9 27 Quantum Invariants

A1 Invariants.

Weight	Invariant
1	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{11}+2 q^9-2 q^7+2 q^5-q^3+q+2 q^{-1} -2 q^{-3} +2 q^{-5} -2 q^{-7} + q^{-9} }
2	$q^{32}-2q^{30}-2q^{28}+7q^{26}-2q^{24}-9q^{22}+11q^{20}+2q^{18}-15q^{16}+9q^{14}+7q^{12}-13q^{10}+3q^{8}+8q^{6}-4q^{4}-4q^{2}+5+9q^{-2}-11q^{-4}-3q^{-6}+15q^{-8}-10q^{-10}-7q^{-12}+13q^{-14}-4q^{-16}-5q^{-18}+6q^{-20}-q^{-22}-2q^{-24}+q^{-26}$
3	$-q^{63}+2q^{61}+2q^{59}-3q^{57}-7q^{55}+2q^{53}+16q^{51}+q^{49}-23q^{47}-11q^{45}+29q^{43}+26q^{41}-31q^{39}-42q^{37}+26q^{35}+55q^{33}-13q^{31}-65q^{29}-q^{27}+67q^{25}+14q^{23}-63q^{21}-25q^{19}+52q^{17}+34q^{15}-39q^{13}-36q^{11}+22q^{9}+39q^{7}-4q^{5}-36q^{3}-18q+34q^{-1}+42q^{-3}-27q^{-5}-55q^{-7}+13q^{-9}+68q^{-11}-2q^{-13}-69q^{-15}-12q^{-17}+62q^{-19}+20q^{-21}-48q^{-23}-23q^{-25}+34q^{-27}+21q^{-29}-21q^{-31}-16q^{-33}+11q^{-35}+11q^{-37}-7q^{-39}-5q^{-41}+3q^{-43}+3q^{-45}-q^{-47}-2q^{-49}+q^{-51}$
4	$q^{104}-2q^{102}-2q^{100}+3q^{98}+3q^{96}+7q^{94}-9q^{92}-16q^{90}-q^{88}+11q^{86}+41q^{84}-2q^{82}-47q^{80}-41q^{78}-7q^{76}+100q^{74}+62q^{72}-42q^{70}-117q^{68}-108q^{66}+117q^{64}+173q^{62}+62q^{60}-141q^{58}-259q^{56}+16q^{54}+223q^{52}+230q^{50}-46q^{48}-346q^{46}-148q^{44}+156q^{42}+333q^{40}+100q^{38}-305q^{36}-255q^{34}+30q^{32}+318q^{30}+195q^{28}-190q^{26}-261q^{24}-69q^{22}+225q^{20}+214q^{18}-58q^{16}-208q^{14}-135q^{12}+100q^{10}+195q^{8}+88q^{6}-124q^{4}-197q^{2}-61+154q^{-2}+254q^{-4}-2q^{-6}-232q^{-8}-236q^{-10}+52q^{-12}+355q^{-14}+151q^{-16}-171q^{-18}-343q^{-20}-94q^{-22}+321q^{-24}+243q^{-26}-34q^{-28}-299q^{-30}-185q^{-32}+176q^{-34}+204q^{-36}+72q^{-38}-160q^{-40}-163q^{-42}+51q^{-44}+96q^{-46}+80q^{-48}-49q^{-50}-85q^{-52}+7q^{-54}+23q^{-56}+41q^{-58}-9q^{-60}-29q^{-62}+4q^{-64}+12q^{-68}-2q^{-70}-8q^{-72}+3q^{-74}+3q^{-78}-q^{-80}-2q^{-82}+q^{-84}$
5	$-q^{155}+2q^{153}+2q^{151}-3q^{149}-3q^{147}-3q^{145}+9q^{141}+16q^{139}+q^{137}-20q^{135}-29q^{133}-19q^{131}+20q^{129}+61q^{127}+62q^{125}-11q^{123}-97q^{121}-121q^{119}-47q^{117}+108q^{115}+220q^{113}+161q^{111}-78q^{109}-309q^{107}-326q^{105}-59q^{103}+348q^{101}+541q^{99}+291q^{97}-284q^{95}-722q^{93}-609q^{91}+62q^{89}+811q^{87}+963q^{85}+295q^{83}-745q^{81}-1264q^{79}-732q^{77}+497q^{75}+1431q^{73}+1192q^{71}-123q^{69}-1433q^{67}-1558q^{65}-315q^{63}+1258q^{61}+1785q^{59}+742q^{57}-978q^{55}-1843q^{53}-1070q^{51}+644q^{49}+1750q^{47}+1273q^{45}-324q^{43}-1556q^{41}-1345q^{39}+50q^{37}+1315q^{35}+1314q^{33}+149q^{31}-1043q^{29}-1228q^{27}-316q^{25}+799q^{23}+1121q^{21}+450q^{19}-541q^{17}-1013q^{15}-623q^{13}+280q^{11}+929q^{9}+805q^{7}+27q^{5}-818q^{3}-1032q-389q^{-1}+672q^{-3}+1265q^{-5}+782q^{-7}-438q^{-9}-1410q^{-11}-1218q^{-13}+110q^{-15}+1477q^{-17}+1587q^{-19}+274q^{-21}-1350q^{-23}-1852q^{-25}-701q^{-27}+1098q^{-29}+1925q^{-31}+1056q^{-33}-717q^{-35}-1801q^{-37}-1283q^{-39}+301q^{-41}+1502q^{-43}+1336q^{-45}+71q^{-47}-1114q^{-49}-1217q^{-51}-315q^{-53}+702q^{-55}+984q^{-57}+430q^{-59}-366q^{-61}-710q^{-63}-417q^{-65}+137q^{-67}+449q^{-69}+335q^{-71}-3q^{-73}-256q^{-75}-239q^{-77}-36q^{-79}+127q^{-81}+138q^{-83}+47q^{-85}-51q^{-87}-81q^{-89}-32q^{-91}+23q^{-93}+34q^{-95}+17q^{-97}-5q^{-99}-13q^{-101}-10q^{-103}+3q^{-105}+8q^{-107}-q^{-109}-3q^{-111}+3q^{-119}-q^{-121}-2q^{-123}+q^{-125}$

