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Label Char Prim Dim AA Field CM RM Minimal twist Traces Fricke sign Sato-Tate qq-expansion
a2a_{2} a3a_{3} a5a_{5} a7a_{7}
1332.1.b.a 1332.b 148.b 11 0.6650.665 Q\Q Q(111)\Q(\sqrt{-111}) , Q(37)\Q(\sqrt{-37}) Q(3)\Q(\sqrt{3}) 1332.1.b.a 1-1 00 00 00 qq2+q4q8+q16+2q23+q25+q-q^{2}+q^{4}-q^{8}+q^{16}+2q^{23}+q^{25}+\cdots
1332.1.b.b 1332.b 148.b 11 0.6650.665 Q\Q Q(111)\Q(\sqrt{-111}) , Q(37)\Q(\sqrt{-37}) Q(3)\Q(\sqrt{3}) 1332.1.b.a 11 00 00 00 q+q2+q4+q8+q162q23+q25+q+q^{2}+q^{4}+q^{8}+q^{16}-2q^{23}+q^{25}+\cdots
1332.1.b.c 1332.b 148.b 22 0.6650.665 Q(1)\Q(\sqrt{-1}) Q(1)\Q(\sqrt{-1}) , Q(111)\Q(\sqrt{-111}) Q(111)\Q(\sqrt{111}) 1332.1.b.c 00 00 00 00 qiq2q42iq5+iq82q10+q-i q^{2}-q^{4}-2 i q^{5}+i q^{8}-2 q^{10}+\cdots
1332.1.b.d 1332.b 148.b 44 0.6650.665 Q(ζ8)\Q(\zeta_{8}) Q(111)\Q(\sqrt{-111}) None 1332.1.b.d 00 00 00 00 qζ8q2+ζ82q4+(ζ8+ζ83)q5+q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots
1332.1.m.a 1332.m 444.j 44 0.6650.665 Q(ζ8)\Q(\zeta_{8}) Q(1)\Q(\sqrt{-1}) None 1332.1.m.a 00 00 00 00 qζ83q2ζ82q4ζ8q8+(1ζ82+)q13+q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{8}+(1-\zeta_{8}^{2}+\cdots)q^{13}+\cdots
1332.1.o.a 1332.o 37.d 22 0.6650.665 Q(1)\Q(\sqrt{-1}) None None 148.1.f.a 00 00 00 2-2 qq7iq11+(i+1)q17+(i+1)q19+q-q^{7}-i q^{11}+(-i+1)q^{17}+(-i+1)q^{19}+\cdots
1332.1.y.a 1332.y 148.i 22 0.6650.665 Q(3)\Q(\sqrt{-3}) Q(1)\Q(\sqrt{-1}) None 148.1.i.a 11 00 1-1 00 qζ62q2ζ6q4ζ6q5q8q10+q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}-q^{8}-q^{10}+\cdots
1332.1.bj.a 1332.bj 148.j 44 0.6650.665 Q(ζ12)\Q(\zeta_{12}) Q(1)\Q(\sqrt{-1}) None 1332.1.bj.a 00 00 00 00 q+ζ125q2ζ124q4ζ12q5+ζ123q8+q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}q^{5}+\zeta_{12}^{3}q^{8}+\cdots
1332.1.cd.a 1332.cd 444.x 88 0.6650.665 Q(ζ24)\Q(\zeta_{24}) Q(1)\Q(\sqrt{-1}) None 1332.1.cd.a 00 00 00 00 qζ247q2ζ242q4+(ζ243+ζ247+)q5+q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(\zeta_{24}^{3}+\zeta_{24}^{7}+\cdots)q^{5}+\cdots
1332.1.cy.a 1332.cy 148.o 1212 0.6650.665 Q(ζ36)\Q(\zeta_{36}) Q(1)\Q(\sqrt{-1}) None 1332.1.cy.a 00 00 00 00 q+ζ3613q2ζ368q4+(ζ367+)q5+q+\zeta_{36}^{13}q^{2}-\zeta_{36}^{8}q^{4}+(-\zeta_{36}^{7}+\cdots)q^{5}+\cdots
1332.1.cz.a 1332.cz 148.p 66 0.6650.665 Q(ζ18)\Q(\zeta_{18}) Q(1)\Q(\sqrt{-1}) None 148.1.p.a 00 00 33 00 qζ184q2+ζ188q4+(ζ186+ζ187+)q5+q-\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+(-\zeta_{18}^{6}+\zeta_{18}^{7}+\cdots)q^{5}+\cdots
