[was@modular counting_slopes-10-23-00]$ [was@modular counting_slopes-10-23-00]$ Magma V2.7-3 Wed Nov 8 2000 14:02:29 on modular [Seed = 3096125942] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x > load "level2slopes_1-5000.m"; Loading "level2slopes_1-5000.m" > time conj:=[ : j in [0..14], n in [1..6], alpha in [0] | IsEven(j) and Dim(j,n,alpha,slopes) gt 0]; time> >> IsEven(j) and Dim(j,n,alpha,slopes) gt 0]; ^ User error: Identifier 'slopes' has not been declared or assigned > slopes:=level2slopes; > time conj:=[ : j in [0..14], n in [1..6], alpha in [0] | IsEven(j) and Dim(j,n,alpha,slopes) gt 0]; time> >> IsEven(j) and Dim(j,n,alpha,slopes) gt 0]; ^ User error: Identifier 'Dim' has not been declared or assigned > Attach("coleman.m"); > time conj:=[ : j in [0..14], n in [1..6], alpha in [0] | IsEven(j) and Dim(j,n,alpha,slopes) gt 0]; time> Time: 2.100 > > conj; [ <0, 1, 0>, <2, 1, 0>, <4, 1, 0>, <6, 1, 0>, <8, 1, 0>, <10, 1, 0>, <12, 1, 0>, <14, 1, 0>, <0, 2, 0>, <2, 2, 0>, <4, 2, 0>, <6, 2, 0>, <8, 2, 0>, <10, 2, 0>, <12, 2, 0>, <14, 2, 0>, <0, 3, 0>, <2, 3, 0>, <4, 3, 0>, <6, 3, 0>, <8, 3, 0>, <10, 3, 0>, <12, 3, 0>, <14, 3, 0>, <0, 4, 0>, <2, 4, 0>, <4, 4, 0>, <6, 4, 0>, <8, 4, 0>, <10, 4, 0>, <12, 4, 0>, <14, 4, 0>, <0, 5, 0>, <2, 5, 0>, <4, 5, 0>, <6, 5, 0>, <8, 5, 0>, <10, 5, 0>, <12, 5, 0>, <14, 5, 0>, <0, 6, 0>, <2, 6, 0>, <4, 6, 0>, <6, 6, 0>, <8, 6, 0>, <10, 6, 0>, <12, 6, 0>, <14, 6, 0> ] > conj:=Sort(conj); > conj; [ <0, 1, 0>, <0, 2, 0>, <0, 3, 0>, <0, 4, 0>, <0, 5, 0>, <0, 6, 0>, <2, 1, 0>, <2, 2, 0>, <2, 3, 0>, <2, 4, 0>, <2, 5, 0>, <2, 6, 0>, <4, 1, 0>, <4, 2, 0>, <4, 3, 0>, <4, 4, 0>, <4, 5, 0>, <4, 6, 0>, <6, 1, 0>, <6, 2, 0>, <6, 3, 0>, <6, 4, 0>, <6, 5, 0>, <6, 6, 0>, <8, 1, 0>, <8, 2, 0>, <8, 3, 0>, <8, 4, 0>, <8, 5, 0>, <8, 6, 0>, <10, 1, 0>, <10, 2, 0>, <10, 3, 0>, <10, 4, 0>, <10, 5, 0>, <10, 6, 0>, <12, 1, 0>, <12, 2, 0>, <12, 3, 0>, <12, 4, 0>, <12, 5, 0>, <12, 6, 0>, <14, 1, 0>, <14, 2, 0>, <14, 3, 0>, <14, 4, 0>, <14, 5, 0>, <14, 6, 0> ] > for c in conj do a,b:=TryConj(c[1],c[2],c[3],slopes); print c, " & ", b, "\\\\"; end for; <0, 1, 0> & 1 \\ <0, 2, 0> & 1 \\ <0, 3, 0> & 1 \\ <0, 4, 0> & 1 \\ <0, 5, 0> & 1 \\ <0, 6, 0> & 1 \\ <2, 1, 0> & 1 \\ <2, 2, 0> & 1 \\ <2, 3, 0> & 1 \\ <2, 4, 0> & 1 \\ <2, 5, 0> & 1 \\ <2, 6, 0> & 1 \\ [Interrupted] > for c in conj do a,b:=TryConj(c[1],c[2],c[3],slopes); print c, " & ", a, b, "\\\\"; end for; <0, 1, 0> & false 1 \\ <0, 2, 0> & false 1 \\ <0, 3, 0> & false 1 \\ <0, 4, 0> & false 1 \\ <0, 5, 0> & false 1 \\ <0, 6, 0> & false 1 \\ <2, 1, 0> & true 1 \\ <2, 2, 0> & true 1 \\ <2, 3, 0> & true 1 \\ <2, 4, 0> & true 1 \\ <2, 5, 0> & true 1 \\ <2, 6, 0> & true 1 \\ <4, 1, 0> & true 1 \\ <4, 2, 0> & true 1 \\ <4, 3, 0> & true 1 \\ <4, 4, 0> & true 1 \\ <4, 5, 0> & true 1 \\ <4, 6, 0> & true 1 \\ <6, 1, 0> & true 1 \\ <6, 2, 0> & true 1 \\ <6, 3, 0> & true 1 \\ <6, 4, 0> & true 1 \\ <6, 5, 0> & true 1 \\ <6, 6, 0> & true 1 \\ <8, 1, 0> & true 1 \\ <8, 2, 0> & true 1 \\ <8, 3, 0> & true 1 \\ <8, 4, 0> & true 1 \\ <8, 5, 0> & true 1 \\ <8, 6, 0> & true 1 \\ <10, 1, 0> & true 1 \\ <10, 2, 0> & true 1 \\ <10, 3, 0> & true 1 \\ <10, 4, 0> & true 1 \\ <10, 5, 0> & true 1 \\ <10, 6, 0> & true 1 \\ <12, 1, 0> & true 1 \\ <12, 2, 0> & true 1 \\ <12, 3, 0> & true 1 \\ <12, 4, 0> & true 1 \\ <12, 5, 0> & true 1 \\ <12, 6, 0> & true 1 \\ <14, 1, 0> & true 1 \\ <14, 2, 0> & true 1 \\ <14, 3, 0> & true 1 \\ <14, 4, 0> & true 1 \\ <14, 5, 0> & true 1 \\ <14, 6, 0> & true 1 \\ > slopes[4000]; [ 3, 7, 15, 15, 15, 24, 28, 31, 35, 39, 46, 47, 48, 57, 61, 66, 69, 73, 79, 79, 79, 85, 89, 92, 97, 101, 111, 112, 113, 120, 124, 128, 131, 135, 145, 145, 145, 153, 157, 160, 164, 168, 175, 176, 177, 185, 189, 195, 198, 202, 207, 207, 207, 212, 216, 219, 225, 229, 237, 238, 239, 246, 250, 254, 257, 261, 269, 269, 269, 280, 284, 287, 291, 295, 302, 303, 304, 315, 319, 324, 327, 331, 337, 337, 337, 343, 347, 350, 355, 359, 368, 369, 370, 377, 381, 385, 388, 392, 401, 401, 401, 409, 413, 416, 420, 424, 431, 432, 433, 