Z7alphabeta[x_]=(49 \[Alpha]^21 (1+\[Beta]^2)-49 \[Alpha]^20 \[Beta] (-5+13 \[Beta]^2)+14 \[Alpha]^19 (-44-281 \[Beta]^2+255 \[Beta]^4)-14 \[Alpha]^18 \[Beta] (356-1679 \[Beta]^2+759 \[Beta]^4)+\[Alpha]^16 \[Beta] (53456-260248 \[Beta]^2+130701 \[Beta]^4+12699 \[Beta]^6)+\[Alpha]^17 (12240+66808 \[Beta]^2-84111 \[Beta]^4+14289 \[Beta]^6)-8 \[Alpha]^15 (8768+74160 \[Beta]^2-63964 \[Beta]^4-22935 \[Beta]^6+11985 \[Beta]^8)+8 \[Alpha]^14 \[Beta] (-51136+96016 \[Beta]^2+135668 \[Beta]^4-155289 \[Beta]^6+24225 \[Beta]^8)+\[Alpha]^13 (557568+309248 \[Beta]^2+5159360 \[Beta]^4-7379744 \[Beta]^6+2353218 \[Beta]^8-173502 \[Beta]^10)-\[Beta] (-1+\[Beta]^2) (1024-2304 \[Beta]^2+2688 \[Beta]^4-672 \[Beta]^6-108 \[Beta]^8+3 \[Beta]^10)^2-2 \[Alpha]^12 \[Beta] (-367872-4472832 \[Beta]^2+10093088 \[Beta]^4-5940304 \[Beta]^6+798315 \[Beta]^8+35581 \[Beta]^10)+4 \[Alpha]^11 (-109568+1462016 \[Beta]^2-7297920 \[Beta]^4+6212832 \[Beta]^6-562988 \[Beta]^8-433237 \[Beta]^10+112931 \[Beta]^12)-4 \[Alpha]^10 \[Beta] (-228352+7639296 \[Beta]^2-8253312 \[Beta]^4-1263712 \[Beta]^6+3863908 \[Beta]^8-1352963 \[Beta]^10+178347 \[Beta]^12)-2 \[Alpha]^8 \[Beta] (1798144-5724160 \[Beta]^2-31098624 \[Beta]^4+61881856 \[Beta]^6-40069872 \[Beta]^8+14142696 \[Beta]^10-2875233 \[Beta]^12+217209 \[Beta]^14)+2 \[Alpha]^9 (-913408-6551552 \[Beta]^2+12086016 \[Beta]^4+12306944 \[Beta]^6-26150672 \[Beta]^8+12759176 \[Beta]^10-3393947 \[Beta]^12+341445 \[Beta]^14)-8 \[Alpha]^6 \[Beta] (-212992-6180864 \[Beta]^2+24314880 \[Beta]^4-30825728 \[Beta]^6+19685440 \[Beta]^8-8710384 \[Beta]^10+2152828 \[Beta]^12-247359 \[Beta]^14+3927 \[Beta]^16)+8 \[Alpha]^7 (311296+4096 \[Beta]^2+8803328 \[Beta]^4-22584064 \[Beta]^6+21324352 \[Beta]^8-10382672 \[Beta]^10+3282060 \[Beta]^12-475809 \[Beta]^14+21879 \[Beta]^16)+\[Alpha]^5 (851968+21168128 \[Beta]^2-147865600 \[Beta]^4+263495680 \[Beta]^6-232813056 \[Beta]^8+132206592 \[Beta]^10-44855360 \[Beta]^12+7820640 \[Beta]^14-669459 \[Beta]^16-8211 \[Beta]^18)+\[Alpha]^4 \[Beta] (3211264-64946176 \[Beta]^2+176406528 \[Beta]^4-221585408 \[Beta]^6+172045824 \[Beta]^8-83879936 \[Beta]^10+21634496 \[Beta]^12-3261920 \[Beta]^14+49665 \[Beta]^16+6615 \[Beta]^18)-2 \[Alpha]^2 \[Beta] (1835008-14745600 \[Beta]^2+38404096 \[Beta]^4-57294848 \[Beta]^6+48424960 \[Beta]^8-22564352 \[Beta]^10+7184128 \[Beta]^12-1194816 \[Beta]^14-76452 \[Beta]^16+10631 \[Beta]^18+17 \[Beta]^20)-2 \[Alpha]^3 (1310720+8847360 \[Beta]^2-48365568 \[Beta]^4+84197376 \[Beta]^6-83101696 \[Beta]^8+50762240 \[Beta]^10-17438464 \[Beta]^12+4297152 \[Beta]^14-478700 \[Beta]^16-31105 \[Beta]^18+727 \[Beta]^20)+\[Alpha] (1048576+3670016 \[Beta]^2-23003136 \[Beta]^4+44236800 \[Beta]^6-42655744 \[Beta]^8+27217920 \[Beta]^10-14689792 \[Beta]^12+4301824 \[Beta]^14-816 \[Beta]^16-118856 \[Beta]^18+101 \[Beta]^20+69 \[Beta]^22)+128 x^7 (256-3 \[Alpha]^8+8 \[Alpha]^7 \[Beta]-512 \[Beta]^2+160 \[Beta]^4+64 \[Beta]^6-3 \[Beta]^8-24 \[Alpha]^5 \[Beta] (-8+3 \[Beta]^2)+4 \[Alpha]^6 (16+3 \[Beta]^2)+8 \[Alpha] \[Beta]^3 (-48+24 \[Beta]^2+\[Beta]^4)-8 \[Alpha]^3 \[Beta] (48-16 \[Beta]^2+9 \[Beta]^4)+10 \[Alpha]^4 (16-32 \[Beta]^2+11 \[Beta]^4)+4 \[Alpha]^2 (-128+112 \[Beta]^2-80 \[Beta]^4+3 \[Beta]^6))^2-128 x^6 (30 \[Alpha]^17-155 \[Alpha]^16 \[Beta]-16 \[Alpha]^15 (73+\[Beta]^2)+8 \[Alpha]^14 \[Beta] (-14+221 \[Beta]^2)+\[Alpha]^13 (9280+17136 \[Beta]^2-4344 \[Beta]^4)+4 \[Alpha]^12 \[Beta] (17664-6620 \[Beta]^2+151 \[Beta]^4)+16 \[Alpha]^11 (2736-2120 \[Beta]^2-2445 \[Beta]^4+977 \[Beta]^6)-8 \[Alpha]^10 \[Beta] (6240+31168 \[Beta]^2-18906 \[Beta]^4+4169 \[Beta]^6)-2 \[Alpha]^8 \[Beta] (251648-464256 \[Beta]^2+291840 \[Beta]^4-78440 \[Beta]^6+4521 \[Beta]^8)+4 \[Alpha]^9 (-30720-81088 \[Beta]^2+88368 \[Beta]^4-48148 \[Beta]^6+7821 \[Beta]^8)-16 \[Alpha]^7 (6912-63488 \[Beta]^2+70432 \[Beta]^4-43344 \[Beta]^6+5915 \[Beta]^8+583 \[Beta]^10)+8 \[Alpha]^6 \[Beta] (120320-163584 \[Beta]^2+120896 \[Beta]^4-23168 \[Beta]^6+406 \[Beta]^8+1187 \[Beta]^10)-8 \[Alpha]^5 (-63488+159232 \[Beta]^2-193536 \[Beta]^4+81088 \[Beta]^6+2504 \[Beta]^8-7258 \[Beta]^10+191 \[Beta]^12)-4 \[Alpha]^4 \[Beta] (122880-211968 \[Beta]^2+135424 \[Beta]^4-21888 \[Beta]^6-4864 \[Beta]^8+8084 \[Beta]^10+513 \[Beta]^12)-8 \[Alpha]^2 \[Beta] (8192+8192 \[Beta]^2-512 \[Beta]^4-17664 \[Beta]^6+14816 \[Beta]^8-576 \[Beta]^10-1310 \[Beta]^12+7 \[Beta]^14)+16 \[Alpha]^3 (-28672+55296 \[Beta]^2-49408 \[Beta]^4+5120 \[Beta]^6+15728 \[Beta]^8-8072 \[Beta]^10-591 \[Beta]^12+71 \[Beta]^14)+\[Beta] (65536-196608 \[Beta]^2+163840 \[Beta]^4+20480 \[Beta]^6-81408 \[Beta]^8+20224 \[Beta]^10+6144 \[Beta]^12-784 \[Beta]^14+21 \[Beta]^16)-2 \[Alpha] (-65536+163840 \[Beta]^2-24576 \[Beta]^4-169984 \[Beta]^6+114688 \[Beta]^8+15232 \[Beta]^10-22176 \[Beta]^12+184 \[Beta]^14+49 \[Beta]^16))+64 x^5 (-262144+77 \[Alpha]^18-382 \[Alpha]^17 \[Beta]+983040 \[Beta]^2-1114112 \[Beta]^4+163840 \[Beta]^6+387072 \[Beta]^8-137728 \[Beta]^10-26880 \[Beta]^12+9216 \[Beta]^14-1092 \[Beta]^16+35 \[Beta]^18-5 \[Alpha]^16 (532+\[Beta]^2)+16 \[Alpha]^15 \[Beta] (54+223 \[Beta]^2)+\[Alpha]^14 (21504+30208 \[Beta]^2-7468 \[Beta]^4)-8 \[Alpha]^13 \[Beta] (-13104+5604 \[Beta]^2+185 \[Beta]^4)-16 \[Alpha]^11 \[Beta] (20256+11440 \[Beta]^2-8958 \[Beta]^4+1591 \[Beta]^6)+4 \[Alpha]^12 (3392-26112 \[Beta]^2-12804 \[Beta]^4+5999 \[Beta]^6)-2 \[Alpha]^10 (150272+14336 \[Beta]^2-104960 \[Beta]^4+23776 \[Beta]^6+9933 \[Beta]^8)+4 \[Alpha]^9 \[Beta] (-32000+306816 \[Beta]^2-96992 \[Beta]^4-31656 \[Beta]^6+17699 \[Beta]^8)+\[Alpha]^8 (428032+1195520 \[Beta]^2-744192 \[Beta]^4+87040 \[Beta]^6+247560 \[Beta]^8-68486 \[Beta]^10)+16 \[Alpha]^7 \[Beta] (111104-126720 \[Beta]^2+4800 \[Beta]^4+53216 \[Beta]^6-20158 \[Beta]^8+1529 \[Beta]^10)-8 \[Alpha]^5 \[Beta] (282624-238592 \[Beta]^2+65280 \[Beta]^4+109952 \[Beta]^6-44880 \[Beta]^8+6380 \[Beta]^10+889 \[Beta]^12)+4 \[Alpha]^6 (122880-630784 \[Beta]^2+452864 \[Beta]^4-65024 \[Beta]^6-177408 \[Beta]^8+62112 \[Beta]^10+1553 \[Beta]^12)+4 \[Alpha]^4 (-376832+712704 \[Beta]^2-797696 \[Beta]^4+69376 \[Beta]^6+234432 \[Beta]^8-81920 \[Beta]^10-9876 \[Beta]^12+43 \[Beta]^14)+16 \[Alpha]^3 \[Beta] (40960-118784 \[Beta]^2+58880 \[Beta]^4-9984 \[Beta]^6+4704 \[Beta]^8+464 \[Beta]^10+522 \[Beta]^12+79 \[Beta]^14)+\[Alpha]^2 (1114112-2621440 \[Beta]^2+1998848 \[Beta]^4-606208 \[Beta]^6-93696 \[Beta]^8+108544 \[Beta]^10+27648 \[Beta]^12+9024 \[Beta]^14-203 \[Beta]^16)-2 \[Alpha] \[Beta] (-65536-196608 \[Beta]^2+671744 \[Beta]^4-438272 \[Beta]^6-42496 \[Beta]^8+87808 \[Beta]^10-17344 \[Beta]^12+368 \[Beta]^14+63 \[Beta]^16))-16 x^4 (189 \[Alpha]^19-889 \[Alpha]^18 \[Beta]+\[Alpha]^17 (-5628+107 \[Beta]^2)+\[Alpha]^16 \[Beta] (6612+5849 \[Beta]^2)+\[Alpha]^15 (53440+35232 \[Beta]^2-7628 \[Beta]^4)-4 \[Alpha]^14 \[Beta] (-15760+13848 \[Beta]^2+3353 \[Beta]^4)+4 \[Alpha]^13 (-60352-83728 \[Beta]^2-2708 \[Beta]^4+6359 \[Beta]^6)+4 \[Alpha]^12 \[Beta] (-338368+129232 \[Beta]^2-25028 \[Beta]^4+13453 \[Beta]^6)-2 \[Alpha]^11 (334080-715520 \[Beta]^2+189216 \[Beta]^4-247408 \[Beta]^6+100845 \[Beta]^8)+2 \[Alpha]^10 \[Beta] (980224+1044224 \[Beta]^2-59232 \[Beta]^4-380688 \[Beta]^6+123145 \[Beta]^8)-2 \[Alpha]^9 (-1268736-697600 \[Beta]^2+282240 \[Beta]^4+416160 \[Beta]^6-395308 \[Beta]^8+58179 \[Beta]^10)+\[Alpha]^8 (4610048 \[Beta]-8720896 \[Beta]^3+1311488 \[Beta]^5+2039360 \[Beta]^7-706120 \[Beta]^9-29570 \[Beta]^11)-4 \[Alpha]^6 \[Beta] (2846720-3266560 \[Beta]^2+1212160 \[Beta]^4+551680 \[Beta]^6-113584 \[Beta]^8-18584 \[Beta]^10+1333 \[Beta]^12)+4 \[Alpha]^7 (12288-2582528 \[Beta]^2+2169600 \[Beta]^4-888576 \[Beta]^6-254576 \[Beta]^8+84632 \[Beta]^10+12985 \[Beta]^12)+4 \[Alpha]^4 \[Beta] (1654784-2256896 \[Beta]^2+1037312 \[Beta]^4-135424 \[Beta]^6+148416 \[Beta]^8+50032 \[Beta]^10-8036 \[Beta]^12+1489 \[Beta]^14)-4 \[Alpha]^5 (1490944-4009984 \[Beta]^2+4062208 \[Beta]^4-1121536 \[Beta]^6-463296 \[Beta]^8+178736 \[Beta]^10+25204 \[Beta]^12+3709 \[Beta]^14)+\[Alpha]^3 (6094848-11927552 \[Beta]^2+9977856 \[Beta]^4-794624 \[Beta]^6-3299840 \[Beta]^8+1672704 \[Beta]^10+69440 \[Beta]^12+32032 \[Beta]^14+773 \[Beta]^16)+\[Alpha]^2 (458752 \[Beta]+1179648 \[Beta]^3-999424 \[Beta]^5-794624 \[Beta]^7+1257984 \[Beta]^9-299520 \[Beta]^11-26176 \[Beta]^13+2592 \[Beta]^15-609 \[Beta]^17)+\[Beta] (-786432+2162688 \[Beta]^2-1507328 \[Beta]^4-606208 \[Beta]^6+989184 \[Beta]^8-117248 \[Beta]^10-133888 \[Beta]^12+16576 \[Beta]^14-1260 \[Beta]^16+49 \[Beta]^18)-\[Alpha] (1835008-4390912 \[Beta]^2+983040 \[Beta]^4+4046848 \[Beta]^6-2816000 \[Beta]^8-418304 \[Beta]^10+596736 \[Beta]^12-10304 \[Beta]^14+1084 \[Beta]^16+77 \[Beta]^18))+2 x^3 (5242880+441 \[Alpha]^20-1932 \[Alpha]^19 \[Beta]-17301504 \[Beta]^2+14483456 \[Beta]^4+5636096 \[Beta]^6-11558912 \[Beta]^8+2461696 \[Beta]^10+1217024 \[Beta]^12-340480 \[Beta]^14+46608 \[Beta]^16-1736 \[Beta]^18+49 \[Beta]^20+14 \[Alpha]^18 (-844+45 \[Beta]^2)+4 \[Alpha]^17 \[Beta] (9004+1353 \[Beta]^2)-16 \[Alpha]^15 \[Beta] (17328+3160 \[Beta]^2+3959 \[Beta]^4)+\[Alpha]^16 (179216-18568 \[Beta]^2+11389 \[Beta]^4)+8 \[Alpha]^14 (-176448-141392 \[Beta]^2+20508 \[Beta]^4+3449 \[Beta]^6)+16 \[Alpha]^13 \[Beta] (-267712+147504 \[Beta]^2-19116 \[Beta]^4+12609 \[Beta]^6)+\[Alpha]^12 (279040+5204480 \[Beta]^2+1030080 \[Beta]^4+141280 \[Beta]^6-346014 \[Beta]^8)+8 \[Alpha]^11 \[Beta] (1575680+764160 \[Beta]^2-511584 \[Beta]^4+24496 \[Beta]^6+2011 \[Beta]^8)-8 \[Alpha]^9 \[Beta] (-74752+4707584 \[Beta]^2-1036160 \[Beta]^4-662112 \[Beta]^6+82748 \[Beta]^8+83321 \[Beta]^10)+4 \[Alpha]^10 (2593792-1147648 \[Beta]^2-692864 \[Beta]^4-106336 \[Beta]^6+47860 \[Beta]^8+134321 \[Beta]^10)-16 \[Alpha]^7 \[Beta] (2650112-2783232 \[Beta]^2-1680128 \[Beta]^4+2472192 \[Beta]^6-424048 \[Beta]^8-90392 \[Beta]^10+643 \[Beta]^12)+2 \[Alpha]^8 (-8204288-12408832 \[Beta]^2+6526720 \[Beta]^4+740608 \[Beta]^6-2851536 \[Beta]^8-125304 \[Beta]^10+160521 \[Beta]^12)-16 \[Alpha]^5 \[Beta] (-3162112+577536 \[Beta]^2+3486720 \[Beta]^4-3776256 \[Beta]^6+690752 \[Beta]^8+87536 \[Beta]^10-25876 \[Beta]^12+355 \[Beta]^14)-8 \[Alpha]^6 (802816-6975488 \[Beta]^2+2108416 \[Beta]^4+3083520 \[Beta]^6-3703360 \[Beta]^8+625968 \[Beta]^10+156788 \[Beta]^12+4631 \[Beta]^14)+4 \[Alpha]^3 \[Beta] (-2818048+393216 \[Beta]^2+9814016 \[Beta]^4-7938048 \[Beta]^6-25088 \[Beta]^8+1044992 \[Beta]^10-218688 \[Beta]^12-6240 \[Beta]^14+21 \[Beta]^16)+\[Alpha]^4 (31784960-52822016 \[Beta]^2+21479424 \[Beta]^4+54468608 \[Beta]^6-52380160 \[Beta]^8+9186816 \[Beta]^10+3564480 \[Beta]^12-21920 \[Beta]^14+10533 \[Beta]^16)+4 \[Alpha] \[Beta] (-1310720+589824 \[Beta]^2+2686976 \[Beta]^4-2408448 \[Beta]^6-407552 \[Beta]^8+978432 \[Beta]^10-360192 \[Beta]^12+16960 \[Beta]^14-84 \[Beta]^16+49 \[Beta]^18)-2 \[Alpha]^2 (11796480-21168128 \[Beta]^2+4653056 \[Beta]^4+13647872 \[Beta]^6-9209856 \[Beta]^8-514560 \[Beta]^10+1613568 \[Beta]^12+208704 \[Beta]^14-6796 \[Beta]^16+805 \[Beta]^18))-2 x (441 \[Alpha]^20-1932 \[Alpha]^19 \[Beta]+14 \[Alpha]^18 (-668+45 \[Beta]^2)+4 \[Alpha]^17 \[Beta] (5948+1353 \[Beta]^2)-16 \[Alpha]^15 \[Beta] (15792-3976 \[Beta]^2+3959 \[Beta]^4)+\[Alpha]^16 (94672-18728 \[Beta]^2+11389 \[Beta]^4)+8 \[Alpha]^14 (-93504-20624 \[Beta]^2-9364 \[Beta]^4+3449 \[Beta]^6)+16 \[Alpha]^13 \[Beta] (-58560+60336 \[Beta]^2-22076 \[Beta]^4+12609 \[Beta]^6)+\[Alpha]^12 (913920+2279936 \[Beta]^2-715584 \[Beta]^4+909152 \[Beta]^6-346014 \[Beta]^8)+8 \[Alpha]^11 \[Beta] (514816-51968 \[Beta]^2+65440 \[Beta]^4-77328 \[Beta]^6+2011 \[Beta]^8)+(1024-1280 \[Beta]^2-384 \[Beta]^4+736 \[Beta]^6-44 \[Beta]^8+7 \[Beta]^10)^2-8 \[Alpha]^9 \[Beta] (404480+832768 \[Beta]^2-91520 \[Beta]^4-16224 \[Beta]^6-200436 \[Beta]^8+83321 \[Beta]^10)+4 \[Alpha]^10 (566272-1522432 \[Beta]^2+710016 \[Beta]^4-381152 \[Beta]^6-111068 \[Beta]^8+134321 \[Beta]^10)-16 \[Alpha]^7 \[Beta] (356352-628736 \[Beta]^2-398080 \[Beta]^4+242944 \[Beta]^6+290704 \[Beta]^8-139320 \[Beta]^10+643 \[Beta]^12)+\[Alpha]^8 (-5365760+528384 \[Beta]^2+2342400 \[Beta]^4-3409408 \[Beta]^6+3684576 \[Beta]^8-2442160 \[Beta]^10+321042 \[Beta]^12)-16 \[Alpha]^5 \[Beta] (-606208+86016 \[Beta]^2+1025024 \[Beta]^4-581376 \[Beta]^6-330944 \[Beta]^8+187760 \[Beta]^10-11652 \[Beta]^12+355 \[Beta]^14)-8 \[Alpha]^6 (-114688-1355776 \[Beta]^2+777216 \[Beta]^4-35584 \[Beta]^6+94656 \[Beta]^8-420624 \[Beta]^10+131940 \[Beta]^12+4631 \[Beta]^14)+4 \[Alpha]^3 \[Beta] (-720896-1179648 \[Beta]^2+4046848 \[Beta]^4-1613824 \[Beta]^6-1491456 \[Beta]^8+936448 \[Beta]^10-141888 \[Beta]^12+3872 \[Beta]^14+21 \[Beta]^16)+\[Alpha]^4 (5570560-11927552 \[Beta]^2-81920 \[Beta]^4+16031744 \[Beta]^6-9269760 \[Beta]^8-2404864 \[Beta]^10+2193600 \[Beta]^12-16416 \[Beta]^14+10533 \[Beta]^16)+4 \[Alpha] \[Beta] (-262144+589824 \[Beta]^2-196608 \[Beta]^4-442368 \[Beta]^6+337920 \[Beta]^8+44544 \[Beta]^10-84736 \[Beta]^12+10304 \[Beta]^14-1092 \[Beta]^16+49 \[Beta]^18)-2 \[Alpha]^2 (2359296-3342336 \[Beta]^2-2162688 \[Beta]^4+5455872 \[Beta]^6-1255424 \[Beta]^8-1960448 \[Beta]^10+962304 \[Beta]^12+64576 \[Beta]^14-3548 \[Beta]^16+805 \[Beta]^18))-2 x^2 (49 \[Alpha]^21-196 \[Alpha]^20 \[Beta]-140 \[Alpha]^18 \[Beta] (-82+3 \[Beta]^2)+14 \[Alpha]^19 (-152+9 \[Beta]^2)-8 \[Alpha]^16 \[Beta] (10524+3113 \[Beta]^2+1546 \[Beta]^4)+\[Alpha]^17 (55344-13184 \[Beta]^2+4701 \[Beta]^4)-16 \[Alpha]^14 \[Beta] (9888-608 \[Beta]^2-19406 \[Beta]^4+1497 \[Beta]^6)+8 \[Alpha]^15 (-52864-24816 \[Beta]^2+360 \[Beta]^4+1741 \[Beta]^6)-8 \[Alpha]^12 \[Beta] (-765952+202944 \[Beta]^2+77296 \[Beta]^4-48796 \[Beta]^6+28151 \[Beta]^8)+2 \[Alpha]^13 (947456+466944 \[Beta]^2+636320 \[Beta]^4-351296 \[Beta]^6+47673 \[Beta]^8)-8 \[Alpha]^10 \[Beta] (1730048+125184 \[Beta]^2+931136 \[Beta]^4-819968 \[Beta]^6+115654 \[Beta]^8+28151 \[Beta]^10)+4 \[Alpha]^11 (526336-2413312 \[Beta]^2+1089792 \[Beta]^4-874528 \[Beta]^6+152712 \[Beta]^8+73997 \[Beta]^10)-16 \[Alpha]^8 \[Beta] (181248-484608 \[Beta]^2-1935232 \[Beta]^4+1689952 \[Beta]^6-285116 \[Beta]^8-66089 \[Beta]^10+1497 \[Beta]^12)+2 \[Alpha]^9 (-7131136+6995968 \[Beta]^2-10482944 \[Beta]^4+9389056 \[Beta]^6-3219056 \[Beta]^8-35904 \[Beta]^10+47673 \[Beta]^12)-16 \[Alpha]^6 \[Beta] (-1892352+1179648 \[Beta]^2+1869312 \[Beta]^4-2100992 \[Beta]^6+159968 \[Beta]^8+161440 \[Beta]^10-15366 \[Beta]^12+773 \[Beta]^14)+8 \[Alpha]^7 (1146880+1773568 \[Beta]^2+759808 \[Beta]^4-2241792 \[Beta]^6+1749632 \[Beta]^8-81296 \[Beta]^10-114328 \[Beta]^12+1741 \[Beta]^14)-4 \[Alpha]^4 \[Beta] (5963776-5144576 \[Beta]^2-843776 \[Beta]^4+964608 \[Beta]^6+1561600 \[Beta]^8-321408 \[Beta]^10-17056 \[Beta]^12+6440 \[Beta]^14+105 \[Beta]^16)+\[Alpha]^5 (16056320-51380224 \[Beta]^2+34095104 \[Beta]^4+9011200 \[Beta]^6-16402944 \[Beta]^8+831488 \[Beta]^10+1812288 \[Beta]^12+60544 \[Beta]^14+4701 \[Beta]^16)-4 \[Alpha]^2 \[Beta] (-393216+1900544 \[Beta]^2-2129920 \[Beta]^4+229376 \[Beta]^6+957440 \[Beta]^8-480768 \[Beta]^10+30592 \[Beta]^12+14592 \[Beta]^14-2310 \[Beta]^16+49 \[Beta]^18)-8 \[Beta] (-262144+589824 \[Beta]^2-196608 \[Beta]^4-442368 \[Beta]^6+337920 \[Beta]^8+44544 \[Beta]^10-84736 \[Beta]^12+10304 \[Beta]^14-1092 \[Beta]^16+49 \[Beta]^18)+2 \[Alpha]^3 (-11010048+23003136 \[Beta]^2-16908288 \[Beta]^4-1163264 \[Beta]^6+7344128 \[Beta]^8-2745856 \[Beta]^10-299520 \[Beta]^12-123328 \[Beta]^14-9256 \[Beta]^16+63 \[Beta]^18)+\[Alpha] (7340032-16777216 \[Beta]^2+5570560 \[Beta]^4+13107200 \[Beta]^6-9674752 \[Beta]^8-1835008 \[Beta]^10+2492928 \[Beta]^12-129024 \[Beta]^14+27184 \[Beta]^16+49 \[Beta]^20)))/(128 (256-3 \[Alpha]^8+8 \[Alpha]^7 \[Beta]-512 \[Beta]^2+160 \[Beta]^4+64 \[Beta]^6-3 \[Beta]^8-24 \[Alpha]^5 \[Beta] (-8+3 \[Beta]^2)+4 \[Alpha]^6 (16+3 \[Beta]^2)+8 \[Alpha] \[Beta]^3 (-48+24 \[Beta]^2+\[Beta]^4)-8 \[Alpha]^3 \[Beta] (48-16 \[Beta]^2+9 \[Beta]^4)+10 \[Alpha]^4 (16-32 \[Beta]^2+11 \[Beta]^4)+4 \[Alpha]^2 (-128+112 \[Beta]^2-80 \[Beta]^4+3 \[Beta]^6))^2);
a7=Coefficient[Z7alphabeta[x],x,7]
1
a6=Coefficient[Z7alphabeta[x],x,6]//Simplify
-((-10 \[Alpha]^9+256 \[Beta]+25 \[Alpha]^8 \[Beta]-256 \[Beta]^3-32 \[Beta]^5+112 \[Beta]^7-7 \[Beta]^9+16 \[Alpha]^7 (11+2 \[Beta]^2)+\[Alpha]^6 (400 \[Beta]-164 \[Beta]^3)-10 \[Alpha]^4 \[Beta] (80-8 \[Beta]^2+\[Beta]^4)+4 \[Alpha]^5 (32-148 \[Beta]^2+43 \[Beta]^4)-16 \[Alpha]^3 (48-56 \[Beta]^2+23 \[Beta]^4+5 \[Beta]^6)+4 \[Alpha]^2 \[Beta] (64+16 \[Beta]^2-20 \[Beta]^4+7 \[Beta]^6)+2 \[Alpha] (256-128 \[Beta]^2-128 \[Beta]^4+136 \[Beta]^6+7 \[Beta]^8))/(256-3 \[Alpha]^8+8 \[Alpha]^7 \[Beta]-512 \[Beta]^2+160 \[Beta]^4+64 \[Beta]^6-3 \[Beta]^8-24 \[Alpha]^5 \[Beta] (-8+3 \[Beta]^2)+4 \[Alpha]^6 (16+3 \[Beta]^2)+8 \[Alpha] \[Beta]^3 (-48+24 \[Beta]^2+\[Beta]^4)-8 \[Alpha]^3 \[Beta] (48-16 \[Beta]^2+9 \[Beta]^4)+10 \[Alpha]^4 (16-32 \[Beta]^2+11 \[Beta]^4)+4 \[Alpha]^2 (-128+112 \[Beta]^2-80 \[Beta]^4+3 \[Beta]^6)))