1332.1.dm.a 1332.dm 444.ai 2424 0.6650.665 Q(ζ72)\Q(\zeta_{72}) Q(1)\Q(\sqrt{-1}) None 1332.1.dm.a 00 00 00 00 qζ7235q2ζ7234q4+(ζ723+)q5+q-\zeta_{72}^{35}q^{2}-\zeta_{72}^{34}q^{4}+(-\zeta_{72}^{3}+\cdots)q^{5}+\cdots
1332.1.dn.a 1332.dn 37.i 1212 0.6650.665 Q(ζ36)\Q(\zeta_{36}) Q(3)\Q(\sqrt{-3}) None 1332.1.dn.a 00 00 00 00 q+(ζ365ζ3615)q7+(ζ368ζ369+)q13+q+(-\zeta_{36}^{5}-\zeta_{36}^{15})q^{7}+(\zeta_{36}^{8}-\zeta_{36}^{9}+\cdots)q^{13}+\cdots
1332.2.a.a 1332.a 1.a 11 10.63610.636 Q\Q None None 1332.2.a.a 00 00 2-2 00 ++ SU(2)\mathrm{SU}(2) q2q5+4q116q13+6q174q19+q-2q^{5}+4q^{11}-6q^{13}+6q^{17}-4q^{19}+\cdots
1332.2.a.b 1332.a 1.a 11 10.63610.636 Q\Q None None 444.2.a.a 00 00 00 00 ++ SU(2)\mathrm{SU}(2) q4q112q13+6q198q23+q-4q^{11}-2q^{13}+6q^{19}-8q^{23}+\cdots
1332.2.a.c 1332.a 1.a 11 10.63610.636 Q\Q None None 444.2.a.b 00 00 22 4-4 ++ SU(2)\mathrm{SU}(2) q+2q54q7+4q116q136q17+q+2q^{5}-4q^{7}+4q^{11}-6q^{13}-6q^{17}+\cdots
1332.2.a.d 1332.a 1.a 11 10.63610.636 Q\Q None None 1332.2.a.a 00 00 22 00 ++ SU(2)\mathrm{SU}(2) q+2q54q116q136q174q19+q+2q^{5}-4q^{11}-6q^{13}-6q^{17}-4q^{19}+\cdots
1332.2.a.e 1332.a 1.a 11 10.63610.636 Q\Q None None 148.2.a.a 00 00 44 3-3 - SU(2)\mathrm{SU}(2) q+4q53q75q11+6q17+2q19+q+4q^{5}-3q^{7}-5q^{11}+6q^{17}+2q^{19}+\cdots
1332.2.a.f 1332.a 1.a 22 10.63610.636 Q(17)\Q(\sqrt{17}) None None 148.2.a.b 00 00 4-4 11 ++ SU(2)\mathrm{SU}(2) q2q5+(1β)q7+(1+β)q11+q-2q^{5}+(1-\beta )q^{7}+(-1+\beta )q^{11}+\cdots
1332.2.a.g 1332.a 1.a 22 10.63610.636 Q(6)\Q(\sqrt{6}) None None 444.2.a.d 00 00 00 44 - SU(2)\mathrm{SU}(2) q+βq5+2q7+(2+2β)q13βq17+q+\beta q^{5}+2q^{7}+(2+2\beta )q^{13}-\beta q^{17}+\cdots
1332.2.a.h 1332.a 1.a 22 10.63610.636 Q(3)\Q(\sqrt{3}) None None 444.2.a.c 00 00 22 00 - SU(2)\mathrm{SU}(2) q+(1+β)q5+2βq7+4q112βq13+q+(1+\beta )q^{5}+2\beta q^{7}+4q^{11}-2\beta q^{13}+\cdots
1332.2.a.i 1332.a 1.a 44 10.63610.636 4.4.7168.1 None None 1332.2.a.i 00 00 00 88 - SU(2)\mathrm{SU}(2) q+β1q5+(2+β3)q7+β2q11+2q13+q+\beta _{1}q^{5}+(2+\beta _{3})q^{7}+\beta _{2}q^{11}+2q^{13}+\cdots
1332.2.c.a 1332.c 12.b 3636 10.63610.636 None None 1332.2.c.a 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}]
1332.2.c.b 1332.c 12.b 3636 10.63610.636 None None 1332.2.c.b 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}]
1332.2.e.a 1332.e 37.b 22 10.63610.636 Q(3)\Q(\sqrt{-3}) None None 148.2.d.a 00 00 00 22 SU(2)[C2]\mathrm{SU}(2)[C_{2}] qβq5+q73q11βq13+βq17+q-\beta q^{5}+q^{7}-3 q^{11}-\beta q^{13}+\beta q^{17}+\cdots
