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Label Char Prim Dim $A$ Field CM RM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1452.1.e.a 1452.e 3.b $1$ $0.725$ \(\Q\) \(\Q(\sqrt{-3}) \) None 1452.1.e.a \(0\) \(1\) \(0\) \(-1\) \(q+q^{3}-q^{7}+q^{9}+2q^{13}-q^{19}-q^{21}+\cdots\)
1452.1.e.b 1452.e 3.b $1$ $0.725$ \(\Q\) \(\Q(\sqrt{-3}) \) None 1452.1.e.a \(0\) \(1\) \(0\) \(1\) \(q+q^{3}+q^{7}+q^{9}-2q^{13}+q^{19}+q^{21}+\cdots\)
1452.1.e.c 1452.e 3.b $2$ $0.725$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-3}) \) None 1452.1.e.c \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}-\beta q^{7}+q^{9}+\beta q^{19}+\beta q^{21}+\cdots\)
1452.1.e.d 1452.e 3.b $2$ $0.725$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-11}) \) None 1452.1.e.d \(0\) \(1\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{3}+(-\zeta_{6}-\zeta_{6}^{2})q^{5}-\zeta_{6}q^{9}+\cdots\)
1452.1.m.a 1452.m 33.h $4$ $0.725$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-3}) \) None 1452.1.e.a \(0\) \(-1\) \(0\) \(-1\) \(q+\zeta_{10}^{2}q^{3}-\zeta_{10}^{3}q^{7}+\zeta_{10}^{4}q^{9}+\cdots\)
1452.1.m.b 1452.m 33.h $4$ $0.725$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-3}) \) None 1452.1.e.a \(0\) \(-1\) \(0\) \(1\) \(q+\zeta_{10}^{2}q^{3}+\zeta_{10}^{3}q^{7}+\zeta_{10}^{4}q^{9}+\cdots\)
1452.1.m.c 1452.m 33.h $8$ $0.725$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-11}) \) None 1452.1.e.d \(0\) \(-1\) \(0\) \(0\) \(q+\zeta_{30}q^{3}+(\zeta_{30}^{8}+\zeta_{30}^{13})q^{5}+\zeta_{30}^{2}q^{9}+\cdots\)
1452.1.m.d 1452.m 33.h $8$ $0.725$ 8.0.324000000.3 \(\Q(\sqrt{-3}) \) None 1452.1.e.c \(0\) \(2\) \(0\) \(0\) \(q+(1+\beta _{2}+\beta _{4}+\beta _{6})q^{3}-\beta _{7}q^{7}+\beta _{6}q^{9}+\cdots\)
1452.2.a.a 1452.a 1.a $1$ $11.594$ \(\Q\) None None 1452.2.a.a \(0\) \(-1\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-2q^{7}+q^{9}+3q^{13}+q^{15}+\cdots\)
1452.2.a.b 1452.a 1.a $1$ $11.594$ \(\Q\) None None 1452.2.a.a \(0\) \(-1\) \(-1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+2q^{7}+q^{9}-3q^{13}+q^{15}+\cdots\)
1452.2.a.c 1452.a 1.a $1$ $11.594$ \(\Q\) None None 132.2.a.a \(0\) \(-1\) \(2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}-2q^{7}+q^{9}-6q^{13}+\cdots\)
1452.2.a.d 1452.a 1.a $1$ $11.594$ \(\Q\) None None 1452.2.a.d \(0\) \(1\) \(-4\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{5}-5q^{7}+q^{9}-2q^{13}+\cdots\)
1452.2.a.e 1452.a 1.a $1$ $11.594$ \(\Q\) None None 1452.2.a.d \(0\) \(1\) \(-4\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{5}+5q^{7}+q^{9}+2q^{13}+\cdots\)
