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Label Char Prim Dim $A$ Field CM RM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2900.1.e.a 2900.e 580.e $2$ $1.447$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-29}) \) None 116.1.d.a \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{8}-q^{11}+\cdots\)
2900.1.e.b 2900.e 580.e $2$ $1.447$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-29}) \) None 116.1.d.a \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{8}+q^{11}+\cdots\)
2900.1.g.a 2900.g 116.d $1$ $1.447$ \(\Q\) \(\Q(\sqrt{-29}) \) None 116.1.d.a \(-1\) \(1\) \(0\) \(0\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}-q^{11}+\cdots\)
2900.1.g.b 2900.g 116.d $1$ $1.447$ \(\Q\) \(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-29}) \) \(\Q(\sqrt{145}) \) 580.1.e.c \(-1\) \(2\) \(0\) \(0\) \(q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{8}+3q^{9}+\cdots\)
2900.1.g.c 2900.g 116.d $1$ $1.447$ \(\Q\) \(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-29}) \) \(\Q(\sqrt{145}) \) 580.1.e.c \(1\) \(-2\) \(0\) \(0\) \(q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{8}+3q^{9}+\cdots\)
2900.1.g.d 2900.g 116.d $1$ $1.447$ \(\Q\) \(\Q(\sqrt{-29}) \) None 116.1.d.a \(1\) \(-1\) \(0\) \(0\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{11}+\cdots\)
2900.1.g.e 2900.g 116.d $2$ $1.447$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-29}) \) None 580.1.e.d \(-2\) \(-2\) \(0\) \(0\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}-\beta q^{11}+\cdots\)
2900.1.g.f 2900.g 116.d $2$ $1.447$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-145}) \) \(\Q(\sqrt{145}) \) 580.1.e.a \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{8}-q^{9}+q^{16}+iq^{17}+\cdots\)
2900.1.g.g 2900.g 116.d $2$ $1.447$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-29}) \) None 580.1.e.d \(2\) \(2\) \(0\) \(0\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}-\beta q^{11}+\cdots\)
2900.1.i.a 2900.i 580.i $2$ $1.447$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) None 2900.1.i.a \(-2\) \(0\) \(0\) \(2\) \(q-q^{2}-iq^{3}+q^{4}+2iq^{6}+(1-i+\cdots)q^{7}+\cdots\)
2900.1.i.b 2900.i 580.i $2$ $1.447$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None 580.1.i.a \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{8}+q^{9}+(-1-i+\cdots)q^{13}+\cdots\)
2900.1.i.c 2900.i 580.i $2$ $1.447$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) None 2900.1.i.a \(2\) \(0\) \(0\) \(-2\) \(q+q^{2}+iq^{3}+q^{4}+2iq^{6}+(-1+i+\cdots)q^{7}+\cdots\)
2900.1.t.a 2900.t 580.t $2$ $1.447$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None 580.1.i.a \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}-q^{9}+(1-i)q^{13}+\cdots\)
2900.1.t.b 2900.t 580.t $2$ $1.447$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) None 2900.1.i.a \(0\) \(-4\) \(0\) \(2\) \(q-iq^{2}-q^{3}-q^{4}+2iq^{6}+(1+i+\cdots)q^{7}+\cdots\)
2900.1.t.c 2900.t 580.t $2$ $1.447$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) None 2900.1.i.a \(0\) \(4\) \(0\) \(-2\) \(q+iq^{2}+q^{3}-q^{4}+2iq^{6}+(-1-i+\cdots)q^{7}+\cdots\)
2900.1.w.a 2900.w 2900.w $4$ $1.447$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-29}) \) None 2900.1.w.a \(-1\) \(3\) \(-1\) \(0\) \(q+\zeta_{10}^{2}q^{2}+(1-\zeta_{10}^{3})q^{3}+\zeta_{10}^{4}q^{4}+\cdots\)
