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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
916.1.c.a	$916$	$1$	916.c	916.c	$2$	$2$	$2$	$0.457$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-229}) \)	None	✓	✓			916.1.c.a	$2$	$0$	\(-2\)	\(0\)	\(-1\)	\(1\)		$1$		\(q-q^{2}+q^{4}+(-1+\beta )q^{5}+\beta q^{7}-q^{8}+\cdots\)
916.1.c.b	$916$	$1$	916.c	916.c	$2$	$2$	$2$	$0.457$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-229}) \)	None	✓	✓			916.1.c.a	$2$	$0$	\(2\)	\(0\)	\(-1\)	\(-1\)		$1$		\(q+q^{2}+q^{4}+(-1+\beta )q^{5}-\beta q^{7}+q^{8}+\cdots\)
916.1.j.a	$916$	$1$	916.j	916.j	$6$	$2$	$1$	$0.457$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-1}) \)	None		✓			916.1.j.a	$4$	$0$	\(2\)	\(0\)	\(1\)	\(0\)		$1$		\(q+q^{2}+q^{4}+\zeta_{6}q^{5}+q^{8}-\zeta_{6}q^{9}+\cdots\)
916.1.j.b	$916$	$1$	916.j	916.j	$6$	$4$	$2$	$0.457$	\(\Q(\zeta_{12})\)	$A_{4}$	None	None		✓	✓		916.1.j.b	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$1$		\(q-\zeta_{12}^{3}q^{2}+\zeta_{12}^{5}q^{3}-q^{4}-\zeta_{12}^{4}q^{5}+\cdots\)
916.1.p.a	$916$	$1$	916.p	916.p	$38$	$18$	$1$	$0.457$	\(\Q(\zeta_{38})\)	$D_{19}$	\(\Q(\sqrt{-1}) \)	None		✓	✓	✓	916.1.p.a	$4$	$0$	\(-1\)	\(0\)	\(-2\)	\(0\)		$1$		\(q-\zeta_{38}^{17}q^{2}-\zeta_{38}^{15}q^{4}+(-\zeta_{38}^{3}+\cdots)q^{5}+\cdots\)
916.1.t.a	$916$	$1$	916.t	916.t	$114$	$36$	$1$	$0.457$	\(\Q(\zeta_{57})\)	$D_{57}$	\(\Q(\sqrt{-1}) \)	None		✓	✓	✓	916.1.t.a	$4$	$0$	\(-2\)	\(0\)	\(-1\)	\(0\)		$1$		\(q+\zeta_{114}^{24}q^{2}+\zeta_{114}^{48}q^{4}+(-\zeta_{114}^{13}+\cdots)q^{5}+\cdots\)
916.2.a.a	$916$	$2$	916.a	1.a	$1$	$1$	$1$	$7.314$	\(\Q\)	$_{}$	None	None	✓	✓			916.2.a.a	$1$	$2$	\(0\)	\(-3\)	\(-3\)	\(-4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-3q^{5}-4q^{7}+6q^{9}-3q^{11}+\cdots\)
916.2.a.b	$916$	$2$	916.a	1.a	$1$	$1$	$1$	$7.314$	\(\Q\)	$_{}$	None	None	✓	✓			916.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+2q^{7}-2q^{9}-5q^{11}+\cdots\)
916.2.a.c	$916$	$2$	916.a	1.a	$1$	$1$	$1$	$7.314$	\(\Q\)	$_{}$	None	None	✓	✓			916.2.a.c	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-2q^{7}-3q^{9}+4q^{11}+2q^{13}+\cdots\)
916.2.a.d	$916$	$2$	916.a	1.a	$1$	$1$	$1$	$7.314$	\(\Q\)	$_{}$	None	None	✓	✓			916.2.a.d	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}+2q^{7}-2q^{9}-3q^{11}+\cdots\)
916.2.a.e	$916$	$2$	916.a	1.a	$1$	$1$	$1$	$7.314$	\(\Q\)	$_{}$	None	None	✓	✓			916.2.a.e	$1$	$0$	\(0\)	\(3\)	\(1\)	\(4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+q^{5}+4q^{7}+6q^{9}-5q^{11}+\cdots\)
