [ 7708, 0 ] [ 7761, -3 ] [ 7973, -10 ] [ 8185, 1 ] [ 8344, -4 ] [ 8556, 2 ] [ 8609, 4 ] [ 8821, 2 ] [ 9033, 4 ] [ 9192, -2 ] [ 9404, -10 ] [ 9669, 4 ] [ 9881, -2 ] /* D = 26 (mod 53 ) [ 185, 3 ] [ 344, 0 ] [ 397, -2 ] [ 556, -2 ] [ 609, -1 ] [ 821, 2 ] [ 1033, 1 ] [ 1192, 1 ] [ 1245, -5 ] [ 1457, 2 ] [ 1669, -2 ] [ 2040, -4 ] [ 2093, 5 ] [ 2252, -3 ] [ 2305, -1 ] [ 2517, 2 ] [ 2729, -4 ] [ 2941, 0 ] [ 3153, 2 ] [ 3365, 2 ] [ 3736, -2 ] [ 3948, -2 ] [ 4001, -1 ] [ 4213, 6 ] [ 4584, 3 ] [ 4637, 2 ] [ 4796, 2 ] [ 4849, 1 ] [ 5061, 3 ] [ 5273, 0 ] [ 5432, -6 ] [ 5485, -1 ] [ 5644, 3 ] [ 5909, -4 ] [ 6121, 2 ] [ 6280, 0 ] [ 6333, 3 ] [ 6492, 4 ] [ 6545, -8 ] [ 6757, -2 ] [ 6969, -1 ] [ 7181, -17 ] [ 7340, -4 ] [ 7393, 0 ] [ 7817, 4 ] [ 7976, 11 ] [ 8029, -2 ] [ 8188, 6 ] [ 8241, 0 ] [ 8453, -5 ] [ 8665, -2 ] [ 8824, 0 ] [ 8877, -3 ] [ 9089, 7 ] [ 9301, 1 ] [ 9672, -2 ] [ 9884, 2 ] [ 9937, -2 ] /* D = 27 (mod 53 ) [ 133, -1 ] [ 345, -1 ] [ 557, -1 ] [ 716, 1 ] [ 769, 0 ] [ 1193, 2 ] [ 1405, 3 ] [ 1564, -1 ] [ 1829, 4 ] [ 2041, 1 ] [ 2253, 0 ] [ 2465, -5 ] [ 2677, -1 ] [ 3048, -7 ] [ 3101, -5 ] [ 3260, 2 ] [ 3313, -1 ] [ 3737, 1 ] [ 3896, 6 ] [ 3949, -1 ] [ 4108, -3 ] [ 4161, -1 ] [ 4373, -10 ] [ 4585, 0 ] [ 4744, 1 ] [ 4956, 0 ] [ 5009, 3 ] [ 5221, -3 ] [ 5433, -2 ] [ 5592, 6 ] [ 5645, 7 ] [ 5804, -9 ] [ 5857, 3 ] [ 6281, 2 ] [ 6440, -6 ] [ 6493, -1 ] [ 6652, 2 ] [ 6917, 1 ] [ 7129, -1 ] [ 7288, 0 ] [ 7341, 7 ] [ 7553, 9 ] [ 7765, 1 ] [ 7977, 2 ] [ 8189, -9 ] [ 8348, -1 ] [ 8401, 0 ] [ 8984, -4 ] [ 9037, -1 ] [ 9249, 1 ] [ 9461, 1 ] [ 9673, -4 ] [ 9832, 3 ] [ 9885, 0 ] /* D = 30 (mod 53 ) [ 136, -1 ] [ 348, -3 ] [ 401, -2 ] [ 613, 0 ] [ 984, 2 ] [ 1037, 1 ] [ 1196, 7 ] [ 1249, -2 ] [ 1461, 0 ] [ 1673, 0 ] [ 1832, 3 ] [ 1885, -1 ] [ 2044, 0 ] [ 2309, -9 ] [ 2521, 0 ] [ 2680, 4 ] [ 2733, 0 ] [ 2892, 1 ] [ 2945, 4 ] [ 3157, 2 ] [ 3369, -1 ] [ 3581, -6 ] [ 3740, -4 ] [ 3793, -1 ] [ 4217, 10 ] [ 4376, 4 ] [ 4429, 1 ] [ 4588, 0 ] [ 4641, 3 ] [ 4853, -2 ] [ 5065, 1 ] [ 5224, 2 ] [ 5277, 2 ] [ 5489, -1 ] [ 5701, 3 ] [ 6072, -6 ] [ 6284, 3 ] [ 6337, -1 ] [ 6549, -2 ] [ 6761, -6 ] [ 6920, -2 ] [ 6973, 3 ] [ 7132, -1 ] [ 7185, -5 ] [ 7397, -8 ] [ 7609, 1 ] [ 7768, 2 ] [ 7980, 2 ] [ 8033, -2 ] [ 8245, -1 ] [ 8457, 1 ] [ 8616, 5 ] [ 8669, 7 ] [ 8828, -2 ] [ 8881, -1 ] [ 9093, 7 ] [ 9305, -1 ] [ 9517, 0 ] [ 9676, -2 ] [ 9941, 3 ] /* D = 31 (mod 53 ) [ 137, -1 ] [ 296, 1 ] [ 349, -1 ] [ 508, -1 ] [ 561, -1 ] [ 773, 5 ] [ 985, 0 ] [ 1144, -2 ] [ 1356, -1 ] [ 1409, 5 ] [ 1621, 1 ] [ 1833, 0 ] [ 1992, -1 ] [ 2045, -3 ] [ 2204, -7 ] [ 2257, -3 ] [ 2469, 2 ] [ 2681, 4 ] [ 2840, -6 ] [ 2893, 0 ] [ 3052, 2 ] [ 3317, -6 ] [ 3529, 1 ] [ 3688, 3 ] [ 3741, -1 ] [ 3953, 0 ] [ 4377, -1 ] [ 4589, 3 ] [ 4748, 7 ] [ 4801, -1 ] [ 5384, 0 ] [ 5437, -4 ] [ 5596, -1 ] [ 5649, -1 ] [ 5861, 7 ] [ 6073, 1 ] [ 6232, 2 ] [ 6285, 4 ] [ 6497, 2 ] [ 6709, 3 ] [ 7080, -2 ] [ 7133, -5 ] [ 7292, 3 ] [ 7345, 1 ] [ 7557, 3 ] [ 7769, -10 ] [ 7928, 4 ] [ 7981, 0 ] [ 8140, -4 ] [ 8193, 1 ] [ 8617, 1 ] [ 8776, 5 ] [ 8988, -6 ] [ 9041, 6 ] [ 9253, 2 ] [ 9465, 3 ] [ 9624, -2 ] [ 9677, 2 ] [ 9836, 4 ] [ 9889, 2 ] /* D = 32 (mod 53 ) [ 85, -1 ] [ 456, -1 ] [ 509, 6 ] [ 668, 5 ] [ 721, 1 ] [ 933, -2 ] [ 1145, 1 ] [ 1304, -6 ] [ 1357, 0 ] [ 1516, -1 ] [ 1569, 0 ] [ 1781, -1 ] [ 1993, 1 ] [ 2152, -1 ] [ 2364, -4 ] [ 2417, -2 ] [ 2629, -2 ] [ 2841, 5 ] [ 3053, 7 ] [ 3212, 0 ] [ 3265, 0 ] [ 3477, -7 ] [ 3689, 2 ] [ 3848, 5 ] [ 3901, 0 ] [ 4060, 2 ] [ 4537, 1 ] [ 4696, -2 ] [ 4749, -1 ] [ 4908, 5 ] [ 5173, -1 ] [ 5385, -1 ] [ 5597, -1 ] [ 5756, -10 ] [ 5809, 3 ] [ 6233, -10 ] [ 6392, 6 ] [ 6445, 0 ] [ 6604, 1 ] [ 6657, 1 ] [ 6869, -5 ] [ 7081, 1 ] [ 7240, 0 ] [ 7293, 7 ] [ 7505, -1 ] [ 7717, -3 ] [ 8088, -4 ] [ 8141, 0 ] [ 8353, -3 ] [ 8565, -4 ] [ 8777, -4 ] [ 8936, 3 ] [ 8989, 2 ] [ 9148, 0 ] [ 9201, 3 ] [ 9413, -2 ] [ 9784, -4 ] /* D = 33 (mod 53 ) [ 33, 1 ] [ 457, 0 ] [ 616, -2 ] [ 669, -3 ] [ 881, -1 ] [ 1093, -1 ] [ 1464, 0 ] [ 1517, -2 ] [ 1676, 6 ] [ 1729, -1 ] [ 1941, 3 ] [ 2153, 2 ] [ 2365, -2 ] [ 2524, 1 ] [ 2577, -2 ] [ 2789, 11 ] [ 3001, 3 ] [ 3160, 2 ] [ 3372, 1 ] [ 3637, 0 ] [ 3849, 5 ] [ 4008, 5 ] [ 4061, -6 ] [ 4220, -8 ] [ 4273, 2 ] [ 4485, -3 ] [ 4697, -2 ] [ 4856, -10 ] [ 4909, 1 ] [ 5068, 2 ] [ 5333, -5 ] [ 5545, -1 ] [ 5704, 0 ] [ 5757, 1 ] [ 5916, -1 ] [ 5969, -2 ] [ 6181, 0 ] [ 6393, 1 ] [ 6605, -1 ] [ 6764, 6 ] [ 6817, -2 ] [ 7241, -3 ] [ 7453, 4 ] [ 7612, -4 ] [ 7665, 4 ] [ 7877, 4 ] [ 8089, 1 ] [ 8248, 4 ] [ 8301, 5 ] [ 8513, -2 ] [ 9096, 1 ] [ 9149, -11 ] [ 9308, -9 ] [ 9361, 1 ] [ 9573, 3 ] [ 9785, -3 ] [ 9944, 0 ] [ 9997, 2 ] /* D = 34 (mod 53 ) [ 140, 2 ] [ 193, -1 ] [ 617, -3 ] [ 776, -1 ] [ 829, -2 ] [ 988, -1 ] [ 1041, 2 ] [ 1253, -1 ] [ 1465, 2 ] [ 1624, 0 ] [ 1677, 1 ] [ 1889, -2 ] [ 2101, -1 ] [ 2472, -1 ] [ 2684, 8 ] [ 2737, 3 ] [ 2949, 2 ] [ 3161, -4 ] [ 3320, 8 ] [ 3373, -1 ] [ 3532, 0 ] [ 3585, 0 ] [ 3797, -6 ] [ 4009, 2 ] [ 4168, -3 ] [ 4380, 2 ] [ 4433, -2 ] [ 4645, 0 ] [ 4857, 7 ] [ 5016, 0 ] [ 5069, -1 ] [ 5228, -15 ] [ 5281, -3 ] [ 5493, -4 ] [ 5705, -8 ] [ 5864, 4 ] [ 5917, 3 ] [ 6341, 11 ] [ 6553, 1 ] [ 6712, 2 ] [ 6765, 4 ] [ 6924, -2 ] [ 6977, 8 ] [ 7189, 1 ] [ 7401, 0 ] [ 7613, 8 ] [ 7772, 0 ] [ 8249, 1 ] [ 8408, 2 ] [ 8461, -1 ] [ 8620, 0 ] [ 8885, 7 ] [ 9097, 1 ] [ 9256, -2 ] [ 9309, -5 ] [ 9521, -1 ] [ 9733, -4 ] /* D = 35 (mod 53 ) [ 88, 0 ] [ 141, 2 ] [ 353, -3 ] [ 565, 3 ] [ 777, -1 ] [ 989, -1 ] [ 1148, 0 ] [ 1201, 0 ] [ 1784, 2 ] [ 1837, -1 ] [ 1996, 1 ] [ 2049, 4 ] [ 2261, 1 ] [ 2473, -2 ] [ 2632, 2 ] [ 2685, 1 ] [ 2897, 5 ] [ 3109, -1 ] [ 3480, -2 ] [ 3533, -5 ] [ 3692, 5 ] [ 3745, 0 ] [ 3957, -1 ] [ 4169, -1 ] [ 4328, -2 ] [ 4381, -1 ] [ 4540, -2 ] [ 4593, -3 ] [ 5017, 0 ] [ 5176, -4 ] [ 5388, 1 ] [ 5441, -1 ] [ 5653, 1 ] [ 5865, 3 ] [ 6024, -4 ] [ 6077, 0 ] [ 6236, -7 ] [ 6289, 0 ] [ 6501, 2 ] [ 6872, 12 ] [ 7084, 2 ] [ 7349, 15 ] [ 7561, -1 ] [ 7720, -2 ] [ 7773, 2 ] [ 7932, 3 ] [ 7985, -7 ] [ 8197, -5 ] [ 8409, 0 ] [ 8621, 0 ] [ 8780, -2 ] [ 9257, 5 ] [ 9416, 2 ] [ 9469, 5 ] [ 9628, 3 ] [ 9681, 1 ] [ 9893, -7 ] /* D = 39 (mod 53 ) [ 92, -1 ] [ 145, 1 ] [ 357, 1 ] [ 569, -2 ] [ 728, -4 ] [ 781, 1 ] [ 940, 0 ] [ 993, 2 ] [ 1205, -5 ] [ 1417, 0 ] [ 1576, 0 ] [ 1788, -1 ] [ 1841, -6 ] [ 2053, 0 ] [ 2265, 1 ] [ 