#=================================================== # # Reduced Relation Curve Polynomials Degree 2-10, H1,H2,H4,H6,H8,H12,H16,H18,H24 # g-sequence (2-12): 0,0,0,1,1,4,5,7,9,16,13 # Version 1.0 - 22/05/20 #=================================================== H21= 2 + \[Alpha] - \[Beta] H32= 4 + \[Alpha]^2 + 2 \[Alpha] \[Beta] - 3 \[Beta]^2 H44= 16 - 8 \[Alpha]^2 + 8 \[Alpha]^3 + \[Alpha]^4 + 16 \[Alpha] \[Beta] + 8 \[Alpha]^2 \[Beta] - 4 \[Alpha]^3 \[Beta] - 8 \[Beta]^2 - 8 \[Alpha] \[Beta]^2 + 6 \[Alpha]^2 \[Beta]^2 - 8 \[Beta]^3 - 4 \[Alpha] \[Beta]^3 + \[Beta]^4 H56= 64 - 80 \[Alpha]^2 + 44 \[Alpha]^4 + \[Alpha]^6 + 96 \[Alpha] \[Beta] - 16 \[Alpha]^3 \[Beta] + 6 \[Alpha]^5 \[Beta] - 16 \[Beta]^2 + 104 \[Alpha]^2 \[Beta]^2 - 29 \[Alpha]^4 \[Beta]^2 - 80 \[Alpha] \[Beta]^3 + 36 \[Alpha]^3 \[Beta]^3 - 52 \[Beta]^4 - 9 \[Alpha]^2 \[Beta]^4 - 10 \[Alpha] \[Beta]^5 + 5 \[Beta]^6 H68= 256 - 256 \[Alpha]^2 - 256 \[Alpha]^3 + 96 \[Alpha]^4 + 256 \[Alpha]^5 - 80 \[Alpha]^6 + 16 \[Alpha]^7 + \[Alpha]^8 + 512 \[Alpha] \[Beta] - 256 \[Alpha]^2 \[Beta] - 384 \[Alpha]^3 \[Beta] + 256 \[Alpha]^4 \[Beta] - 32 \[Alpha]^5 \[Beta] + 80 \[Alpha]^6 \[Beta] - 8 \[Alpha]^7 \[Beta] - 256 \[Beta]^2 + 256 \[Alpha] \[Beta]^2 + 576 \[Alpha]^2 \[Beta]^2 - 176 \[Alpha]^4 \[Beta]^2 - 112 \[Alpha]^5 \[Beta]^2 + 28 \[Alpha]^6 \[Beta]^2 + 256 \[Beta]^3 - 384 \[Alpha] \[Beta]^3 + 576 \[Alpha]^3 \[Beta]^3 - 176 \[Alpha]^4 \[Beta]^3 - 56 \[Alpha]^5 \[Beta]^3 + 96 \[Beta]^4 - 256 \[Alpha] \[Beta]^4 - 176 \[Alpha]^2 \[Beta]^4 + 176 \[Alpha]^3 \[Beta]^4 + 70 \[Alpha]^4 \[Beta]^4 - 256 \[Beta]^5 - 32 \[Alpha] \[Beta]^5 + 112 \[Alpha]^2 \[Beta]^5 - 56 \[Alpha]^3 \[Beta]^5 - 80 \[Beta]^6 - 80 \[Alpha] \[Beta]^6 + 28 \[Alpha]^2 \[Beta]^6 - 16 \[Beta]^7 - 8 \[Alpha] \[Beta]^7 + \[Beta]^8 H712= 4096 - 2048 \[Alpha]^2 - 8448 \[Alpha]^4 + 7424 \[Alpha]^6 - 1040 \[Alpha]^8 + 184 \[Alpha]^10 + \[Alpha]^12 + 12288 \[Alpha] \[Beta] - 17408 \[Alpha]^3 \[Beta] + 1536 \[Alpha]^5 \[Beta] + 4992 \[Alpha]^7 \[Beta] - 144 \[Alpha]^9 \[Beta] + 12 \[Alpha]^11 \[Beta] - 10240 \[Beta]^2 + 25088 \[Alpha]^2 \[Beta]^2 - 8448 \[Alpha]^4 \[Beta]^2 - 4288 \[Alpha]^6 \[Beta]^2 + 1976 \[Alpha]^8 \[Beta]^2 - 118 \[Alpha]^10 \[Beta]^2 - 13312 \[Alpha] \[Beta]^3 + 33792 \[Alpha]^3 \[Beta]^3 - 10624 \[Alpha]^5 \[Beta]^3 - 4032 \[Alpha]^7 \[Beta]^3 + 364 \[Alpha]^9 \[Beta]^3 + 14080 \[Beta]^4 - 29952 \[Alpha]^2 \[Beta]^4 + 23712 \[Alpha]^4 \[Beta]^4 - 3472 \[Alpha]^6 \[Beta]^4 - 441 \[Alpha]^8 \[Beta]^4 + 5632 \[Alpha] \[Beta]^5 - 19328 \[Alpha]^3 \[Beta]^5 + 11680 \[Alpha]^5 \[Beta]^5 - 168 \[Alpha]^7 \[Beta]^5 - 9984 \[Beta]^6 + 10560 \[Alpha]^2 \[Beta]^6 - 7632 \[Alpha]^4 \[Beta]^6 + 1260 \[Alpha]^6 \[Beta]^6 - 5760 \[Alpha] \[Beta]^7 + 3648 \[Alpha]^3 \[Beta]^7 - 1800 \[Alpha]^5 \[Beta]^7 + 1776 \[Beta]^8 - 3624 \[Alpha]^2 \[Beta]^8 + 1311 \[Alpha]^4 \[Beta]^8 + 1136 \[Alpha] \[Beta]^9 - 484 \[Alpha]^3 \[Beta]^9 + 280 \[Beta]^10 + 42 \[Alpha]^2 \[Beta]^10 + 28 \[Alpha] \[Beta]^11 - 7 \[Beta]^12 H816= 65536 - 131072 \[Alpha]^2 + 131072 \[Alpha]^3 + 114688 \[Alpha]^4 - 327680 \[Alpha]^5 - 90112 \[Alpha]^6 + 253952 \[Alpha]^7 + 50688 \[Alpha]^8 - 57344 \[Alpha]^9 - 15872 \[Alpha]^10 - 512 \[Alpha]^11 + 6592 \[Alpha]^12 + 768 \[Alpha]^13 - 160 \[Alpha]^14 + 32 \[Alpha]^15 + \[Alpha]^16 + 262144 \[Alpha] \[Beta] + 131072 \[Alpha]^2 \[Beta] - 458752 \[Alpha]^3 \[Beta] - 196608 \[Alpha]^4 \[Beta] + 278528 \[Alpha]^5 \[Beta] - 106496 \[Alpha]^6 \[Beta] - 143360 \[Alpha]^7 \[Beta] + 221184 \[Alpha]^8 \[Beta] + 60416 \[Alpha]^9 \[Beta] - 45568 \[Alpha]^10 \[Beta] + 2816 \[Alpha]^11 \[Beta] - 768 \[Alpha]^12 \[Beta] + 1216 \[Alpha]^13 \[Beta] + 160 \[Alpha]^14 \[Beta] - 16 \[Alpha]^15 \[Beta] - 131072 \[Beta]^2 - 131072 \[Alpha] \[Beta]^2 + 688128 \[Alpha]^2 \[Beta]^2 + 131072 \[Alpha]^3 \[Beta]^2 - 827392 \[Alpha]^4 \[Beta]^2 + 122880 \[Alpha]^5 \[Beta]^2 + 370688 \[Alpha]^6 \[Beta]^2 - 262144 \[Alpha]^7 \[Beta]^2 - 124416 \[Alpha]^8 \[Beta]^2 + 170496 \[Alpha]^9 \[Beta]^2 + 41856 \[Alpha]^10 \[Beta]^2 - 16896 \[Alpha]^11 \[Beta]^2 - 4320 \[Alpha]^12 \[Beta]^2 - 864 \[Alpha]^13 \[Beta]^2 + 120 \[Alpha]^14 \[Beta]^2 - 131072 \[Beta]^3 - 458752 \[Alpha] \[Beta]^3 - 131072 \[Alpha]^2 \[Beta]^3 + 1277952 \[Alpha]^3 \[Beta]^3 + 483328 \[Alpha]^4 \[Beta]^3 - 1003520 \[Alpha]^5 \[Beta]^3 - 65536 \[Alpha]^6 \[Beta]^3 + 331776 \[Alpha]^7 \[Beta]^3 - 185856 \[Alpha]^8 \[Beta]^3 - 123136 \[Alpha]^9 \[Beta]^3 + 66048 \[Alpha]^10 \[Beta]^3 + 11136 \[Alpha]^11 \[Beta]^3 - 1504 \[Alpha]^12 \[Beta]^3 - 560 \[Alpha]^13 \[Beta]^3 + 114688 \[Beta]^4 + 196608 \[Alpha] \[Beta]^4 - 827392 \[Alpha]^2 \[Beta]^4 - 483328 \[Alpha]^3 \[Beta]^4 + 1451008 \[Alpha]^4 \[Beta]^4 + 475136 \[Alpha]^5 \[Beta]^4 - 777216 \[Alpha]^6 \[Beta]^4 - 62464 \[Alpha]^7 \[Beta]^4 + 117312 \[Alpha]^8 \[Beta]^4 - 86784 \[Alpha]^9 \[Beta]^4 - 27040 \[Alpha]^10 \[Beta]^4 + 12192 \[Alpha]^11 \[Beta]^4 + 1820 \[Alpha]^12 \[Beta]^4 + 327680 \[Beta]^5 + 278528 \[Alpha] \[Beta]^5 - 122880 \[Alpha]^2 \[Beta]^5 - 1003520 \[Alpha]^3 \[Beta]^5 - 475136 \[Alpha]^4 \[Beta]^5 + 1050624 \[Alpha]^5 \[Beta]^5 + 338944 \[Alpha]^6 \[Beta]^5 - 338432 \[Alpha]^7 \[Beta]^5 - 11520 \[Alpha]^8 \[Beta]^5 + 59200 \[Alpha]^9 \[Beta]^5 - 19424 \[Alpha]^10 \[Beta]^5 - 4368 \[Alpha]^11 \[Beta]^5 - 90112 \[Beta]^6 + 106496 \[Alpha] \[Beta]^6 + 370688 \[Alpha]^2 \[Beta]^6 + 65536 \[Alpha]^3 \[Beta]^6 - 777216 \[Alpha]^4 \[Beta]^6 - 338944 \[Alpha]^5 \[Beta]^6 + 585984 \[Alpha]^6 \[Beta]^6 + 156672 \[Alpha]^7 \[Beta]^6 - 99552 \[Alpha]^8 \[Beta]^6 + 32 \[Alpha]^9 \[Beta]^6 + 8008 \[Alpha]^10 \[Beta]^6 - 253952 \[Beta]^7 - 143360 \[Alpha] \[Beta]^7 + 262144 \[Alpha]^2 \[Beta]^7 + 331776 \[Alpha]^3 \[Beta]^7 + 62464 \[Alpha]^4 \[Beta]^7 - 338432 \[Alpha]^5 \[Beta]^7 - 156672 \[Alpha]^6 \[Beta]^7 + 119040 \[Alpha]^7 \[Beta]^7 + 32160 \[Alpha]^8 \[Beta]^7 - 11440 \[Alpha]^9 \[Beta]^7 + 50688 \[Beta]^8 - 221184 \[Alpha] \[Beta]^8 - 124416 \[Alpha]^2 \[Beta]^8 + 185856 \[Alpha]^3 \[Beta]^8 + 117312 \[Alpha]^4 \[Beta]^8 + 11520 \[Alpha]^5 \[Beta]^8 - 99552 \[Alpha]^6 \[Beta]^8 - 32160 \[Alpha]^7 \[Beta]^8 + 12870 \[Alpha]^8 \[Beta]^8 + 57344 \[Beta]^9 + 60416 \[Alpha] \[Beta]^9 - 170496 \[Alpha]^2 \[Beta]^9 - 123136 \[Alpha]^3 \[Beta]^9 + 86784 \[Alpha]^4 \[Beta]^9 + 59200 \[Alpha]^5 \[Beta]^9 - 32 \[Alpha]^6 \[Beta]^9 - 11440 \[Alpha]^7 \[Beta]^9 - 15872 \[Beta]^10 + 45568 \[Alpha] \[Beta]^10 + 41856 \[Alpha]^2 \[Beta]^10 - 66048 \[Alpha]^3 \[Beta]^10 - 27040 \[Alpha]^4 \[Beta]^10 + 19424 \[Alpha]^5 \[Beta]^10 + 8008 \[Alpha]^6 \[Beta]^10 + 512 \[Beta]^11 + 2816 \[Alpha] \[Beta]^11 + 16896 \[Alpha]^2 \[Beta]^11 + 11136 \[Alpha]^3 \[Beta]^11 - 12192 \[Alpha]^4 \[Beta]^11 - 4368 \[Alpha]^5 \[Beta]^11 + 6592 \[Beta]^12 + 768 \[Alpha] \[Beta]^12 - 4320 \[Alpha]^2 \[Beta]^12 + 1504 \[Alpha]^3 \[Beta]^12 + 1820 \[Alpha]^4 \[Beta]^12 - 768 \[Beta]^13 + 1216 \[Alpha] \[Beta]^13 + 864 \[Alpha]^2 \[Beta]^13 - 560 \[Alpha]^3 \[Beta]^13 - 160 \[Beta]^14 - 160 \[Alpha] \[Beta]^14 + 120 \[Alpha]^2 \[Beta]^14 - 32 \[Beta]^15 - 16 \[Alpha] \[Beta]^15 + \[Beta]^16 H918= 262144 - 983040 \[Alpha]^2 + 2293760 \[Alpha]^4 - 3424256 \[Alpha]^6 + 2791424 \[Alpha]^8 - 1149440 \[Alpha]^10 + 217856 \[Alpha]^12 - 8768 \[Alpha]^14 + 516 \[Alpha]^16 + \[Alpha]^18 + 1179648 \[Alpha] \[Beta] - 2097152 \[Alpha]^3 \[Beta] + 1409024 \[Alpha]^5 \[Beta] - 1638400 \[Alpha]^7 \[Beta] + 1649664 \[Alpha]^9 \[Beta] - 598016 \[Alpha]^11 \[Beta] + 99712 \[Alpha]^13 \[Beta] - 1792 \[Alpha]^15 \[Beta] + 18 \[Alpha]^17 \[Beta] - 196608 \[Beta]^2 + 3538944 \[Alpha]^2 \[Beta]^2 - 7454720 \[Alpha]^4 \[Beta]^2 + 6479872 \[Alpha]^6 \[Beta]^2 - 4073984 \[Alpha]^8 \[Beta]^2 + 2126336 \[Alpha]^10 \[Beta]^2 - 425152 \[Alpha]^12 \[Beta]^2 + 22688 \[Alpha]^14 \[Beta]^2 - 363 \[Alpha]^16 \[Beta]^2 - 2621440 \[Alpha] \[Beta]^3 + 8454144 \[Alpha]^3 \[Beta]^3 - 10125312 \[Alpha]^5 \[Beta]^3 + 6328320 \[Alpha]^7 \[Beta]^3 - 2791424 \[Alpha]^9 \[Beta]^3 + 938752 \[Alpha]^11 \[Beta]^3 - 121216 \[Alpha]^13 \[Beta]^3 + 2608 \[Alpha]^15 \[Beta]^3 - 1114112 \[Beta]^4 - 2080768 \[Alpha]^2 \[Beta]^4 + 9359360 \[Alpha]^4 \[Beta]^4 - 8295424 \[Alpha]^6 \[Beta]^4 + 3371264 \[Alpha]^8 \[Beta]^4 - 1351744 \[Alpha]^10 \[Beta]^4 + 284464 \[Alpha]^12 \[Beta]^4 - 10860 \[Alpha]^14 \[Beta]^4 + 1146880 \[Alpha] \[Beta]^5 - 6422528 \[Alpha]^3 \[Beta]^5 + 11339776 \[Alpha]^5 \[Beta]^5 - 7282688 \[Alpha]^7 \[Beta]^5 + 1859200 \[Alpha]^9 \[Beta]^5 - 390656 \[Alpha]^11 \[Beta]^5 + 30072 \[Alpha]^13 \[Beta]^5 + 1949696 \[Beta]^6 - 1089536 \[Alpha]^2 \[Beta]^6 - 4924416 \[Alpha]^4 \[Beta]^6 + 6687744 \[Alpha]^6 \[Beta]^6 - 2740416 \[Alpha]^8 \[Beta]^6 + 498400 \[Alpha]^10 \[Beta]^6 - 58604 \[Alpha]^12 \[Beta]^6 + 1671168 \[Alpha] \[Beta]^7 - 1470464 \[Alpha]^3 \[Beta]^7 - 2215936 \[Alpha]^5 \[Beta]^7 + 2857472 \[Alpha]^7 \[Beta]^7 - 717440 \[Alpha]^9 \[Beta]^7 + 81744 \[Alpha]^11 \[Beta]^7 - 1026048 \[Beta]^8 + 1728000 \[Alpha]^2 \[Beta]^8 - 137984 \[Alpha]^4 \[Beta]^8 - 1215680 \[Alpha]^6 \[Beta]^8 + 703192 \[Alpha]^8 \[Beta]^8 - 79794 \[Alpha]^10 \[Beta]^8 - 1332224 \[Alpha] \[Beta]^9 + 1900544 \[Alpha]^3 \[Beta]^9 - 628096 \[Alpha]^5 \[Beta]^9 - 214784 \[Alpha]^7 \[Beta]^9 + 48620 \[Alpha]^9 \[Beta]^9 + 200192 \[Beta]^10 - 1170944 \[Alpha]^2 \[Beta]^10 + 945088 \[Alpha]^4 \[Beta]^10 - 235168 \[Alpha]^6 \[Beta]^10 - 7722 \[Alpha]^8 \[Beta]^10 - 22528 \[Alpha] \[Beta]^11 - 384256 \[Alpha]^3 \[Beta]^11 + 242048 \[Alpha]^5 \[Beta]^11 - 18096 \[Alpha]^7 \[Beta]^11 - 84224 \[Beta]^12 + 69440 \[Alpha]^2 \[Beta]^12 - 82768 \[Alpha]^4 \[Beta]^12 + 21476 \[Alpha]^6 \[Beta]^12 - 24192 \[Alpha] \[Beta]^13 + 21504 \[Alpha]^3 \[Beta]^13 - 12936 \[Alpha]^5 \[Beta]^13 + 8640 \[Beta]^14 - 12000 \[Alpha]^2 \[Beta]^14 + 4740 \[Alpha]^4 \[Beta]^14 + 2688 \[Alpha] \[Beta]^15 - 976 \[Alpha]^3 \[Beta]^15 + 324 \[Beta]^16 + 57 \[Alpha]^2 \[Beta]^16 + 18 \[Alpha] \[Beta]^17 - 3 \[Beta]^18 H1024= 16777216 - 50331648 \[Alpha]^2 - 