A2 Invariants.

Weight	Invariant
1,0	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{16}+q^{12}-q^{10}+2 q^8+2 q^2-1+2 q^{-2} -2 q^{-4} + q^{-8} - q^{-10} + q^{-12} }
1,1	$q^{44}-4q^{42}+12q^{40}-28q^{38}+52q^{36}-86q^{34}+130q^{32}-180q^{30}+222q^{28}-248q^{26}+258q^{24}-236q^{22}+176q^{20}-88q^{18}-24q^{16}+144q^{14}-267q^{12}+376q^{10}-450q^{8}+492q^{6}-483q^{4}+440q^{2}-352+244q^{-2}-120q^{-4}-4q^{-6}+102q^{-8}-176q^{-10}+222q^{-12}-238q^{-14}+228q^{-16}-196q^{-18}+162q^{-20}-126q^{-22}+88q^{-24}-58q^{-26}+36q^{-28}-20q^{-30}+10q^{-32}-4q^{-34}+q^{-36}$
2,0	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{42}-2 q^{38}-2 q^{36}+2 q^{34}+4 q^{32}-3 q^{30}-3 q^{28}+4 q^{26}+4 q^{24}-5 q^{22}-5 q^{20}+5 q^{18}+2 q^{16}-6 q^{14}+6 q^{10}-2 q^8-q^6+6 q^4+q^2-2+3 q^{-2} +5 q^{-4} -7 q^{-6} -5 q^{-8} +7 q^{-10} +2 q^{-12} -7 q^{-14} +6 q^{-18} -3 q^{-22} +2 q^{-26} - q^{-28} - q^{-30} + q^{-32} }

A3 Invariants.

Weight	Invariant
0,1,0	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{34}-2 q^{32}+q^{30}+3 q^{28}-7 q^{26}+3 q^{24}+4 q^{22}-12 q^{20}+5 q^{18}+8 q^{16}-10 q^{14}+5 q^{12}+10 q^{10}-5 q^8-q^6+4 q^4+q^2-4-4 q^{-2} +9 q^{-4} -5 q^{-6} -8 q^{-8} +13 q^{-10} -2 q^{-12} -8 q^{-14} +10 q^{-16} -6 q^{-20} +4 q^{-22} -2 q^{-26} + q^{-28} }
1,0,0	$-q^{21}-q^{17}+q^{15}-q^{13}+3q^{11}+2q^{7}+q^{3}-q^{-1}+q^{-3}-2q^{-5}+q^{-7}-q^{-9}+2q^{-11}-q^{-13}+q^{-15}$

A4 Invariants.

