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, 1, 0]); /* 83A */ wp=ellrootno(e,p); /* 1 */ mxl=qsetprime(83); Is=qidcl(mxl); /* # = 8 */ f=vector(8,i,ellap(e,prime(i))); /* [-1, -1, -2, -3, 3, -6, 5, 2] */ ef=get_ef(mxl,f,Is); /* [0, 0, 0, -1/2, 0, 0, 0, 1/2]~ */ ht=hprod(ef,ef); /* 1/2 */ b0=qzero_modp(19); /* [0, 1, 1, 8], norm = 5396 */ Qs=vector(#Is,i,qtheta_lp(Is[i],b0,-19,83)); ks=vector(#Qs,i,qfrep_lk(Qs[i]),1,1)); kf=sum(i=1,#ef,ef[i]*ks[i]); kfs=sum(i=1,#kf,kronecker(i,p)*kf[i])/2; 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 83 ) [ 85, 1 ] [ 168, -3 ] [ 417, 1 ] [ 749, 4 ] [ 1081, 0 ] [ 1164, 2 ] [ 1496, -1 ] [ 1745, 1 ] [ 2077, 2 ] [ 2409, -1 ] [ 2492, 2 ] [ 2741, -3 ] [ 2824, 1 ] [ 3073, -5 ] [ 3405, 2 ] [ 3737, 2 ] [ 3820, 4 ] [ 4069, -1 ] [ 4152, 5 ] [ 4733, 1 ] [ 5065, 0 ] [ 5397, -9 ] [ 5480, 4 ] [ 5729, -2 ] [ 6061, 1 ] [ 6393, -3 ] [ 6476, -4 ] [ 6808, -2 ] [ 7057, 3 ] [ 7721, 0 ] [ 7804, -6 ] [ 8053, -10 ] [ 8385, 4 ] [ 8717, 12 ] [ 9049, 2 ] [ 9132, 0 ] [ 9381, 6 ] [ 9713, -2 ] /* D = 5 (mod 83 ) [ 5, 1 ] [ 88, 1 ] [ 337, 0 ] [ 669, 1 ] [ 1001, -3 ] [ 1084, -2 ] [ 1333, -2 ] [ 1416, 1 ] [ 1997, 3 ] [ 2329, -2 ] [ 2661, 1 ] [ 2993, -4 ] [ 3657, 4 ] [ 3740, 2 ] [ 3989, 0 ] [ 4072, 3 ] [ 4321, 2 ] [ 4985, 5 ] [ 5068, 4 ] [ 5317, 1 ] [ 5649, 0 ] [ 5981, 2 ] [ 6313, 0 ] [ 6396, 4 ] [ 6645, -3 ] [ 6977, -4 ] [ 7309, 2 ] [ 7724, 0 ] [ 7973, -10 ] [ 8056, 2 ] [ 8305, 7 ] [ 8637, 2 ] [ 8969, -1 ] [ 9052, 4 ] [ 9301, -4 ] [ 9384, -2 ] [ 9965, -2 ] /* D = 6 (mod 83 ) [ 89, 2 ] [ 172, 0 ] [ 421, 2 ] [ 753, 1 ] [ 1085, -3 ] [ 1417, -1 ] [ 1749, 0 ] [ 1832, -2 ] [ 2081, 1 ] [ 2413, -7 ] [ 2828, -8 ] [ 3077, -3 ] [ 3160, 0 ] [ 3409, 1 ] [ 3741, 2 ] [ 4073, 0 ] [ 4156, 2 ] [ 4405, 7 ] [ 4488, 1 ] [ 4737, -6 ] [ 5069, 0 ] [ 5401, -1 ] [ 5484, -2 ] [ 5816, 1 ] [ 6065, 3 ] [ 6397, -2 ] [ 6729, -1 ] [ 6812, 8 ] [ 7061, 8 ] [ 7144, -6 ] [ 7393, 1 ] [ 8057, -1 ] [ 8140, -4 ] [ 8389, 1 ] [ 8472, -1 ] [ 9053, -5 ] [ 9385, 1 ] [ 9717, 10 ] /* D = 8 (mod 83 ) [ 8, -1 ] [ 257, 3 ] [ 589, 1 ] [ 921, -1 ] [ 1004, 4 ] [ 1253, 1 ] [ 1336, -1 ] [ 1585, -3 ] [ 2249, 1 ] [ 2332, 2 ] [ 2581, -2 ] [ 2913, -1 ] [ 3245, 5 ] [ 3660, 0 ] [ 3909, -4 ] [ 3992, 1 ] [ 4241, -2 ] [ 4573, 2 ] [ 4988, 0 ] [ 5237, 2 ] [ 5320, -2 ] [ 5569, -3 ] [ 5901, -3 ] [ 6233, -2 ] [ 6316, 2 ] [ 6565, 2 ] [ 6648, 4 ] [ 7229, 1 ] [ 7561, -2 ] [ 7976, 1 ] [ 8557, 4 ] [ 8889, 1 ] [ 8972, -16 ] [ 9221, 1 ] [ 9304, -1 ] [ 9553, 6 ] [ 9885, -2 ] /* D = 13 (mod 83 ) [ 13, 1 ] [ 345, 2 ] [ 