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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}
735.1.f.a 735.f 15.d 11 0.3670.367 Q\Q Q(15)\Q(\sqrt{-15}) , Q(35)\Q(\sqrt{-35}) Q(21)\Q(\sqrt{21}) 735.1.f.a 00 1-1 1-1 00 qq3q4q5+q9+q12+q15+q-q^{3}-q^{4}-q^{5}+q^{9}+q^{12}+q^{15}+\cdots
735.1.f.b 735.f 15.d 11 0.3670.367 Q\Q Q(15)\Q(\sqrt{-15}) , Q(35)\Q(\sqrt{-35}) Q(21)\Q(\sqrt{21}) 735.1.f.a 00 11 11 00 q+q3q4+q5+q9q12+q15+q+q^{3}-q^{4}+q^{5}+q^{9}-q^{12}+q^{15}+\cdots
735.1.f.c 735.f 15.d 22 0.3670.367 Q(2)\Q(\sqrt{2}) Q(15)\Q(\sqrt{-15}) None 735.1.f.c 00 2-2 22 00 qβq2q3+q4+q5+βq6+q9+q-\beta q^{2}-q^{3}+q^{4}+q^{5}+\beta q^{6}+q^{9}+\cdots
735.1.f.d 735.f 15.d 22 0.3670.367 Q(2)\Q(\sqrt{2}) Q(15)\Q(\sqrt{-15}) None 735.1.f.c 00 22 2-2 00 qβq2+q3+q4q5βq6+q9+q-\beta q^{2}+q^{3}+q^{4}-q^{5}-\beta q^{6}+q^{9}+\cdots
735.1.o.a 735.o 105.o 22 0.3670.367 Q(3)\Q(\sqrt{-3}) Q(15)\Q(\sqrt{-15}) , Q(35)\Q(\sqrt{-35}) Q(21)\Q(\sqrt{21}) 735.1.f.a 00 1-1 1-1 00 qζ6q3+ζ6q4+ζ62q5+ζ62q9+q-\zeta_{6}q^{3}+\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{9}+\cdots
735.1.o.b 735.o 105.o 22 0.3670.367 Q(3)\Q(\sqrt{-3}) Q(15)\Q(\sqrt{-15}) , Q(35)\Q(\sqrt{-35}) Q(21)\Q(\sqrt{21}) 735.1.f.a 00 11 11 00 q+ζ6q3+ζ6q4ζ62q5+ζ62q9+q+\zeta_{6}q^{3}+\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{9}+\cdots
735.1.o.c 735.o 105.o 44 0.3670.367 Q(2,3)\Q(\sqrt{2}, \sqrt{-3}) Q(15)\Q(\sqrt{-15}) None 735.1.f.c 00 2-2 22 00 qβ1q2+β2q3+β2q4+(1+β2+)q5+q-\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots
735.1.o.d 735.o 105.o 44 0.3670.367 Q(2,3)\Q(\sqrt{2}, \sqrt{-3}) Q(15)\Q(\sqrt{-15}) None 735.1.f.c 00 22 2-2 00 qβ1q2β2q3+β2q4+(1β2+)q5+q-\beta _{1}q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots
735.2.a.a 735.a 1.a 11 5.8695.869 Q\Q None None 105.2.i.b 2-2 1-1 1-1 00 - SU(2)\mathrm{SU}(2) q2q2q3+2q4q5+2q6+q9+q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}+q^{9}+\cdots
735.2.a.b 735.a 1.a 11 5.8695.869 Q\Q None None 105.2.i.b 2-2 11 11 00 ++ SU(2)\mathrm{SU}(2) q2q2+q3+2q4+q52q6+q9+q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}+q^{9}+\cdots
735.2.a.c 735.a 1.a 11 5.8695.869 Q\Q None None 15.2.a.a 1-1 11 1-1 00 ++ SU(2)\mathrm{SU}(2) qq2+q3q4q5q6+3q8+q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}+3q^{8}+\cdots
735.2.a.d 735.a 1.a 11 5.8695.869 Q\Q None None 105.2.i.a 00 1-1 11 00 ++ SU(2)\mathrm{SU}(2) qq32q4+q5+q9+2q12+q13+q-q^{3}-2q^{4}+q^{5}+q^{9}+2q^{12}+q^{13}+\cdots
735.2.a.e 735.a 1.a 11 5.8695.869 Q\Q None None 105.2.i.a 00 11 1-1 00 - SU(2)\mathrm{SU}(2) q+q32q4q5+q92q12q13+q+q^{3}-2q^{4}-q^{5}+q^{9}-2q^{12}-q^{13}+\cdots
735.2.a.f 735.a 1.a 11 5.8695.869 Q\Q None None 105.2.a.a 11 1-1 1-1 00 - SU(2)\mathrm{SU}(2) q+q2q3q4q5q63q8+q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}-3q^{8}+\cdots
