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Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
204.1.g.a 204.g 51.c $1$ $0.102$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-51}) \) None \(0\) \(-1\) \(1\) \(0\) \(q-q^{3}+q^{5}+q^{9}+q^{11}-q^{13}-q^{15}+\cdots\)
204.1.g.b 204.g 51.c $1$ $0.102$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-51}) \) None \(0\) \(1\) \(-1\) \(0\) \(q+q^{3}-q^{5}+q^{9}-q^{11}-q^{13}-q^{15}+\cdots\)
255.1.h.e 255.h 255.h $2$ $0.127$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-51}) \) \(\Q(\sqrt{85}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-q^{4}-iq^{5}-q^{9}+iq^{12}+\cdots\)
459.1.c.a 459.c 51.c $1$ $0.229$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(-1\) \(0\) \(q+q^{4}-q^{5}+2q^{11}-q^{13}+q^{16}+\cdots\)
459.1.c.b 459.c 51.c $1$ $0.229$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(1\) \(0\) \(q+q^{4}+q^{5}-2q^{11}-q^{13}+q^{16}+\cdots\)
561.1.u.a 561.u 561.u $4$ $0.280$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-51}) \) None \(0\) \(-1\) \(3\) \(0\) \(q+\zeta_{10}^{2}q^{3}-\zeta_{10}^{3}q^{4}+(1+\zeta_{10}^{2}+\cdots)q^{5}+\cdots\)
561.1.u.b 561.u 561.u $4$ $0.280$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-51}) \) None \(0\) \(1\) \(-3\) \(0\) \(q-\zeta_{10}^{2}q^{3}-\zeta_{10}^{3}q^{4}+(-1-\zeta_{10}^{2}+\cdots)q^{5}+\cdots\)
663.1.g.a 663.g 663.g $1$ $0.331$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-51}) \), \(\Q(\sqrt{-663}) \) \(\Q(\sqrt{13}) \) \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}-q^{4}+q^{9}+q^{12}+q^{13}+q^{16}+\cdots\)
663.1.g.b 663.g 663.g $1$ $0.331$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-51}) \), \(\Q(\sqrt{-663}) \) \(\Q(\sqrt{13}) \) \(0\) \(1\) \(0\) \(0\) \(q+q^{3}-q^{4}+q^{9}-q^{12}+q^{13}+q^{16}+\cdots\)
663.1.v.a 663.v 663.v $2$ $0.331$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-51}) \) None \(0\) \(-1\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{3}+\zeta_{6}q^{4}+(-\zeta_{6}-\zeta_{6}^{2})q^{5}+\cdots\)
663.1.v.b 663.v 663.v $2$ $0.331$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-51}) \) None \(0\) \(1\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{3}+\zeta_{6}q^{4}+(\zeta_{6}+\zeta_{6}^{2})q^{5}+\cdots\)
663.1.bb.a 663.bb 663.ab $2$ $0.331$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-51}) \) None \(0\) \(-1\) \(-2\) \(0\) \(q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-q^{5}+\zeta_{6}^{2}q^{9}+\cdots\)
663.1.bb.b 663.bb 663.ab $2$ $0.331$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-51}) \) None \(0\) \(1\) \(2\) \(0\) \(q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+\zeta_{6}^{2}q^{9}+\cdots\)
765.1.o.a 765.o 85.g $4$ $0.382$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+(\zeta_{8}+\zeta_{8}^{3})q^{11}+\cdots\)
816.1.m.a 816.m 51.c $1$ $0.407$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-51}) \) None \(0\) \(-1\) \(-1\) \(0\) \(q-q^{3}-q^{5}+q^{9}+q^{11}-q^{13}+q^{15}+\cdots\)
816.1.m.b 816.m 51.c $1$ $0.407$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-51}) \) None \(0\) \(1\) \(1\) \(0\) \(q+q^{3}+q^{5}+q^{9}-q^{11}-q^{13}+q^{15}+\cdots\)