428, -2 ] [ 677, 3 ] [ 760, 2 ] [ 1009, -1 ] [ 1673, -2 ] [ 1756, 0 ] [ 2005, 0 ] [ 2337, -2 ] [ 2669, -1 ] [ 3001, -5 ] [ 3084, 0 ] [ 3333, -6 ] [ 3416, 3 ] [ 3665, 1 ] [ 3997, -2 ] [ 4412, 6 ] [ 4661, 1 ] [ 4744, 5 ] [ 4993, 1 ] [ 5657, 5 ] [ 5740, 4 ] [ 5989, 2 ] [ 6072, 2 ] [ 6653, 4 ] [ 6985, 3 ] [ 7068, 0 ] [ 7649, 0 ] [ 7981, -2 ] [ 8313, 1 ] [ 8396, -2 ] [ 8645, 2 ] [ 8728, -7 ] [ 8977, 11 ] [ 9309, -6 ] [ 9641, 2 ] [ 9724, 0 ] [ 9973, -8 ] /* D = 14 (mod 83 ) [ 97, -2 ] [ 429, -1 ] [ 761, -2 ] [ 844, 0 ] [ 1093, -2 ] [ 1757, 7 ] [ 2089, -1 ] [ 2172, -6 ] [ 2504, 1 ] [ 2753, -2 ] [ 3085, 7 ] [ 3417, 4 ] [ 3749, 2 ] [ 3832, -1 ] [ 4081, 2 ] [ 4413, -4 ] [ 4745, 0 ] [ 4828, -8 ] [ 5077, -7 ] [ 5160, -6 ] [ 5741, -3 ] [ 6073, -1 ] [ 6405, 3 ] [ 6488, 4 ] [ 6737, 5 ] [ 7069, 3 ] [ 7401, -2 ] [ 7484, 0 ] [ 7733, -13 ] [ 7816, 3 ] [ 8065, -1 ] [ 8729, 0 ] [ 8812, 6 ] [ 9061, -2 ] [ 9393, -8 ] /* D = 15 (mod 83 ) [ 181, -1 ] [ 264, -3 ] [ 1177, 0 ] [ 1509, 0 ] [ 1592, 0 ] [ 1841, 1 ] [ 2173, 0 ] [ 2505, 1 ] [ 2588, 6 ] [ 2837, -2 ] [ 2920, 4 ] [ 3169, -2 ] [ 3833, -4 ] [ 3916, -2 ] [ 4497, 0 ] [ 4829, 9 ] [ 5161, 0 ] [ 5244, 0 ] [ 5493, -15 ] [ 5576, -2 ] [ 6157, 2 ] [ 6572, -10 ] [ 6821, -1 ] [ 6904, -3 ] [ 7153, 2 ] [ 7485, 1 ] [ 7817, -2 ] [ 8149, 1 ] [ 8481, 5 ] [ 8813, 1 ] [ 9145, 11 ] [ 9228, 2 ] [ 9560, -2 ] [ 9809, -2 ] /* D = 18 (mod 83 ) [ 101, 0 ] [ 184, 0 ] [ 433, -2 ] [ 1097, 0 ] [ 1180, 2 ] [ 1429, 0 ] [ 1761, 1 ] [ 2093, 4 ] [ 2508, 2 ] [ 2757, 0 ] [ 2840, -6 ] [ 3089, 5 ] [ 3421, 2 ] [ 3836, -2 ] [ 4085, 2 ] [ 4168, 4 ] [ 4417, 0 ] [ 4749, -1 ] [ 5081, 4 ] [ 5164, -4 ] [ 5413, 0 ] [ 5496, -2 ] [ 5745, -3 ] [ 6077, -8 ] [ 6409, 3 ] [ 6492, 8 ] [ 6824, -3 ] [ 7073, -5 ] [ 7405, 1 ] [ 7737, -4 ] [ 7820, -4 ] [ 8069, -1 ] [ 8152, 6 ] [ 8401, 0 ] [ 8733, 0 ] [ 9148, 4 ] [ 9397, -4 ] [ 9480, 4 ] /* D = 19 (mod 83 ) [ 185, -1 ] [ 268, 2 ] [ 517, 1 ] [ 849, 1 ] [ 1181, -5 ] [ 1513, -2 ] [ 1596, -4 ] [ 1928, -5 ] [ 2177, -6 ] [ 2509, 0 ] [ 2841, 6 ] [ 2924, -4 ] [ 3173, 5 ] [ 3256, -3 ] [ 3505, 2 ] [ 3837, -2 ] [ 4169, 0 ] [ 4252, -2 ] [ 4501, 3 ] [ 4584, -1 ] [ 5165, -1 ] [ 5497, 0 ] [ 5829, 6 ] [ 5912, 4 ] [ 6161, 2 ] [ 6493, -10 ] [ 6908, 0 ] [ 7157, 0 ] [ 7240, 2 ] [ 7489, 5 ] [ 8153, -9 ] [ 8236, 0 ] [ 8485, 3 ] [ 8817, 0 ] [ 9149, -2 ] [ 9481, 3 ] [ 9564, -4 ] [ 9813, -6 ] [ 9896, -5 ] /* D = 20 (mod 83 ) [ 269, 2 ] [ 601, -1 ] [ 933, 2 ] [ 1016, -1 ] [ 1265, -4 ] [ 1597, -4 ] [ 1929, -1 ] [ 2012, -6 ] [ 2261, -1 ] [ 2344, 0 ] [ 2593, 4 ] [ 3257, 2 ] [ 3340, 0 ] [ 3589, 2 ] [ 3921, 2 ] [ 4253, 6 ] [ 4585, 0 ] [ 4668, 4 ] [ 4917, 0 ] [ 5249, -1 ] [ 5581, -3 ] [ 5996, 0 ] [ 6245, 5 ] [ 6328, 7 ] [ 6577, -1 ] [ 7241, 0 ] [ 7324, 0 ] [ 7573, 5 ] [ 7656, 5 ] [ 7905, -3 ] [ 8237, -8 ] [ 8569, -2 ] [ 8652, 10 ] [ 8984, -3 ] [ 9233, 6 ] [ 9565, -2 ] [ 9897, 2 ] [ 9980, -2 ] /* D = 22 (mod 83 ) [ 105, -1 ] [ 188, 4 ] [ 437, 0 ] [ 520, 2 ] [ 769, -3 ] [ 1101, 2 ] [ 1433, 1 ] [ 1516, 2 ] [ 1765, -1 ] [ 1848, -7 ] [ 2429, -2 ] [ 2761, -3 ] [ 3093, 4 ] [ 3176, 4 ] [ 4089, 1 ] [ 4172, -2 ] [ 4421, -3 ] [ 4504, 7 ] [ 5417, 3 ] [ 5749, 2 ] [ 6081, 1 ] [ 6745, 0 ] [ 6828, 6 ] [ 7077, -2 ] [ 7160, 2 ] [ 7409, -2 ] [ 7741, 0 ] [ 8156, 2 ] [ 8488, 2 ] [ 8737, 3 ] [ 9069, -4 ] [ 9401, -3 ] [ 9484, 4 ] [ 9733, -10 ] [ 9816, 5 ] /* D = 24 (mod 83 ) [ 24, 1 ] [ 273, -3 ] [ 937, -1 ] [ 1020, 2 ] [ 1601, 2 ] [ 1933, 1 ] [ 2265, -3 ] [ 2348, -6 ] [ 2680, -4 ] [ 2929, 0 ] [ 3261, 0 ] [ 3593, 2 ] [ 3676, 0 ] [ 4008, 1 ] [ 4589, 3 ] [ 4921, 3 ] [ 5253, -4 ] [ 5336, -4 ] [ 5585, 6 ] [ 5917, 4 ] [ 6249, -2 ] [ 6332, 0 ] [ 6581, -3 ] [ 6913, -3 ] [ 7577, 7 ] [ 7660, 0 ] [ 7909, -8 ] [ 8241, -2 ] [ 8573, 1 ] [ 8905, 0 ] [ 8988, -2 ] [ 9237, 6 ] [ 9320, 8 ] [ 9569, -2 ] [ 9901, -8 ] /* D = 32 (mod 83 ) [ 281, 1 ] [ 364, -2 ] [ 613, 1 ] [ 696, -5 ] [ 1277, 2 ] [ 1609, 1 ] [ 1941, -2 ] [ 2024, 2 ] [ 2273, -4 ] [ 2605, 2 ] [ 2937, -4 ] [ 3020, 4 ] [ 3269, 1 ] [ 3352, 1 ] [ 3601, 0 ] [ 4265, -3 ] [ 4348, 8 ] [ 4597, -6 ] [ 4929, 6 ] [ 5261, -2 ] [ 5593, -1 ] [ 5676, -8 ] [ 6008, 4 ] [ 6257, -6 ] [ 6589, 1 ] [ 7004, -2 ] [ 7253, -3 ] [ 7336, 0 ] [ 7585, 2 ] [ 7917, 1 ] [ 8249, 3 ] [ 8332, -2 ] [ 8581, 5 ] [ 8913, 4 ] [ 9577, -1 ] [ 9660, -4 ] [ 9992, 1 ] /* D = 34 (mod 83 ) [ 449, -1 ] [ 781, 2 ] [ 1113, -2 ] [ 1196, 0 ] [ 1528, -1 ] [ 1777, 2 ] [ 2109, -1 ] [ 2441, 0 ] [ 2524, 2 ] [ 2773, -3 ] [ 2856, 3 ] [ 3437, 9 ] [ 3769, 1 ] [ 4101, -10 ] [ 4184, 5 ] [ 4433, -1 ] [ 4765, -1 ] [ 5097, -1 ] [ 5180, -6 ] [ 5429, 0 ] [ 5512, -8 ] [ 5761, -3 ] [ 6508, 2 ] [ 6757, -1 ] [ 7089, 1 ] [ 7421, -2 ] [ 7753, 3 ] [ 7836, -4 ] [ 8168, -1 ] [ 8417, 7 ] [ 8749, -1 ] [ 9164, -2 ] [ 9413, -2 ] [ 9496, 5 ] [ 9745, 1 ] /* D = 35 (mod 83 ) [ 201, 2 ] [ 284, 0 ] [ 533, 0 ] [ 616, 1 ] [ 865, 1 ] [ 1529, 1 ] [ 1612, -2 ] [ 1861, -4 ] [ 2193, -2 ] [ 2857, -3 ] [ 3189, 0 ] [ 3272, 1 ] [ 3521, 6 ] [ 3853, 1 ] [ 4268, 6 ] [ 4517, 2 ] [ 4849, 1 ] [ 5181, 3 ] [ 5513, -2 ] [ 5596, -4 ] [ 5845, 3 ] [ 5928, 6 ] [ 6177, -6 ] [ 6509, -2 ] [ 6841, 0 ] [ 6924, -4 ] [ 7256, -1 ] [ 7505, -2 ] [ 7837, 8 ] [ 8169, 5 ] [ 8252, 0 ] [ 8501, -5 ] [ 8584, -3 ] [ 9165, -2 ] [ 9497, 4 ] [ 9580, 4 ] [ 9829, 0 ] [ 9912, -3 ] /* D = 39 (mod 83 ) [ 205, -2 ] [ 537, -3 ] [ 620, 0 ] [ 869, 1 ] [ 952, -1 ] [ 1201, -2 ] [ 1533, 1 ] [ 1865, 3 ] [ 1948, 0 ] [ 2280, 2 ] [ 2861, 1 ] [ 3193, 2 ] [ 3608, -14 ] [ 3857, -1 ] [ 4189, -4 ] [ 4521, -4 ] [ 4604, -2 ] [ 4853, 4 ] [ 4936, 1 ] [ 5185, 1 ] [ 5849, 0 ] [ 5932, -4 ] [ 6181, -2 ] [ 6513, 7 ] [ 7177, 3 ] [ 7509, -11 ] [ 7592, -2 ] [ 7841, -1 ] [ 8173, -2 ] [ 8588, 2 ] [ 8837, 11 ] [ 8920, 4 ] [ 9169, -2 ] [ 9501, -6 ] [ 9833, -4 ] [ 9916, -2 ] /* D = 42 (mod 83 ) [ 457, 2 ] [ 789, -1 ] [ 872, 1 ] [ 1121, -1 ] [ 1453, 1 ] [ 1785, -1 ] [ 1868, 8 ] [ 2117, -3 ] [ 2449, 1 ] [ 3113, -5 ] [ 3196, 4 ] [ 3445, -2 ] [ 3777, 1 ] [ 4109, 1 ] [ 4441, 3 ] [ 4524, 2 ] [ 4773, -8 ] [ 4856, 4 ] [ 5105, 1 ] [ 5437, -1 ] [ 5852, 8 ] [ 6101, 2 ] [ 6184, -4 ] [ 6433, -4 ] [ 6765, 14 ] [ 7097, -1 ] [ 7180, 4 ] [ 7429, -6 ] [ 7512, -3 ] [ 7761, -2 ] [ 8093, -4 ] [ 8508, -18 ] [ 8840, 2 ] [ 9089, 6 ] [ 9421, 3 ] [ 9753, 1 ] [ 9836, -2 ] /* D = 43 (mod 83 ) [ 209, -1 ] [ 541, -2 ] [ 956, -2 ] [ 1205, -1 ] [ 1288, 2 ] [ 1537, 2 ] [ 1869, 2 ] [ 2201, -4 ] [ 2284, 0 ] [ 2533, 6 ] [ 2616, 1 ] [ 2865, 1 ] [ 3197, -6 ] [ 3529, -3 ] [ 3612, -4 ] [ 3944, 5 ] [ 4193, 1 ] [ 4857, 3 ] [ 4940, 0 ] [ 5189, 0 ] [ 5272, -6 ] [ 5521, -2 ] [ 5853, -2 ] [ 6185, -3 ] [ 6268, -6 ] [ 7181, 2 ] [ 7513, 3 ] [ 7845, 3 ] [ 7928, -1 ] [ 8177, -5 ] [ 8509, 0 ] [ 8841, 2 ] [ 8924, -4 ] [ 9173, 10 ] [ 9256, 0 ] [ 9505, -1 ] /* D = 45 (mod 83 ) [ 377, 1 ] [ 460, 4 ] [ 709, -1 ] [ 1041, 0 ] [ 1373, -3 ] [ 1705, 1 ] [ 1788, -2 ] [ 2037, -2 ] [ 2120, -2 ] [ 2369, 0 ] [ 2701, -1 ] [ 3116, 0 ] [ 3365, 7 ] [ 3448, -1 ] [ 3697, -1 ] [ 4029, 3 ] [ 4444, 0 ] [ 4776, -2 ] [ 5357, 5 ] [ 5689, 1 ] [ 5772, 2 ] [ 6104, 9 ] [ 6353, 0 ] [ 6685, 3 ] [ 7017, 3 ] [ 7349, -3 ] [ 7432, 3 ] [ 7681, -2 ] [ 8013, -8 ] [ 8345, -4 ] [ 8677, 5 ] [ 8760, 0 ] [ 9341, 6 ] [ 9673, -1 ] /* D = 46 (mod 83 ) [ 129, 0 ] [ 461, 2 ] [ 793, -1 ] [ 876, -2 ] [ 1208, -3 ] [ 1457, 1 ] [ 1789, 1 ] [ 2121, 0 ] [ 2204, -4 ] [ 2453, -5 ] [ 2536, -1 ] [ 2785, 0 ] [ 3117, -1 ] [ 3449, 3 ] [ 3532, 4 ] [ 3781, -2 ] [ 3864, 2 ] [ 4445, 5 ] [ 4777, -3 ] [ 5109, -2 ] [ 5192, -5 ] [ 5441, 1 ] [ 5773, -2 ] [ 6105, 1 ] [ 6188, 2 ] [ 6437, 6 ] [ 6520, 2 ] [ 6769, 4 ] [ 7433, 3 ] [ 7516, -10 ] [ 7765, 0 ] [ 8097, -4 ] [ 8429, -2 ] [ 8761, -2 ] [ 8844, -2 ] [ 9093, -6 ] [ 9176, -5 ] [ 9757, 9 ] /* D = 47 (mod 83 ) [ 213, 4 ] [ 296, -1 ] [ 545, -1 ] [ 877, 2 ] [ 1209, 1 ] [ 1292, 2 ] [ 1541, -4 ] [ 1624, 1 ] [ 1873, -1 ] [ 2537, -6 ] [ 2620, 4 ] [ 2869, -3 ] [ 3201, 2 ] [ 3533, -1 ] [ 3865, -2 ] [ 3948, -2 ] [ 4197, 8 ] [ 4280, 6 ] [ 4529, -2 ] [ 4861, -6 ] [ 5276, 6 ] [ 5608, -4 ] [ 5857, 1 ] [ 6189, -3 ] [ 6521, 0 ] [ 6604, 2 ] [ 6853, 8 ] [ 7185, 1 ] [ 7517, -3 ] [ 7849, 1 ] [ 7932, -6 ] [ 8264, 5 ] [ 8513, 0 ] [ 8845, 3 ] [ 9177, 2 ] [ 9260, 0 ] [ 9509, 3 ] [ 9592, -5 ] [ 9841, 1 ] /* D = 50 (mod 83 ) [ 133, 1 ] [ 465, 1 ] [ 797, 2 ] [ 1129, -1 ] [ 1212, 0 ] [ 1461, -7 ] [ 1544, 0 ] [ 1793, -1 ] [ 2540, 4 ] [ 2789, -4 ] [ 2872, -5 ] [ 3121, 0 ] [ 3453, 3 ] [ 3785, 1 ] [ 3868, 0 ] [ 4117, -2 ] [ 4449, 2 ] [ 4781, 3 ] [ 5113, 0 ] [ 5196, -2 ] [ 5528, -1 ] [ 5777, -4 ] [ 6109, 4 ] [ 6441, -1 ] [ 6524, 6 ] [ 6773, -2 ] [ 6856, 7 ] [ 7437, 6 ] [ 7769, -8 ] [ 7852, -6 ] [ 8101, 0 ] [ 8184, 1 ] [ 8765, 0 ] [ 9097, 1 ] [ 9429, -1 ] [ 9512, -2 ] [ 9761, -4 ] /* D = 52 (mod 83 ) [ 301, 2 ] [ 633, -1 ] [ 716, -2 ] [ 965, 4 ] [ 1048, -4 ] [ 1297, -1 ] [ 1961, 0 ] [ 2044, 0 ] [ 2293, -2 ] [ 2957, -6 ] [ 3289, 0 ] [ 3372, 10 ] [ 3621, -2 ] [ 3704, -3 ] [ 3953, -2 ] [ 4285, -1 ] [ 5032, 5 ] [ 5281, 1 ] [ 5613, -3 ] [ 5945, 0 ] [ 6028, 2 ] [ 6277, 6 ] [ 6360, 2 ] [ 6609, 7 ] [ 6941, 2 ] [ 7273, -1 ] [ 7356, -6 ] [ 7937, 1 ] [ 8269, 0 ] [ 8601, 5 ] [ 8684, -2 ] [ 8933, 1 ] [ 9265, 1 ] [ 9597, -6 ] [ 9929, 5 ] /* D = 53 (mod 83 ) [ 53, 0 ] [ 136, 1 ] [ 385, 1 ] [ 717, -4 ] [ 1049, 2 ] [ 1132, -2 ] [ 1381, 0 ] [ 1464, 5 ] [ 1713, 2 ] [ 2045, 1 ] [ 2377, 1 ] [ 2460, 4 ] [ 2792, -5 ] [ 3041, -3 ] [ 3373, 3 ] [ 3705, -2 ] [ 3788, 2 ] [ 4037, 8 ] [ 4120, -2 ] [ 4369, -1 ] [ 4701, -7 ] [ 5033, 2 ] [ 5116, 4 ] [ 5365, -1 ] [ 5448, 2 ] [ 6029, 1 ] [ 6361, -1 ] [ 6693, 8 ] [ 7357, 0 ] [ 7689, -5 ] [ 7772, 2 ] [ 8021, -5 ] [ 8104, 0 ] [ 8353, 0 ] [ 9017, 0 ] [ 9349, -5 ] [ 9681, -4 ] /* D = 54 (mod 83 ) [ 137, 2 ] [ 220, -2 ] [ 469, 0 ] [ 552, -4 ] [ 1133, 2 ] [ 1465, 0 ] [ 1797, -1 ] [ 1880, 0 ] [ 2129, 1 ] [ 2461, 0 ] [ 2876, 2 ] [ 3208, -2 ] [ 3457, 0 ] [ 4121, -1 ] [ 4204, 4 ] [ 4453, -5 ] [ 4785, -1 ] [ 5117, 8 ] [ 5449, -3 ] [ 5532, -4 ] [ 5781, 0 ] [ 5864, -1 ] [ 6113, 0 ] [ 6445, 0 ] [ 7109, -5 ] [ 7192, -7 ] [ 7441, 0 ] [ 7773, 3 ] [ 8105, 11 ] [ 8188, -8 ] [ 8437, 3 ] [ 8520, -2 ] [ 8769, -3 ] [ 9101, -3 ] [ 9433, 7 ] [ 9516, 2 ] [ 9848, -6 ] /* D = 55 (mod 83 ) [ 221, -1 ] [ 553, 3 ] [ 636, 2 ] [ 885, 1 ] [ 1217, 3 ] [ 1549, -3 ] [ 1964, 2 ] [ 2213, 1 ] [ 2296, 2 ] [ 2545, -1 ] [ 