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Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2001.1.i.a 2001.i 2001.i $2$ $0.999$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-23}) \) None \(-2\) \(2\) \(0\) \(0\) \(q+(-1+i)q^{2}+q^{3}-iq^{4}+(-1+i+\cdots)q^{6}+\cdots\)
2001.1.i.b 2001.i 2001.i $2$ $0.999$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-23}) \) None \(2\) \(0\) \(0\) \(0\) \(q+(1-i)q^{2}+iq^{3}-iq^{4}+(1+i)q^{6}+\cdots\)
2001.1.i.c 2001.i 2001.i $4$ $0.999$ \(\Q(\zeta_{12})\) $D_{12}$ \(\Q(\sqrt{-23}) \) None \(-2\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}^{4}+\zeta_{12}^{5})q^{2}-\zeta_{12}^{5}q^{3}+(-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
2001.1.i.d 2001.i 2001.i $4$ $0.999$ \(\Q(\zeta_{12})\) $D_{12}$ \(\Q(\sqrt{-23}) \) None \(2\) \(-2\) \(0\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}-\zeta_{12}^{2}q^{3}+(\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
2001.1.bf.a 2001.bf 2001.af $12$ $0.999$ \(\Q(\zeta_{28})\) $D_{28}$ \(\Q(\sqrt{-23}) \) None \(-2\) \(0\) \(0\) \(0\) \(q+(-\zeta_{28}^{7}-\zeta_{28}^{10})q^{2}-\zeta_{28}^{9}q^{3}+\cdots\)
2001.1.bf.b 2001.bf 2001.af $12$ $0.999$ \(\Q(\zeta_{28})\) $D_{28}$ \(\Q(\sqrt{-23}) \) None \(2\) \(-2\) \(0\) \(0\) \(q+(\zeta_{28}^{7}+\zeta_{28}^{10})q^{2}-\zeta_{28}^{6}q^{3}+(-1+\cdots)q^{4}+\cdots\)
2001.1.bf.c 2001.bf 2001.af $24$ $0.999$ \(\Q(\zeta_{84})\) $D_{84}$ \(\Q(\sqrt{-23}) \) None \(-2\) \(2\) \(0\) \(0\) \(q+(-\zeta_{84}^{7}-\zeta_{84}^{20})q^{2}-\zeta_{84}^{26}q^{3}+\cdots\)
2001.1.bf.d 2001.bf 2001.af $24$ $0.999$ \(\Q(\zeta_{84})\) $D_{84}$ \(\Q(\sqrt{-23}) \) None \(2\) \(0\) \(0\) \(0\) \(q+(\zeta_{84}^{7}+\zeta_{84}^{20})q^{2}+\zeta_{84}^{25}q^{3}+\cdots\)
2003.1.b.a 2003.b 2003.b $1$ $1.000$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-2003}) \) None \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}+q^{4}-q^{12}-q^{13}+q^{16}+2q^{19}+\cdots\)
2003.1.b.b 2003.b 2003.b $3$ $1.000$ \(\Q(\zeta_{18})^+\) $D_{9}$ \(\Q(\sqrt{-2003}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+q^{4}+(1+\beta _{2})q^{9}-\beta _{1}q^{12}+\cdots\)
2004.1.g.a 2004.g 2004.g $1$ $1.000$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-167}) \), \(\Q(\sqrt{-501}) \) \(\Q(\sqrt{3}) \) \(-1\) \(-1\) \(0\) \(0\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
2004.1.g.b 2004.g 2004.g $1$ $1.000$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-167}) \), \(\Q(\sqrt{-501}) \) \(\Q(\sqrt{3}) \) \(1\) \(1\) \(0\) \(0\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
2004.1.g.c 2004.g 2004.g $2$ $1.000$ \(\Q(\sqrt{2}) \) $D_{4}$ \(\Q(\sqrt{-501}) \) None \(-2\) \(2\) \(0\) \(0\) \(q-q^{2}+q^{3}+q^{4}-\beta q^{5}-q^{6}-q^{8}+\cdots\)
2004.1.g.d 2004.g 2004.g $2$ $1.000$ \(\Q(\sqrt{2}) \) $D_{4}$ \(\Q(\sqrt{-501}) \) None \(2\) \(-2\) \(0\) \(0\) \(q+q^{2}-q^{3}+q^{4}-\beta q^{5}-q^{6}+q^{8}+\cdots\)
2004.1.g.e 2004.g 2004.g $10$ $1.000$ \(\Q(\zeta_{22})\) $D_{22}$ \(\Q(\sqrt{-167}) \) None \(-1\) \(-1\) \(0\) \(0\) \(q+\zeta_{22}^{6}q^{2}+\zeta_{22}^{2}q^{3}-\zeta_{22}q^{4}+\zeta_{22}^{8}q^{6}+\cdots\)
