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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}
308.1.g.a 308.g 308.g 11 0.1540.154 Q\Q Q(7)\Q(\sqrt{-7}) , Q(77)\Q(\sqrt{-77}) Q(11)\Q(\sqrt{11}) 308.1.g.a 1-1 00 00 11 qq2+q4+q7q8q9+q11+q-q^{2}+q^{4}+q^{7}-q^{8}-q^{9}+q^{11}+\cdots
308.1.g.b 308.g 308.g 11 0.1540.154 Q\Q Q(7)\Q(\sqrt{-7}) , Q(77)\Q(\sqrt{-77}) Q(11)\Q(\sqrt{11}) 308.1.g.a 11 00 00 1-1 q+q2+q4q7+q8q9q11+q+q^{2}+q^{4}-q^{7}+q^{8}-q^{9}-q^{11}+\cdots
308.1.s.a 308.s 308.s 44 0.1540.154 Q(ζ10)\Q(\zeta_{10}) Q(7)\Q(\sqrt{-7}) None 308.1.s.a 1-1 00 00 11 q+ζ104q2ζ103q4ζ102q7+q+\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}-\zeta_{10}^{2}q^{7}+\cdots
308.1.s.b 308.s 308.s 44 0.1540.154 Q(ζ10)\Q(\zeta_{10}) Q(7)\Q(\sqrt{-7}) None 308.1.s.a 11 00 00 1-1 q+ζ103q2ζ10q4+ζ102q7ζ104q8+q+\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+\zeta_{10}^{2}q^{7}-\zeta_{10}^{4}q^{8}+\cdots
308.2.a.a 308.a 1.a 11 2.4592.459 Q\Q None None 308.2.a.a 00 1-1 1-1 1-1 ++ SU(2)\mathrm{SU}(2) qq3q5q72q9+q114q13+q-q^{3}-q^{5}-q^{7}-2q^{9}+q^{11}-4q^{13}+\cdots
308.2.a.b 308.a 1.a 22 2.4592.459 Q(6)\Q(\sqrt{6}) None None 308.2.a.b 00 00 44 2-2 - SU(2)\mathrm{SU}(2) q+βq3+2q5q7+3q9q11+q+\beta q^{3}+2q^{5}-q^{7}+3q^{9}-q^{11}+\cdots
308.2.a.c 308.a 1.a 33 2.4592.459 3.3.1016.1 None None 308.2.a.c 00 1-1 1-1 33 - SU(2)\mathrm{SU}(2) qβ1q3+(β1β2)q5+q7+(1+)q9+q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+q^{7}+(1+\cdots)q^{9}+\cdots
308.2.c.a 308.c 77.b 44 2.4592.459 Q(2,5)\Q(\sqrt{2}, \sqrt{-5}) None None 308.2.c.a 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] qβ3q3β3q5+(β1β2)q72q9+q-\beta _{3}q^{3}-\beta _{3}q^{5}+(\beta _{1}-\beta _{2})q^{7}-2q^{9}+\cdots
308.2.c.b 308.c 77.b 44 2.4592.459 Q(2,7)\Q(\sqrt{-2}, \sqrt{-7}) None None 308.2.c.b 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+β2q32β2q5β3q7+q9+(2+)q11+q+\beta _{2}q^{3}-2\beta _{2}q^{5}-\beta _{3}q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots
308.2.d.a 308.d 44.c 1818 2.4592.459 Q[x]/(x18)\mathbb{Q}[x]/(x^{18} - \cdots) None None 308.2.d.a 1-1 00 00 1818 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+β12q2β4q3β8q4β10q5+q+\beta _{12}q^{2}-\beta _{4}q^{3}-\beta _{8}q^{4}-\beta _{10}q^{5}+\cdots