2877, -2 ] [ 3209, -4 ] [ 3292, 2 ] [ 3541, 1 ] [ 3624, 5 ] [ 3873, -1 ] [ 4537, -1 ] [ 4620, 8 ] [ 4952, -1 ] [ 5201, 0 ] [ 5533, 2 ] [ 5865, 0 ] [ 5948, -12 ] [ 6197, 1 ] [ 6280, 0 ] [ 6529, -3 ] [ 6861, -3 ] [ 7193, 4 ] [ 7276, 2 ] [ 7608, -7 ] [ 8189, 5 ] [ 8521, -2 ] [ 8853, 10 ] [ 8936, 6 ] [ 9185, -3 ] [ 9517, -1 ] [ 9932, 2 ] /* D = 56 (mod 83 ) [ 56, -1 ] [ 305, 1 ] [ 969, 3 ] [ 1052, -2 ] [ 1301, 1 ] [ 1384, 5 ] [ 1633, 0 ] [ 1965, 0 ] [ 2297, -1 ] [ 2380, 4 ] [ 2629, 2 ] [ 2712, 5 ] [ 3293, 0 ] [ 3957, -4 ] [ 4040, 2 ] [ 4289, -1 ] [ 4621, -5 ] [ 4953, -1 ] [ 5036, -6 ] [ 5285, 5 ] [ 5368, 1 ] [ 5617, 2 ] [ 6281, -4 ] [ 6364, -4 ] [ 6613, -1 ] [ 6945, -3 ] [ 7277, 3 ] [ 7609, 2 ] [ 7692, 4 ] [ 7941, 6 ] [ 8024, -5 ] [ 8273, -3 ] [ 8605, 3 ] [ 9020, 4 ] [ 9269, 2 ] [ 9352, 3 ] [ 9601, 5 ] [ 9933, 0 ] /* D = 57 (mod 83 ) [ 57, 1 ] [ 140, 0 ] [ 389, 3 ] [ 472, -1 ] [ 721, 0 ] [ 1385, -4 ] [ 1468, -4 ] [ 1717, 2 ] [ 2049, -3 ] [ 2381, -7 ] [ 2713, 1 ] [ 2796, 0 ] [ 3045, 5 ] [ 3128, -10 ] [ 3377, 1 ] [ 3709, -2 ] [ 4124, -2 ] [ 4373, 5 ] [ 4456, 2 ] [ 4705, 1 ] [ 5037, 0 ] [ 5369, -3 ] [ 5452, -2 ] [ 5701, 3 ] [ 5784, 1 ] [ 6033, 4 ] [ 6365, -4 ] [ 6697, 3 ] [ 6780, 6 ] [ 7112, 3 ] [ 7361, -2 ] [ 8108, -6 ] [ 8357, 8 ] [ 8440, 6 ] [ 8689, -3 ] [ 9021, -4 ] [ 9353, 6 ] [ 9436, 6 ] [ 9685, 0 ] [ 9768, -9 ] /* D = 58 (mod 83 ) [ 141, 1 ] [ 473, 2 ] [ 556, 0 ] [ 805, 0 ] [ 888, -5 ] [ 1137, 6 ] [ 1469, -5 ] [ 1801, -1 ] [ 1884, 0 ] [ 2216, 0 ] [ 2465, -5 ] [ 2797, -5 ] [ 3129, 0 ] [ 3212, 6 ] [ 3461, -3 ] [ 3544, 3 ] [ 3793, -2 ] [ 4457, -3 ] [ 4540, 0 ] [ 4789, 1 ] [ 4872, 1 ] [ 5453, -6 ] [ 5785, 4 ] [ 6117, 8 ] [ 6449, -2 ] [ 6781, 0 ] [ 7113, 2 ] [ 7196, -2 ] [ 7445, 3 ] [ 7528, -9 ] [ 7777, 2 ] [ 8441, -6 ] [ 8524, 4 ] [ 8773, 7 ] [ 9105, -6 ] [ 9437, 6 ] [ 9769, 4 ] [ 9852, -14 ] /* D = 60 (mod 83 ) [ 60, 2 ] [ 309, -2 ] [ 641, 0 ] [ 973, -3 ] [ 1388, 2 ] [ 1637, 2 ] [ 1720, -2 ] [ 1969, 3 ] [ 2301, -3 ] [ 2633, -4 ] [ 2716, -2 ] [ 2965, 1 ] [ 3048, -3 ] [ 3297, 1 ] [ 3629, 3 ] [ 3961, 3 ] [ 4044, 2 ] [ 4376, -3 ] [ 4957, 1 ] [ 5289, 6 ] [ 5372, 4 ] [ 5621, 3 ] [ 5704, 0 ] [ 5953, -3 ] [ 6285, 9 ] [ 6617, -3 ] [ 6949, 4 ] [ 7032, 2 ] [ 7613, -6 ] [ 7945, -2 ] [ 8277, -8 ] [ 8360, 2 ] [ 8609, 0 ] [ 8941, 2 ] [ 9273, -5 ] [ 9356, 2 ] [ 9605, 1 ] [ 9688, 9 ] [ 9937, -3 ] /* D = 62 (mod 83 ) [ 145, -1 ] [ 809, -1 ] [ 892, 2 ] [ 1141, 3 ] [ 1473, -1 ] [ 2137, -2 ] [ 2220, -4 ] [ 2469, 1 ] [ 2552, -1 ] [ 2801, 0 ] [ 3133, 3 ] [ 3548, 4 ] [ 3797, 0 ] [ 3880, -2 ] [ 4129, 3 ] [ 4461, 1 ] [ 4793, 3 ] [ 4876, 0 ] [ 5208, 9 ] [ 5457, 0 ] [ 5789, 1 ] [ 6121, 4 ] [ 6204, -4 ] [ 6536, 4 ] [ 6785, -2 ] [ 7117, -12 ] [ 7449, 1 ] [ 7532, 8 ] [ 7781, 1 ] [ 7864, 0 ] [ 8113, -1 ] [ 8445, 5 ] [ 8777, 6 ] [ 8860, 6 ] [ 9109, -1 ] [ 9192, -1 ] [ 9773, -8 ] /* D = 66 (mod 83 ) [ 149, 2 ] [ 232, -1 ] [ 481, 1 ] [ 813, 0 ] [ 1145, 0 ] [ 1228, 2 ] [ 1477, -5 ] [ 1560, -6 ] [ 2141, 4 ] [ 2473, -1 ] [ 2805, -1 ] [ 3137, -1 ] [ 3469, 2 ] [ 3801, -1 ] [ 3884, -6 ] [ 4133, -1 ] [ 4216, -3 ] [ 4465, 0 ] [ 5129, 2 ] [ 5212, 2 ] [ 5461, 2 ] [ 5793, 0 ] [ 6457, 3 ] [ 6540, 0 ] [ 6789, -1 ] [ 6872, -1 ] [ 7121, 4 ] [ 7453, 1 ] [ 7868, 4 ] [ 8117, -5 ] [ 8449, 0 ] [ 8781, 7 ] [ 9113, -2 ] [ 9445, -3 ] [ 9528, 0 ] [ 9777, -3 ] /* D = 67 (mod 83 ) [ 233, 1 ] [ 316, 0 ] [ 565, -1 ] [ 897, -2 ] [ 1229, 1 ] [ 1561, 1 ] [ 1644, 2 ] [ 1893, -10 ] [ 1976, 2 ] [ 2557, 3 ] [ 2972, -4 ] [ 3221, 0 ] [ 3304, 3 ] [ 3553, 3 ] [ 3885, 5 ] [ 4217, 5 ] [ 4549, 0 ] [ 4632, 0 ] [ 4881, -4 ] [ 5213, 4 ] [ 5545, -3 ] [ 5628, 2 ] [ 5960, 4 ] [ 6209, -3 ] [ 6541, 1 ] [ 6873, -5 ] [ 6956, 2 ] [ 7205, 0 ] [ 7288, -3 ] [ 7537, -1 ] [ 7869, -2 ] [ 8201, 1 ] [ 8284, 4 ] [ 8533, -4 ] [ 8616, -3 ] [ 9197, 10 ] [ 9529, -3 ] [ 9861, -1 ] [ 9944, 1 ] /* D = 71 (mod 83 ) [ 237, -3 ] [ 569, -1 ] [ 652, 4 ] [ 901, -2 ] [ 984, 2 ] [ 1565, -1 ] [ 1897, 2 ] [ 2229, 4 ] [ 2561, 3 ] [ 2893, 1 ] [ 3308, -6 ] [ 3557, 10 ] [ 3640, -2 ] [ 3889, 0 ] [ 4553, 3 ] [ 4636, 0 ] [ 4885, 1 ] [ 5217, -3 ] [ 5549, -7 ] [ 5881, 1 ] [ 5964, 0 ] [ 6213, -5 ] [ 6296, -4 ] [ 6545, -1 ] [ 7292, 2 ] [ 7541, -2 ] [ 7624, 5 ] [ 7873, -2 ] [ 8205, -1 ] [ 8537, 1 ] [ 8620, 4 ] [ 8952, 13 ] [ 9201, 1 ] [ 9533, 8 ] [ 9865, -3 ] [ 9948, 2 ] /* D = 72 (mod 83 ) [ 321, 2 ] [ 653, 4 ] [ 985, 1 ] [ 1068, -2 ] [ 1317, -1 ] [ 1649, 0 ] [ 1981, -5 ] [ 2396, 2 ] [ 2728, 7 ] [ 2977, -2 ] [ 3309, -4 ] [ 3641, 0 ] [ 3973, -2 ] [ 4305, -6 ] [ 4637, 6 ] [ 4969, 0 ] [ 5052, -2 ] [ 5384, 3 ] [ 5633, 2 ] [ 5965, 5 ] [ 6297, -2 ] [ 6380, -4 ] [ 6629, 0 ] [ 6712, -5 ] [ 6961, 5 ] [ 7293, 11 ] [ 7708, 0 ] [ 7957, 3 ] [ 8040, -4 ] [ 8621, -5 ] [ 8953, 0 ] [ 9285, -3 ] [ 9368, -1 ] [ 9617, 3 ] [ 9949, -1 ] /* D = 73 (mod 83 ) [ 73, -1 ] [ 156, 0 ] [ 488, 3 ] [ 737, 0 ] [ 1069, -1 ] [ 1401, 1 ] [ 1484, 2 ] [ 1733, -4 ] [ 1816, 2 ] [ 2065, 3 ] [ 2397, 7 ] [ 2729, 4 ] [ 2812, 0 ] [ 3061, -2 ] [ 3144, 0 ] [ 4057, 3 ] [ 4389, -7 ] [ 4472, -2 ] [ 4721, 1 ] [ 5053, 3 ] [ 5385, -1 ] [ 5468, 6 ] [ 5717, 0 ] [ 6049, -2 ] [ 6796, 0 ] [ 7045, 0 ] [ 