735.2.a.g 735.a 1.a 22 5.8695.869 Q(3)\Q(\sqrt{3}) None None 105.2.i.d 2-2 2-2 22 00 - SU(2)\mathrm{SU}(2) q+(1+β)q2q3+(22β)q4+q5+q+(-1+\beta )q^{2}-q^{3}+(2-2\beta )q^{4}+q^{5}+\cdots
735.2.a.h 735.a 1.a 22 5.8695.869 Q(3)\Q(\sqrt{3}) None None 105.2.i.d 2-2 22 2-2 00 ++ SU(2)\mathrm{SU}(2) q+(1+β)q2+q3+(22β)q4q5+q+(-1+\beta )q^{2}+q^{3}+(2-2\beta )q^{4}-q^{5}+\cdots
735.2.a.i 735.a 1.a 22 5.8695.869 Q(2)\Q(\sqrt{2}) None None 105.2.i.c 00 2-2 2-2 00 ++ SU(2)\mathrm{SU}(2) q+βq2q3q5βq62βq8+q+\beta q^{2}-q^{3}-q^{5}-\beta q^{6}-2\beta q^{8}+\cdots
735.2.a.j 735.a 1.a 22 5.8695.869 Q(2)\Q(\sqrt{2}) None None 105.2.i.c 00 22 22 00 - SU(2)\mathrm{SU}(2) q+βq2+q3+q5+βq62βq8+q+\beta q^{2}+q^{3}+q^{5}+\beta q^{6}-2\beta q^{8}+\cdots
735.2.a.k 735.a 1.a 22 5.8695.869 Q(5)\Q(\sqrt{5}) None None 105.2.a.b 00 22 22 00 - SU(2)\mathrm{SU}(2) qβq2+q3+3q4+q5βq6βq8+q-\beta q^{2}+q^{3}+3q^{4}+q^{5}-\beta q^{6}-\beta q^{8}+\cdots
735.2.a.l 735.a 1.a 22 5.8695.869 Q(2)\Q(\sqrt{2}) None None 735.2.a.l 22 2-2 2-2 00 - SU(2)\mathrm{SU}(2) q+(1+β)q2q3+(1+2β)q4q5+q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}-q^{5}+\cdots
735.2.a.m 735.a 1.a 22 5.8695.869 Q(2)\Q(\sqrt{2}) None None 735.2.a.l 22 22 22 00 - SU(2)\mathrm{SU}(2) q+(1+β)q2+q3+(1+2β)q4+q5+q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}+q^{5}+\cdots
735.2.a.n 735.a 1.a 44 5.8695.869 4.4.4352.1 None None 735.2.a.n 44 4-4 44 00 - SU(2)\mathrm{SU}(2) q+(1+β1β3)q2q3+(2+β1β2+)q4+q+(1+\beta _{1}-\beta _{3})q^{2}-q^{3}+(2+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots
735.2.a.o 735.a 1.a 44 5.8695.869 4.4.4352.1 None None 735.2.a.n 44 44 4-4 00 - SU(2)\mathrm{SU}(2) q+(1+β1β3)q2+q3+(2+β1β2+)q4+q+(1+\beta _{1}-\beta _{3})q^{2}+q^{3}+(2+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots
735.2.b.a 735.b 21.c 22 5.8695.869 Q(3)\Q(\sqrt{-3}) None None 105.2.s.a 00 3-3 2-2 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(12ζ6)q2+(1ζ6)q3q4+q+(1-2\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-q^{4}+\cdots
735.2.b.b 735.b 21.c 22 5.8695.869 Q(3)\Q(\sqrt{-3}) None None 105.2.s.a 00 33 22 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(12ζ6)q2+(1+ζ6)q3q4+q5+q+(1-2\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-q^{4}+q^{5}+\cdots
735.2.b.c 735.b 21.c 88 5.8695.869 8.0.856615824.2 None None 105.2.s.c 00 1-1 88 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] qβ1q2+β3q3+(1+β2)q4+q5+q-\beta _{1}q^{2}+\beta _{3}q^{3}+(-1+\beta _{2})q^{4}+q^{5}+\cdots
735.2.b.d 735.b 21.c 88 5.8695.869 8.0.856615824.2 None None 105.2.s.c 00 11 8-8 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] qβ1q2β3q3+(1+β2)q4q5+q-\beta _{1}q^{2}-\beta _{3}q^{3}+(-1+\beta _{2})q^{4}-q^{5}+\cdots