308.2.d.b 308.d 44.c 1818 2.4592.459 Q[x]/(x18)\mathbb{Q}[x]/(x^{18} - \cdots) None None 308.2.d.a 11 00 00 18-18 SU(2)[C2]\mathrm{SU}(2)[C_{2}] qβ12q2β4q3β8q4β10q5+q-\beta _{12}q^{2}-\beta _{4}q^{3}-\beta _{8}q^{4}-\beta _{10}q^{5}+\cdots
308.2.f.a 308.f 28.d 4040 2.4592.459 None None 308.2.f.a 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}]
308.2.i.a 308.i 7.c 66 2.4592.459 6.0.309123.1 None None 308.2.i.a 00 1-1 22 44 SU(2)[C3]\mathrm{SU}(2)[C_{3}] qβ2q3+(β1β2β3+β5)q5+q-\beta _{2}q^{3}+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{5}+\cdots
308.2.i.b 308.i 7.c 66 2.4592.459 6.0.1783323.2 None None 308.2.i.b 00 33 22 22 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(1β4+β5)q3+(β1+β2+β4+)q5+q+(1-\beta _{4}+\beta _{5})q^{3}+(\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots
308.2.j.a 308.j 11.c 44 2.4592.459 Q(ζ10)\Q(\zeta_{10}) None None 308.2.j.a 00 44 2-2 11 SU(2)[C5]\mathrm{SU}(2)[C_{5}] q+(2ζ10+2ζ103)q32ζ10q5+ζ103q7+q+(2\zeta_{10}+2\zeta_{10}^{3})q^{3}-2\zeta_{10}q^{5}+\zeta_{10}^{3}q^{7}+\cdots
308.2.j.b 308.j 11.c 88 2.4592.459 Q[x]/(x8)\mathbb{Q}[x]/(x^{8} - \cdots) None None 308.2.j.b 00 8-8 1-1 22 SU(2)[C5]\mathrm{SU}(2)[C_{5}] q+(22β2β3β6)q3+β7q5+q+(-2-2\beta _{2}-\beta _{3}-\beta _{6})q^{3}+\beta _{7}q^{5}+\cdots
308.2.j.c 308.j 11.c 1212 2.4592.459 Q[x]/(x12)\mathbb{Q}[x]/(x^{12} - \cdots) None None 308.2.j.c 00 66 11 3-3 SU(2)[C5]\mathrm{SU}(2)[C_{5}] q+(β1+β3β4+β5+β8β9+β11)q3+q+(\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{8}-\beta _{9}+\beta _{11})q^{3}+\cdots
308.2.l.a 308.l 28.f 8080 2.4592.459 None None 308.2.l.a 00 00 00 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}]
308.2.n.a 308.n 308.n 44 2.4592.459 Q(3,7)\Q(\sqrt{-3}, \sqrt{-7}) None None 308.2.n.a 1-1 00 00 2-2 SU(2)[C6]\mathrm{SU}(2)[C_{6}] qβ3q2+(12β1β2)q3+(1+β1+)q4+q-\beta _{3}q^{2}+(1-2\beta _{1}-\beta _{2})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots
308.2.n.b 308.n 308.n 44 2.4592.459 Q(3,7)\Q(\sqrt{-3}, \sqrt{-7}) None None 308.2.n.a 11 00 00 22 SU(2)[C6]\mathrm{SU}(2)[C_{6}] q+β3q2+(12β1β2)q3+(1+β1+)q4+q+\beta _{3}q^{2}+(1-2\beta _{1}-\beta _{2})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots
308.2.n.c 308.n 308.n 8080 2.4592.459 None None 308.2.n.c 00 00 4-4 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}]
308.2.q.a 308.q 77.i 1616 2.4592.459 Q[x]/(x16+)\mathbb{Q}[x]/(x^{16} + \cdots) None None 308.2.q.a 00 00 66 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}] qβ3q3+β5q5+β9q7+β7q9+q-\beta _{3}q^{3}+\beta _{5}q^{5}+\beta _{9}q^{7}+\beta _{7}q^{9}+\cdots