2004.1.g.f 2004.g 2004.g $10$ $1.000$ \(\Q(\zeta_{22})\) $D_{22}$ \(\Q(\sqrt{-167}) \) None \(1\) \(1\) \(0\) \(0\) \(q-\zeta_{22}^{6}q^{2}+\zeta_{22}^{9}q^{3}-\zeta_{22}q^{4}+\zeta_{22}^{4}q^{6}+\cdots\)
2005.1.g.a 2005.g 2005.g $2$ $1.001$ \(\Q(\sqrt{-1}) \) $D_{4}$ None \(\Q(\sqrt{401}) \) \(2\) \(0\) \(2\) \(-2\) \(q+(1-i)q^{2}-iq^{4}+q^{5}+(-1+i+\cdots)q^{7}+\cdots\)
2005.1.g.b 2005.g 2005.g $8$ $1.001$ \(\Q(\zeta_{20})\) $D_{20}$ None \(\Q(\sqrt{401}) \) \(-2\) \(0\) \(-2\) \(2\) \(q+(-\zeta_{20}+\zeta_{20}^{4})q^{2}+(\zeta_{20}^{2}-\zeta_{20}^{5}+\cdots)q^{4}+\cdots\)
2007.1.d.a 2007.d 223.b $1$ $1.002$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-223}) \) \(\Q(\sqrt{669}) \) \(0\) \(0\) \(0\) \(-2\) \(q-q^{4}-2q^{7}+q^{16}+2q^{19}+q^{25}+\cdots\)
2007.1.d.b 2007.d 223.b $3$ $1.002$ \(\Q(\zeta_{14})^+\) $D_{7}$ \(\Q(\sqrt{-223}) \) None \(1\) \(0\) \(0\) \(-1\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{1}-\beta _{2})q^{7}+\cdots\)
2007.1.d.c 2007.d 223.b $6$ $1.002$ \(\Q(\zeta_{28})^+\) $D_{14}$ \(\Q(\sqrt{-223}) \) None \(0\) \(0\) \(0\) \(2\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)
2007.1.v.a 2007.v 223.f $36$ $1.002$ \(\Q(\zeta_{74})\) $D_{74}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q-\zeta_{74}^{20}q^{4}+(\zeta_{74}^{21}+\zeta_{74}^{27})q^{7}+\cdots\)
2008.1.c.a 2008.c 2008.c $3$ $1.002$ \(\Q(\zeta_{14})^+\) $D_{7}$ \(\Q(\sqrt{-502}) \) None \(-3\) \(0\) \(0\) \(-1\) \(q-q^{2}+q^{4}-\beta _{1}q^{7}-q^{8}+q^{9}-\beta _{2}q^{11}+\cdots\)
2008.1.c.b 2008.c 2008.c $3$ $1.002$ \(\Q(\zeta_{14})^+\) $D_{7}$ \(\Q(\sqrt{-502}) \) None \(3\) \(0\) \(0\) \(-1\) \(q+q^{2}+q^{4}-\beta _{1}q^{7}+q^{8}+q^{9}+\beta _{2}q^{11}+\cdots\)
2008.1.j.a 2008.j 2008.j $4$ $1.002$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-2}) \) None \(4\) \(-2\) \(0\) \(0\) \(q+q^{2}+(-\zeta_{10}+\zeta_{10}^{2})q^{3}+q^{4}+(-\zeta_{10}+\cdots)q^{6}+\cdots\)
2008.1.w.a 2008.w 2008.w $20$ $1.002$ \(\Q(\zeta_{50})\) $D_{25}$ \(\Q(\sqrt{-2}) \) None \(-5\) \(0\) \(0\) \(0\) \(q-\zeta_{50}^{5}q^{2}+(\zeta_{50}^{2}+\zeta_{50}^{4})q^{3}+\zeta_{50}^{10}q^{4}+\cdots\)
2008.1.bd.a 2008.bd 2008.ad $100$ $1.002$ \(\Q(\zeta_{250})\) $D_{125}$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{250}^{35}q^{2}+(\zeta_{250}^{14}-\zeta_{250}^{53})q^{3}+\cdots\)
2009.1.i.a 2009.i 287.i $6$ $1.003$ 6.0.64827.1 $D_{7}$ \(\Q(\sqrt{-287}) \) None \(1\) \(-1\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3}-\beta _{4}-\beta _{5})q^{3}+\cdots\)
2009.1.i.b 2009.i 287.i $6$ $1.003$ 6.0.64827.1 $D_{7}$ \(\Q(\sqrt{-287}) \) None \(1\) \(1\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{3}+\cdots\)
2011.1.b.a 2011.b 2011.b $3$ $1.004$ \(\Q(\zeta_{14})^+\) $D_{7}$ \(\Q(\sqrt{-2011}) \) None \(0\) \(0\) \(-1\) \(0\) \(q+q^{4}-\beta _{1}q^{5}+q^{9}+(-1+\beta _{1}-\beta _{2})q^{13}+\cdots\)
2013.1.bm.a 2013.bm 2013.am $4$ $1.005$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-183}) \) None \(-3\) \(-1\) \(0\) \(0\) \(q+(-1+\zeta_{10})q^{2}+\zeta_{10}^{4}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