1452.2.a.f 1452.a 1.a $1$ $11.594$ \(\Q\) None None 132.2.a.b \(0\) \(1\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+2q^{7}+q^{9}+2q^{13}+\cdots\)
1452.2.a.g 1452.a 1.a $1$ $11.594$ \(\Q\) None None 1452.2.a.g \(0\) \(1\) \(3\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{5}-2q^{7}+q^{9}-5q^{13}+\cdots\)
1452.2.a.h 1452.a 1.a $1$ $11.594$ \(\Q\) None None 1452.2.a.g \(0\) \(1\) \(3\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{5}+2q^{7}+q^{9}+5q^{13}+\cdots\)
1452.2.a.i 1452.a 1.a $2$ $11.594$ \(\Q(\sqrt{5}) \) None None 132.2.i.b \(0\) \(-2\) \(-1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(1-3\beta )q^{5}+(-3+2\beta )q^{7}+\cdots\)
1452.2.a.j 1452.a 1.a $2$ $11.594$ \(\Q(\sqrt{5}) \) None None 132.2.i.b \(0\) \(-2\) \(-1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(1-3\beta )q^{5}+(3-2\beta )q^{7}+q^{9}+\cdots\)
1452.2.a.k 1452.a 1.a $2$ $11.594$ \(\Q(\sqrt{3}) \) None None 1452.2.a.k \(0\) \(-2\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-\beta q^{7}+q^{9}+\beta q^{19}+\beta q^{21}+\cdots\)
1452.2.a.l 1452.a 1.a $2$ $11.594$ \(\Q(\sqrt{5}) \) None None 132.2.i.a \(0\) \(2\) \(-1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta q^{5}+(-3+2\beta )q^{7}+q^{9}+\cdots\)
1452.2.a.m 1452.a 1.a $2$ $11.594$ \(\Q(\sqrt{5}) \) None None 132.2.i.a \(0\) \(2\) \(-1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta q^{5}+(3-2\beta )q^{7}+q^{9}+(1+\cdots)q^{13}+\cdots\)
1452.2.b.a 1452.b 33.d $4$ $11.594$ \(\Q(\sqrt{-2}, \sqrt{-11})\) None None 1452.2.b.a \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{3}+(-1+2\beta _{3})q^{5}-3\beta _{2}q^{7}+\cdots\)
1452.2.b.b 1452.b 33.d $4$ $11.594$ \(\Q(\sqrt{-2}, \sqrt{3})\) \(\Q(\sqrt{-3}) \) None 1452.2.b.b \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{2}q^{3}+(-2\beta _{1}+\beta _{3})q^{7}+3q^{9}+\cdots\)
1452.2.b.c 1452.b 33.d $4$ $11.594$ \(\Q(\sqrt{-2}, \sqrt{3})\) \(\Q(\sqrt{-3}) \) None 1452.2.b.c \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{2}q^{3}+(2\beta _{1}+\beta _{3})q^{7}+3q^{9}+(-\beta _{1}+\cdots)q^{13}+\cdots\)
1452.2.b.d 1452.b 33.d $8$ $11.594$ 8.0.3588489216.5 None None 1452.2.b.d \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{1})q^{3}+\beta _{2}q^{5}+(-1+\beta _{1}+\cdots)q^{9}+\cdots\)
1452.2.b.e 1452.b 33.d $16$ $11.594$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None 132.2.p.a \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{3}+\beta _{15}q^{5}+(\beta _{1}+\beta _{2}+\beta _{14}+\cdots)q^{7}+\cdots\)