735.2.b.e 735.b 21.c 1616 5.8695.869 Q[x]/(x16+)\mathbb{Q}[x]/(x^{16} + \cdots) None None 735.2.b.e 00 4-4 1616 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+β1q2+β7q3+(β3β4+β6+)q4+q+\beta _{1}q^{2}+\beta _{7}q^{3}+(-\beta _{3}-\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots
735.2.b.f 735.b 21.c 1616 5.8695.869 Q[x]/(x16+)\mathbb{Q}[x]/(x^{16} + \cdots) None None 735.2.b.e 00 44 16-16 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+β1q2β7q3+(β3β4+β6+)q4+q+\beta _{1}q^{2}-\beta _{7}q^{3}+(-\beta _{3}-\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots
735.2.d.a 735.d 5.b 22 5.8695.869 Q(1)\Q(\sqrt{-1}) None None 105.2.d.a 00 00 2-2 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+iq2iq3+q4+(2i1)q5+q+i q^{2}-i q^{3}+q^{4}+(2 i-1)q^{5}+\cdots
735.2.d.b 735.d 5.b 66 5.8695.869 6.0.350464.1 None None 105.2.d.b 00 00 2-2 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] qβ1q2β4q3+(1+β3+β5)q4+q-\beta _{1}q^{2}-\beta _{4}q^{3}+(-1+\beta _{3}+\beta _{5})q^{4}+\cdots
735.2.d.c 735.d 5.b 88 5.8695.869 8.0.309760000.3 None None 735.2.d.c 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] qβ5q2β4q3+(2+β6β7)q4+q-\beta _{5}q^{2}-\beta _{4}q^{3}+(-2+\beta _{6}-\beta _{7})q^{4}+\cdots
735.2.d.d 735.d 5.b 88 5.8695.869 8.0.2058981376.2 None None 105.2.q.a 00 00 2-2 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+β6q2β4q3+(1+β1+β3+)q4+q+\beta _{6}q^{2}-\beta _{4}q^{3}+(-1+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots
735.2.d.e 735.d 5.b 88 5.8695.869 8.0.2058981376.2 None None 105.2.q.a 00 00 22 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+β6q2+β4q3+(1+β1+β3+)q4+q+\beta _{6}q^{2}+\beta _{4}q^{3}+(-1+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots
735.2.d.f 735.d 5.b 88 5.8695.869 Q(ζ24)\Q(\zeta_{24}) None None 735.2.d.f 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+β4q2+β1q3+β3q4+(β6+β5β2)q5+q+\beta_{4} q^{2}+\beta_1 q^{3}+\beta_{3} q^{4}+(\beta_{6}+\beta_{5}-\beta_{2})q^{5}+\cdots
735.2.g.a 735.g 105.g 1616 5.8695.869 16.0.\cdots.5 Q(15)\Q(\sqrt{-15}) None 735.2.g.a 00 00 00 00 U(1)[D2]\mathrm{U}(1)[D_{2}] qβ3q2+β5q3+(2β8)q4+β11q5+q-\beta _{3}q^{2}+\beta _{5}q^{3}+(2-\beta _{8})q^{4}+\beta _{11}q^{5}+\cdots
735.2.g.b 735.g 105.g 2424 5.8695.869 None None 105.2.p.a 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}]
735.2.g.c 735.g 105.g 3232 5.8695.869 None None 735.2.g.c 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}]
735.2.i.a 735.i 7.c 22 5.8695.869 Q(3)\Q(\sqrt{-3}) None None 105.2.a.a 1-1 1-1 1-1 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] qζ6q2+(1+ζ6)q3+(1ζ6)q4+q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots
735.2.i.b 735.i 7.c 22 5.8695.869 Q(3)\Q(\sqrt{-3}) None None 105.2.a.a 1-1 11 11 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] qζ6q2+(1ζ6)q3+(1ζ6)q4+q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots
735.2.i.c 735.i 7.c 22 5.8695.869 Q(3)\Q(\sqrt{-3}) None None 105.2.i.a 00 11 1-1 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(1ζ6)q3+(22ζ6)q4ζ6q5+q+(1-\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}-\zeta_{6}q^{5}+\cdots
735.2.i.d 735.i 7.c 22 5.8695.869 Q(3)\Q(\sqrt{-3}) None None 15.2.a.a 11 1-1 11 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+ζ6q2+(1+ζ6)q3+(1ζ6)q4+q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots
735.2.i.e 735.i 7.c 22 5.8695.869 Q(3)\Q(\sqrt{-3}) None None 15.2.a.a 11 11 1-1 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+ζ6q2+(1ζ6)q3+(1ζ6)q4+q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots
735.2.i.f 735.i 7.c 22 5.8695.869 Q(3)\Q(\sqrt{-3}) None None 105.2.i.b 22 11 11 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+2ζ6q2+(1ζ6)q3+(2+2ζ6)q4+q+2\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots
735.2.i.g 735.i 7.c 44 5.8695.869 Q(2,3)\Q(\sqrt{2}, \sqrt{-3}) None None 735.2.a.l 2-2 2-2 2-2 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(1+β1β2)q2+β2q3+(2β1+)q4+q+(-1+\beta _{1}-\beta _{2})q^{2}+\beta _{2}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots
735.2.i.h 735.i 7.c 44 5.8695.869 Q(2,3)\Q(\sqrt{2}, \sqrt{-3}) None None 735.2.a.l 2-2 22 22 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(1+β1β2)q2β2q3+(2β1+)q4+q+(-1+\beta _{1}-\beta _{2})q^{2}-\beta _{2}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots
735.2.i.i 735.i 7.c 44 5.8695.869 Q(3,5)\Q(\sqrt{-3}, \sqrt{5}) None None 105.2.a.b 00 2-2 2-2 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] qβ2q2+β1q3+3β1q4+(1β1+)q5+q-\beta _{2}q^{2}+\beta _{1}q^{3}+3\beta _{1}q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots
735.2.i.j 735.i 7.c 44 5.8695.869 Q(2,3)\Q(\sqrt{2}, \sqrt{-3}) None None 105.2.i.c 00 2-2 2-2 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+β1q2+β2q3+(1β2)q5+β3q6+q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-1-\beta _{2})q^{5}+\beta _{3}q^{6}+\cdots
735.2.i.k 735.i 7.c 44 5.8695.869 Q(3,5)\Q(\sqrt{-3}, \sqrt{5}) None None 105.2.a.b 00 22 22 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] qβ2q2β1q3+3β1q4+(1+β1+)q5+q-\beta _{2}q^{2}-\beta _{1}q^{3}+3\beta _{1}q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots
735.2.i.l 735.i 7.c 44 5.8695.869 Q(ζ12)\Q(\zeta_{12}) None None 105.2.i.d 22 2-2 22 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(β2+β1)q2+(β11)q3+q+(-\beta_{2}+\beta_1)q^{2}+(\beta_1-1)q^{3}+\cdots
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