7377, -3 ] [ 7709, 3 ] [ 8041, -4 ] [ 8124, 0 ] [ 8373, 0 ] [ 8456, 5 ] [ 8705, -3 ] [ 9037, -3 ] [ 9452, 4 ] [ 9701, -2 ] [ 9784, 7 ] /* D = 74 (mod 83 ) [ 157, 3 ] [ 489, -1 ] [ 572, -4 ] [ 821, 1 ] [ 904, 1 ] [ 1153, 0 ] [ 1817, 0 ] [ 2149, -3 ] [ 2481, -5 ] [ 2813, 6 ] [ 3145, -1 ] [ 3228, 0 ] [ 3477, -9 ] [ 3560, -4 ] [ 3809, 2 ] [ 4141, 0 ] [ 4556, 2 ] [ 4888, 0 ] [ 5137, 5 ] [ 5469, 0 ] [ 5801, -1 ] [ 5884, 4 ] [ 6133, 1 ] [ 6216, 1 ] [ 6465, -1 ] [ 6797, 5 ] [ 7129, 2 ] [ 7212, -4 ] [ 7544, 0 ] [ 7793, 2 ] [ 8457, 7 ] [ 8540, -2 ] [ 8789, -7 ] [ 8872, -9 ] [ 9121, -4 ] [ 9453, 8 ] [ 9785, -2 ] [ 9868, 4 ] /* D = 76 (mod 83 ) [ 76, -2 ] [ 408, -3 ] [ 989, -2 ] [ 1321, -1 ] [ 1653, 7 ] [ 1736, 5 ] [ 1985, -4 ] [ 2317, 0 ] [ 2649, -2 ] [ 2732, 0 ] [ 2981, 0 ] [ 3064, 3 ] [ 3313, -2 ] [ 3977, 2 ] [ 4060, 2 ] [ 4309, -1 ] [ 4641, -1 ] [ 4973, -16 ] [ 5305, 0 ] [ 5388, -12 ] [ 5637, 1 ] [ 5720, 6 ] [ 5969, 1 ] [ 6301, 0 ] [ 6716, 12 ] [ 6965, 2 ] [ 7048, -5 ] [ 7297, 1 ] [ 7629, -3 ] [ 7961, 1 ] [ 8044, 2 ] [ 8293, 1 ] [ 8376, -3 ] [ 9289, 1 ] [ 9372, 4 ] [ 9704, 5 ] [ 9953, 12 ] /* D = 79 (mod 83 ) [ 328, 0 ] [ 577, -4 ] [ 1241, -3 ] [ 1324, 4 ] [ 1905, 3 ] [ 2237, 2 ] [ 2569, 2 ] [ 2652, -4 ] [ 2901, 4 ] [ 2984, -5 ] [ 3233, 4 ] [ 3565, -2 ] [ 3980, 0 ] [ 4229, -3 ] [ 4561, 0 ] [ 4893, 5 ] [ 5308, -2 ] [ 5557, -2 ] [ 5640, 0 ] [ 5889, -1 ] [ 6221, -5 ] [ 6553, 0 ] [ 6636, 6 ] [ 6968, 6 ] [ 7217, -6 ] [ 7549, -4 ] [ 7881, -2 ] [ 7964, 2 ] [ 8213, 0 ] [ 8296, 1 ] [ 8545, 2 ] [ 8877, -6 ] [ 9209, 1 ] [ 9292, 4 ] [ 9541, 1 ] [ 9624, 4 ] /* D = 80 (mod 83 ) [ 329, 1 ] [ 412, -2 ] [ 661, 3 ] [ 744, 1 ] [ 993, -2 ] [ 1657, -2 ] [ 1740, 4 ] [ 2072, 1 ] [ 2321, 1 ] [ 2653, 0 ] [ 2985, -4 ] [ 3068, 0 ] [ 3317, 6 ] [ 3649, 0 ] [ 3981, -1 ] [ 4313, 0 ] [ 4396, 2 ] [ 4645, -1 ] [ 4728, 3 ] [ 5309, -8 ] [ 5641, 3 ] [ 5973, 1 ] [ 6056, -3 ] [ 6305, 6 ] [ 6637, -5 ] [ 6969, 2 ] [ 7052, 8 ] [ 7384, 0 ] [ 7633, 5 ] [ 8297, 3 ] [ 8380, -6 ] [ 8629, 2 ] [ 8961, 0 ] [ 9293, 5 ] [ 9708, -4 ] [ 9957, 5 ] /* D = 82 (mod 83 ) [ 165, 1 ] [ 248, 1 ] [ 497, 2 ] [ 829, 2 ] [ 1244, -4 ] [ 1493, 0 ] [ 1576, -1 ] [ 2157, -4 ] [ 2489, 0 ] [ 2572, 4 ] [ 2821, 3 ] [ 3153, -6 ] [ 3485, -4 ] [ 3817, -6 ] [ 4481, 0 ] [ 4813, 0 ] [ 5228, 10 ] [ 5477, 2 ] [ 5560, -2 ] [ 5809, 3 ] [ 6141, 2 ] [ 6473, 6 ] [ 6556, -2 ] [ 6805, -5 ] [ 6888, 4 ] [ 7469, 6 ] [ 7801, 4 ] [ 8133, -3 ] [ 8216, -4 ] [ 8465, 4 ] [ 8797, 1 ] [ 9129, 1 ] [ 9461, 1 ] [ 9544, -5 ] [ 9793, 0 ] Total time: 142.630 seconds Goodbye!