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Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
231.1.h.a 231.h 231.h $1$ $0.115$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-231}) \) None \(-1\) \(-1\) \(1\) \(-1\) \(q-q^{2}-q^{3}+q^{5}+q^{6}-q^{7}+q^{8}+\cdots\)
231.1.h.b 231.h 231.h $1$ $0.115$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-231}) \) None \(-1\) \(1\) \(-1\) \(1\) \(q-q^{2}+q^{3}-q^{5}-q^{6}+q^{7}+q^{8}+\cdots\)
231.1.h.c 231.h 231.h $1$ $0.115$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-231}) \) None \(1\) \(-1\) \(1\) \(1\) \(q+q^{2}-q^{3}+q^{5}-q^{6}+q^{7}-q^{8}+\cdots\)
231.1.h.d 231.h 231.h $1$ $0.115$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-231}) \) None \(1\) \(1\) \(-1\) \(-1\) \(q+q^{2}+q^{3}-q^{5}+q^{6}-q^{7}-q^{8}+\cdots\)
1155.1.e.a 1155.e 1155.e $2$ $0.576$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-231}) \) \(\Q(\sqrt{165}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+q^{4}-iq^{5}+iq^{7}-q^{9}-q^{11}+\cdots\)
1155.1.e.b 1155.e 1155.e $2$ $0.576$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-231}) \) \(\Q(\sqrt{165}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+q^{4}-iq^{5}-iq^{7}-q^{9}+q^{11}+\cdots\)
1155.1.e.c 1155.e 1155.e $4$ $0.576$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-231}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}^{2}+\zeta_{12}^{4})q^{2}+\zeta_{12}^{3}q^{3}+(-1+\cdots)q^{4}+\cdots\)
1155.1.e.d 1155.e 1155.e $4$ $0.576$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-231}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{2}+\zeta_{12}^{3}q^{3}+\cdots\)
1617.1.k.a 1617.k 231.k $2$ $0.807$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-231}) \) None \(-1\) \(-1\) \(1\) \(0\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}q^{5}+q^{6}-q^{8}+\cdots\)
1617.1.k.b 1617.k 231.k $2$ $0.807$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-231}) \) None \(-1\) \(1\) \(-1\) \(0\) \(q-\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{5}-q^{6}-q^{8}+\cdots\)
1617.1.k.c 1617.k 231.k $2$ $0.807$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-231}) \) None \(1\) \(-1\) \(1\) \(0\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}q^{5}-q^{6}+q^{8}+\cdots\)
1617.1.k.d 1617.k 231.k $2$ $0.807$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-231}) \) None \(1\) \(1\) \(-1\) \(0\) \(q+\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{5}+q^{6}+q^{8}+\cdots\)
1848.1.b.a 1848.b 1848.b $2$ $0.922$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-231}) \) \(\Q(\sqrt{154}) \) \(0\) \(0\) \(0\) \(-2\) \(q-iq^{2}-iq^{3}-q^{4}-iq^{5}-q^{6}-q^{7}+\cdots\)
1848.1.b.b 1848.b 1848.b $2$ $0.922$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-231}) \) \(\Q(\sqrt{154}) \) \(0\) \(0\) \(0\) \(2\) \(q+iq^{2}-iq^{3}-q^{4}-iq^{5}+q^{6}+q^{7}+\cdots\)
1848.1.b.c 1848.b 1848.b $4$ $0.922$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-231}) \) None \(0\) \(0\) \(0\) \(4\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}+\cdots\)
1848.1.b.d 1848.b 1848.b $4$ $0.922$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-231}) \) None \(0\) \(0\) \(0\) \(-4\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{4}q^{4}+\cdots\)
2079.1.h.a 2079.h 231.h $3$ $1.038$ \(\Q(\zeta_{18})^+\) $D_{9}$ \(\Q(\sqrt{-231}) \) None \(0\) \(0\) \(0\) \(-3\) \(q+\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+\beta _{1}q^{5}+\cdots\)