50331648 \[Alpha]^3 + 69206016 \[Alpha]^4 + 218103808 \[Alpha]^5 - 87031808 \[Alpha]^6 - 353370112 \[Alpha]^7 + 107937792 \[Alpha]^8 + 260046848 \[Alpha]^9 - 89522176 \[Alpha]^10 - 79560704 \[Alpha]^11 + 48349184 \[Alpha]^12 + 1703936 \[Alpha]^13 - 21422080 \[Alpha]^14 + 5234688 \[Alpha]^15 + 5992192 \[Alpha]^16 - 1769472 \[Alpha]^17 + 14592 \[Alpha]^18 - 61184 \[Alpha]^19 + 31776 \[Alpha]^20 + 4352 \[Alpha]^21 - 496 \[Alpha]^22 + 48 \[Alpha]^23 + \[Alpha]^24 + 100663296 \[Alpha] \[Beta] - 50331648 \[Alpha]^2 \[Beta] - 276824064 \[Alpha]^3 \[Beta] + 150994944 \[Alpha]^4 \[Beta] + 287309824 \[Alpha]^5 \[Beta] + 11534336 \[Alpha]^6 \[Beta] - 192413696 \[Alpha]^7 \[Beta] - 402653184 \[Alpha]^8 \[Beta] + 165412864 \[Alpha]^9 \[Beta] + 420610048 \[Alpha]^10 \[Beta] - 110428160 \[Alpha]^11 \[Beta] - 139853824 \[Alpha]^12 \[Beta] + 22822912 \[Alpha]^13 \[Beta] + 11952128 \[Alpha]^14 \[Beta] - 978944 \[Alpha]^15 \[Beta] - 1146880 \[Alpha]^16 \[Beta] + 4357632 \[Alpha]^17 \[Beta] - 1089280 \[Alpha]^18 \[Beta] + 85376 \[Alpha]^19 \[Beta] - 6912 \[Alpha]^20 \[Beta] + 3232 \[Alpha]^21 \[Beta] + 496 \[Alpha]^22 \[Beta] - 24 \[Alpha]^23 \[Beta] - 50331648 \[Beta]^2 + 50331648 \[Alpha] \[Beta]^2 + 415236096 \[Alpha]^2 \[Beta]^2 - 67108864 \[Alpha]^3 \[Beta]^2 - 835715072 \[Alpha]^4 \[Beta]^2 - 110100480 \[Alpha]^5 \[Beta]^2 + 740556800 \[Alpha]^6 \[Beta]^2 + 461373440 \[Alpha]^7 \[Beta]^2 - 421396480 \[Alpha]^8 \[Beta]^2 - 729415680 \[Alpha]^9 \[Beta]^2 + 263421952 \[Alpha]^10 \[Beta]^2 + 526909440 \[Alpha]^11 \[Beta]^2 - 166305792 \[Alpha]^12 \[Beta]^2 - 130260992 \[Alpha]^13 \[Beta]^2 + 58984448 \[Alpha]^14 \[Beta]^2 - 3047424 \[Alpha]^15 \[Beta]^2 - 5435136 \[Alpha]^16 \[Beta]^2 + 1570560 \[Alpha]^17 \[Beta]^2 + 1089472 \[Alpha]^18 \[Beta]^2 - 160768 \[Alpha]^19 \[Beta]^2 - 17296 \[Alpha]^20 \[Beta]^2 - 3536 \[Alpha]^21 \[Beta]^2 + 276 \[Alpha]^22 \[Beta]^2 + 50331648 \[Beta]^3 - 276824064 \[Alpha] \[Beta]^3 + 67108864 \[Alpha]^2 \[Beta]^3 + 1270874112 \[Alpha]^3 \[Beta]^3 - 475004928 \[Alpha]^4 \[Beta]^3 - 1883766784 \[Alpha]^5 \[Beta]^3 + 360710144 \[Alpha]^6 \[Beta]^3 + 1280311296 \[Alpha]^7 \[Beta]^3 + 412483584 \[Alpha]^8 \[Beta]^3 - 637599744 \[Alpha]^9 \[Beta]^3 - 767033344 \[Alpha]^10 \[Beta]^3 + 349077504 \[Alpha]^11 \[Beta]^3 + 416014336 \[Alpha]^12 \[Beta]^3 - 111857664 \[Alpha]^13 \[Beta]^3 - 67010560 \[Alpha]^14 \[Beta]^3 + 14438400 \[Alpha]^15 \[Beta]^3 + 2049792 \[Alpha]^16 \[Beta]^3 - 4308608 \[Alpha]^17 \[Beta]^3 + 