916.2.a.f	$916$	$2$	916.a	1.a	$1$	$5$	$5$	$7.314$	5.5.205225.1	$_{}$	None	None	✓	✓	✓		916.2.a.f	$1$	$1$	\(0\)	\(-1\)	\(-4\)	\(-9\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}+(-1+\beta _{1})q^{5}+(-2-\beta _{3}+\cdots)q^{7}+\cdots\)
916.2.a.g	$916$	$2$	916.a	1.a	$1$	$9$	$9$	$7.314$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	$_{}$	None	None	✓	✓	✓		916.2.a.g	$1$	$0$	\(0\)	\(-1\)	\(10\)	\(3\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{3}+\beta _{8})q^{3}+(1-\beta _{2}+\beta _{7})q^{5}+(1+\cdots)q^{7}+\cdots\)
916.2.d.a	$916$	$2$	916.d	229.b	$2$	$2$	$2$	$7.314$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		✓			916.2.d.a	$2$	$0$	\(0\)	\(-2\)	\(6\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+3 q^{5}-\beta q^{7}-2 q^{9}-3 q^{11}+\cdots\)
916.2.d.b	$916$	$2$	916.d	229.b	$2$	$2$	$2$	$7.314$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		✓			916.2.d.b	$2$	$1$	\(0\)	\(2\)	\(-2\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}-q^{5}-\beta q^{7}-2 q^{9}-5 q^{11}+\cdots\)
916.2.d.c	$916$	$2$	916.d	229.b	$2$	$4$	$4$	$7.314$	\(\Q(\sqrt{-14 +2 \sqrt{37}})\)	$_{}$	None	None		✓			916.2.d.c	$2$	$0$	\(0\)	\(8\)	\(2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{3}+(1-\beta _{2})q^{5}+(\beta _{1}-\beta _{3})q^{7}+\cdots\)
916.2.d.d	$916$	$2$	916.d	229.b	$2$	$10$	$10$	$7.314$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	$_{}$	None	None		✓	✓		916.2.d.d	$2$	$0$	\(0\)	\(-6\)	\(-4\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{4})q^{3}-\beta _{6}q^{5}-\beta _{1}q^{7}+(1+\cdots)q^{9}+\cdots\)
916.2.e.a	$916$	$2$	916.e	229.c	$3$	$40$	$20$	$7.314$		$_{}$	None	None		✓	✓	✓	916.2.e.a	$2$	$0$	\(0\)	\(-2\)	\(3\)	\(-1\)			$\mathrm{SU}(2)[C_{3}]$
916.2.f.a	$916$	$2$	916.f	916.f	$4$	$2$	$1$	$7.314$	\(\Q(\sqrt{-1}) \)	$_{}$	\(\Q(\sqrt{-1}) \)	None		✓			916.2.f.a	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(-i-1)q^{2}+2 i q^{4}-4 i q^{5}+\cdots\)
916.2.f.b	$916$	$2$	916.f	916.f	$4$	$224$	$112$	$7.314$		$_{}$	None	None		✓	✓		916.2.f.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
916.2.h.a	$916$	$2$	916.h	229.e	$6$	$2$	$1$	$7.314$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		✓			916.2.h.a	$2$	$0$	\(0\)	\(-2\)	\(3\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+2\zeta_{6})q^{3}+3\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
916.2.h.b	$916$	$2$	916.h	229.e	$6$	$36$	$18$	$7.314$		$_{}$	None	None		✓	✓		916.2.h.b	$2$	$0$	\(0\)	\(4\)	\(-5\)	\(9\)			$\mathrm{SU}(2)[C_{6}]$
916.2.l.a	$916$	$2$	916.l	916.l	$12$	$4$	$1$	$7.314$	\(\Q(\zeta_{12})\)	$_{}$	\(\Q(\sqrt{-1}) \)	None		✓			916.2.l.a	$4$	$0$	\(-4\)	\(0\)	\(6\)	\(0\)		$1$	$\mathrm{U}(1)[D_{12}]$	\(q+(-1+\zeta_{12}^{3})q^{2}-2\zeta_{12}^{3}q^{4}+(1+\cdots)q^{5}+\cdots\)