(* This term a6 is equal to -7*s *)
a5=Coefficient[Z7alphabeta[x],x,5]//Simplify
(-262144+77 \[Alpha]^18-382 \[Alpha]^17 \[Beta]+983040 \[Beta]^2-1114112 \[Beta]^4+163840 \[Beta]^6+387072 \[Beta]^8-137728 \[Beta]^10-26880 \[Beta]^12+9216 \[Beta]^14-1092 \[Beta]^16+35 \[Beta]^18-5 \[Alpha]^16 (532+\[Beta]^2)+16 \[Alpha]^15 \[Beta] (54+223 \[Beta]^2)+\[Alpha]^14 (21504+30208 \[Beta]^2-7468 \[Beta]^4)-8 \[Alpha]^13 \[Beta] (-13104+5604 \[Beta]^2+185 \[Beta]^4)-16 \[Alpha]^11 \[Beta] (20256+11440 \[Beta]^2-8958 \[Beta]^4+1591 \[Beta]^6)+4 \[Alpha]^12 (3392-26112 \[Beta]^2-12804 \[Beta]^4+5999 \[Beta]^6)-2 \[Alpha]^10 (150272+14336 \[Beta]^2-104960 \[Beta]^4+23776 \[Beta]^6+9933 \[Beta]^8)+4 \[Alpha]^9 \[Beta] (-32000+306816 \[Beta]^2-96992 \[Beta]^4-31656 \[Beta]^6+17699 \[Beta]^8)+\[Alpha]^8 (428032+1195520 \[Beta]^2-744192 \[Beta]^4+87040 \[Beta]^6+247560 \[Beta]^8-68486 \[Beta]^10)+16 \[Alpha]^7 \[Beta] (111104-126720 \[Beta]^2+4800 \[Beta]^4+53216 \[Beta]^6-20158 \[Beta]^8+1529 \[Beta]^10)-8 \[Alpha]^5 \[Beta] (282624-238592 \[Beta]^2+65280 \[Beta]^4+109952 \[Beta]^6-44880 \[Beta]^8+6380 \[Beta]^10+889 \[Beta]^12)+4 \[Alpha]^6 (122880-630784 \[Beta]^2+452864 \[Beta]^4-65024 \[Beta]^6-177408 \[Beta]^8+62112 \[Beta]^10+1553 \[Beta]^12)+4 \[Alpha]^4 (-376832+712704 \[Beta]^2-797696 \[Beta]^4+69376 \[Beta]^6+234432 \[Beta]^8-81920 \[Beta]^10-9876 \[Beta]^12+43 \[Beta]^14)+16 \[Alpha]^3 \[Beta] (40960-118784 \[Beta]^2+58880 \[Beta]^4-9984 \[Beta]^6+4704 \[Beta]^8+464 \[Beta]^10+522 \[Beta]^12+79 \[Beta]^14)+\[Alpha]^2 (1114112-2621440 \[Beta]^2+1998848 \[Beta]^4-606208 \[Beta]^6-93696 \[Beta]^8+108544 \[Beta]^10+27648 \[Beta]^12+9024 \[Beta]^14-203 \[Beta]^16)-2 \[Alpha] \[Beta] (-65536-196608 \[Beta]^2+671744 \[Beta]^4-438272 \[Beta]^6-42496 \[Beta]^8+87808 \[Beta]^10-17344 \[Beta]^12+368 \[Beta]^14+63 \[Beta]^16))/(2 (256-3 \[Alpha]^8+8 \[Alpha]^7 \[Beta]-512 \[Beta]^2+160 \[Beta]^4+64 \[Beta]^6-3 \[Beta]^8-24 \[Alpha]^5 \[Beta] (-8+3 \[Beta]^2)+4 \[Alpha]^6 (16+3 \[Beta]^2)+8 \[Alpha] \[Beta]^3 (-48+24 \[Beta]^2+\[Beta]^4)-8 \[Alpha]^3 \[Beta] (48-16 \[Beta]^2+9 \[Beta]^4)+10 \[Alpha]^4 (16-32 \[Beta]^2+11 \[Beta]^4)+4 \[Alpha]^2 (-128+112 \[Beta]^2-80 \[Beta]^4+3 \[Beta]^6))^2)
a4=Coefficient[Z7alphabeta[x],x,4]//Simplify
(-189 \[Alpha]^19+786432 \[Beta]+889 \[Alpha]^18 \[Beta]-2162688 \[Beta]^3+1507328 \[Beta]^5+606208 \[Beta]^7-989184 \[Beta]^9+117248 \[Beta]^11+133888 \[Beta]^13-16576 \[Beta]^15+1260 \[Beta]^17-49 \[Beta]^19+\[Alpha]^17 (5628-107 \[Beta]^2)-\[Alpha]^16 \[Beta] (6612+5849 \[Beta]^2)+4 \[Alpha]^15 (-13360-8808 \[Beta]^2+1907 \[Beta]^4)+4 \[Alpha]^14 \[Beta] (-15760+13848 \[Beta]^2+3353 \[Beta]^4)-4 \[Alpha]^13 (-60352-83728 \[Beta]^2-2708 \[Beta]^4+6359 \[Beta]^6)-4 \[Alpha]^12 \[Beta] (-338368+129232 \[Beta]^2-25028 \[Beta]^4+13453 \[Beta]^6)+2 \[Alpha]^11 (334080-715520 \[Beta]^2+189216 \[Beta]^4-247408 \[Beta]^6+100845 \[Beta]^8)-2 \[Alpha]^10 \[Beta] (980224+1044224 \[Beta]^2-59232 \[Beta]^4-380688 \[Beta]^6+123145 \[Beta]^8)+2 \[Alpha]^8 \[Beta] (-2305024+4360448 \[Beta]^2-655744 \[Beta]^4-1019680 \[Beta]^6+353060 \[Beta]^8+14785 \[Beta]^10)+2 \[Alpha]^9 (-1268736-697600 \[Beta]^2+282240 \[Beta]^4+416160 \[Beta]^6-395308 \[Beta]^8+58179 \[Beta]^10)+4 \[Alpha]^6 \[Beta] (2846720-3266560 \[Beta]^2+1212160 \[Beta]^4+551680 \[Beta]^6-113584 \[Beta]^8-18584 \[Beta]^10+1333 \[Beta]^12)-4 \[Alpha]^7 (12288-2582528 \[Beta]^2+2169600 \[Beta]^4-888576 \[Beta]^6-254576 \[Beta]^8+84632 \[Beta]^10+12985 \[Beta]^12)-4 \[Alpha]^4 \[Beta] (1654784-2256896 \[Beta]^2+1037312 \[Beta]^4-135424 \[Beta]^6+148416 \[Beta]^8+50032 \[Beta]^10-8036 \[Beta]^12+1489 \[Beta]^14)+4 \[Alpha]^5 (1490944-4009984 \[Beta]^2+4062208 \[Beta]^4-1121536 \[Beta]^6-463296 \[Beta]^8+178736 \[Beta]^10+25204 \[Beta]^12+3709 \[Beta]^14)+\[Alpha]^2 \[Beta] (-458752-1179648 \[Beta]^2+999424 \[Beta]^4+794624 \[Beta]^6-1257984 \[Beta]^8+299520 \[Beta]^10+26176 \[Beta]^12-2592 \[Beta]^14+609 \[Beta]^16)-\[Alpha]^3 (6094848-11927552 \[Beta]^2+9977856 \[Beta]^4-794624 \[Beta]^6-3299840 \[Beta]^8+1672704 \[Beta]^10+69440 \[Beta]^12+32032 \[Beta]^14+773 \[Beta]^16)+\[Alpha] (1835008-4390912 \[Beta]^2+983040 \[Beta]^4+4046848 \[Beta]^6-2816000 \[Beta]^8-418304 \[Beta]^10+596736 \[Beta]^12-10304 \[Beta]^14+1084 \[Beta]^16+77 \[Beta]^18))/(8 (256-3 \[Alpha]^8+8 \[Alpha]^7 \[Beta]-512 \[Beta]^2+160 \[Beta]^4+64 \[Beta]^6-3 \[Beta]^8-24 \[Alpha]^5 \[Beta] (-8+3 \[Beta]^2)+4 \[Alpha]^6 (16+3 \[Beta]^2)+8 \[Alpha] \[Beta]^3 (-48+24 \[Beta]^2+\[Beta]^4)-8 \[Alpha]^3 \[Beta] (48-16 \[Beta]^2+9 \[Beta]^4)+10 \[Alpha]^4 (16-32 \[Beta]^2+11 \[Beta]^4)+4 \[Alpha]^2 (-128+112 \[Beta]^2-80 \[Beta]^4+3 \[Beta]^6))^2)
a3=Coefficient[Z7alphabeta[x],x,3]//Simplify
(5242880+441 \[Alpha]^20-1932 \[Alpha]^19 \[Beta]-17301504 \[Beta]^2+14483456 \[Beta]^4+5636096 \[Beta]^6-11558912 \[Beta]^8+2461696 \[Beta]^10+1217024 \[Beta]^12-340480 \[Beta]^14+46608 \[Beta]^16-1736 \[Beta]^18+49 \[Beta]^20+14 \[Alpha]^18 (-844+45 \[Beta]^2)+4 \[Alpha]^17 \[Beta] (9004+1353 \[Beta]^2)-16 \[Alpha]^15 \[Beta] (17328+3160 \[Beta]^2+3959 \[Beta]^4)+\[Alpha]^16 (179216-18568 \[Beta]^2+11389 \[Beta]^4)+8 \[Alpha]^14 (-176448-141392 \[Beta]^2+20508 \[Beta]^4+3449 \[Beta]^6)+16 \[Alpha]^13 \[Beta] (-267712+147504 \[Beta]^2-19116 \[Beta]^4+12609 \[Beta]^6)+\[Alpha]^12 (279040+5204480 \[Beta]^2+1030080 \[Beta]^4+141280 \[Beta]^6-346014 \[Beta]^8)+8 \[Alpha]^11 \[Beta] (1575680+764160 \[Beta]^2-511584 \[Beta]^4+24496 \[Beta]^6+2011 \[Beta]^8)-8 \[Alpha]^9 \[Beta] (-74752+4707584 \[Beta]^2-1036160 \[Beta]^4-662112 \[Beta]^6+82748 \[Beta]^8+83321 \[Beta]^10)+4 \[Alpha]^10 (2593792-1147648 \[Beta]^2-692864 \[Beta]^4-106336 \[Beta]^6+47860 \[Beta]^8+134321 \[Beta]^10)-16 \[Alpha]^7 \[Beta] (2650112-2783232 \[Beta]^2-1680128 \[Beta]^4+2472192 \[Beta]^6-424048 \[Beta]^8-90392 \[Beta]^10+643 \[Beta]^12)+2 \[Alpha]^8 (-8204288-12408832 \[Beta]^2+6526720 \[Beta]^4+740608 \[Beta]^6-2851536 \[Beta]^8-125304 \[Beta]^10+160521 \[Beta]^12)-16 \[Alpha]^5 \[Beta] (-3162112+577536 \[Beta]^2+3486720 \[Beta]^4-3776256 \[Beta]^6+690752 \[Beta]^8+87536 \[Beta]^10-25876 \[Beta]^12+355 \[Beta]^14)-8 \[Alpha]^6 (802816-6975488 \[Beta]^2+2108416 \[Beta]^4+3083520 \[Beta]^6-3703360 \[Beta]^8+625968 \[Beta]^10+156788 \[Beta]^12+4631 \[Beta]^14)+4 \[Alpha]^3 \[Beta] (-2818048+393216 \[Beta]^2+9814016 \[Beta]^4-7938048 \[Beta]^6-25088 \[Beta]^8+1044992 \[Beta]^10-218688 \[Beta]^12-6240 \[Beta]^14+21 \[Beta]^16)+\[Alpha]^4 (31784960-52822016 \[Beta]^2+21479424 \[Beta]^4+54468608 \[Beta]^6-52380160 \[Beta]^8+9186816 \[Beta]^10+3564480 \[Beta]^12-21920 \[Beta]^14+10533 \[Beta]^16)+4 \[Alpha] \[Beta] (-1310720+589824 \[Beta]^2+2686976 \[Beta]^4-2408448 \[Beta]^6-407552 \[Beta]^8+978432 \[Beta]^10-360192 \[Beta]^12+16960 \[Beta]^14-84 \[Beta]^16+49 \[Beta]^18)-2 \[Alpha]^2 (11796480-21168128 \[Beta]^2+4653056 \[Beta]^4+13647872 \[Beta]^6-9209856 \[Beta]^8-514560 \[Beta]^10+1613568 \[Beta]^12+208704 \[Beta]^14-6796 \[Beta]^16+805 \[Beta]^18))/(64 (256-3 \[Alpha]^8+8 \[Alpha]^7 \[Beta]-512 \[Beta]^2+160 \[Beta]^4+64 \[Beta]^6-3 \[Beta]^8-24 \[Alpha]^5 \[Beta] (-8+3 \[Beta]^2)+4 \[Alpha]^6 (16+3 \[Beta]^2)+8 \[Alpha] \[Beta]^3 (-48+24 \[Beta]^2+\[Beta]^4)-8 \[Alpha]^3 \[Beta] (48-16 \[Beta]^2+9 \[Beta]^4)+10 \[Alpha]^4 (16-32 \[Beta]^2+11 \[Beta]^4)+4 \[Alpha]^2 (-128+112 \[Beta]^2-80 \[Beta]^4+3 \[Beta]^6))^2)
a2=Coefficient[Z7alphabeta[x],x,2]//Simplify