2079.1.h.b 2079.h 231.h $3$ $1.038$ \(\Q(\zeta_{18})^+\) $D_{9}$ \(\Q(\sqrt{-231}) \) None \(0\) \(0\) \(0\) \(-3\) \(q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}-\beta _{1}q^{5}+\cdots\)
2079.1.h.c 2079.h 231.h $3$ $1.038$ \(\Q(\zeta_{18})^+\) $D_{9}$ \(\Q(\sqrt{-231}) \) None \(0\) \(0\) \(0\) \(3\) \(q+\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}-\beta _{1}q^{5}+\cdots\)
2079.1.h.d 2079.h 231.h $3$ $1.038$ \(\Q(\zeta_{18})^+\) $D_{9}$ \(\Q(\sqrt{-231}) \) None \(0\) \(0\) \(0\) \(3\) \(q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+\beta _{1}q^{5}+\cdots\)
2541.1.r.a 2541.r 231.r $4$ $1.268$ \(\Q(\zeta_{10})\) $D_{3}$ \(\Q(\sqrt{-231}) \) None \(-1\) \(-1\) \(1\) \(1\) \(q-\zeta_{10}q^{2}-\zeta_{10}^{3}q^{3}-\zeta_{10}^{4}q^{5}+\zeta_{10}^{4}q^{6}+\cdots\)
2541.1.r.b 2541.r 231.r $4$ $1.268$ \(\Q(\zeta_{10})\) $D_{3}$ \(\Q(\sqrt{-231}) \) None \(-1\) \(1\) \(-1\) \(-1\) \(q-\zeta_{10}q^{2}+\zeta_{10}^{3}q^{3}+\zeta_{10}^{4}q^{5}-\zeta_{10}^{4}q^{6}+\cdots\)
2541.1.r.c 2541.r 231.r $4$ $1.268$ \(\Q(\zeta_{10})\) $D_{3}$ \(\Q(\sqrt{-231}) \) None \(1\) \(-1\) \(1\) \(-1\) \(q+\zeta_{10}q^{2}-\zeta_{10}^{3}q^{3}-\zeta_{10}^{4}q^{5}-\zeta_{10}^{4}q^{6}+\cdots\)
2541.1.r.d 2541.r 231.r $4$ $1.268$ \(\Q(\zeta_{10})\) $D_{3}$ \(\Q(\sqrt{-231}) \) None \(1\) \(1\) \(-1\) \(1\) \(q+\zeta_{10}q^{2}+\zeta_{10}^{3}q^{3}+\zeta_{10}^{4}q^{5}+\zeta_{10}^{4}q^{6}+\cdots\)
2772.1.h.c 2772.h 308.g $2$ $1.383$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-21}) \), \(\Q(\sqrt{-231}) \) \(\Q(\sqrt{11}) \) \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-iq^{5}+iq^{7}-q^{8}+2iq^{10}+\cdots\)
2772.1.h.f 2772.h 308.g $2$ $1.383$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-21}) \), \(\Q(\sqrt{-231}) \) \(\Q(\sqrt{11}) \) \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}-iq^{5}-iq^{7}+q^{8}-2iq^{10}+\cdots\)
2772.1.h.g 2772.h 308.g $4$ $1.383$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-231}) \) None \(-2\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{4}q^{2}-\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}+\cdots\)
2772.1.h.h 2772.h 308.g $4$ $1.383$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-231}) \) None \(2\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{4}q^{2}-\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}+\cdots\)
3003.1.b.a 3003.b 3003.b $2$ $1.499$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-143}) \), \(\Q(\sqrt{-231}) \) \(\Q(\sqrt{273}) \) \(0\) \(-2\) \(0\) \(0\) \(q-iq^{2}-q^{3}-3q^{4}+2iq^{6}-iq^{7}+\cdots\)
3003.1.b.b 3003.b 3003.b $2$ $1.499$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-143}) \), \(\Q(\sqrt{-231}) \) \(\Q(\sqrt{273}) \) \(0\) \(2\) \(0\) \(0\) \(q-iq^{2}+q^{3}-3q^{4}-2iq^{6}+iq^{7}+\cdots\)
3003.1.b.c 3003.b 3003.b $4$ $1.499$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-231}) \) None \(0\) \(-4\) \(0\) \(0\) \(q-\zeta_{12}^{3}q^{2}-q^{3}+(-\zeta_{12}^{2}-\zeta_{12}^{4}+\cdots)q^{5}+\cdots\)
3003.1.b.d 3003.b 3003.b $4$ $1.499$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-231}) \) None \(0\) \(4\) \(0\) \(0\) \(q-\zeta_{12}^{3}q^{2}+q^{3}+(-\zeta_{12}^{2}-\zeta_{12}^{4}+\cdots)q^{5}+\cdots\)
3003.1.ce.a 3003.ce 3003.be $6$ $1.499$ \(\Q(\zeta_{18})\) $D_{9}$ \(\Q(\sqrt{-231}) \) None \(0\) \(-3\) \(0\) \(-3\) \(q+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{2}+\zeta_{18}^{6}q^{3}+(-\zeta_{18}^{3}+\cdots)q^{4}+\cdots\)