441, 445, 452, 455, 459, 463, 463, 463, 467, 471, 474, 481, 485, 493, 494, 495, 502, 506, 510, 513, 517, 525, 525, 525, 534, 538, 541, 545, 549, 556, 557, 558, 567, 571, 576, 579, 583, 589, 589, 589, 595, 599, 602, 607, 611, 623, 624, 625, 632, 636, 640, 643, 647, 659, 659, 659, 667, 671, 674, 678, 682, 689, 690, 691, 699, 703, 709, 712, 716, 721, 721, 721, 726, 730, 733, 739, 743, 751, 752, 753, 760, 764, 768, 771, 775, 783, 783, 783, 793, 797, 800, 804, 808, 815, 816, 817, 827, 831, 836, 839, 843, 849, 849, 849, 855, 859, 862, 867, 871, 880, 881, 882, 889, 893, 897, 900, 904, 913, 913, 913, 921, 925, 928, 932, 936, 943, 944, 945, 953, 957, 965, 968, 972, 975, 975, 975, 978, 982, 985, 993, 997, 1005, 1006, 1007, 1014, 1018, 1022, 1025, 1029, 1037, 1037, 1037, 1046, 1050, 1053, 1057, 1061, 1068, 1069, 1070, 1079, 1083, 1088, 1091, 1095, 1101, 1101, 1101, 1107, 1111, 1114, 1119, 1123, 1133, 1134, 1135, 1142, 1146, 1150, 1153, 1157, 1167, 1167, 1167, 1175, 1179, 1182, 1186, 1190, 1197, 1198, 1199, 1207, 1211, 1217, 1220, 1224, 1229, 1229, 1229, 1234, 1238, 1241, 1247, 1251, 1259, 1260, 1261, 1268, 1272, 1276, 1279, 1283, 1291, 1291, 1291, 1304, 1308, 1311, 1315, 1319, 1326, 1327, 1328, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 1999, 2671, 2672, 2673, 2680, 2684, 2688, 2691, 2695, 2708, 2708, 2708, 2716, 2720, 2723, 2727, 2731, 2738, 2739, 2740, 2748, 2752, 2758, 2761, 2765, 2770, 2770, 2770, 2775, 2779, 2782, 2788, 2792, 2800, 2801, 2802, 2809, 2813, 2817, 2820, 2824, 2832, 2832, 2832, 2842, 2846, 2849, 2853, 2857, 2864, 2865, 2866, 2876, 2880, 2885, 2888, 2892, 2898, 2898, 2898, 2904, 2908, 2911, 2916, 2920, 2929, 2930, 2931, 2938, 2942, 2946, 2949, 2953, 2962, 2962, 2962, 2970, 2974, 2977, 2981, 2985, 2992, 2993, 2994, 3002, 3006, 3014, 3017, 3021, 3024, 3024, 3024, 3027, 3031, 3034, 3042, 3046, 3054, 3055, 3056, 3063, 3067, 3071, 3074, 3078, 3086, 3086, 3086, 3095, 3099, 3102, 3106, 3110, 3117, 3118, 3119, 3128, 3132, 3137, 3140, 3144, 3150, 3150, 3150, 3156, 3160, 3163, 3168, 3172, 3182, 3183, 3184, 3191, 3195, 3199, 3202, 3206, 3216, 3216, 3216, 3224, 3228, 3231, 3235, 3239, 3246, 3247, 3248, 3256, 3260, 3266, 3269, 3273, 3278, 3278, 3278, 3283, 3287, 3290, 3296, 3300, 3308, 3309, 3310, 3317, 3321, 3325, 3328, 3332, 3340, 3340, 3340, 3352, 3356, 3359, 3363, 3367, 3374, 3375, 3376, 3388, 3392, 3397, 3400, 3404, 3410, 3410, 3410, 3416, 3420, 3423, 3428, 3432, 3441, 3442, 3443, 3450, 3454, 3458, 3461, 3465, 3474, 3474, 3474, 3482, 3486, 3489, 3493, 3497, 3504, 3505, 3506, 3514, 3518, 3525, 3528, 3532, 3536, 3536, 3536, 3540, 3544, 3547, 3554, 3558, 3566, 3567, 3568, 3575, 3579, 3583, 3586, 3590, 3598, 3598, 3598, 3607, 3611, 3614, 3618, 3622, 3629, 3630, 3631, 3640, 3644, 3649, 3652, 3656, 3662, 3662, 3662, 3668, 3672, 3675, 3680, 3684, 3695, 3696, 3697, 3704, 3708, 3712, 3715, 3719, 3730, 3730, 3730, 3738, 3742, 3745, 3749, 3753, 3760, 3761, 3762, 3770, 3774, 3780, 3783, 3787, 3792, 3792, 3792, 3797, 3801, 3804, 3810, 3814, 3822, 3823, 3824, 3831, 3835, 3839, 3842, 3846, 3854, 3854, 3854, 3864, 3868, 3871, 3875, 3879, 3886, 3887, 3888, 3898, 3902, 3907, 3910, 3914, 3920, 3920, 3920, 3926, 3930, 3933, 3938, 3942, 3951, 3952, 3953, 3960, 3964, 3968, 3971, 3975, 3984, 3984, 3984, 3992, 3996, 0 ] > function f(n) return slopes[2^n-2]; end function; > f(5); [ 6, 6, 14, 14, 23, 23, 0 ] > function f(n) return 2^n, Sort(slopes[2^n-2]); end function; > f(5); 32 [ 0, 6, 6, 14, 14, 23, 23 ] > Log(5000)/Log(2); > Log(5000)/Log(2); 12.28771237954944939148127771 > for n in [5..12] do f(n); end for; 32 [ 0, 6, 6, 14, 14, 23, 23 ] 64 [ 0, 6, 6, 14, 14, 30, 30, 30, 30, 30, 30, 47, 47, 55, 55 ] 128 [ 0, 6, 6, 14, 14, 24, 24, 30, 30, 36, 36, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 89, 89, 95, 95, 101, 101, 111, 111, 119, 119 ] 256 [ 0, 6, 6, 14, 14, 24, 24, 30, 30, 36, 36, 48, 48, 56, 56, 62, 62, 68, 68, 76, 76, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 177, 177, 185, 185, 191, 191, 197, 197, 205, 205, 217, 217, 223, 223, 229, 229, 239, 