2900.1.w.b 2900.w 2900.w $4$ $1.447$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-29}) \) None 2900.1.w.a \(1\) \(-3\) \(-1\) \(0\) \(q-\zeta_{10}^{2}q^{2}+(-1+\zeta_{10}^{3})q^{3}+\zeta_{10}^{4}q^{4}+\cdots\)
2900.1.w.c 2900.w 2900.w $8$ $1.447$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-29}) \) None 2900.1.w.c \(-2\) \(-3\) \(1\) \(0\) \(q+\zeta_{30}^{6}q^{2}+(\zeta_{30}^{4}-\zeta_{30}^{5})q^{3}+\zeta_{30}^{12}q^{4}+\cdots\)
2900.1.w.d 2900.w 2900.w $8$ $1.447$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-29}) \) None 2900.1.w.c \(2\) \(3\) \(1\) \(0\) \(q-\zeta_{30}^{6}q^{2}+(-\zeta_{30}^{10}-\zeta_{30}^{14})q^{3}+\cdots\)
2900.1.bb.a 2900.bb 2900.ab $4$ $1.447$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-1}) \) None 2900.1.bb.a \(-1\) \(0\) \(1\) \(0\) \(q+\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}-\zeta_{10}^{2}q^{5}+\cdots\)
2900.1.bb.b 2900.bb 2900.ab $4$ $1.447$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-1}) \) None 2900.1.bb.a \(1\) \(0\) \(1\) \(0\) \(q-\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}-\zeta_{10}^{2}q^{5}+\cdots\)
2900.1.bb.c 2900.bb 2900.ab $8$ $1.447$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-29}) \) None 2900.1.bb.c \(0\) \(0\) \(-2\) \(0\) \(q-\zeta_{20}^{3}q^{2}+(\zeta_{20}^{5}-\zeta_{20}^{7})q^{3}+\zeta_{20}^{6}q^{4}+\cdots\)
2900.1.bb.d 2900.bb 2900.ab $16$ $1.447$ \(\Q(\zeta_{60})\) \(\Q(\sqrt{-29}) \) None 2900.1.bb.d \(0\) \(0\) \(2\) \(0\) \(q-\zeta_{60}^{21}q^{2}+(-\zeta_{60}^{5}+\zeta_{60}^{19})q^{3}+\cdots\)
2900.1.bd.a 2900.bd 580.v $12$ $1.447$ \(\Q(\zeta_{28})\) \(\Q(\sqrt{-1}) \) None 116.1.j.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{28}q^{2}+\zeta_{28}^{2}q^{4}+\zeta_{28}^{3}q^{8}+\zeta_{28}^{10}q^{9}+\cdots\)
2900.1.be.a 2900.be 116.h $6$ $1.447$ \(\Q(\zeta_{14})\) \(\Q(\sqrt{-5}) \) None 580.1.y.c \(-1\) \(2\) \(0\) \(-7\) \(q+\zeta_{14}^{6}q^{2}+(\zeta_{14}+\zeta_{14}^{3})q^{3}-\zeta_{14}^{5}q^{4}+\cdots\)
2900.1.be.b 2900.be 116.h $6$ $1.447$ \(\Q(\zeta_{14})\) \(\Q(\sqrt{-5}) \) None 580.1.y.c \(1\) \(-2\) \(0\) \(7\) \(q-\zeta_{14}^{6}q^{2}+(-\zeta_{14}-\zeta_{14}^{3})q^{3}-\zeta_{14}^{5}q^{4}+\cdots\)
2900.1.be.c 2900.be 116.h $12$ $1.447$ \(\Q(\zeta_{28})\) \(\Q(\sqrt{-1}) \) None 580.1.y.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{28}^{5}q^{2}+\zeta_{28}^{10}q^{4}-\zeta_{28}q^{8}+\cdots\)
2900.1.bj.a 2900.bj 116.j $6$ $1.447$ \(\Q(\zeta_{14})\) \(\Q(\sqrt{-1}) \) None 116.1.j.a \(1\) \(0\) \(0\) \(0\) \(q-\zeta_{14}^{2}q^{2}+\zeta_{14}^{4}q^{4}-\zeta_{14}^{6}q^{8}+\cdots\)
2900.1.bj.b 2900.bj 116.j $12$ $1.447$ \(\Q(\zeta_{28})\) \(\Q(\sqrt{-5}) \) None 580.1.v.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{28}^{11}q^{2}+(-\zeta_{28}^{3}+\zeta_{28}^{9})q^{3}+\cdots\)
2900.1.bk.a 2900.bk 2900.ak $8$ $1.447$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-1}) \) None 2900.1.bk.a \(-2\) \(0\) \(0\) \(0\) \(q+\zeta_{20}^{4}q^{2}+\zeta_{20}^{8}q^{4}-\zeta_{20}^{7}q^{5}+\cdots\)
2900.1.bv.a 2900.bv 2900.av $8$ $1.447$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-1}) \) None 2900.1.bk.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}^{3}q^{2}+\zeta_{20}^{6}q^{4}+\zeta_{20}^{9}q^{5}+\cdots\)
2900.1.bx.a 2900.bx 580.ad $12$ $1.447$ \(\Q(\zeta_{28})\) \(\Q(\sqrt{-5}) \) None 2900.1.bx.a \(0\) \(-4\) \(0\) \(-12\) \(q-\zeta_{28}^{11}q^{2}+(-\zeta_{28}^{2}-\zeta_{28}^{10})q^{3}+\cdots\)