820224 \[Alpha]^18 \[Beta]^3 + 121792 \[Alpha]^19 \[Beta]^3 - 7568 \[Alpha]^20 \[Beta]^3 - 2024 \[Alpha]^21 \[Beta]^3 + 69206016 \[Beta]^4 - 150994944 \[Alpha] \[Beta]^4 - 835715072 \[Alpha]^2 \[Beta]^4 + 475004928 \[Alpha]^3 \[Beta]^4 + 2455371776 \[Alpha]^4 \[Beta]^4 - 763363328 \[Alpha]^5 \[Beta]^4 - 2810970112 \[Alpha]^6 \[Beta]^4 + 443809792 \[Alpha]^7 \[Beta]^4 + 1417822208 \[Alpha]^8 \[Beta]^4 + 393347072 \[Alpha]^9 \[Beta]^4 - 410640384 \[Alpha]^10 \[Beta]^4 - 655728640 \[Alpha]^11 \[Beta]^4 + 190391296 \[Alpha]^12 \[Beta]^4 + 279412736 \[Alpha]^13 \[Beta]^4 - 78490624 \[Alpha]^14 \[Beta]^4 - 19053568 \[Alpha]^15 \[Beta]^4 + 5319072 \[Alpha]^16 \[Beta]^4 - 846080 \[Alpha]^17 \[Beta]^4 - 606416 \[Alpha]^18 \[Beta]^4 + 99792 \[Alpha]^19 \[Beta]^4 + 10626 \[Alpha]^20 \[Beta]^4 - 218103808 \[Beta]^5 + 287309824 \[Alpha] \[Beta]^5 + 110100480 \[Alpha]^2 \[Beta]^5 - 1883766784 \[Alpha]^3 \[Beta]^5 + 763363328 \[Alpha]^4 \[Beta]^5 + 3752329216 \[Alpha]^5 \[Beta]^5 - 1198260224 \[Alpha]^6 \[Beta]^5 - 3127508992 \[Alpha]^7 \[Beta]^5 + 501350400 \[Alpha]^8 \[Beta]^5 + 1304936448 \[Alpha]^9 \[Beta]^5 + 307552256 \[Alpha]^10 \[Beta]^5 - 437121024 \[Alpha]^11 \[Beta]^5 - 347504640 \[Alpha]^12 \[Beta]^5 + 123619328 \[Alpha]^13 \[Beta]^5 + 90964992 \[Alpha]^14 \[Beta]^5 - 17125888 \[Alpha]^15 \[Beta]^5 - 4760832 \[Alpha]^16 \[Beta]^5 + 1886240 \[Alpha]^17 \[Beta]^5 - 228592 \[Alpha]^18 \[Beta]^5 - 42504 \[Alpha]^19 \[Beta]^5 - 87031808 \[Beta]^6 - 11534336 \[Alpha] \[Beta]^6 + 740556800 \[Alpha]^2 \[Beta]^6 - 360710144 \[Alpha]^3 \[Beta]^6 - 2810970112 \[Alpha]^4 \[Beta]^6 + 1198260224 \[Alpha]^5 \[Beta]^6 + 4291887104 \[Alpha]^6 \[Beta]^6 - 1327497216 \[Alpha]^7 \[Beta]^6 - 2723520512 \[Alpha]^8 \[Beta]^6 + 505864192 \[Alpha]^9 \[Beta]^6 + 687880192 \[Alpha]^10 \[Beta]^6 + 152272896 \[Alpha]^11 \[Beta]^6 - 135764992 \[Alpha]^12 \[Beta]^6 - 168096768 \[Alpha]^13 \[Beta]^6 + 49761536 \[Alpha]^14 \[Beta]^6 + 20406272 \[Alpha]^15 \[Beta]^6 - 4031152 \[Alpha]^16 \[Beta]^6 - 198064 \[Alpha]^17 \[Beta]^6 + 134596 \[Alpha]^18 \[Beta]^6 + 353370112 \[Beta]^7 - 192413696 \[Alpha] \[Beta]^7 - 461373440 \[Alpha]^2 \[Beta]^7 + 1280311296 \[Alpha]^3 \[Beta]^7 - 443809792 \[Alpha]^4 \[Beta]^7 - 3127508992 \[Alpha]^5 \[Beta]^7 + 1327497216 \[Alpha]^6 \[Beta]^7 + 3290103808 \[Alpha]^7 \[Beta]^7 - 1010409472 \[Alpha]^8 \[Beta]^7 - 1526222848 \[Alpha]^9 \[Beta]^7 + 205750272 \[Alpha]^10 \[Beta]^7 + 343945216 \[Alpha]^11 \[Beta]^7 + 75484160 \[Alpha]^12 \[Beta]^7 - 62036480 \[Alpha]^13 \[Beta]^7 - 35979264 \[Alpha]^14 \[Beta]^7 + 7056640 \[Alpha]^15 \[Beta]^7 + 2012944 \[Alpha]^16 \[Beta]^7 - 346104 \[Alpha]^17 \[Beta]^7 + 107937792 \[Beta]^8 + 402653184 \[Alpha] \[Beta]^8 - 421396480 \[Alpha]^2 \[Beta]^8 - 412483584 \[Alpha]^3 \[Beta]^8 + 1417822208 \[Alpha]^4 \[Beta]^8 - 501350400 \[Alpha]^5 \[Beta]^8 - 2723520512 \[Alpha]^6 \[Beta]^8 + 1010409472 \[Alpha]^7 \[Beta]^8 + 2265864704 \[Alpha]^8 \[Beta]^8 - 636780544 \[Alpha]^9 \[Beta]^8 - 703070720 \[Alpha]^10 \[Beta]^8 + 128171520 \[Alpha]^11 \[Beta]^8 + 80886336 \[Alpha]^12 \[Beta]^8 + 25819648 \[Alpha]^13 \[Beta]^8 - 12399200 \[Alpha]^14 \[Beta]^8 - 4315168 \[Alpha]^15 \[Beta]^8 + 735471 \[Alpha]^16 \[Beta]^8 - 260046848 \[Beta]^9 + 165412864 \[Alpha] \[Beta]^9 + 729415680 \[Alpha]^2 \[Beta]^9 - 637599744 \[Alpha]^3 \[Beta]^9 - 393347072 \[Alpha]^4 \[Beta]^9 + 1304936448 \[Alpha]^5 \[Beta]^9 - 505864192 \[Alpha]^6 \[Beta]^9 - 1526222848 \[Alpha]^7 \[Beta]^9 + 636780544 \[Alpha]^8 \[Beta]^9 + 872772608 \[Alpha]^9 \[Beta]^9 - 224879104 \[Alpha]^10 \[Beta]^9 - 193438464 \[Alpha]^11 \[Beta]^9 + 19522048 \[Alpha]^12 \[Beta]^9 + 21973824 \[Alpha]^13 \[Beta]^9 + 3638624 \[Alpha]^14 \[Beta]^9 - 1307504 \[Alpha]^15 \[Beta]^9 - 89522176 \[Beta]^10 - 420610048 \[Alpha] \[Beta]^10 + 263421952 \[Alpha]^2 \[Beta]^10 + 767033344 \[Alpha]^3 \[Beta]^10 - 410640384 \[Alpha]^4 \[Beta]^10 - 307552256 \[Alpha]^5 \[Beta]^10 + 687880192 \[Alpha]^6 \[Beta]^10 - 205750272 \[Alpha]^7 \[Beta]^10 - 703070720 \[Alpha]^8 \[Beta]^10 + 224879104 \[Alpha]^9 \[Beta]^10 + 279471744 \[Alpha]^10 \[Beta]^10 - 65628160 \[Alpha]^11 \[Beta]^10 - 33277088 \[Alpha]^12 \[Beta]^10 + 1891808 \[Alpha]^13 \[Beta]^10 + 1961256 \[Alpha]^14 \[Beta]^10 + 79560704 \[Beta]^11 - 110428160 \[Alpha] \[Beta]^11 - 526909440 \[Alpha]^2 \[Beta]^11 + 349077504 \[Alpha]^3 \[Beta]^11 + 655728640 \[Alpha]^4 \[Beta]^11 - 437121024 \[Alpha]^5 \[Beta]^11 - 152272896 \[Alpha]^6 \[Beta]^11 + 343945216 \[Alpha]^7 \[Beta]^11 - 128171520 \[Alpha]^8 \[Beta]^11 - 193438464 \[Alpha]^9 \[Beta]^11 + 65628160 \[Alpha]^10 \[Beta]^11 + 38579840 \[Alpha]^11 \[Beta]^11 - 7941024 \[Alpha]^12 \[Beta]^11 - 2496144 \[Alpha]^13 \[Beta]^11 + 48349184 \[Beta]^12 + 139853824 \[Alpha] \[Beta]^12 - 166305792 \[Alpha]^2 \[Beta]^12 - 416014336 \[Alpha]^3 \[Beta]^12 + 190391296 \[Alpha]^4 \[Beta]^12 + 347504640 \[Alpha]^5 \[Beta]^12 - 135764992 \[Alpha]^6 \[Beta]^12 - 75484160 \[Alpha]^7 \[Beta]^12 + 80886336 \[Alpha]^8 \[Beta]^12 - 19522048 \[Alpha]^9 \[Beta]^12 - 33277088 \[Alpha]^10 \[Beta]^12 + 7941024 \[Alpha]^11 \[Beta]^12 + 2704156 \[Alpha]^12 \[Beta]^12 - 1703936 \[Beta]^13 + 22822912 \[Alpha] \[Beta]^13 + 130260992 \[Alpha]^2 \[Beta]^13 - 111857664 \[Alpha]^3 \[Beta]^13 - 279412736 \[Alpha]^4 \[Beta]^13 + 123619328 \[Alpha]^5 \[Beta]^13 + 168096768 \[Alpha]^6 \[Beta]^13 - 62036480 \[Alpha]^7 \[Beta]^13 - 25819648 \[Alpha]^8 \[Beta]^13 + 21973824 \[Alpha]^9 \[Beta]^13 - 1891808 \[Alpha]^10 \[Beta]^13 - 2496144 \[Alpha]^11 \[Beta]^13 - 21422080 \[Beta]^14 - 11952128 \[Alpha] \[Beta]^14 + 58984448 \[Alpha]^2 \[Beta]^14 + 67010560 \[Alpha]^3 \[Beta]^14 - 78490624 \[Alpha]^4 \[Beta]^14 - 90964992 \[Alpha]^5 \[Beta]^14 + 49761536 \[Alpha]^6 \[Beta]^14 + 35979264 \[Alpha]^7 \[Beta]^14 - 12399200 \[Alpha]^8 \[Beta]^14 - 3638624 \[Alpha]^9 \[Beta]^14 + 1961256 \[Alpha]^10 \[Beta]^14 - 5234688 \[Beta]^15 - 978944 \[Alpha] \[Beta]^15 + 3047424 \[Alpha]^2 \[Beta]^15 + 14438400 \[Alpha]^3 \[Beta]^15 + 19053568 \[Alpha]^4 \[Beta]^15 - 17125888 \[Alpha]^5 \[Beta]^15 - 20406272 \[Alpha]^6 \[Beta]^15 + 7056640 \[Alpha]^7 \[Beta]^15 + 4315168 \[Alpha]^8 \[Beta]^15 - 1307504 \[Alpha]^9 \[Beta]^15 + 5992192 \[Beta]^16 + 1146880 \[Alpha] \[Beta]^16 - 5435136 \[Alpha]^2 \[Beta]^16 - 2049792 \[Alpha]^3 \[Beta]^16 + 5319072 \[Alpha]^4 \[Beta]^16 + 4760832 \[Alpha]^5 \[Beta]^16 - 4031152 \[Alpha]^6 \[Beta]^16 - 2012944 \[Alpha]^7 \[Beta]^16 + 735471 \[Alpha]^8 \[Beta]^16 + 1769472 \[Beta]^17 + 4357632 \[Alpha] \[Beta]^17 - 1570560 \[Alpha]^2 \[Beta]^17 - 4308608 \[Alpha]^3 \[Beta]^17 + 846080 \[Alpha]^4 \[Beta]^17 + 1886240 \[Alpha]^5 \[Beta]^17 + 198064 \[Alpha]^6 \[Beta]^17 - 346104 \[Alpha]^7 \[Beta]^17 + 14592 \[Beta]^18 + 1089280 \[Alpha] \[Beta]^18 + 1089472 \[Alpha]^2 \[Beta]^18 - 820224 \[Alpha]^3 \[Beta]^18 - 606416 \[Alpha]^4 \[Beta]^18 + 228592 \[Alpha]^5 \[Beta]^18 + 134596 \[Alpha]^6 \[Beta]^18 + 61184 \[Beta]^19 + 85376 \[Alpha] \[Beta]^19 + 160768 \[Alpha]^2 \[Beta]^19 + 121792 \[Alpha]^3 \[Beta]^19 - 99792 \[Alpha]^4 \[Beta]^19 - 42504 \[Alpha]^5 \[Beta]^19 + 31776 \[Beta]^20 + 6912 \[Alpha] \[Beta]^20 - 17296 \[Alpha]^2 \[Beta]^20 + 7568 \[Alpha]^3 \[Beta]^20 + 10626 \[Alpha]^4 \[Beta]^20 - 4352 \[Beta]^21 + 3232 \[Alpha] \[Beta]^21 + 3536 \[Alpha]^2 \[Beta]^21 - 2024 \[Alpha]^3 \[Beta]^21 - 496 \[Beta]^22 - 496 \[Alpha] \[Beta]^22 + 276 \[Alpha]^2 \[Beta]^22 - 48 \[Beta]^23 - 24 \[Alpha] \[Beta]^23 + \[Beta]^24