239, 247, 247 ] 512 [ 0, 6, 6, 14, 14, 24, 24, 30, 30, 36, 36, 48, 48, 56, 56, 62, 62, 68, 68, 76, 76, 90, 90, 96, 96, 102, 102, 112, 112, 120, 120, 126, 126, 132, 132, 140, 140, 150, 150, 156, 156, 162, 162, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 347, 347, 353, 353, 359, 359, 369, 369, 377, 377, 383, 383, 389, 389, 397, 397, 407, 407, 413, 413, 419, 419, 433, 433, 441, 441, 447, 447, 453, 453, 461, 461, 473, 473, 479, 479, 485, 485, 495, 495, 503, 503 ] 1024 [ 0, 6, 6, 14, 14, 24, 24, 30, 30, 36, 36, 48, 48, 56, 56, 62, 62, 68, 68, 76, 76, 90, 90, 96, 96, 102, 102, 112, 112, 120, 120, 126, 126, 132, 132, 140, 140, 150, 150, 156, 156, 162, 162, 178, 178, 186, 186, 192, 192, 198, 198, 206, 206, 218, 218, 224, 224, 230, 230, 240, 240, 248, 248, 254, 254, 260, 260, 268, 268, 278, 278, 284, 284, 290, 290, 302, 302, 310, 310, 316, 316, 322, 322, 330, 330, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 691, 691, 699, 699, 705, 705, 711, 711, 719, 719, 731, 731, 737, 737, 743, 743, 753, 753, 761, 761, 767, 767, 773, 773, 781, 781, 791, 791, 797, 797, 803, 803, 815, 815, 823, 823, 829, 829, 835, 835, 843, 843, 859, 859, 865, 865, 871, 871, 881, 881, 889, 889, 895, 895, 901, 901, 909, 909, 919, 919, 925, 925, 931, 931, 945, 945, 953, 953, 959, 959, 965, 965, 973, 973, 985, 985, 991, 991, 997, 997, 1007, 1007, 1015, 1015 ] 2048 [ 0, 6, 6, 14, 14, 24, 24, 30, 30, 36, 36, 48, 48, 56, 56, 62, 62, 68, 68, 76, 76, 90, 90, 96, 96, 102, 102, 112, 112, 120, 120, 126, 126, 132, 132, 140, 140, 150, 150, 156, 156, 162, 162, 178, 178, 186, 186, 192, 192, 198, 198, 206, 206, 218, 218, 224, 224, 230, 230, 240, 240, 248, 248, 254, 254, 260, 260, 268, 268, 278, 278, 284, 284, 290, 290, 302, 302, 310, 310, 316, 316, 322, 322, 330, 330, 348, 348, 354, 354, 360, 360, 370, 370, 378, 378, 384, 384, 390, 390, 398, 398, 408, 408, 414, 414, 420, 420, 434, 434, 442, 442, 448, 448, 454, 454, 462, 462, 474, 474, 480, 480, 486, 486, 496, 496, 504, 504, 510, 510, 516, 516, 524, 524, 534, 534, 540, 540, 546, 546, 558, 558, 566, 566, 572, 572, 578, 578, 586, 586, 600, 600, 606, 606, 612, 612, 622, 622, 630, 630, 636, 636, 642, 642, 650, 650, 660, 660, 666, 666, 672, 672, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1373, 1373, 1379, 1379, 1385, 1385, 1395, 1395, 1403, 1403, 1409, 1409, 1415, 1415, 1423, 1423, 1433, 1433, 1439, 1439, 1445, 1445, 1459, 1459, 1467, 1467, 1473, 1473, 1479, 1479, 1487, 1487, 1499, 1499, 1505, 1505, 1511, 1511, 1521, 1521, 1529, 1529, 1535, 1535, 1541, 1541, 1549, 1549, 1559, 1559, 1565, 1565, 1571, 1571, 1583, 1583, 1591, 1591, 1597, 1597, 1603, 1603, 1611, 1611, 1625, 1625, 1631, 1631, 1637, 1637, 1647, 1647, 1655, 1655, 1661, 1661, 1667, 1667, 1675, 1675, 1685, 1685, 1691, 1691, 1697, 1697, 1715, 1715, 1723, 1723, 1729, 1729, 1735, 1735, 1743, 1743, 1755, 1755, 1761, 1761, 1767, 1767, 1777, 1777, 1785, 1785, 1791, 1791, 1797, 1797, 1805, 1805, 1815, 1815, 1821, 1821, 1827, 1827, 1839, 1839, 1847, 1847, 1853, 1853, 1859, 1859, 1867, 1867, 1883, 1883, 1889, 1889, 1895, 1895, 1905, 1905, 1913, 1913, 1919, 1919, 1925, 1925, 1933, 1933, 1943, 1943, 1949, 1949, 1955, 1955, 1969, 1969, 1977, 1977, 1983, 1983, 1989, 1989, 1997, 1997, 2009, 2009, 2015, 2015, 2021, 2021, 2031, 2031, 2039, 2039 ] 4096 [ 0, 6, 6, 14, 14, 24, 24, 30, 30, 36, 36, 48, 48, 56, 56, 62, 62, 68, 68, 76, 76, 90, 90, 96, 96, 102, 102, 112, 112, 120, 120, 126, 126, 132, 132, 140, 140, 150, 150, 156, 156, 162, 162, 178, 178, 186, 186, 192, 192, 198, 198, 206, 206, 218, 218, 224, 224, 230, 230, 240, 240, 248, 248, 254, 254, 260, 260, 268, 268, 278, 278, 284, 284, 290, 290, 302, 302, 310, 310, 316, 316, 322, 322, 330, 330, 348, 348, 354, 354, 360, 360, 370, 370, 378, 378, 384, 384, 390, 390, 398, 398, 408, 408, 414, 414, 420, 420, 434, 434, 442, 442, 448, 448, 454, 454, 462, 462, 474, 474, 480, 480, 486, 486, 496, 496, 504, 504, 510, 510, 516, 516, 524, 524, 534, 534, 540, 540, 546, 546, 558, 558, 566, 566, 572, 572, 578, 578, 586, 586, 600, 600, 606, 606, 612, 612, 622, 622, 630, 