1452.2.i.a 1452.i 11.c $4$ $11.594$ \(\Q(\zeta_{10})\) None None 1452.2.a.g \(0\) \(-1\) \(-3\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+\zeta_{10}^{2}q^{3}-3\zeta_{10}q^{5}-2\zeta_{10}^{3}q^{7}+\cdots\)
1452.2.i.b 1452.i 11.c $4$ $11.594$ \(\Q(\zeta_{10})\) None None 1452.2.a.g \(0\) \(-1\) \(-3\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q+\zeta_{10}^{2}q^{3}-3\zeta_{10}q^{5}+2\zeta_{10}^{3}q^{7}+\cdots\)
1452.2.i.c 1452.i 11.c $4$ $11.594$ \(\Q(\zeta_{10})\) None None 132.2.i.a \(0\) \(-1\) \(-2\) \(-3\) $\mathrm{SU}(2)[C_{5}]$ \(q+\zeta_{10}^{2}q^{3}+(-1+\zeta_{10}-\zeta_{10}^{2})q^{5}+\cdots\)
1452.2.i.d 1452.i 11.c $4$ $11.594$ \(\Q(\zeta_{10})\) None None 132.2.a.b \(0\) \(-1\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+\zeta_{10}^{2}q^{3}-2\zeta_{10}q^{5}-2\zeta_{10}^{3}q^{7}+\cdots\)
1452.2.i.e 1452.i 11.c $4$ $11.594$ \(\Q(\zeta_{10})\) None None 132.2.a.b \(0\) \(-1\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q+\zeta_{10}^{2}q^{3}-2\zeta_{10}q^{5}+2\zeta_{10}^{3}q^{7}+\cdots\)
1452.2.i.f 1452.i 11.c $4$ $11.594$ \(\Q(\zeta_{10})\) None None 132.2.i.a \(0\) \(-1\) \(-2\) \(3\) $\mathrm{SU}(2)[C_{5}]$ \(q+\zeta_{10}^{2}q^{3}+(-1+\zeta_{10}-\zeta_{10}^{2})q^{5}+\cdots\)
1452.2.i.g 1452.i 11.c $4$ $11.594$ \(\Q(\zeta_{10})\) None None 132.2.i.a \(0\) \(-1\) \(3\) \(-7\) $\mathrm{SU}(2)[C_{5}]$ \(q+\zeta_{10}^{2}q^{3}+(1+\zeta_{10}^{2})q^{5}+(-2+2\zeta_{10}+\cdots)q^{7}+\cdots\)
1452.2.i.h 1452.i 11.c $4$ $11.594$ \(\Q(\zeta_{10})\) None None 1452.2.a.d \(0\) \(-1\) \(4\) \(-5\) $\mathrm{SU}(2)[C_{5}]$ \(q+\zeta_{10}^{2}q^{3}+4\zeta_{10}q^{5}-5\zeta_{10}^{3}q^{7}+\cdots\)
1452.2.i.i 1452.i 11.c $4$ $11.594$ \(\Q(\zeta_{10})\) None None 1452.2.a.d \(0\) \(-1\) \(4\) \(5\) $\mathrm{SU}(2)[C_{5}]$ \(q+\zeta_{10}^{2}q^{3}+4\zeta_{10}q^{5}+5\zeta_{10}^{3}q^{7}+\cdots\)
1452.2.i.j 1452.i 11.c $4$ $11.594$ \(\Q(\zeta_{10})\) None None 132.2.i.b \(0\) \(1\) \(-7\) \(-3\) $\mathrm{SU}(2)[C_{5}]$ \(q-\zeta_{10}^{2}q^{3}+(-3+2\zeta_{10}-3\zeta_{10}^{2}+\cdots)q^{5}+\cdots\)
1452.2.i.k 1452.i 11.c $4$ $11.594$ \(\Q(\zeta_{10})\) None None 132.2.a.a \(0\) \(1\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q-\zeta_{10}^{2}q^{3}-2\zeta_{10}q^{5}-2\zeta_{10}^{3}q^{7}+\cdots\)
1452.2.i.l 1452.i 11.c $4$ $11.594$ \(\Q(\zeta_{10})\) None None 132.2.a.a \(0\) \(1\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q-\zeta_{10}^{2}q^{3}-2\zeta_{10}q^{5}+2\zeta_{10}^{3}q^{7}+\cdots\)