969.1.q.a 969.q 969.q $2$ $0.484$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-51}) \) None \(0\) \(-1\) \(1\) \(0\) \(q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{9}+\cdots\)
969.1.q.b 969.q 969.q $2$ $0.484$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-51}) \) None \(0\) \(1\) \(-1\) \(0\) \(q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+\zeta_{6}^{2}q^{9}+\cdots\)
969.1.bm.a 969.bm 969.am $6$ $0.484$ \(\Q(\zeta_{18})\) $D_{9}$ \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(-6\) \(0\) \(q+\zeta_{18}^{5}q^{3}-\zeta_{18}^{7}q^{4}+(-1-\zeta_{18}^{4}+\cdots)q^{5}+\cdots\)
969.1.bm.b 969.bm 969.am $6$ $0.484$ \(\Q(\zeta_{18})\) $D_{9}$ \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(6\) \(0\) \(q-\zeta_{18}^{5}q^{3}-\zeta_{18}^{7}q^{4}+(1+\zeta_{18}^{4}+\cdots)q^{5}+\cdots\)
1020.1.o.a 1020.o 255.h $4$ $0.509$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{3}q^{3}-\zeta_{12}q^{5}-q^{9}+(-\zeta_{12}+\cdots)q^{11}+\cdots\)
1173.1.y.a 1173.y 1173.y $10$ $0.585$ \(\Q(\zeta_{22})\) $D_{11}$ \(\Q(\sqrt{-51}) \) None \(0\) \(-1\) \(-2\) \(0\) \(q+\zeta_{22}^{6}q^{3}-\zeta_{22}^{7}q^{4}+(\zeta_{22}^{2}-\zeta_{22}^{7}+\cdots)q^{5}+\cdots\)
1173.1.y.b 1173.y 1173.y $10$ $0.585$ \(\Q(\zeta_{22})\) $D_{11}$ \(\Q(\sqrt{-51}) \) None \(0\) \(1\) \(2\) \(0\) \(q-\zeta_{22}^{6}q^{3}-\zeta_{22}^{7}q^{4}+(-\zeta_{22}^{2}+\zeta_{22}^{7}+\cdots)q^{5}+\cdots\)
1275.1.c.a 1275.c 51.c $1$ $0.636$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-51}) \) \(\Q(\sqrt{85}) \) \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}+q^{4}+q^{9}-q^{12}+q^{16}+q^{17}+\cdots\)
1275.1.c.b 1275.c 51.c $1$ $0.636$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-51}) \) \(\Q(\sqrt{85}) \) \(0\) \(1\) \(0\) \(0\) \(q+q^{3}+q^{4}+q^{9}+q^{12}+q^{16}-q^{17}+\cdots\)
1275.1.bf.a 1275.bf 1275.af $8$ $0.636$ \(\Q(\zeta_{20})\) $D_{10}$ \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}^{9}q^{3}-\zeta_{20}^{4}q^{4}+\zeta_{20}^{5}q^{5}+\cdots\)
1275.1.bg.a 1275.bg 1275.ag $4$ $0.636$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-51}) \) None \(0\) \(-1\) \(4\) \(0\) \(q-\zeta_{10}^{3}q^{3}-\zeta_{10}^{3}q^{4}+q^{5}-\zeta_{10}q^{9}+\cdots\)
1275.1.bg.b 1275.bg 1275.ag $4$ $0.636$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-51}) \) None \(0\) \(1\) \(-4\) \(0\) \(q+\zeta_{10}^{3}q^{3}-\zeta_{10}^{3}q^{4}-q^{5}-\zeta_{10}q^{9}+\cdots\)
1377.1.i.a 1377.i 153.i $2$ $0.687$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(-1\) \(0\) \(q-\zeta_{6}q^{4}-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{11}+\zeta_{6}q^{13}+\cdots\)
1377.1.i.b 1377.i 153.i $2$ $0.687$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(1\) \(0\) \(q-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{11}+\zeta_{6}q^{13}+\cdots\)
1479.1.h.a 1479.h 1479.h $2$ $0.738$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-51}) \), \(\Q(\sqrt{-87}) \) \(\Q(\sqrt{493}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-q^{4}-q^{9}+iq^{11}+iq^{12}+\cdots\)
1479.1.bd.a 1479.bd 1479.ad $12$ $0.738$ \(\Q(\zeta_{28})\) $D_{14}$ \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{28}^{3}q^{3}-\zeta_{28}^{4}q^{4}+(-\zeta_{28}^{5}+\zeta_{28}^{13}+\cdots)q^{5}+\cdots\)
1479.1.bh.a 1479.bh 1479.ah $6$ $0.738$ \(\Q(\zeta_{14})\) $D_{7}$ \(\Q(\sqrt{-51}) \) None \(0\) \(-1\) \(-2\) \(0\) \(q+\zeta_{14}^{6}q^{3}-\zeta_{14}q^{4}+(-\zeta_{14}^{3}-\zeta_{14}^{5}+\cdots)q^{5}+\cdots\)