630, 636, 636, 642, 642, 650, 650, 660, 660, 666, 666, 672, 672, 692, 692, 700, 700, 706, 706, 712, 712, 720, 720, 732, 732, 738, 738, 744, 744, 754, 754, 762, 762, 768, 768, 774, 774, 782, 782, 792, 792, 798, 798, 804, 804, 816, 816, 824, 824, 830, 830, 836, 836, 844, 844, 860, 860, 866, 866, 872, 872, 882, 882, 890, 890, 896, 896, 902, 902, 910, 910, 920, 920, 926, 926, 932, 932, 946, 946, 954, 954, 960, 960, 966, 966, 974, 974, 986, 986, 992, 992, 998, 998, 1008, 1008, 1016, 1016, 1022, 1022, 1028, 1028, 1036, 1036, 1046, 1046, 1052, 1052, 1058, 1058, 1070, 1070, 1078, 1078, 1084, 1084, 1090, 1090, 1098, 1098, 1112, 1112, 1118, 1118, 1124, 1124, 1134, 1134, 1142, 1142, 1148, 1148, 1154, 1154, 1162, 1162, 1172, 1172, 1178, 1178, 1184, 1184, 1200, 1200, 1208, 1208, 1214, 1214, 1220, 1220, 1228, 1228, 1240, 1240, 1246, 1246, 1252, 1252, 1262, 1262, 1270, 1270, 1276, 1276, 1282, 1282, 1290, 1290, 1300, 1300, 1306, 1306, 1312, 1312, 1324, 1324, 1332, 1332, 1338, 1338, 1344, 1344, 1352, 1352, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2046, 2741, 2741, 2749, 2749, 2755, 2755, 2761, 2761, 2769, 2769, 2781, 2781, 2787, 2787, 2793, 2793, 2803, 2803, 2811, 2811, 2817, 2817, 2823, 2823, 2831, 2831, 2841, 2841, 2847, 2847, 2853, 2853, 2865, 2865, 2873, 2873, 2879, 2879, 2885, 2885, 2893, 2893, 2909, 2909, 2915, 2915, 2921, 2921, 2931, 2931, 2939, 2939, 2945, 2945, 2951, 2951, 2959, 2959, 2969, 2969, 2975, 2975, 2981, 2981, 2995, 2995, 3003, 3003, 3009, 3009, 3015, 3015, 3023, 3023, 3035, 3035, 3041, 3041, 3047, 3047, 3057, 3057, 3065, 3065, 3071, 3071, 3077, 3077, 3085, 3085, 3095, 3095, 3101, 3101, 3107, 3107, 3119, 3119, 3127, 3127, 3133, 3133, 3139, 3139, 3147, 3147, 3161, 3161, 3167, 3167, 3173, 3173, 3183, 3183, 3191, 3191, 3197, 3197, 3203, 3203, 3211, 3211, 3221, 3221, 3227, 3227, 3233, 3233, 3249, 3249, 3257, 3257, 3263, 3263, 3269, 3269, 3277, 3277, 3289, 3289, 3295, 3295, 3301, 3301, 3311, 3311, 3319, 3319, 3325, 3325, 3331, 3331, 3339, 3339, 3349, 3349, 3355, 3355, 3361, 3361, 3373, 3373, 3381, 3381, 3387, 3387, 3393, 3393, 3401, 3401, 3421, 3421, 3427, 3427, 3433, 3433, 3443, 3443, 3451, 3451, 3457, 3457, 3463, 3463, 3471, 3471, 3481, 3481, 3487, 3487, 3493, 3493, 3507, 3507, 3515, 3515, 3521, 3521, 3527, 3527, 3535, 3535, 3547, 3547, 3553, 3553, 3559, 3559, 3569, 3569, 3577, 3577, 3583, 3583, 3589, 3589, 3597, 3597, 3607, 3607, 3613, 3613, 3619, 3619, 3631, 3631, 3639, 3639, 3645, 3645, 3651, 3651, 3659, 3659, 3673, 3673, 3679, 3679, 3685, 3685, 3695, 3695, 3703, 3703, 3709, 3709, 3715, 3715, 3723, 3723, 3733, 3733, 3739, 3739, 3745, 3745, 3763, 3763, 3771, 3771, 3777, 3777, 3783, 3783, 3791, 3791, 3803, 3803, 3809, 3809, 3815, 3815, 3825, 3825, 3833, 3833, 3839, 3839, 3845, 3845, 3853, 3853, 3863, 3863, 3869, 3869, 3875, 3875, 3887, 3887, 3895, 3895, 3901, 3901, 3907, 3907, 3915, 3915, 3931, 3931, 3937, 3937, 3943, 3943, 3953, 3953, 3961, 3961, 3967, 3967, 3973, 3973, 3981, 3981, 3991, 3991, 3997, 3997, 4003, 4003, 4017, 4017, 4025, 4025, 4031, 4031, 4037, 4037, 4045, 4045, 4057, 4057, 4063, 4063, 4069, 4069, 4079, 4079, 4087, 4087 ] > load "slopes.m"; >> load "slopes.m"; ^ User error: Could not open file "slopes.m" (No such file or directory) > DimensionNewCuspFormsGamma0(2,2048); 171 > DimensionNewCuspFormsGamma0(2,4); 0 > DimensionNewCuspFormsGamma0(2,8); 1 > DimensionNewCuspFormsGamma0(2,1024); 85 > DimensionNewCuspFormsGamma0(2,512); 43 > DimensionNewCuspFormsGamma0(2,256); 21 > DimensionNewCuspFormsGamma0(2,128); 11 > DimensionNewCuspFormsGamma0(2,4096); 341 > DimensionNewCuspFormsGamma0(2,2048-2); 170 > DimensionNewCuspFormsGamma0(2,4096-2); 342 > DimensionNewCuspFormsGamma0(2,1024-2); 86 > DimensionNewCuspFormsGamma0(2,512-2); 42 > slopes[2^10-2]; [ 6, 6, 14, 14, 24, 24, 30, 30, 36, 36, 48, 48, 56, 56, 62, 62, 68, 68, 76, 76, 90, 90, 96, 96, 102, 102, 112, 112, 120, 120, 126, 126, 132, 132, 140, 140, 150, 150, 156, 156, 162, 162, 178, 178, 186, 186, 192, 192, 198, 198, 206, 206, 218, 218, 224, 224, 230, 230, 240, 240, 248, 248, 254, 