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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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
195.1.e.a	$195$	$1$	195.e	195.e	$2$	$4$	$4$	$0.097$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-39}) \)	None		✓	✓	✓	195.1.e.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\cdots\)
195.2.a.a	$195$	$2$	195.a	1.a	$1$	$1$	$1$	$1.557$	\(\Q\)	$_{}$	None	None	✓	✓			195.2.a.a	$1$	$0$	\(-1\)	\(1\)	\(1\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+3q^{8}+\cdots\)
195.2.a.b	$195$	$2$	195.a	1.a	$1$	$1$	$1$	$1.557$	\(\Q\)	$_{}$	None	None	✓	✓	✓	✓	195.2.a.b	$1$	$0$	\(2\)	\(-1\)	\(1\)	\(3\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-q^{3}+2q^{4}+q^{5}-2q^{6}+3q^{7}+\cdots\)
195.2.a.c	$195$	$2$	195.a	1.a	$1$	$1$	$1$	$1.557$	\(\Q\)	$_{}$	None	None	✓	✓	✓	✓	195.2.a.c	$1$	$0$	\(2\)	\(1\)	\(-1\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}-q^{7}+\cdots\)
195.2.a.d	$195$	$2$	195.a	1.a	$1$	$1$	$1$	$1.557$	\(\Q\)	$_{}$	None	None	✓	✓			195.2.a.d	$1$	$0$	\(2\)	\(1\)	\(1\)	\(-3\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}-3q^{7}+\cdots\)
195.2.a.e	$195$	$2$	195.a	1.a	$1$	$3$	$3$	$1.557$	3.3.316.1	$_{}$	None	None	✓	✓	✓	✓	195.2.a.e	$1$	$0$	\(0\)	\(-3\)	\(-3\)	\(1\)	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(3+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
195.2.b.a	$195$	$2$	195.b	13.b	$2$	$2$	$2$	$1.557$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		✓			195.2.b.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+2 q^{4}+i q^{5}+3 i q^{7}+q^{9}+\cdots\)
195.2.b.b	$195$	$2$	195.b	13.b	$2$	$2$	$2$	$1.557$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		✓			195.2.b.b	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{3}+q^{4}+i q^{5}+i q^{6}+\cdots\)
195.2.b.c	$195$	$2$	195.b	13.b	$2$	$4$	$4$	$1.557$	\(\Q(i, \sqrt{17})\)	$_{}$	None	None		✓	✓		195.2.b.c	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+q^{3}+(-3+\beta _{3})q^{4}-\beta _{2}q^{5}+\cdots\)
195.2.c.a	$195$	$2$	195.c	5.b	$2$	$2$	$2$	$1.557$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		✓			195.2.c.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+2 q^{4}+(2 i-1)q^{5}+i q^{7}+\cdots\)
195.2.c.b	$195$	$2$	195.c	5.b	$2$	$10$	$10$	$1.557$	10.0.\(\cdots\).1	$_{}$	None	None		✓	✓		195.2.c.b	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-1-\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)
195.2.h.a	$195$	$2$	195.h	65.d	$2$	$2$	$2$	$1.557$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		✓			195.2.h.a	$2$	$0$	\(-4\)	\(0\)	\(-4\)	\(6\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2 q^{2}+i q^{3}+2 q^{4}+(-i-2)q^{5}+\cdots\)
195.2.h.b	$195$	$2$	195.h	65.d	$2$	$2$	$2$	$1.557$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		✓			195.2.h.a	$2$	$0$	\(4\)	\(0\)	\(4\)	\(-6\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 q^{2}+i q^{3}+2 q^{4}+(i+2)q^{5}+\cdots\)
195.2.h.c	$195$	$2$	195.h	65.d	$2$	$12$	$12$	$1.557$	12.0.\(\cdots\).1	$_{}$	None	None		✓	✓		195.2.h.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{10}q^{2}+\beta _{1}q^{3}+(1+\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
195.2.i.a	$195$	$2$	195.i	13.c	$3$	$2$	$1$	$1.557$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		✓			195.2.i.a	$2$	$1$	\(-2\)	\(-1\)	\(-2\)	\(-5\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots\)
195.2.i.b	$195$	$2$	195.i	13.c	$3$	$2$	$1$	$1.557$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		✓			195.2.i.b	$2$	$0$	\(0\)	\(-1\)	\(-2\)	\(1\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{4}-q^{5}+\zeta_{6}q^{7}+\cdots\)