(-49 \[Alpha]^21+196 \[Alpha]^20 \[Beta]+140 \[Alpha]^18 \[Beta] (-82+3 \[Beta]^2)-14 \[Alpha]^19 (-152+9 \[Beta]^2)+\[Alpha]^17 (-55344+13184 \[Beta]^2-4701 \[Beta]^4)+8 \[Alpha]^16 \[Beta] (10524+3113 \[Beta]^2+1546 \[Beta]^4)+16 \[Alpha]^14 \[Beta] (9888-608 \[Beta]^2-19406 \[Beta]^4+1497 \[Beta]^6)-8 \[Alpha]^15 (-52864-24816 \[Beta]^2+360 \[Beta]^4+1741 \[Beta]^6)+8 \[Alpha]^12 \[Beta] (-765952+202944 \[Beta]^2+77296 \[Beta]^4-48796 \[Beta]^6+28151 \[Beta]^8)-2 \[Alpha]^13 (947456+466944 \[Beta]^2+636320 \[Beta]^4-351296 \[Beta]^6+47673 \[Beta]^8)+8 \[Alpha]^10 \[Beta] (1730048+125184 \[Beta]^2+931136 \[Beta]^4-819968 \[Beta]^6+115654 \[Beta]^8+28151 \[Beta]^10)-4 \[Alpha]^11 (526336-2413312 \[Beta]^2+1089792 \[Beta]^4-874528 \[Beta]^6+152712 \[Beta]^8+73997 \[Beta]^10)+16 \[Alpha]^8 \[Beta] (181248-484608 \[Beta]^2-1935232 \[Beta]^4+1689952 \[Beta]^6-285116 \[Beta]^8-66089 \[Beta]^10+1497 \[Beta]^12)-2 \[Alpha]^9 (-7131136+6995968 \[Beta]^2-10482944 \[Beta]^4+9389056 \[Beta]^6-3219056 \[Beta]^8-35904 \[Beta]^10+47673 \[Beta]^12)+16 \[Alpha]^6 \[Beta] (-1892352+1179648 \[Beta]^2+1869312 \[Beta]^4-2100992 \[Beta]^6+159968 \[Beta]^8+161440 \[Beta]^10-15366 \[Beta]^12+773 \[Beta]^14)-8 \[Alpha]^7 (1146880+1773568 \[Beta]^2+759808 \[Beta]^4-2241792 \[Beta]^6+1749632 \[Beta]^8-81296 \[Beta]^10-114328 \[Beta]^12+1741 \[Beta]^14)+4 \[Alpha]^4 \[Beta] (5963776-5144576 \[Beta]^2-843776 \[Beta]^4+964608 \[Beta]^6+1561600 \[Beta]^8-321408 \[Beta]^10-17056 \[Beta]^12+6440 \[Beta]^14+105 \[Beta]^16)-\[Alpha]^5 (16056320-51380224 \[Beta]^2+34095104 \[Beta]^4+9011200 \[Beta]^6-16402944 \[Beta]^8+831488 \[Beta]^10+1812288 \[Beta]^12+60544 \[Beta]^14+4701 \[Beta]^16)+2 \[Alpha]^3 (11010048-23003136 \[Beta]^2+16908288 \[Beta]^4+1163264 \[Beta]^6-7344128 \[Beta]^8+2745856 \[Beta]^10+299520 \[Beta]^12+123328 \[Beta]^14+9256 \[Beta]^16-63 \[Beta]^18)+4 \[Alpha]^2 \[Beta] (-393216+1900544 \[Beta]^2-2129920 \[Beta]^4+229376 \[Beta]^6+957440 \[Beta]^8-480768 \[Beta]^10+30592 \[Beta]^12+14592 \[Beta]^14-2310 \[Beta]^16+49 \[Beta]^18)+8 \[Beta] (-262144+589824 \[Beta]^2-196608 \[Beta]^4-442368 \[Beta]^6+337920 \[Beta]^8+44544 \[Beta]^10-84736 \[Beta]^12+10304 \[Beta]^14-1092 \[Beta]^16+49 \[Beta]^18)-\[Alpha] (7340032-16777216 \[Beta]^2+5570560 \[Beta]^4+13107200 \[Beta]^6-9674752 \[Beta]^8-1835008 \[Beta]^10+2492928 \[Beta]^12-129024 \[Beta]^14+27184 \[Beta]^16+49 \[Beta]^20))/(64 (256-3 \[Alpha]^8+8 \[Alpha]^7 \[Beta]-512 \[Beta]^2+160 \[Beta]^4+64 \[Beta]^6-3 \[Beta]^8-24 \[Alpha]^5 \[Beta] (-8+3 \[Beta]^2)+4 \[Alpha]^6 (16+3 \[Beta]^2)+8 \[Alpha] \[Beta]^3 (-48+24 \[Beta]^2+\[Beta]^4)-8 \[Alpha]^3 \[Beta] (48-16 \[Beta]^2+9 \[Beta]^4)+10 \[Alpha]^4 (16-32 \[Beta]^2+11 \[Beta]^4)+4 \[Alpha]^2 (-128+112 \[Beta]^2-80 \[Beta]^4+3 \[Beta]^6))^2)
a1=Coefficient[Z7alphabeta[x],x,1]//Simplify
-((441 \[Alpha]^20-1932 \[Alpha]^19 \[Beta]+14 \[Alpha]^18 (-668+45 \[Beta]^2)+4 \[Alpha]^17 \[Beta] (5948+1353 \[Beta]^2)-16 \[Alpha]^15 \[Beta] (15792-3976 \[Beta]^2+3959 \[Beta]^4)+\[Alpha]^16 (94672-18728 \[Beta]^2+11389 \[Beta]^4)+8 \[Alpha]^14 (-93504-20624 \[Beta]^2-9364 \[Beta]^4+3449 \[Beta]^6)+16 \[Alpha]^13 \[Beta] (-58560+60336 \[Beta]^2-22076 \[Beta]^4+12609 \[Beta]^6)+\[Alpha]^12 (913920+2279936 \[Beta]^2-715584 \[Beta]^4+909152 \[Beta]^6-346014 \[Beta]^8)+8 \[Alpha]^11 \[Beta] (514816-51968 \[Beta]^2+65440 \[Beta]^4-77328 \[Beta]^6+2011 \[Beta]^8)+(1024-1280 \[Beta]^2-384 \[Beta]^4+736 \[Beta]^6-44 \[Beta]^8+7 \[Beta]^10)^2-8 \[Alpha]^9 \[Beta] (404480+832768 \[Beta]^2-91520 \[Beta]^4-16224 \[Beta]^6-200436 \[Beta]^8+83321 \[Beta]^10)+4 \[Alpha]^10 (566272-1522432 \[Beta]^2+710016 \[Beta]^4-381152 \[Beta]^6-111068 \[Beta]^8+134321 \[Beta]^10)-16 \[Alpha]^7 \[Beta] (356352-628736 \[Beta]^2-398080 \[Beta]^4+242944 \[Beta]^6+290704 \[Beta]^8-139320 \[Beta]^10+643 \[Beta]^12)+\[Alpha]^8 (-5365760+528384 \[Beta]^2+2342400 \[Beta]^4-3409408 \[Beta]^6+3684576 \[Beta]^8-2442160 \[Beta]^10+321042 \[Beta]^12)-16 \[Alpha]^5 \[Beta] (-606208+86016 \[Beta]^2+1025024 \[Beta]^4-581376 \[Beta]^6-330944 \[Beta]^8+187760 \[Beta]^10-11652 \[Beta]^12+355 \[Beta]^14)-8 \[Alpha]^6 (-114688-1355776 \[Beta]^2+777216 \[Beta]^4-35584 \[Beta]^6+94656 \[Beta]^8-420624 \[Beta]^10+131940 \[Beta]^12+4631 \[Beta]^14)+4 \[Alpha]^3 \[Beta] (-720896-1179648 \[Beta]^2+4046848 \[Beta]^4-1613824 \[Beta]^6-1491456 \[Beta]^8+936448 \[Beta]^10-141888 \[Beta]^12+3872 \[Beta]^14+21 \[Beta]^16)+\[Alpha]^4 (5570560-11927552 \[Beta]^2-81920 \[Beta]^4+16031744 \[Beta]^6-9269760 \[Beta]^8-2404864 \[Beta]^10+2193600 \[Beta]^12-16416 \[Beta]^14+10533 \[Beta]^16)+4 \[Alpha] \[Beta] (-262144+589824 \[Beta]^2-196608 \[Beta]^4-442368 \[Beta]^6+337920 \[Beta]^8+44544 \[Beta]^10-84736 \[Beta]^12+10304 \[Beta]^14-1092 \[Beta]^16+49 \[Beta]^18)-2 \[Alpha]^2 (2359296-3342336 \[Beta]^2-2162688 \[Beta]^4+5455872 \[Beta]^6-1255424 \[Beta]^8-1960448 \[Beta]^10+962304 \[Beta]^12+64576 \[Beta]^14-3548 \[Beta]^16+805 \[Beta]^18))/(64 (256-3 \[Alpha]^8+8 \[Alpha]^7 \[Beta]-512 \[Beta]^2+160 \[Beta]^4+64 \[Beta]^6-3 \[Beta]^8-24 \[Alpha]^5 \[Beta] (-8+3 \[Beta]^2)+4 \[Alpha]^6 (16+3 \[Beta]^2)+8 \[Alpha] \[Beta]^3 (-48+24 \[Beta]^2+\[Beta]^4)-8 \[Alpha]^3 \[Beta] (48-16 \[Beta]^2+9 \[Beta]^4)+10 \[Alpha]^4 (16-32 \[Beta]^2+11 \[Beta]^4)+4 \[Alpha]^2 (-128+112 \[Beta]^2-80 \[Beta]^4+3 \[Beta]^6))^2))
a0=Coefficient[Z7alphabeta[x],x,0]//Simplify
(49 \[Alpha]^21 (1+\[Beta]^2)-49 \[Alpha]^20 \[Beta] (-5+13 \[Beta]^2)+14 \[Alpha]^19 (-44-281 \[Beta]^2+255 \[Beta]^4)-14 \[Alpha]^18 \[Beta] (356-1679 \[Beta]^2+759 \[Beta]^4)+\[Alpha]^16 \[Beta] (53456-260248 \[Beta]^2+130701 \[Beta]^4+12699 \[Beta]^6)+\[Alpha]^17 (12240+66808 \[Beta]^2-84111 \[Beta]^4+14289 \[Beta]^6)-8 \[Alpha]^15 (8768+74160 \[Beta]^2-63964 \[Beta]^4-22935 \[Beta]^6+11985 \[Beta]^8)+8 \[Alpha]^14 \[Beta] (-51136+96016 \[Beta]^2+135668 \[Beta]^4-155289 \[Beta]^6+24225 \[Beta]^8)+\[Alpha]^13 (557568+309248 \[Beta]^2+5159360 \[Beta]^4-7379744 \[Beta]^6+2353218 \[Beta]^8-173502 \[Beta]^10)-\[Beta] (-1+\[Beta]^2) (1024-2304 \[Beta]^2+2688 \[Beta]^4-672 \[Beta]^6-108 \[Beta]^8+3 \[Beta]^10)^2-2 \[Alpha]^12 \[Beta] (-367872-4472832 \[Beta]^2+10093088 \[Beta]^4-5940304 \[Beta]^6+798315 \[Beta]^8+35581 \[Beta]^10)+4 \[Alpha]^11 (-109568+1462016 \[Beta]^2-7297920 \[Beta]^4+6212832 \[Beta]^6-562988 \[Beta]^8-433237 \[Beta]^10+112931 \[Beta]^12)-4 \[Alpha]^10 \[Beta] (-228352+7639296 \[Beta]^2-8253312 \[Beta]^4-1263712 \[Beta]^6+3863908 \[Beta]^8-1352963 \[Beta]^10+178347 \[Beta]^12)-2 \[Alpha]^8 \[Beta] (1798144-5724160 \[Beta]^2-31098624 \[Beta]^4+61881856 \[Beta]^6-40069872 \[Beta]^8+14142696 \[Beta]^10-2875233 \[Beta]^12+217209 \[Beta]^14)+2 \[Alpha]^9 (-913408-6551552 \[Beta]^2+12086016 \[Beta]^4+12306944 \[Beta]^6-26150672 \[Beta]^8+12759176 \[Beta]^10-3393947 \[Beta]^12+341445 \[Beta]^14)-8 \[Alpha]^6 \[Beta] (-212992-6180864 \[Beta]^2+24314880 \[Beta]^4-30825728 \[Beta]^6+19685440 \[Beta]^8-8710384 \[Beta]^10+2152828 \[Beta]^12-247359 \[Beta]^14+3927 \[Beta]^16)+8 \[Alpha]^7 (311296+4096 \[Beta]^2+8803328 \[Beta]^4-22584064 \[Beta]^6+21324352 \[Beta]^8-10382672 \[Beta]^10+3282060 \[Beta]^12-475809 \[Beta]^14+21879 \[Beta]^16)+\[Alpha]^5 (851968+21168128 \[Beta]^2-147865600 \[Beta]^4+263495680 \[Beta]^6-232813056 \[Beta]^8+132206592 \[Beta]^10-44855360 \[Beta]^12+7820640 \[Beta]^14-669459 \[Beta]^16-8211 \[Beta]^18)+\[Alpha]^4 \[Beta] (3211264-64946176 \[Beta]^2+176406528 \[Beta]^4-221585408 \[Beta]^6+172045824 \[Beta]^8-83879936 \[Beta]^10+21634496 \[Beta]^12-3261920 \[Beta]^14+49665 \[Beta]^16+6615 \[Beta]^18)-2 \[Alpha]^2 \[Beta] (1835008-14745600 \[Beta]^2+38404096 \[Beta]^4-57294848 \[Beta]^6+48424960 \[Beta]^8-22564352 \[Beta]^10+7184128 \[Beta]^12-1194816 \[Beta]^14-76452 \[Beta]^16+10631 \[Beta]^18+17 \[Beta]^20)-2 \[Alpha]^3 (1310720+8847360 \[Beta]^2-48365568 \[Beta]^4+84197376 \[Beta]^6-83101696 \[Beta]^8+50762240 \[Beta]^10-17438464 \[Beta]^12+4297152 \[Beta]^14-478700 \[Beta]^16-31105 \[Beta]^18+727 \[Beta]^20)+\[Alpha] (1048576+3670016 \[Beta]^2-23003136 \[Beta]^4+44236800 \[Beta]^6-42655744 \[Beta]^8+27217920 \[Beta]^10-14689792 \[Beta]^12+4301824 \[Beta]^14-816 \[Beta]^16-118856 \[Beta]^18+101 \[Beta]^20+69 \[Beta]^22))/(128 (256-3 \[Alpha]^8+8 \[Alpha]^7 \[Beta]-512 \[Beta]^2+160 \[Beta]^4+64 \[Beta]^6-3 \[Beta]^8-24 \[Alpha]^5 \[Beta] (-8+3 \[Beta]^2)+4 \[Alpha]^6 (16+3 \[Beta]^2)+8 \[Alpha] \[Beta]^3 (-48+24 \[Beta]^2+\[Beta]^4)-8 \[Alpha]^3 \[Beta] (48-16 \[Beta]^2+9 \[Beta]^4)+10 \[Alpha]^4 (16-32 \[Beta]^2+11 \[Beta]^4)+4 \[Alpha]^2 (-128+112 \[Beta]^2-80 \[Beta]^4+3 \[Beta]^6))^2)
S7alphabeta[x_]=a0+a1 x+a2 x^2+a3 x^3+a4 x^4+a5 x^5+a6 x^6+a7 x^7