254, 260, 260, 268, 268, 278, 278, 284, 284, 290, 290, 302, 302, 310, 310, 316, 316, 322, 322, 330, 330, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 510, 691, 691, 699, 699, 705, 705, 711, 711, 719, 719, 731, 731, 737, 737, 743, 743, 753, 753, 761, 761, 767, 767, 773, 773, 781, 781, 791, 791, 797, 797, 803, 803, 815, 815, 823, 823, 829, 829, 835, 835, 843, 843, 859, 859, 865, 865, 871, 871, 881, 881, 889, 889, 895, 895, 901, 901, 909, 909, 919, 919, 925, 925, 931, 931, 945, 945, 953, 953, 959, 959, 965, 965, 973, 973, 985, 985, 991, 991, 997, 997, 1007, 1007, 1015, 1015, 0 ] > 2^10-2; 1022 > slopes[2^11-2]; [ 6, 6, 14, 14, 24, 24, 30, 30, 36, 36, 48, 48, 56, 56, 62, 62, 68, 68, 76, 76, 90, 90, 96, 96, 102, 102, 112, 112, 120, 120, 126, 126, 132, 132, 140, 140, 150, 150, 156, 156, 162, 162, 178, 178, 186, 186, 192, 192, 198, 198, 206, 206, 218, 218, 224, 224, 230, 230, 240, 240, 248, 248, 254, 254, 260, 260, 268, 268, 278, 278, 284, 284, 290, 290, 302, 302, 310, 310, 316, 316, 322, 322, 330, 330, 348, 348, 354, 354, 360, 360, 370, 370, 378, 378, 384, 384, 390, 390, 398, 398, 408, 408, 414, 414, 420, 420, 434, 434, 442, 442, 448, 448, 454, 454, 462, 462, 474, 474, 480, 480, 486, 486, 496, 496, 504, 504, 510, 510, 516, 516, 524, 524, 534, 534, 540, 540, 546, 546, 558, 558, 566, 566, 572, 572, 578, 578, 586, 586, 600, 600, 606, 606, 612, 612, 622, 622, 630, 630, 636, 636, 642, 642, 650, 650, 660, 660, 666, 666, 672, 672, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1373, 1373, 1379, 1379, 1385, 1385, 1395, 1395, 1403, 1403, 1409, 1409, 1415, 1415, 1423, 1423, 1433, 1433, 1439, 1439, 1445, 1445, 1459, 1459, 1467, 1467, 1473, 1473, 1479, 1479, 1487, 1487, 1499, 1499, 1505, 1505, 1511, 1511, 1521, 1521, 1529, 1529, 1535, 1535, 1541, 1541, 1549, 1549, 1559, 1559, 1565, 1565, 1571, 1571, 1583, 1583, 1591, 1591, 1597, 1597, 1603, 1603, 1611, 1611, 1625, 1625, 1631, 1631, 1637, 1637, 1647, 1647, 1655, 1655, 1661, 1661, 1667, 1667, 1675, 1675, 1685, 1685, 1691, 1691, 1697, 1697, 1715, 1715, 1723, 1723, 1729, 1729, 1735, 1735, 1743, 1743, 1755, 1755, 1761, 1761, 1767, 1767, 1777, 1777, 1785, 1785, 1791, 1791, 1797, 1797, 1805, 1805, 1815, 1815, 1821, 1821, 1827, 1827, 1839, 1839, 1847, 1847, 1853, 1853, 1859, 1859, 1867, 1867, 1883, 1883, 1889, 1889, 1895, 1895, 1905, 1905, 1913, 1913, 1919, 1919, 1925, 1925, 1933, 1933, 1943, 1943, 1949, 1949, 1955, 1955, 1969, 1969, 1977, 1977, 1983, 1983, 1989, 1989, 1997, 1997, 2009, 2009, 2015, 2015, 2021, 2021, 2031, 2031, 2039, 2039, 0 ] > [a : a in slopes[2^11-2] | a eq 254]; [ 254, 254 ] > [a : a in slopes[2^12-2] | a eq 254]; [ 254, 254 ] > 2^13-2; 8190 > DimensionNewCuspFormsGamma0(2,126); 0 > DimensionNewCuspFormsGamma0(2,126); 10 > DimensionNewCuspFormsGamma0(2,62); 6 > DimensionNewCuspFormsGamma0(2,30); 2 > level1slopes[30]; >> level1slopes[30]; ^ User error: Identifier 'level1slopes' has not been declared or assigned > function MultSeq(v) ans := []; i := 1; while i le #v do x := v[i]; mult := 1; for j in [0..#v-i] do i +:= 1; if v[i] eq x then mult +:= 1; end if; end for; Append(~ans, [mult, x]); end for; return ans; end function; function> function> function> function|while> function|while> function|while> function|while|for> function|while|for> function|while|for|if> function|while|for|if> function|while|for> function|while> function|while> >> end for; ^ User error: bad syntax > function MultSeq(v) ans := []; i := 1; while i le #v do x := v[i]; mult := 1; for j in [0..#v-i] do i +:= 1; if v[i] eq x then mult +:= 1; end if; end for; Append(~ans, [mult, x]); end while; return ans; end function; >> return ans; ^ User error: A 'return' can only be used inside a procedure or function > >> end function; ^ User error: bad syntax > > > function MultSeq(v) ans := []; i := 1; while i le #v do x := v[i]; mult := 1; for j in [0..