195.2.i.c	$195$	$2$	195.i	13.c	$3$	$4$	$2$	$1.557$	\(\Q(\zeta_{12})\)	$_{}$	None	None		✓			195.2.i.c	$2$	$0$	\(2\)	\(-2\)	\(4\)	\(0\)		$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta_{2}+\beta_1)q^{2}-\beta_1 q^{3}+(2\beta_{3}-2\beta_{2}+2\beta_1-2)q^{4}+\cdots\)
195.2.i.d	$195$	$2$	195.i	13.c	$3$	$6$	$3$	$1.557$	6.0.1714608.1	$_{}$	None	None		✓			195.2.i.d	$2$	$0$	\(0\)	\(3\)	\(6\)	\(-3\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{3}+\beta _{5})q^{2}+(1+\beta _{4})q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
195.2.i.e	$195$	$2$	195.i	13.c	$3$	$6$	$3$	$1.557$	6.0.591408.1	$_{}$	None	None		✓			195.2.i.e	$2$	$0$	\(0\)	\(3\)	\(-6\)	\(5\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{5}q^{2}+(1-\beta _{4})q^{3}+(\beta _{1}-\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
195.2.k.a	$195$	$2$	195.k	65.f	$4$	$28$	$14$	$1.557$		$_{}$	None	None		✓	✓	✓	195.2.k.a	$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
195.2.m.a	$195$	$2$	195.m	15.e	$4$	$48$	$24$	$1.557$		$_{}$	None	None		✓	✓	✓	195.2.m.a	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(-8\)			$\mathrm{SU}(2)[C_{4}]$
195.2.n.a	$195$	$2$	195.n	195.n	$4$	$48$	$24$	$1.557$		$_{}$	None	None		✓	✓	✓	195.2.n.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
195.2.o.a	$195$	$2$	195.o	39.f	$4$	$40$	$20$	$1.557$		$_{}$	None	None		✓	✓	✓	195.2.o.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)			$\mathrm{SU}(2)[C_{4}]$
195.2.s.a	$195$	$2$	195.s	195.s	$4$	$16$	$8$	$1.557$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	$_{}$	\(\Q(\sqrt{-39}) \)	None		✓			195.2.s.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}\cdot 5$	$\mathrm{U}(1)[D_{4}]$	\(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(2\beta _{2}+\beta _{12})q^{4}+\cdots\)
195.2.s.b	$195$	$2$	195.s	195.s	$4$	$32$	$16$	$1.557$		$_{}$	None	None		✓	✓		195.2.s.b	$8$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
195.2.t.a	$195$	$2$	195.t	65.k	$4$	$28$	$14$	$1.557$		$_{}$	None	None		✓	✓	✓	195.2.k.a	$2$	$0$	\(-4\)	\(0\)	\(-4\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
195.2.v.a	$195$	$2$	195.v	65.l	$6$	$32$	$16$	$1.557$		$_{}$	None	None		✓	✓	✓	195.2.v.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
195.2.ba.a	$195$	$2$	195.ba	65.n	$6$	$24$	$12$	$1.557$		$_{}$	None	None		✓	✓	✓	195.2.ba.a	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
195.2.bb.a	$195$	$2$	195.bb	13.e	$6$	$4$	$2$	$1.557$	\(\Q(\zeta_{12})\)	$_{}$	None	None		✓			195.2.bb.a	$2$	$1$	\(-6\)	\(-2\)	\(0\)	\(-12\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{12}-\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
195.2.bb.b	$195$	$2$	195.bb	13.e	$6$	$8$	$4$	$1.557$	8.0.191102976.5	$_{}$	None	None		✓			195.2.bb.b	$2$	$0$	\(0\)	\(4\)	\(0\)	\(12\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2\beta _{1}+\beta _{3}-\beta _{5}-\beta _{7})q^{2}+(1-\beta _{4}+\cdots)q^{3}+\cdots\)
195.2.bb.c	$195$	$2$	195.bb	13.e	$6$	$8$	$4$	$1.557$	8.0.56070144.2	$_{}$	None	None		✓			195.2.bb.c	$2$	$0$	\(6\)	\(-4\)	\(0\)	\(6\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{1}-\beta _{2}-\beta _{4}+\beta _{5}+\beta _{6})q^{2}+\cdots\)
195.2.bd.a	$195$	$2$	195.bd	65.o	$12$	$56$	$14$	$1.557$		$_{}$	None	None		✓	✓	✓	195.2.bd.a	$2$	$0$	\(4\)	\(0\)	\(4\)	\(0\)			$\mathrm{SU}(2)[C_{12}]$
195.2.bf.a	$195$	$2$	195.bf	195.af	$12$	$96$	$24$	$1.557$		$_{}$	None	None		✓	✓	✓	195.2.bf.a	$8$	$0$	\(0\)	\(-2\)	\(0\)	\(-12\)			$\mathrm{SU}(2)[C_{12}]$