1332.2.e.b 1332.e 37.b 22 10.63610.636 Q(3)\Q(\sqrt{-3}) Q(3)\Q(\sqrt{-3}) None 1332.2.e.b 00 00 00 88 U(1)[D2]\mathrm{U}(1)[D_{2}] q+4q72βq13+βq19+5q25+q+4 q^{7}-2\beta q^{13}+\beta q^{19}+5 q^{25}+\cdots
1332.2.e.c 1332.e 37.b 44 10.63610.636 Q(i,6)\Q(i, \sqrt{6}) None None 1332.2.e.c 00 00 00 8-8 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+β2q52q7+β3q11β2q17+q+\beta _{2}q^{5}-2q^{7}+\beta _{3}q^{11}-\beta _{2}q^{17}+\cdots
1332.2.e.d 1332.e 37.b 44 10.63610.636 4.0.32448.1 None None 444.2.e.b 00 00 00 4-4 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+β1q5+(1+β2)q72β1q13+q+\beta _{1}q^{5}+(-1+\beta _{2})q^{7}-2\beta _{1}q^{13}+\cdots
1332.2.e.e 1332.e 37.b 44 10.63610.636 Q(2,5)\Q(\sqrt{-2}, \sqrt{5}) None None 444.2.e.a 00 00 00 44 SU(2)[C2]\mathrm{SU}(2)[C_{2}] qβ1q5+(1β3)q7+(22β3)q11+q-\beta _{1}q^{5}+(1-\beta _{3})q^{7}+(2-2\beta _{3})q^{11}+\cdots
1332.2.g.a 1332.g 444.g 44 10.63610.636 Q(2,37)\Q(\sqrt{-2}, \sqrt{37}) Q(37)\Q(\sqrt{-37}) None 1332.2.g.a 00 00 00 00 U(1)[D2]\mathrm{U}(1)[D_{2}] q+β1q22q42β1q8+4q16+q+\beta _{1}q^{2}-2q^{4}-2\beta _{1}q^{8}+4q^{16}+\cdots
1332.2.g.b 1332.g 444.g 44 10.63610.636 Q(2,37)\Q(\sqrt{-2}, \sqrt{37}) Q(37)\Q(\sqrt{-37}) None 1332.2.g.a 00 00 00 00 U(1)[D2]\mathrm{U}(1)[D_{2}] q+β1q22q42β1q8+4q16+q+\beta _{1}q^{2}-2q^{4}-2\beta _{1}q^{8}+4q^{16}+\cdots
1332.2.g.c 1332.g 444.g 44 10.63610.636 Q(ζ8)\Q(\zeta_{8}) Q(1)\Q(\sqrt{-1}) None 1332.2.g.c 00 00 00 00 U(1)[D2]\mathrm{U}(1)[D_{2}] qβ2q2+2q4+β2q52β2q8+q-\beta_{2} q^{2}+2 q^{4}+\beta_{2} q^{5}-2\beta_{2} q^{8}+\cdots
1332.2.g.d 1332.g 444.g 6464 10.63610.636 None None 1332.2.g.d 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}]
1332.2.i.a 1332.i 9.c 22 10.63610.636 Q(3)\Q(\sqrt{-3}) None None 1332.2.i.a 00 00 11 11 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(1+2ζ6)q3+ζ6q5+(1ζ6)q7+q+(-1+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots
1332.2.i.b 1332.i 9.c 22 10.63610.636 Q(3)\Q(\sqrt{-3}) None None 1332.2.i.b 00 00 33 11 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(1+2ζ6)q3+3ζ6q5+(1ζ6)q7+q+(-1+2\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots
1332.2.i.c 1332.i 9.c 3434 10.63610.636 None None 1332.2.i.c 00 11 7-7 1-1 SU(2)[C3]\mathrm{SU}(2)[C_{3}]
1332.2.i.d 1332.i 9.c 3434 10.63610.636 None None 1332.2.i.d 00 11 77 1-1 SU(2)[C3]\mathrm{SU}(2)[C_{3}]
1332.2.j.a 1332.j 37.c 22 10.63610.636 Q(3)\Q(\sqrt{-3}) Q(3)\Q(\sqrt{-3}) None 1332.2.j.a 00 00 00 5-5 U(1)[D3]\mathrm{U}(1)[D_{3}] q5ζ6q7+7ζ6q138ζ6q19+(5+)q25+q-5\zeta_{6}q^{7}+7\zeta_{6}q^{13}-8\zeta_{6}q^{19}+(5+\cdots)q^{25}+\cdots