#v-i] do i +:= 1; if v[i] eq x then mult +:= 1; end if; end for; Append(~ans, [mult, x]); end while; return ans; end function; function> function> function> function|while> function|while> function|while> function|while|for> function|while|for> function|while|for|if> function|while|for|if> function|while|for> function|while> function|while> function> function> > > > > > MultSeq([1,1]); MultSeq( v: [ 1, 1 ] ) >> if v[i] eq x then ^ Runtime error in '[]': Sequence element 3 not defined > function MultSeq(v) ans := []; i := 1; while i le #v do x := v[i]; mult := 1; while i le #v and v[i] eq x do i +:= 1; if v[i] eq x then mult +:= 1; end if; end for; Append(~ans, [mult, x]); end while; return ans; end function; function> function> function> function|while> function|while> function|while> function|while|while> function|while|while> function|while|while|if> function|while|while|if> function|while|while> >> end for; ^ User error: bad syntax > >> Append(~ans, [mult, x]); ^ User error: Identifier 'mult' has not been declared or assigned > >> end while; ^ User error: bad syntax > >> return ans; ^ User error: A 'return' can only be used inside a procedure or function > >> end function; ^ User error: bad syntax > > > function MultSeq(v) ans := []; i := 1; while i le #v do x := v[i]; mult := 1; while i le #v and v[i] eq x do i +:= 1; if v[i] eq x then mult +:= 1; end if; end while; Append(~ans, [mult, x]); end while; return ans; end function; function> function> function> function|while> function|while> function|while> function|while|while> function|while|while> function|while|while|if> function|while|while|if> function|while|while> function|while> function|while> function> function> > > > > > MultSeq([1,1,2]); MultSeq( v: [ 1, 1, 2 ] ) >> if v[i] eq x then ^ Runtime error in '[]': Sequence element 4 not defined > function MultSeq(v) ans := []; i := 1; while i le #v do x := v[i]; mult := 1; while i le #v and v[i] eq x do mult +:= 1; i +:= 1; end while; Append(~ans, [mult, x]); end while; return ans; end function; > function> function> function> function|while> function|while> function|while> function|while|while> function|while|while> function|while|while> function|while> function|while> function> function> > > > > MultSeq([1,1,2]); [ [ 3, 1 ], [ 2, 2 ] ] > function MultSeq(v) ans := []; i := 1; while i le #v do x := v[i]; mult := 0; while i le #v and v[i] eq x do mult +:= 1; i +:= 1; end while; Append(~ans, [mult, x]); end while; return ans; end function; function> function> function> function|while> function|while> function|while> function|while|while> function|while|while> function|while|while> function|while> function|while> function> function> > > > > > MultSeq([1,1,2,3,3,3]); [ [ 2, 1 ], [ 1, 2 ], [ 3, 3 ] ] > function MultSeq(v) ans := []; i := 1; while i le #v do x := v[i]; mult := 0; while i le #v and v[i] eq x do mult +:= 1; i +:= 1; end while; Append(~ans, [mult, x]); end while; return ans; end function; mult := []; for k in [1..#slopes] do Append(~mult,MultSeq(slopes[k])); end for; function> function> function> function|while> function|while> function|while> function|while|while> function|while|while> function|while|while> function|while> function|while> function> function> > > > for> for> > > > > mult[2^8-2]; [ [ 2, 6 ], [ 2, 14 ], [ 2, 24 ], [ 2, 30 ], [ 2, 36 ], [ 2, 48 ], [ 2, 56 ], [ 2, 62 ], [ 2, 68 ], [ 2, 76 ], [ 22, 126 ], [ 2, 177 ], [ 2, 185 ], [ 2, 191 ], [ 2, 197 ], [ 2, 205 ], [ 2, 217 ], [ 2, 223 ], [ 2, 229 ], [ 2, 239 ], [ 2, 247 ], [ 1, 0 ] ] > > > slopes[32]; [ 3, 7, 15, 15, 15, 24, 28, 0 ] > slopes[30]; [ 6, 6, 14, 14, 23, 23, 0 ] > mult[2^12-2]; [ [ 2, 6 ], [ 2, 14 ], [ 2, 24 ], [ 2, 30 ], [ 2, 36 ], [ 2, 48 ], [ 2, 56 ], [ 2, 62 ], [ 2, 68 ], [ 2, 76 ], [ 2, 90 ], [ 2, 96 ], [ 2, 102 ], [ 2, 112 ], [ 2, 120 ], [ 2, 126 ], [ 2, 132 ], [ 2, 140 ], [ 2, 150 ], [ 2, 156 ], [ 2, 162 ], [ 2, 178 ], [ 2, 186 ], [ 2, 192 ], [ 2, 198 ], [ 2, 206 ], [ 2, 218 ], [ 2, 224 ], [ 2, 230 ], [ 2, 240 ], [ 2, 248 ], [ 2, 254 ], [ 2, 260 ], [ 2, 268 ], [ 2, 278 ], [ 2, 284 ], [ 2, 290 ], [ 2, 302 ], [ 2, 310 ], [ 2, 316 ], [ 2, 322 ], [ 2, 330 ], [ 2, 348 ], [ 2, 354 ], [ 2, 360 ], [ 2, 370 ], [ 2, 378 ], [ 2, 384 ], [ 2, 390 ], [ 2, 398 ], [ 2, 408 ], [ 2, 414 ], [ 2, 420 ], [ 2, 434 ], [ 2, 442 ], [ 2, 448 ], [ 2, 454 ], [ 2, 462 ], [ 2, 474 ], [ 2, 480 ], [ 2, 486 ], [ 2, 496 ], [ 2, 504 ], [ 2, 510 ], [ 2, 516 ], [ 2, 524 ], [ 2, 534 ], [ 2, 540 ], [ 2, 546 ], [ 2, 558 ], [ 2, 566 ], [ 2, 572 ], [ 2, 578 ], [ 2, 586 ], [ 2, 600 ], [ 2, 606 ], [ 2, 612 ], [ 2, 622 ], [ 2, 630 ], [ 2, 636 ], [ 2, 642 ], [ 2, 650 ], [ 2, 660 ], [ 2, 666 ], [ 2, 672 ], [ 2, 692 ], [ 2, 700 ], [ 2, 706 ], [ 2, 712 ], [ 2, 720 ], [ 2, 732 ], [ 2, 738 ], [ 2, 744 ], [ 2, 754 ], [ 2, 762 ], [ 2, 768 ], [ 2, 774 ], [ 2, 782 ], [ 2, 792 ], [ 2, 798 ], [ 2, 804 ], [ 2, 816 ], [ 2, 824 ], [ 2, 830 ], [ 2, 836 ], [ 2, 844 ], [ 2, 860 ], [ 2, 866 ], [ 2, 872 ], [ 2, 882 ], [ 2, 890 ], [ 2, 896 ], [ 2, 902 ], [ 2, 910 ], [ 2, 920 ], [ 2, 926 ], [ 2, 932 ], [ 2, 946 ], [ 2, 954 ], [ 2, 960 ], [ 2, 966 ], [ 2, 974 ], [ 2, 986 ], [ 2, 992 ], [ 2, 998 ], [ 2, 1008 ], [ 2, 1016 ], [ 2, 1022 ], [ 2, 1028 ], [ 2, 1036 ], [ 2, 1046 ], [ 2, 1052 ], [ 2, 1058 ], [ 2, 1070 ], [ 2, 1078 ], [ 2, 1084 ], [ 2, 1090 ], [ 2, 1098 ], [ 2, 1112 ], [ 2, 1118 ], [ 2, 1124 ], [ 2, 1134 ], [ 2, 1142 ], [ 2, 1148 ], [ 2, 1154 ], [ 2, 1162 ], [ 2, 1172 ], [ 2, 1178 ], [ 2, 1184 ], [ 2, 1200 ], [ 2, 1208 ], [ 2, 1214 ], [ 2, 1220 ], [ 2, 1228 ], [ 2, 1240 ], [ 2, 1246 ], [ 2, 1252 ], [ 2, 1262 ], [ 2, 1270 ], [ 2, 1276 ], [ 2, 1282 ], [ 2, 1290 ], [ 2, 1300 ], [ 2, 1306 ], [ 2, 1312 ], [ 2, 1324 ], [ 2, 1332 ], [ 2, 1338 ], [ 2, 1344 ], [ 2, 1352 ], [ 342, 2046 ], [ 2, 2741 ], [ 2, 2749 ], [ 2, 2755 ], [ 2, 2761 ], [ 2, 2769 ], [ 2, 2781 ], [ 2, 2787 ], [ 2, 2793 ], [ 2, 2803 ], [ 2, 2811 ], [ 2, 2817 ], [ 2, 2823 ], [ 2, 2831 ], [ 2, 2841 ], [ 2, 2847 ], [ 2, 2853 ], [ 2, 2865 ], [ 2, 2873 ], [ 2, 2879 ], [ 2, 2885 ], [ 2, 2893 ], [ 2, 2909 ], [ 2, 2915 ], [ 2, 2921 ], [ 2, 2931 ], [ 2, 2939 ], [ 2, 2945 ], [ 2, 2951 ], [ 2, 2959 ], [ 2, 2969 ], [ 2, 2975 ], [ 2, 2981 ], [ 2, 2995 ], [ 2, 3003 ], [ 2, 3009 ], [ 2, 3015 ], [ 2, 3023 ], [ 2, 3035 ], [ 2, 3041 ], [ 2, 3047 ], [ 2, 3057 ], [ 2, 3065 ], [ 2, 3071 ], [ 2, 3077 ], [ 2, 3085 ], [ 2, 3095 ], [ 2, 3101 ], [ 2, 3107 ], [ 2, 3119 ], [ 2, 3127 ], [ 2, 3133 ], [ 2, 3139 ], [ 2, 3147 ], [ 2, 3161 ], [ 2, 3167 ], [ 2, 3173 ], [ 2, 3183 ], [ 2, 3191 ], [ 2, 3197 ], [ 2, 3203 ], [ 2, 3211 ], [ 2, 3221 ], [ 2, 3227 ], [ 2, 3233 ], [ 2, 3249 ], [ 2, 3257 ], [ 2, 3263 ], [ 2, 3269 ], [ 2, 3277 ], [ 2, 3289 ], [ 2, 3295 ], [ 2, 3301 ], [ 2, 3311 ], [ 2, 3319 ], [ 2, 3325 ], [ 2, 3331 ], [ 2, 3339 ], [ 2, 3349 ], [ 2, 3355 ], [ 2, 3361 ], [ 2, 3373 ], [ 2, 3381 ], [ 2, 3387 ], [ 2, 3393 ], [ 2, 3401 ], [ 2, 3421 ], [ 2, 3427 ], [ 2, 3433 ], [ 2, 3443 ], [ 2, 3451 ], [ 2, 3457 ], [ 2, 3463 ], [ 2, 3471 ], [ 2, 3481 ], [ 2, 3487 ], [ 2, 3493 ], [ 2, 3507 ], [ 2, 3515 ], [ 2, 3521 ], [ 2, 3527 ], [ 2, 3535 ], [ 2, 3547 ], [ 2, 3553 ], [ 2, 3559 ], [ 2, 3569 ], [ 2, 3577 ], [ 2, 3583 ], [ 2, 3589 ], [ 2, 3597 ], [ 2, 3607 ], [ 2, 3613 ], [ 2, 3619 ], [ 2, 3631 ], [ 2, 3639 ], [ 2, 3645 ], [ 2, 3651 ], [ 2, 3659 ], [ 2, 3673 ], [ 2, 3679 ], [ 2, 3685 ], [ 2, 3695 ], [ 2, 3703 ], [ 2, 3709 ], [ 2, 3715 ], [ 2, 3723 ], [ 2, 3733 ], [ 2, 3739 ], [ 2, 3745 ], [ 2, 3763 ], [ 2, 3771 ], [ 2, 3777 ], [ 2, 3783 ], [ 2, 3791 ], [ 2, 3803 ], [ 2, 3809 ], [ 2, 3815 ], [ 2, 3825 ], [ 2, 3833 ], [ 2, 3839 ], [ 2, 3845 ], [ 2, 3853 ], [ 2, 3863 ], [ 2, 3869 ], [ 2, 3875 ], [ 2, 3887 ], [ 2, 3895 ], [ 2, 3901 ], [ 2, 3907 ], [ 2, 3915 ], [ 2, 3931 ], [ 2, 3937 ], [ 2, 3943 ], [ 2, 3953 ], [ 2, 3961 ], [ 2, 3967 ], [ 2, 3973 ], [ 2, 3981 ], [ 2, 3991 ], [ 2, 3997 ], [ 2, 4003 ], [ 2, 4017 ], [ 2, 4025 ], [ 2, 4031 ], [ 2, 4037 ], [ 2, 4045 ], [ 2, 4057 ], [ 2, 4063 ], [ 2, 4069 ], [ 2, 4079 ], [ 2, 4087 ], [ 1, 0 ] ] > Sort(mult[2^12-2]); [ [ 1, 0 ], [ 2, 6 ], [ 2, 14 ], [ 2, 24 ], [ 2, 30 ], [ 2, 36 ], [ 2, 48 ], [ 2, 56 ], [ 2, 62 ], [ 2, 68 ], [ 2, 76 ], [ 2, 90 ], [ 2, 96 ], [ 2, 102 ], [ 2, 112 ], [ 2, 120 ], [ 2, 126 ], [ 2, 132 ], [ 2, 140 ], [ 2, 150 ], [ 2, 156 ], [ 2, 162 ], [ 2, 178 ], [ 2, 186 ], [ 2, 