1452.2.i.m 1452.i 11.c $4$ $11.594$ \(\Q(\zeta_{10})\) None None 1452.2.a.a \(0\) \(1\) \(1\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q-\zeta_{10}^{2}q^{3}+\zeta_{10}q^{5}-2\zeta_{10}^{3}q^{7}+\cdots\)
1452.2.i.n 1452.i 11.c $4$ $11.594$ \(\Q(\zeta_{10})\) None None 1452.2.a.a \(0\) \(1\) \(1\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q-\zeta_{10}^{2}q^{3}+\zeta_{10}q^{5}+2\zeta_{10}^{3}q^{7}+\cdots\)
1452.2.i.o 1452.i 11.c $4$ $11.594$ \(\Q(\zeta_{10})\) None None 132.2.i.b \(0\) \(1\) \(8\) \(-7\) $\mathrm{SU}(2)[C_{5}]$ \(q-\zeta_{10}^{2}q^{3}+(3-\zeta_{10}+3\zeta_{10}^{2})q^{5}+\cdots\)
1452.2.i.p 1452.i 11.c $4$ $11.594$ \(\Q(\zeta_{10})\) None None 132.2.i.b \(0\) \(1\) \(8\) \(7\) $\mathrm{SU}(2)[C_{5}]$ \(q-\zeta_{10}^{2}q^{3}+(3-\zeta_{10}+3\zeta_{10}^{2})q^{5}+\cdots\)
1452.2.i.q 1452.i 11.c $8$ $11.594$ 8.0.324000000.3 None None 1452.2.a.k \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1+\beta _{2}+\beta _{4}+\beta _{6})q^{3}+\beta _{7}q^{7}+\beta _{6}q^{9}+\cdots\)
1452.3.e.a 1452.e 3.b $1$ $39.564$ \(\Q\) \(\Q(\sqrt{-3}) \) None 1452.3.e.a \(0\) \(-3\) \(0\) \(-13\) $\mathrm{U}(1)[D_{2}]$ \(q-3q^{3}-13q^{7}+9q^{9}-22q^{13}-37q^{19}+\cdots\)
1452.3.e.b 1452.e 3.b $1$ $39.564$ \(\Q\) \(\Q(\sqrt{-3}) \) None 12.3.c.a \(0\) \(-3\) \(0\) \(-2\) $\mathrm{U}(1)[D_{2}]$ \(q-3q^{3}-2q^{7}+9q^{9}+22q^{13}-26q^{19}+\cdots\)
1452.3.e.c 1452.e 3.b $1$ $39.564$ \(\Q\) \(\Q(\sqrt{-3}) \) None 1452.3.e.a \(0\) \(-3\) \(0\) \(13\) $\mathrm{U}(1)[D_{2}]$ \(q-3q^{3}+13q^{7}+9q^{9}+22q^{13}+37q^{19}+\cdots\)
1452.3.e.d 1452.e 3.b $2$ $39.564$ \(\Q(\sqrt{-11}) \) None None 132.3.e.a \(0\) \(5\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(3-\beta )q^{3}+(1-2\beta )q^{5}-2q^{7}+(6+\cdots)q^{9}+\cdots\)
1452.3.e.e 1452.e 3.b $2$ $39.564$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-3}) \) None 1452.3.e.e \(0\) \(6\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+3q^{3}-3\beta q^{7}+9q^{9}+8\beta q^{13}-5\beta q^{19}+\cdots\)
1452.3.e.f 1452.e 3.b $2$ $39.564$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-3}) \) None 1452.3.e.f \(0\) \(6\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+3q^{3}+\beta q^{7}+9q^{9}+\beta q^{13}-2\beta q^{19}+\cdots\)
1452.3.e.g 1452.e 3.b $4$ $39.564$ \(\Q(\sqrt{-3}, \sqrt{-11})\) \(\Q(\sqrt{-11}) \) None 1452.3.e.g \(0\) \(-5\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-1+\beta _{2})q^{3}+\beta _{3}q^{5}+(-3-2\beta _{1}+\cdots)q^{9}+\cdots\)
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