2424, 2 ] [ 2477, 11 ] [ 2636, 2 ] [ 2689, 1 ] [ 2901, -5 ] [ 3113, 5 ] [ 3272, -3 ] [ 3484, -2 ] [ 3749, -1 ] [ 3961, 0 ] [ 4120, -2 ] [ 4173, 1 ] [ 4385, -6 ] [ 4597, -7 ] [ 4809, -3 ] [ 5021, 5 ] [ 5180, -6 ] [ 5233, 2 ] [ 5657, 4 ] [ 5816, 4 ] [ 5869, -4 ] [ 6028, -2 ] [ 6081, 2 ] [ 6293, -6 ] [ 6505, 0 ] [ 6717, -2 ] [ 7141, 1 ] [ 7512, -2 ] [ 7565, 10 ] [ 7724, 15 ] [ 7777, 0 ] [ 7989, -1 ] [ 8201, -6 ] [ 8360, 4 ] [ 8413, 6 ] [ 8572, -5 ] [ 8837, 7 ] [ 9049, -3 ] [ 9208, 2 ] [ 9420, 4 ] [ 9473, 2 ] [ 9685, 1 ] [ 9897, 3 ] /* D = 41 (mod 53 ) [ 41, 2 ] [ 253, 1 ] [ 412, -1 ] [ 465, 2 ] [ 677, -6 ] [ 889, 1 ] [ 1048, 4 ] [ 1101, -1 ] [ 1313, -3 ] [ 1896, 5 ] [ 1949, 4 ] [ 2108, 4 ] [ 2161, 1 ] [ 2373, 5 ] [ 2585, -2 ] [ 2797, -1 ] [ 2956, -3 ] [ 3009, -2 ] [ 3221, 6 ] [ 3433, -1 ] [ 3592, -1 ] [ 3804, -3 ] [ 3857, 3 ] [ 4069, -1 ] [ 4281, 0 ] [ 4440, -6 ] [ 4493, 0 ] [ 4652, 0 ] [ 4705, 0 ] [ 4917, -3 ] [ 5129, 5 ] [ 5288, 5 ] [ 5765, -2 ] [ 5977, -2 ] [ 6136, -2 ] [ 6189, 4 ] [ 6401, 4 ] [ 6613, 0 ] [ 7037, -6 ] [ 7196, 2 ] [ 7249, 2 ] [ 7673, -2 ] [ 7832, 16 ] [ 7885, -5 ] [ 8044, 2 ] [ 8097, -1 ] [ 8309, -1 ] [ 8521, 0 ] [ 8680, 0 ] [ 8733, -4 ] [ 8945, -1 ] [ 9157, 3 ] [ 9528, 0 ] [ 9581, 8 ] [ 9740, -2 ] [ 9793, 3 ] /* D = 45 (mod 53 ) [ 204, -1 ] [ 257, -2 ] [ 469, 2 ] [ 681, 1 ] [ 840, 2 ] [ 893, 2 ] [ 1052, 0 ] [ 1105, 3 ] [ 1317, 2 ] [ 1529, -2 ] [ 1688, -2 ] [ 1741, -2 ] [ 2165, 5 ] [ 2377, -2 ] [ 2536, 1 ] [ 2589, -6 ] [ 2748, -1 ] [ 2801, -1 ] [ 3013, -3 ] [ 3437, -1 ] [ 3596, 8 ] [ 3649, 0 ] [ 4073, 2 ] [ 4285, -2 ] [ 4444, -2 ] [ 4497, 1 ] [ 4709, 0 ] [ 4921, -1 ] [ 5080, -2 ] [ 5133, -4 ] [ 5345, -1 ] [ 5557, 3 ] [ 5928, -5 ] [ 5981, -1 ] [ 6140, -6 ] [ 6193, 1 ] [ 6405, -2 ] [ 6617, 2 ] [ 6829, -2 ] [ 6988, -3 ] [ 7041, 3 ] [ 7253, -2 ] [ 7465, 3 ] [ 7624, 0 ] [ 7836, -6 ] [ 8101, -1 ] [ 8313, 1 ] [ 8472, 2 ] [ 8684, -1 ] [ 8737, -1 ] [ 8949, 9 ] [ 9161, -7 ] [ 9320, -2 ] [ 9373, -3 ] [ 9532, -3 ] [ 9797, -1 ] /* D = 48 (mod 53 ) [ 101, -3 ] [ 313, 1 ] [ 472, -2 ] [ 737, 2 ] [ 949, -1 ] [ 1320, -4 ] [ 1373, 4 ] [ 1532, -6 ] [ 1585, -1 ] [ 1797, -4 ] [ 2168, -2 ] [ 2221, -1 ] [ 2380, 2 ] [ 2433, 1 ] [ 2857, 0 ] [ 3016, 1 ] [ 3228, -1 ] [ 3281, -5 ] [ 3493, -1 ] [ 3705, -1 ] [ 3864, 4 ] [ 3917, 0 ] [ 4076, -1 ] [ 4129, -1 ] [ 4341, 1 ] [ 4553, -3 ] [ 4712, -2 ] [ 4765, 6 ] [ 4924, -1 ] [ 5189, -7 ] [ 5401, 1 ] [ 5560, 0 ] [ 5613, 3 ] [ 5772, -1 ] [ 6037, -2 ] [ 6249, 2 ] [ 6461, -1 ] [ 6620, -10 ] [ 6673, 0 ] [ 7097, 10 ] [ 7256, 4 ] [ 7309, 2 ] [ 7468, -5 ] [ 7521, -4 ] [ 7733, 13 ] [ 7945, 2 ] [ 8104, 3 ] [ 8157, -1 ] [ 8369, 4 ] [ 8581, -5 ] [ 8952, -2 ] [ 9005, -13 ] [ 9164, 3 ] [ 9217, 4 ] [ 9429, -3 ] [ 9641, -6 ] [ 9853, 2 ] /* D = 50 (mod 53 ) [ 156, -1 ] [ 209, 3 ] [ 421, 0 ] [ 633, 0 ] [ 1004, 2 ] [ 1057, -1 ] [ 1481, -2 ] [ 1640, -2 ] [ 1693, 2 ] [ 1852, -1 ] [ 1905, -1 ] [ 2117, 7 ] [ 2329, -1 ] [ 2488, 2 ] [ 2753, -3 ] [ 2965, 1 ] [ 3336, 2 ] [ 3389, 4 ] [ 3548, -11 ] [ 3601, -4 ] [ 3813, 6 ] [ 4184, -8 ] [ 4237, -1 ] [ 4396, 4 ] [ 4449, -3 ] [ 4661, -6 ] [ 4873, 1 ] [ 5032, -3 ] [ 5244, 5 ] [ 5297, 4 ] [ 5509, 2 ] [ 5721, 0 ] [ 5933, 3 ] [ 6092, 1 ] [ 6145, 3 ] [ 6357, -1 ] [ 6569, -9 ] [ 6781, -1 ] [ 6940, 2 ] [ 7205, 2 ] [ 7417, -1 ] [ 7576, 2 ] [ 7629, 6 ] [ 7788, 2 ] [ 7841, 5 ] [ 8053, 4 ] [ 8265, 5 ] [ 8636, -7 ] [ 8689, 0 ] [ 9113, -3 ] [ 9272, -4 ] [ 9484, -1 ] [ 9749, -11 ] [ 9961, -2 ] /* D = 51 (mod 53 ) [ 104, 3 ] [ 157, 1 ] [ 316, 1 ] [ 581, -1 ] [ 793, 1 ] [ 952, -2 ] [ 1005, 0 ] [ 1164, 1 ] [ 1217, 4 ] [ 1429, -1 ] [ 1641, -1 ] [ 1853, 10 ] [ 2012, -6 ] [ 2065, 2 ] [ 2489, 1 ] [ 2648, 2 ] [ 2701, -3 ] [ 2860, 4 ] [ 2913, 1 ] [ 3337, 0 ] [ 3496, -1 ] [ 3761, -1 ] [ 3973, -3 ] [ 4344, 0 ] [ 4397, 0 ] [ 4556, 12 ] [ 4609, 0 ] [ 4821, 0 ] [ 5033, 2 ] [ 5192, 6 ] [ 5245, -1 ] [ 5404, -2 ] [ 5457, 1 ] [ 5669, -1 ] [ 5881, 0 ] [ 6040, -2 ] [ 6252, -1 ] [ 6305, -3 ] [ 6729, 2 ] [ 6888, -4 ] [ 6941, -3 ] [ 7153, 2 ] [ 7365, -1 ] [ 7577, 7 ] [ 7736, -4 ] [ 7789, -3 ] [ 7948, -5 ] [ 8213, 3 ] [ 8584, 1 ] [ 8637, 7 ] [ 8796, -2 ] [ 8849, -2 ] [ 9061, 2 ] [ 9273, 1 ] [ 9485, 6 ] [ 9644, 2 ] [ 9697, -1 ] Total time: 26.460 seconds Goodbye!