916.2.l.b	$916$	$2$	916.l	916.l	$12$	$448$	$112$	$7.314$		$_{}$	None	None		✓	✓		916.2.l.b	$4$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)			$\mathrm{SU}(2)[C_{12}]$
916.2.m.a	$916$	$2$	916.m	229.g	$19$	$342$	$19$	$7.314$		$_{}$	None	None		✓	✓	✓	916.2.m.a	$2$	$0$	\(0\)	\(2\)	\(-19\)	\(4\)			$\mathrm{SU}(2)[C_{19}]$
916.2.n.a	$916$	$2$	916.n	229.h	$38$	$324$	$18$	$7.314$		$_{}$	None	None		✓	✓	✓	916.2.n.a	$2$	$0$	\(0\)	\(-2\)	\(17\)	\(0\)			$\mathrm{SU}(2)[C_{38}]$
916.2.q.a	$916$	$2$	916.q	229.i	$57$	$720$	$20$	$7.314$		$_{}$	None	None		✓	✓	✓	916.2.q.a	$2$	$0$	\(0\)	\(2\)	\(16\)	\(1\)			$\mathrm{SU}(2)[C_{57}]$
916.2.s.a	$916$	$2$	916.s	916.s	$76$	$36$	$1$	$7.314$		$_{}$	\(\Q(\sqrt{-1}) \)	None		✓			916.2.s.a	$4$	$0$	\(2\)	\(0\)	\(0\)	\(0\)			$\mathrm{U}(1)[D_{76}]$
916.2.s.b	$916$	$2$	916.s	916.s	$76$	$4032$	$112$	$7.314$		$_{}$	None	None		✓	✓		916.2.s.b	$4$	$0$	\(-38\)	\(0\)	\(-76\)	\(0\)			$\mathrm{SU}(2)[C_{76}]$
916.2.v.a	$916$	$2$	916.v	229.k	$114$	$684$	$19$	$7.314$		$_{}$	None	None		✓	✓	✓	916.2.v.a	$2$	$0$	\(0\)	\(-2\)	\(-17\)	\(-9\)			$\mathrm{SU}(2)[C_{114}]$
916.2.w.a	$916$	$2$	916.w	916.w	$228$	$72$	$1$	$7.314$		$_{}$	\(\Q(\sqrt{-1}) \)	None		✓			916.2.w.a	$4$	$0$	\(4\)	\(0\)	\(-6\)	\(0\)			$\mathrm{U}(1)[D_{228}]$
916.2.w.b	$916$	$2$	916.w	916.w	$228$	$8064$	$112$	$7.314$		$_{}$	None	None		✓	✓		916.2.w.b	$4$	$0$	\(-76\)	\(0\)	\(-140\)	\(0\)			$\mathrm{SU}(2)[C_{228}]$
916.3.g.a	$916$	$3$	916.g	229.d	$4$	$78$	$39$	$24.959$		$_{}$	None	None		✓	✓	✓	916.3.g.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
916.4.a.a	$916$	$4$	916.a	1.a	$1$	$26$	$26$	$54.046$		$_{}$	None	None	✓	✓	✓	✓	916.4.a.a	$1$	$1$	\(0\)	\(-1\)	\(-30\)	\(-15\)	$-$		$\mathrm{SU}(2)$
916.4.a.b	$916$	$4$	916.a	1.a	$1$	$31$	$31$	$54.046$		$_{}$	None	None	✓	✓	✓	✓	916.4.a.b	$1$	$0$	\(0\)	\(-1\)	\(30\)	\(27\)	$+$		$\mathrm{SU}(2)$
916.4.d.a	$916$	$4$	916.d	229.b	$2$	$58$	$58$	$54.046$		$_{}$	None	None		✓	✓	✓	916.4.d.a	$2$	$0$	\(0\)	\(2\)	\(-38\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
916.6.a.a	$916$	$6$	916.a	1.a	$1$	$45$	$45$	$146.912$		$_{}$	None	None	✓	✓	✓	✓	916.6.a.a	$1$	$1$	\(0\)	\(11\)	\(-150\)	\(-109\)	$+$		$\mathrm{SU}(2)$
916.6.a.b	$916$	$6$	916.a	1.a	$1$	$50$	$50$	$146.912$		$_{}$	None	None	✓	✓	✓	✓	916.6.a.b	$1$	$0$	\(0\)	\(11\)	\(150\)	\(185\)	$-$		$\mathrm{SU}(2)$
916.6.d.a	$916$	$6$	916.d	229.b	$2$	$96$	$96$	$146.912$		$_{}$	None	None		✓	✓	✓	916.6.d.a	$2$	$0$	\(0\)	\(2\)	\(70\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$

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