Weight	Invariant
0,1,0,0	$q^{44}-q^{40}+q^{38}+q^{36}-3q^{34}-3q^{32}+2q^{30}-8q^{26}-2q^{24}+9q^{22}+q^{20}-5q^{18}+9q^{16}+11q^{14}-3q^{12}-2q^{10}+7q^{8}-10q^{4}+2q^{2}+4-9q^{-2}-4q^{-4}+10q^{-6}-2q^{-8}-7q^{-10}+7q^{-12}+8q^{-14}-4q^{-16}-4q^{-18}+6q^{-20}+2q^{-22}-5q^{-24}-q^{-26}+3q^{-28}-q^{-30}-q^{-32}+q^{-34}$
1,0,0,0	$-q^{26}-q^{22}-q^{20}+q^{18}-q^{16}+3q^{14}+q^{12}+2q^{10}+2q^{8}+q^{4}-q^{2}-2q^{-2}+q^{-4}-2q^{-6}+q^{-8}+2q^{-14}-q^{-16}+q^{-18}$

B2 Invariants.

Weight	Invariant
0,1	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{34}+2 q^{32}-5 q^{30}+7 q^{28}-9 q^{26}+11 q^{24}-12 q^{22}+12 q^{20}-9 q^{18}+6 q^{16}-5 q^{12}+12 q^{10}-17 q^8+21 q^6-22 q^4+23 q^2-20+16 q^{-2} -9 q^{-4} +3 q^{-6} +2 q^{-8} -7 q^{-10} +10 q^{-12} -12 q^{-14} +12 q^{-16} -10 q^{-18} +8 q^{-20} -6 q^{-22} +4 q^{-24} -2 q^{-26} + q^{-28} }
1,0	$q^{56}-2q^{52}-2q^{50}+3q^{48}+5q^{46}-2q^{44}-8q^{42}-3q^{40}+9q^{38}+8q^{36}-7q^{34}-13q^{32}+13q^{28}+7q^{26}-9q^{24}-9q^{22}+5q^{20}+11q^{18}-8q^{14}-q^{12}+8q^{10}+3q^{8}-7q^{6}-5q^{4}+7q^{2}+7-5q^{-2}-9q^{-4}+4q^{-6}+10q^{-8}-q^{-10}-12q^{-12}-4q^{-14}+11q^{-16}+9q^{-18}-6q^{-20}-12q^{-22}+11q^{-26}+6q^{-28}-5q^{-30}-7q^{-32}+5q^{-36}+2q^{-38}-2q^{-40}-2q^{-42}+q^{-46}$

D4 Invariants.

Weight

Invariant

1,0,0,0

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{46}-2 q^{44}+3 q^{42}-4 q^{40}+6 q^{38}-8 q^{36}+7 q^{34}-10 q^{32}+9 q^{30}-11 q^{28}+6 q^{26}-6 q^{24}+6 q^{22}-q^{18}+9 q^{16}-4 q^{14}+15 q^{12}-14 q^{10}+16 q^8-16 q^6+18 q^4-19 q^2+12-15 q^{-2} +10 q^{-4} -6 q^{-6} + q^{-8} - q^{-10} -2 q^{-12} +9 q^{-14} -6 q^{-16} +8 q^{-18} -9 q^{-20} +11 q^{-22} -7 q^{-24} +6 q^{-26} -7 q^{-28} +5 q^{-30} -3 q^{-32} +2 q^{-34} -2 q^{-36} + q^{-38} }

G2 Invariants.

Weight

Invariant

1,0

$q^{80}-2q^{78}+5q^{76}-8q^{74}+7q^{72}-4q^{70}-6q^{68}+19q^{66}-29q^{64}+33q^{62}-29q^{60}+6q^{58}+22q^{56}-50q^{54}+65q^{52}-56q^{50}+32q^{48}+6q^{46}-42q^{44}+61q^{42}-58q^{40}+33q^{38}+3q^{36}-32q^{34}+41q^{32}-25q^{30}-q^{28}+36q^{26}-53q^{24}+50q^{22}-24q^{20}-20q^{18}+64q^{16}-89q^{14}+88q^{12}-53q^{10}+8q^{8}+45q^{6}-81q^{4}+87q^{2}-67+26q^{-2}+16q^{-4}-47q^{-6}+48q^{-8}-25q^{-10}-5q^{-12}+31q^{-14}-41q^{-16}+24q^{-18}+q^{-20}-35q^{-22}+58q^{-24}-59q^{-26}+43q^{-28}-9q^{-30}-22q^{-32}+45q^{-34}-51q^{-36}+45q^{-38}-28q^{-40}+7q^{-42}+11q^{-44}-23q^{-46}+24q^{-48}-18q^{-50}+13q^{-52}-4q^{-54}-2q^{-56}+4q^{-58}-6q^{-60}+4q^{-62}-2q^{-64}+q^{-66}$