1332.2.j.b 1332.j 37.c 22 10.63610.636 Q(3)\Q(\sqrt{-3}) Q(3)\Q(\sqrt{-3}) None 1332.2.j.b 00 00 00 11 U(1)[D3]\mathrm{U}(1)[D_{3}] q+ζ6q75ζ6q138ζ6q19+(5+)q25+q+\zeta_{6}q^{7}-5\zeta_{6}q^{13}-8\zeta_{6}q^{19}+(5+\cdots)q^{25}+\cdots
1332.2.j.c 1332.j 37.c 22 10.63610.636 Q(3)\Q(\sqrt{-3}) None None 444.2.i.a 00 00 22 33 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+2ζ6q5+3ζ6q72q11+3ζ6q13+q+2\zeta_{6}q^{5}+3\zeta_{6}q^{7}-2q^{11}+3\zeta_{6}q^{13}+\cdots
1332.2.j.d 1332.j 37.c 44 10.63610.636 Q(3,37)\Q(\sqrt{-3}, \sqrt{37}) None None 444.2.i.b 00 00 1-1 6-6 SU(2)[C3]\mathrm{SU}(2)[C_{3}] qβ1q53β2q7+(2+β3)q11+q-\beta _{1}q^{5}-3\beta _{2}q^{7}+(-2+\beta _{3})q^{11}+\cdots
1332.2.j.e 1332.j 37.c 66 10.63610.636 6.0.27870912.1 None None 148.2.e.a 00 00 3-3 1-1 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(1+β4)q5+(β1+β2+β5)q7+q+(-1+\beta _{4})q^{5}+(\beta _{1}+\beta _{2}+\beta _{5})q^{7}+\cdots
1332.2.j.f 1332.j 37.c 66 10.63610.636 6.0.27379323.1 None None 444.2.i.c 00 00 11 33 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+β1q5β4q7+β3q11+(β1+)q13+q+\beta _{1}q^{5}-\beta _{4}q^{7}+\beta _{3}q^{11}+(-\beta _{1}+\cdots)q^{13}+\cdots
1332.2.j.g 1332.j 37.c 1212 10.63610.636 Q[x]/(x12+)\mathbb{Q}[x]/(x^{12} + \cdots) None None 1332.2.j.g 00 00 00 44 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(β1+β6)q5+(β4β5β7)q7+q+(\beta _{1}+\beta _{6})q^{5}+(-\beta _{4}-\beta _{5}-\beta _{7})q^{7}+\cdots
1332.2.k.a 1332.k 333.g 22 10.63610.636 Q(3)\Q(\sqrt{-3}) None None 1332.2.k.a 00 00 11 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(12ζ6)q3+(1ζ6)q53q9+q+(1-2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-3q^{9}+\cdots
1332.2.k.b 1332.k 333.g 7474 10.63610.636 None None 1332.2.k.b 00 1-1 3-3 22 SU(2)[C3]\mathrm{SU}(2)[C_{3}]
1332.2.l.a 1332.l 333.h 22 10.63610.636 Q(3)\Q(\sqrt{-3}) None None 1332.2.k.a 00 3-3 2-2 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(1ζ6)q3q5+3ζ6q95ζ6q11+q+(-1-\zeta_{6})q^{3}-q^{5}+3\zeta_{6}q^{9}-5\zeta_{6}q^{11}+\cdots
1332.2.l.b 1332.l 333.h 7474 10.63610.636 None None 1332.2.k.b 00 55 66 1-1 SU(2)[C3]\mathrm{SU}(2)[C_{3}]
1332.2.p.a 1332.p 111.g 2828 10.63610.636 None None 1332.2.p.a 00 00 00 00 SU(2)[C4]\mathrm{SU}(2)[C_{4}]
1332.2.q.a 1332.q 333.k 7676 10.63610.636 None None 1332.2.q.a 00 2-2 00 11 SU(2)[C6]\mathrm{SU}(2)[C_{6}]
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