192 ], [ 2, 198 ], [ 2, 206 ], [ 2, 218 ], [ 2, 224 ], [ 2, 230 ], [ 2, 240 ], [ 2, 248 ], [ 2, 254 ], [ 2, 260 ], [ 2, 268 ], [ 2, 278 ], [ 2, 284 ], [ 2, 290 ], [ 2, 302 ], [ 2, 310 ], [ 2, 316 ], [ 2, 322 ], [ 2, 330 ], [ 2, 348 ], [ 2, 354 ], [ 2, 360 ], [ 2, 370 ], [ 2, 378 ], [ 2, 384 ], [ 2, 390 ], [ 2, 398 ], [ 2, 408 ], [ 2, 414 ], [ 2, 420 ], [ 2, 434 ], [ 2, 442 ], [ 2, 448 ], [ 2, 454 ], [ 2, 462 ], [ 2, 474 ], [ 2, 480 ], [ 2, 486 ], [ 2, 496 ], [ 2, 504 ], [ 2, 510 ], [ 2, 516 ], [ 2, 524 ], [ 2, 534 ], [ 2, 540 ], [ 2, 546 ], [ 2, 558 ], [ 2, 566 ], [ 2, 572 ], [ 2, 578 ], [ 2, 586 ], [ 2, 600 ], [ 2, 606 ], [ 2, 612 ], [ 2, 622 ], [ 2, 630 ], [ 2, 636 ], [ 2, 642 ], [ 2, 650 ], [ 2, 660 ], [ 2, 666 ], [ 2, 672 ], [ 2, 692 ], [ 2, 700 ], [ 2, 706 ], [ 2, 712 ], [ 2, 720 ], [ 2, 732 ], [ 2, 738 ], [ 2, 744 ], [ 2, 754 ], [ 2, 762 ], [ 2, 768 ], [ 2, 774 ], [ 2, 782 ], [ 2, 792 ], [ 2, 798 ], [ 2, 804 ], [ 2, 816 ], [ 2, 824 ], [ 2, 830 ], [ 2, 836 ], [ 2, 844 ], [ 2, 860 ], [ 2, 866 ], [ 2, 872 ], [ 2, 882 ], [ 2, 890 ], [ 2, 896 ], [ 2, 902 ], [ 2, 910 ], [ 2, 920 ], [ 2, 926 ], [ 2, 932 ], [ 2, 946 ], [ 2, 954 ], [ 2, 960 ], [ 2, 966 ], [ 2, 974 ], [ 2, 986 ], [ 2, 992 ], [ 2, 998 ], [ 2, 1008 ], [ 2, 1016 ], [ 2, 1022 ], [ 2, 1028 ], [ 2, 1036 ], [ 2, 1046 ], [ 2, 1052 ], [ 2, 1058 ], [ 2, 1070 ], [ 2, 1078 ], [ 2, 1084 ], [ 2, 1090 ], [ 2, 1098 ], [ 2, 1112 ], [ 2, 1118 ], [ 2, 1124 ], [ 2, 1134 ], [ 2, 1142 ], [ 2, 1148 ], [ 2, 1154 ], [ 2, 1162 ], [ 2, 1172 ], [ 2, 1178 ], [ 2, 1184 ], [ 2, 1200 ], [ 2, 1208 ], [ 2, 1214 ], [ 2, 1220 ], [ 2, 1228 ], [ 2, 1240 ], [ 2, 1246 ], [ 2, 1252 ], [ 2, 1262 ], [ 2, 1270 ], [ 2, 1276 ], [ 2, 1282 ], [ 2, 1290 ], [ 2, 1300 ], [ 2, 1306 ], [ 2, 1312 ], [ 2, 1324 ], [ 2, 1332 ], [ 2, 1338 ], [ 2, 1344 ], [ 2, 1352 ], [ 2, 2741 ], [ 2, 2749 ], [ 2, 2755 ], [ 2, 2761 ], [ 2, 2769 ], [ 2, 2781 ], [ 2, 2787 ], [ 2, 2793 ], [ 2, 2803 ], [ 2, 2811 ], [ 2, 2817 ], [ 2, 2823 ], [ 2, 2831 ], [ 2, 2841 ], [ 2, 2847 ], [ 2, 2853 ], [ 2, 2865 ], [ 2, 2873 ], [ 2, 2879 ], [ 2, 2885 ], [ 2, 2893 ], [ 2, 2909 ], [ 2, 2915 ], [ 2, 2921 ], [ 2, 2931 ], [ 2, 2939 ], [ 2, 2945 ], [ 2, 2951 ], [ 2, 2959 ], [ 2, 2969 ], [ 2, 2975 ], [ 2, 2981 ], [ 2, 2995 ], [ 2, 3003 ], [ 2, 3009 ], [ 2, 3015 ], [ 2, 3023 ], [ 2, 3035 ], [ 2, 3041 ], [ 2, 3047 ], [ 2, 3057 ], [ 2, 3065 ], [ 2, 3071 ], [ 2, 3077 ], [ 2, 3085 ], [ 2, 3095 ], [ 2, 3101 ], [ 2, 3107 ], [ 2, 3119 ], [ 2, 3127 ], [ 2, 3133 ], [ 2, 3139 ], [ 2, 3147 ], [ 2, 3161 ], [ 2, 3167 ], [ 2, 3173 ], [ 2, 3183 ], [ 2, 3191 ], [ 2, 3197 ], [ 2, 3203 ], [ 2, 3211 ], [ 2, 3221 ], [ 2, 3227 ], [ 2, 3233 ], [ 2, 3249 ], [ 2, 3257 ], [ 2, 3263 ], [ 2, 3269 ], [ 2, 3277 ], [ 2, 3289 ], [ 2, 3295 ], [ 2, 3301 ], [ 2, 3311 ], [ 2, 3319 ], [ 2, 3325 ], [ 2, 3331 ], [ 2, 3339 ], [ 2, 3349 ], [ 2, 3355 ], [ 2, 3361 ], [ 2, 3373 ], [ 2, 3381 ], [ 2, 3387 ], [ 2, 3393 ], [ 2, 3401 ], [ 2, 3421 ], [ 2, 3427 ], [ 2, 3433 ], [ 2, 3443 ], [ 2, 3451 ], [ 2, 3457 ], [ 2, 3463 ], [ 2, 3471 ], [ 2, 3481 ], [ 2, 3487 ], [ 2, 3493 ], [ 2, 3507 ], [ 2, 3515 ], [ 2, 3521 ], [ 2, 3527 ], [ 2, 3535 ], [ 2, 3547 ], [ 2, 3553 ], [ 2, 3559 ], [ 2, 3569 ], [ 2, 3577 ], [ 2, 3583 ], [ 2, 3589 ], [ 2, 3597 ], [ 2, 3607 ], [ 2, 3613 ], [ 2, 3619 ], [ 2, 3631 ], [ 2, 3639 ], [ 2, 3645 ], [ 2, 3651 ], [ 2, 3659 ], [ 2, 3673 ], [ 2, 3679 ], [ 2, 3685 ], [ 2, 3695 ], [ 2, 3703 ], [ 2, 3709 ], [ 2, 3715 ], [ 2, 3723 ], [ 2, 3733 ], [ 2, 3739 ], [ 2, 3745 ], [ 2, 3763 ], [ 2, 3771 ], [ 2, 3777 ], [ 2, 3783 ], [ 2, 3791 ], [ 2, 3803 ], [ 2, 3809 ], [ 2, 3815 ], [ 2, 3825 ], [ 2, 3833 ], [ 2, 3839 ], [ 2, 3845 ], [ 2, 3853 ], [ 2, 3863 ], [ 2, 3869 ], [ 2, 3875 ], [ 2, 3887 ], [ 2, 3895 ], [ 2, 3901 ], [ 2, 3907 ], [ 2, 3915 ], [ 2, 3931 ], [ 2, 3937 ], [ 2, 3943 ], [ 2, 3953 ], [ 2, 3961 ], [ 2, 3967 ], [ 2, 3973 ], [ 2, 3981 ], [ 2, 3991 ], [ 2, 3997 ], [ 2, 4003 ], [ 2, 4017 ], [ 2, 4025 ], [ 2, 4031 ], [ 2, 4037 ], [ 2, 4045 ], [ 2, 4057 ], [ 2, 4063 ], [ 2, 4069 ], [ 2, 4079 ], [ 2, 4087 ], [ 342, 2046 ] ] >