308.2.t.a 308.t 308.t 88 2.4592.459 8.0.37515625.1 Q(7)\Q(\sqrt{-7}) None 308.2.t.a 11 00 00 00 U(1)[D10]\mathrm{U}(1)[D_{10}] qβ2q2+(1β1β2β3+β4+)q4+q-\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots
308.2.t.b 308.t 308.t 88 2.4592.459 8.0.37515625.1 Q(7)\Q(\sqrt{-7}) None 308.2.t.a 11 00 00 00 U(1)[D10]\mathrm{U}(1)[D_{10}] qβ2q2+(1β1β2β3+β4+)q4+q-\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots
308.2.t.c 308.t 308.t 160160 2.4592.459 None None 308.2.t.c 10-10 00 00 00 SU(2)[C10]\mathrm{SU}(2)[C_{10}]
308.2.v.a 308.v 44.g 7272 2.4592.459 None None 308.2.v.a 1-1 00 00 1818 SU(2)[C10]\mathrm{SU}(2)[C_{10}]
308.2.v.b 308.v 44.g 7272 2.4592.459 None None 308.2.v.a 11 00 00 18-18 SU(2)[C10]\mathrm{SU}(2)[C_{10}]
308.2.w.a 308.w 77.l 3232 2.4592.459 None None 308.2.w.a 00 00 00 5-5 SU(2)[C10]\mathrm{SU}(2)[C_{10}]
308.2.y.a 308.y 77.m 1616 2.4592.459 16.0.\cdots.1 None None 308.2.y.a 00 11 5-5 1414 SU(2)[C15]\mathrm{SU}(2)[C_{15}] q+(β3+β6+β7+β12β15)q3+q+(-\beta _{3}+\beta _{6}+\beta _{7}+\beta _{12}-\beta _{15})q^{3}+\cdots
308.2.y.b 308.y 77.m 4848 2.4592.459 None None 308.2.y.b 00 1-1 77 7-7 SU(2)[C15]\mathrm{SU}(2)[C_{15}]
308.2.z.a 308.z 77.n 6464 2.4592.459 None None 308.2.z.a 00 00 6-6 55 SU(2)[C30]\mathrm{SU}(2)[C_{30}]
308.2.bc.a 308.bc 308.ac 352352 2.4592.459 None None 308.2.bc.a 5-5 00 6-6 00 SU(2)[C30]\mathrm{SU}(2)[C_{30}]
308.2.be.a 308.be 308.ae 352352 2.4592.459 None None 308.2.be.a 1-1 00 18-18 00 SU(2)[C30]\mathrm{SU}(2)[C_{30}]
308.3.b.a 308.b 7.b 1212 8.3928.392 Q[x]/(x12+)\mathbb{Q}[x]/(x^{12} + \cdots) None None 308.3.b.a 00 00 00 6-6 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+β1q3β5q5+(β1β7)q7+(1+)q9+q+\beta _{1}q^{3}-\beta _{5}q^{5}+(\beta _{1}-\beta _{7})q^{7}+(1+\cdots)q^{9}+\cdots
308.3.e.a 308.e 4.b 6060 8.3928.392 None None 308.3.e.a 00 00 88 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}]
308.3.g.a 308.g 308.g 22 8.3928.392 Q(14)\Q(\sqrt{14}) Q(77)\Q(\sqrt{-77}) None 308.3.g.a 4-4 00 00 14-14 U(1)[D2]\mathrm{U}(1)[D_{2}] q2q2+βq3+4q42βq67q7+q-2q^{2}+\beta q^{3}+4q^{4}-2\beta q^{6}-7q^{7}+\cdots
308.3.g.b 308.g 308.g 22 8.3928.392 Q(22)\Q(\sqrt{22}) Q(77)\Q(\sqrt{-77}) None 308.3.g.b 4-4 00 00 1414 U(1)[D2]\mathrm{U}(1)[D_{2}] q2q2+βq3+4q42βq6+7q7+q-2q^{2}+\beta q^{3}+4q^{4}-2\beta q^{6}+7q^{7}+\cdots