1479.1.bh.b 1479.bh 1479.ah $6$ $0.738$ \(\Q(\zeta_{14})\) $D_{7}$ \(\Q(\sqrt{-51}) \) None \(0\) \(1\) \(2\) \(0\) \(q-\zeta_{14}^{6}q^{3}-\zeta_{14}q^{4}+(\zeta_{14}^{3}+\zeta_{14}^{5}+\cdots)q^{5}+\cdots\)
1683.1.b.a 1683.b 187.b $1$ $0.840$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-51}) \), \(\Q(\sqrt{-187}) \) \(\Q(\sqrt{33}) \) \(0\) \(0\) \(0\) \(0\) \(q+q^{4}-q^{11}+q^{16}+q^{17}+q^{25}+\cdots\)
1683.1.b.b 1683.b 187.b $1$ $0.840$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-51}) \), \(\Q(\sqrt{-187}) \) \(\Q(\sqrt{33}) \) \(0\) \(0\) \(0\) \(0\) \(q+q^{4}+q^{11}+q^{16}-q^{17}+q^{25}+\cdots\)
1683.1.bf.a 1683.bf 187.l $4$ $0.840$ \(\Q(\zeta_{10})\) $D_{10}$ \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(-5\) \(0\) \(q+\zeta_{10}^{2}q^{4}+(-1-\zeta_{10}^{3})q^{5}+\zeta_{10}^{4}q^{11}+\cdots\)
1683.1.bf.b 1683.bf 187.l $4$ $0.840$ \(\Q(\zeta_{10})\) $D_{10}$ \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(5\) \(0\) \(q+\zeta_{10}^{2}q^{4}+(1+\zeta_{10}^{3})q^{5}-\zeta_{10}^{4}q^{11}+\cdots\)
1836.1.g.a 1836.g 51.c $1$ $0.916$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-2q^{5}+q^{11}-q^{13}-q^{17}+2q^{19}+\cdots\)
1836.1.g.b 1836.g 51.c $1$ $0.916$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(-1\) \(0\) \(q-q^{5}-q^{11}+2q^{13}+q^{17}-q^{19}+\cdots\)
1836.1.g.c 1836.g 51.c $1$ $0.916$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(1\) \(0\) \(q+q^{5}+q^{11}+2q^{13}-q^{17}-q^{19}+\cdots\)
1836.1.g.d 1836.g 51.c $1$ $0.916$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(2\) \(0\) \(q+2q^{5}-q^{11}-q^{13}+q^{17}+2q^{19}+\cdots\)
1989.1.s.b 1989.s 221.g $2$ $0.993$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{4}+(-1-i)q^{5}+(1-i)q^{11}+\cdots\)
1989.1.s.c 1989.s 221.g $2$ $0.993$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(2\) \(0\) \(q+iq^{4}+(1+i)q^{5}+(-1+i)q^{11}+\cdots\)
1989.1.dg.a 1989.dg 221.w $4$ $0.993$ \(\Q(\zeta_{12})\) $D_{12}$ \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-\zeta_{12}^{5}q^{4}+(-\zeta_{12}-\zeta_{12}^{2})q^{5}+(-1+\cdots)q^{11}+\cdots\)
1989.1.dg.b 1989.dg 221.w $4$ $0.993$ \(\Q(\zeta_{12})\) $D_{12}$ \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(2\) \(0\) \(q-\zeta_{12}^{5}q^{4}+(\zeta_{12}+\zeta_{12}^{2})q^{5}+(1+\zeta_{12}^{5}+\cdots)q^{11}+\cdots\)
2091.1.e.e 2091.e 2091.e $2$ $1.044$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-51}) \), \(\Q(\sqrt{-123}) \) \(\Q(\sqrt{697}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+q^{4}-q^{9}-iq^{11}-iq^{12}+\cdots\)
2091.1.o.a 2091.o 2091.o $4$ $1.044$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}-q^{4}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{9}+\cdots\)
2091.1.bw.a 2091.bw 2091.aw $8$ $1.044$ \(\Q(\zeta_{20})\) $D_{10}$ \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}^{5}q^{3}-\zeta_{20}^{6}q^{4}+(-\zeta_{20}^{5}-\zeta_{20}^{7}+\cdots)q^{5}+\cdots\)
2091.1.bx.a 2091.bx 2091.ax $4$ $1.044$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-51}) \) None \(0\) \(-4\) \(-3\) \(0\) \(q-q^{3}+\zeta_{10}^{2}q^{4}+(-1-\zeta_{10}^{4})q^{5}+\cdots\)
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