2900.1.bx.b 2900.bx 580.ad $12$ $1.447$ \(\Q(\zeta_{28})\) \(\Q(\sqrt{-5}) \) None 2900.1.bx.a \(0\) \(4\) \(0\) \(12\) \(q+\zeta_{28}^{11}q^{2}+(\zeta_{28}^{2}+\zeta_{28}^{10})q^{3}+\cdots\)
2900.1.bx.c 2900.bx 580.ad $12$ $1.447$ \(\Q(\zeta_{28})\) \(\Q(\sqrt{-1}) \) None 580.1.bd.a \(2\) \(0\) \(0\) \(0\) \(q-\zeta_{28}^{4}q^{2}+\zeta_{28}^{8}q^{4}-\zeta_{28}^{12}q^{8}+\cdots\)
2900.1.cg.a 2900.cg 580.am $12$ $1.447$ \(\Q(\zeta_{28})\) \(\Q(\sqrt{-5}) \) None 2900.1.bx.a \(-2\) \(0\) \(0\) \(2\) \(q-\zeta_{28}^{6}q^{2}+(-\zeta_{28}+\zeta_{28}^{3})q^{3}+\zeta_{28}^{12}q^{4}+\cdots\)
2900.1.cg.b 2900.cg 580.am $12$ $1.447$ \(\Q(\zeta_{28})\) \(\Q(\sqrt{-1}) \) None 580.1.bd.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{28}^{13}q^{2}-\zeta_{28}^{12}q^{4}+\zeta_{28}^{11}q^{8}+\cdots\)
2900.1.cg.c 2900.cg 580.am $12$ $1.447$ \(\Q(\zeta_{28})\) \(\Q(\sqrt{-5}) \) None 2900.1.bx.a \(2\) \(0\) \(0\) \(-2\) \(q+\zeta_{28}^{6}q^{2}+(\zeta_{28}-\zeta_{28}^{3})q^{3}+\zeta_{28}^{12}q^{4}+\cdots\)
2900.1.ck.a 2900.ck 2900.bk $24$ $1.447$ \(\Q(\zeta_{35})\) \(\Q(\sqrt{-1}) \) None 2900.1.ck.a \(-1\) \(0\) \(-1\) \(0\) \(q+\zeta_{70}^{19}q^{2}-\zeta_{70}^{3}q^{4}-\zeta_{70}^{32}q^{5}+\cdots\)
2900.1.ck.b 2900.ck 2900.bk $24$ $1.447$ \(\Q(\zeta_{35})\) \(\Q(\sqrt{-1}) \) None 2900.1.ck.a \(1\) \(0\) \(-1\) \(0\) \(q-\zeta_{70}^{19}q^{2}-\zeta_{70}^{3}q^{4}+\zeta_{70}^{27}q^{5}+\cdots\)
2900.1.cl.a 2900.cl 2900.bl $24$ $1.447$ \(\Q(\zeta_{35})\) \(\Q(\sqrt{-1}) \) None 2900.1.cl.a \(1\) \(0\) \(1\) \(0\) \(q+\zeta_{70}^{8}q^{2}+\zeta_{70}^{16}q^{4}+\zeta_{70}^{4}q^{5}+\cdots\)
2900.1.cl.b 2900.cl 2900.bl $24$ $1.447$ \(\Q(\zeta_{35})\) \(\Q(\sqrt{-1}) \) None 2900.1.cl.a \(1\) \(0\) \(1\) \(0\) \(q+\zeta_{70}^{8}q^{2}+\zeta_{70}^{16}q^{4}-\zeta_{70}^{19}q^{5}+\cdots\)
2900.1.cr.a 2900.cr 2900.br $48$ $1.447$ \(\Q(\zeta_{140})\) \(\Q(\sqrt{-1}) \) None 2900.1.cr.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{140}^{53}q^{2}-\zeta_{140}^{36}q^{4}-\zeta_{140}^{69}q^{5}+\cdots\)
2900.1.da.a 2900.da 2900.ca $48$ $1.447$ \(\Q(\zeta_{140})\) \(\Q(\sqrt{-1}) \) None 2900.1.cr.a \(2\) \(0\) \(0\) \(0\) \(q+\zeta_{140}^{8}q^{2}+\zeta_{140}^{16}q^{4}-\zeta_{140}^{39}q^{5}+\cdots\)
2900.2.a.a 2900.a 1.a $1$ $23.157$ \(\Q\) None None 116.2.a.c \(0\) \(-2\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-4q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots\)
2900.2.a.b 2900.a 1.a $1$ $23.157$ \(\Q\) None None 116.2.a.b \(0\) \(-1\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{7}-2q^{9}+3q^{11}-5q^{13}+\cdots\)
2900.2.a.c 2900.a 1.a $1$ $23.157$ \(\Q\) None None 580.2.a.a \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-3q^{9}-2q^{11}+2q^{13}-2q^{19}+8q^{23}+\cdots\)
2900.2.a.d 2900.a 1.a $1$ $23.157$ \(\Q\) None None 580.2.a.b \(0\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{7}-3q^{9}-4q^{11}+6q^{13}+4q^{17}+\cdots\)
2900.2.a.e 2900.a 1.a $1$ $23.157$ \(\Q\) None None 116.2.a.a \(0\) \(3\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-4q^{7}+6q^{9}-q^{11}+3q^{13}+\cdots\)
2900.2.a.f 2900.a 1.a $3$ $23.157$ 3.3.148.1 None None 580.2.a.d \(0\) \(-2\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-1+\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots\)
2900.2.a.g 2900.a 1.a $3$ $23.157$ 3.3.564.1 None None 580.2.a.c \(0\) \(-2\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+(1-\beta _{2})q^{7}+(4+\beta _{1}+\cdots)q^{9}+\cdots\)
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