195.2.bg.a	$195$	$2$	195.bg	39.k	$12$	$72$	$18$	$1.557$		$_{}$	None	None		✓	✓	✓	195.2.bg.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(12\)			$\mathrm{SU}(2)[C_{12}]$
195.2.bh.a	$195$	$2$	195.bh	195.ah	$12$	$96$	$24$	$1.557$		$_{}$	None	None		✓	✓	✓	195.2.bh.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{12}]$
195.2.bl.a	$195$	$2$	195.bl	195.al	$12$	$96$	$24$	$1.557$		$_{}$	None	None		✓	✓	✓	195.2.bl.a	$8$	$0$	\(0\)	\(-2\)	\(0\)	\(-4\)			$\mathrm{SU}(2)[C_{12}]$
195.2.bm.a	$195$	$2$	195.bm	65.t	$12$	$56$	$14$	$1.557$		$_{}$	None	None		✓	✓	✓	195.2.bd.a	$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)			$\mathrm{SU}(2)[C_{12}]$
195.3.d.a	$195$	$3$	195.d	3.b	$2$	$32$	$32$	$5.313$		$_{}$	None	None		✓	✓	✓	195.3.d.a	$2$	$0$	\(0\)	\(8\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
195.3.e.a	$195$	$3$	195.e	195.e	$2$	$1$	$1$	$5.313$	\(\Q\)	$_{}$	\(\Q(\sqrt{-195}) \)	None	✓	✓			195.3.e.a	$2$	$0$	\(0\)	\(-3\)	\(-5\)	\(1\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3q^{3}+4q^{4}-5q^{5}+q^{7}+9q^{9}+\cdots\)
195.3.e.b	$195$	$3$	195.e	195.e	$2$	$1$	$1$	$5.313$	\(\Q\)	$_{}$	\(\Q(\sqrt{-195}) \)	None	✓	✓			195.3.e.a	$2$	$0$	\(0\)	\(-3\)	\(5\)	\(-1\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3q^{3}+4q^{4}+5q^{5}-q^{7}+9q^{9}+\cdots\)
195.3.e.c	$195$	$3$	195.e	195.e	$2$	$1$	$1$	$5.313$	\(\Q\)	$_{}$	\(\Q(\sqrt{-195}) \)	None	✓	✓			195.3.e.a	$2$	$0$	\(0\)	\(3\)	\(-5\)	\(-1\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3q^{3}+4q^{4}-5q^{5}-q^{7}+9q^{9}+\cdots\)
195.3.e.d	$195$	$3$	195.e	195.e	$2$	$1$	$1$	$5.313$	\(\Q\)	$_{}$	\(\Q(\sqrt{-195}) \)	None	✓	✓			195.3.e.a	$2$	$0$	\(0\)	\(3\)	\(5\)	\(1\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3q^{3}+4q^{4}+5q^{5}+q^{7}+9q^{9}+\cdots\)
195.3.e.e	$195$	$3$	195.e	195.e	$2$	$8$	$8$	$5.313$	8.0.\(\cdots\).2	$_{}$	\(\Q(\sqrt{-39}) \)	None		✓			195.3.e.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}\cdot 5$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{6}q^{2}-3\beta _{1}q^{3}+(-4+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
195.3.e.f	$195$	$3$	195.e	195.e	$2$	$40$	$40$	$5.313$		$_{}$	None	None		✓	✓		195.3.e.f	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
195.3.f.a	$195$	$3$	195.f	15.d	$2$	$48$	$48$	$5.313$		$_{}$	None	None		✓	✓	✓	195.3.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
195.3.g.a	$195$	$3$	195.g	39.d	$2$	$4$	$4$	$5.313$	\(\Q(\sqrt{-2}, \sqrt{5})\)	$_{}$	None	None		✓			195.3.g.a	$4$	$0$	\(0\)	\(-12\)	\(0\)	\(0\)		$2^{6}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-3q^{3}+q^{4}-\beta _{2}q^{5}+3\beta _{2}q^{6}+\cdots\)
195.3.g.b	$195$	$3$	195.g	39.d	$2$	$32$	$32$	$5.313$		$_{}$	None	None		✓	✓		195.3.g.b	$4$	$0$	\(0\)	\(12\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
195.3.j.a	$195$	$3$	195.j	195.j	$4$	$2$	$1$	$5.313$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		✓			195.3.j.a	$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+i q^{2}-3 q^{3}+3 q^{4}+5 i q^{5}-3 i q^{6}+\cdots\)
195.3.j.b	$195$	$3$	195.j	195.j	$4$	$2$	$1$	$5.313$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		✓			195.3.j.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-i q^{2}-3 i q^{3}+3 q^{4}-5 i q^{5}+\cdots\)
195.3.j.c	$195$	$3$	195.j	195.j	$4$	$4$	$2$	$5.313$	\(\Q(\zeta_{8})\)	$_{}$	None	None		✓			195.3.j.c	$4$	$0$	\(0\)	\(8\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2\zeta_{8}+2\zeta_{8}^{3})q^{2}+(2+2\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\cdots\)

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