308.3.g.c 308.g 308.g 22 8.3928.392 Q(7)\Q(\sqrt{-7}) Q(7)\Q(\sqrt{-7}) None 308.3.g.c 3-3 00 00 1414 U(1)[D2]\mathrm{U}(1)[D_{2}] q+(1β)q2+(1+3β)q4+7q7+q+(-1-\beta )q^{2}+(-1+3\beta )q^{4}+7q^{7}+\cdots
308.3.g.d 308.g 308.g 22 8.3928.392 Q(7)\Q(\sqrt{-7}) Q(7)\Q(\sqrt{-7}) None 308.3.g.c 33 00 00 14-14 U(1)[D2]\mathrm{U}(1)[D_{2}] q+(1+β)q2+(1+3β)q47q7+q+(1+\beta )q^{2}+(-1+3\beta )q^{4}-7q^{7}+\cdots
308.3.g.e 308.g 308.g 22 8.3928.392 Q(22)\Q(\sqrt{22}) Q(77)\Q(\sqrt{-77}) None 308.3.g.b 44 00 00 14-14 U(1)[D2]\mathrm{U}(1)[D_{2}] q+2q2+βq3+4q4+2βq67q7+q+2q^{2}+\beta q^{3}+4q^{4}+2\beta q^{6}-7q^{7}+\cdots
308.3.g.f 308.g 308.g 22 8.3928.392 Q(14)\Q(\sqrt{14}) Q(77)\Q(\sqrt{-77}) None 308.3.g.a 44 00 00 1414 U(1)[D2]\mathrm{U}(1)[D_{2}] q+2q2+βq3+4q4+2βq6+7q7+q+2q^{2}+\beta q^{3}+4q^{4}+2\beta q^{6}+7q^{7}+\cdots
308.3.g.g 308.g 308.g 8080 8.3928.392 None None 308.3.g.g 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}]
308.3.h.a 308.h 11.b 1212 8.3928.392 Q[x]/(x12)\mathbb{Q}[x]/(x^{12} - \cdots) None None 308.3.h.a 00 10-10 6-6 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+(1+β3)q3+(1+β4)q5+β5q7+q+(-1+\beta _{3})q^{3}+(-1+\beta _{4})q^{5}+\beta _{5}q^{7}+\cdots
308.3.k.a 308.k 77.h 3232 8.3928.392 None None 308.3.k.a 00 00 2-2 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}]
308.3.m.a 308.m 308.m 184184 8.3928.392 None None 308.3.m.a 00 00 12-12 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}]
308.3.o.a 308.o 28.g 160160 8.3928.392 None None 308.3.o.a 00 00 00 00 SU(2)[C6]\mathrm{SU}(2)[C_{6}]
308.3.p.a 308.p 7.d 2828 8.3928.392 None None 308.3.p.a 00 6-6 00 1414 SU(2)[C6]\mathrm{SU}(2)[C_{6}]
308.3.r.a 308.r 11.d 4848 8.3928.392 None None 308.3.r.a 00 1010 66 00 SU(2)[C10]\mathrm{SU}(2)[C_{10}]
308.3.s.a 308.s 308.s 88 8.3928.392 8.0.37515625.1 Q(7)\Q(\sqrt{-7}) None 308.3.s.a 3-3 00 00 1414 U(1)[D10]\mathrm{U}(1)[D_{10}] q+(β4+β5)q2+(3β2+β7)q47β3q7+q+(-\beta _{4}+\beta _{5})q^{2}+(3\beta _{2}+\beta _{7})q^{4}-7\beta _{3}q^{7}+\cdots
308.3.s.b 308.s 308.s 88 8.3928.392 8.0.37515625.1 Q(7)\Q(\sqrt{-7}) None 308.3.s.a 33 00 00 14-14 U(1)[D10]\mathrm{U}(1)[D_{10}] q+(1β1β2β3+β4+β5β6+)q2+q+(1-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{4}+\beta _{5}-\beta _{6}+\cdots)q^{2}+\cdots
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