3003.1.ce.b 3003.ce 3003.be $6$ $1.499$ \(\Q(\zeta_{18})\) $D_{9}$ \(\Q(\sqrt{-231}) \) None \(0\) \(-3\) \(0\) \(3\) \(q+(\zeta_{18}^{5}+\zeta_{18}^{7})q^{2}+\zeta_{18}^{6}q^{3}+(-\zeta_{18}+\cdots)q^{4}+\cdots\)
3003.1.ce.c 3003.ce 3003.be $6$ $1.499$ \(\Q(\zeta_{18})\) $D_{9}$ \(\Q(\sqrt{-231}) \) None \(0\) \(3\) \(0\) \(-3\) \(q+(\zeta_{18}-\zeta_{18}^{2})q^{2}-\zeta_{18}^{6}q^{3}+(\zeta_{18}^{2}+\cdots)q^{4}+\cdots\)
3003.1.ce.d 3003.ce 3003.be $6$ $1.499$ \(\Q(\zeta_{18})\) $D_{9}$ \(\Q(\sqrt{-231}) \) None \(0\) \(3\) \(0\) \(3\) \(q+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{2}-\zeta_{18}^{6}q^{3}+(-\zeta_{18}^{3}+\cdots)q^{4}+\cdots\)
3003.1.cj.a 3003.cj 3003.bj $12$ $1.499$ \(\Q(\zeta_{36})\) $D_{18}$ \(\Q(\sqrt{-231}) \) None \(0\) \(-6\) \(0\) \(0\) \(q+(-\zeta_{36}^{5}+\zeta_{36}^{7})q^{2}-\zeta_{36}^{6}q^{3}+\cdots\)
3003.1.cj.b 3003.cj 3003.bj $12$ $1.499$ \(\Q(\zeta_{36})\) $D_{18}$ \(\Q(\sqrt{-231}) \) None \(0\) \(6\) \(0\) \(0\) \(q+(-\zeta_{36}^{5}+\zeta_{36}^{7})q^{2}+\zeta_{36}^{6}q^{3}+\cdots\)
3465.1.u.a 3465.u 385.l $4$ $1.729$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-231}) \) None \(-4\) \(0\) \(0\) \(0\) \(q+(-1+\zeta_{8}^{2})q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+\cdots\)
3465.1.u.b 3465.u 385.l $4$ $1.729$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-231}) \) None \(4\) \(0\) \(0\) \(0\) \(q+(1-\zeta_{8}^{2})q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+\cdots\)
3465.1.u.c 3465.u 385.l $8$ $1.729$ \(\Q(\zeta_{24})\) $D_{12}$ \(\Q(\sqrt{-231}) \) None \(-4\) \(0\) \(0\) \(0\) \(q+(-\zeta_{24}^{2}-\zeta_{24}^{4})q^{2}+(\zeta_{24}^{4}+\zeta_{24}^{6}+\cdots)q^{4}+\cdots\)
3465.1.u.d 3465.u 385.l $8$ $1.729$ \(\Q(\zeta_{24})\) $D_{12}$ \(\Q(\sqrt{-231}) \) None \(4\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}^{2}+\zeta_{24}^{4})q^{2}+(\zeta_{24}^{4}+\zeta_{24}^{6}+\cdots)q^{4}+\cdots\)
3696.1.bb.a 3696.bb 231.h $1$ $1.845$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-231}) \) None \(0\) \(-1\) \(-1\) \(-1\) \(q-q^{3}-q^{5}-q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
3696.1.bb.b 3696.bb 231.h $1$ $1.845$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-231}) \) None \(0\) \(-1\) \(-1\) \(1\) \(q-q^{3}-q^{5}+q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
3696.1.bb.c 3696.bb 231.h $1$ $1.845$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-231}) \) None \(0\) \(1\) \(1\) \(-1\) \(q+q^{3}+q^{5}-q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
3696.1.bb.d 3696.bb 231.h $1$ $1.845$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-231}) \) None \(0\) \(1\) \(1\) \(1\) \(q+q^{3}+q^{5}+q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
3696.1.bm.a 3696.bm 3696.am $4$ $1.845$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-231}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{2}-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{2}q^{6}+\cdots\)
3696.1.bm.b 3696.bm 3696.am $4$ $1.845$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-231}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{2}q^{6}+\cdots\)
3696.1.bm.c 3696.bm 3696.am $8$ $1.845$ \(\Q(\zeta_{24})\) $D_{12}$ \(\Q(\sqrt{-231}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{5}q^{2}+\zeta_{24}^{9}q^{3}+\zeta_{24}^{10}q^{4}+\cdots\)
3696.1.bm.d 3696.bm 3696.am $8$ $1.845$ \(\Q(\zeta_{24})\) $D_{12}$ \(\Q(\sqrt{-231}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{3}q^{3}-\zeta_{24}^{2}q^{4}+\cdots\)
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