2013.1.bm.b 2013.bm 2013.am $4$ $1.005$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-183}) \) None \(3\) \(-1\) \(0\) \(0\) \(q+(1-\zeta_{10})q^{2}+\zeta_{10}^{4}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
2013.1.bm.c 2013.bm 2013.am $8$ $1.005$ \(\Q(\zeta_{20})\) $D_{10}$ \(\Q(\sqrt{-183}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+(\zeta_{20}^{5}+\zeta_{20}^{7})q^{2}+\zeta_{20}^{8}q^{3}+(-1+\cdots)q^{4}+\cdots\)
2013.1.bm.d 2013.bm 2013.am $16$ $1.005$ \(\Q(\zeta_{40})\) $D_{20}$ \(\Q(\sqrt{-183}) \) None \(0\) \(4\) \(0\) \(0\) \(q+(\zeta_{40}^{9}+\zeta_{40}^{15})q^{2}-\zeta_{40}^{16}q^{3}+\cdots\)
2015.1.h.a 2015.h 2015.h $4$ $1.006$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-155}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}-q^{4}+\zeta_{8}^{2}q^{5}+q^{9}+\cdots\)
2015.1.h.b 2015.h 2015.h $6$ $1.006$ \(\Q(\zeta_{26})^+\) $D_{13}$ \(\Q(\sqrt{-2015}) \) None \(-1\) \(-1\) \(6\) \(-1\) \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
2015.1.h.c 2015.h 2015.h $6$ $1.006$ \(\Q(\zeta_{26})^+\) $D_{13}$ \(\Q(\sqrt{-2015}) \) None \(-1\) \(1\) \(6\) \(-1\) \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
2015.1.h.d 2015.h 2015.h $6$ $1.006$ \(\Q(\zeta_{26})^+\) $D_{13}$ \(\Q(\sqrt{-2015}) \) None \(1\) \(-1\) \(-6\) \(1\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
2015.1.h.e 2015.h 2015.h $6$ $1.006$ \(\Q(\zeta_{26})^+\) $D_{13}$ \(\Q(\sqrt{-2015}) \) None \(1\) \(1\) \(-6\) \(1\) \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
2015.1.bf.a 2015.bf 2015.af $8$ $1.006$ \(\Q(\zeta_{24})\) $D_{12}$ \(\Q(\sqrt{-155}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}^{5}+\zeta_{24}^{11})q^{3}+\zeta_{24}^{4}q^{4}-\zeta_{24}^{6}q^{5}+\cdots\)
2015.1.bq.a 2015.bq 2015.aq $2$ $1.006$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-155}) \) None \(0\) \(-2\) \(2\) \(0\) \(q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+3\zeta_{6}^{2}q^{9}+\cdots\)
2015.1.bq.b 2015.bq 2015.aq $2$ $1.006$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-155}) \) None \(0\) \(2\) \(2\) \(0\) \(q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+3\zeta_{6}^{2}q^{9}+\cdots\)
2015.1.bq.c 2015.bq 2015.aq $4$ $1.006$ \(\Q(\zeta_{12})\) $A_{4}$ None None \(0\) \(-2\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{4}q^{3}+\zeta_{12}^{3}q^{5}+\zeta_{12}^{5}q^{6}+\cdots\)
2015.1.bq.d 2015.bq 2015.aq $4$ $1.006$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-155}) \) None \(0\) \(0\) \(-4\) \(0\) \(q-\zeta_{12}^{2}q^{4}-q^{5}+\zeta_{12}^{2}q^{9}+\zeta_{12}^{5}q^{13}+\cdots\)
2015.1.bq.e 2015.bq 2015.aq $4$ $1.006$ \(\Q(\zeta_{12})\) $A_{4}$ None None \(0\) \(2\) \(0\) \(0\) \(q-\zeta_{12}q^{2}-\zeta_{12}^{4}q^{3}-\zeta_{12}^{3}q^{5}+\zeta_{12}^{5}q^{6}+\cdots\)
2016.1.e.a 2016.e 168.e $4$ $1.006$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{7}+(\zeta_{8}+\zeta_{8}^{3})q^{11}+(-\zeta_{8}+\cdots)q^{23}+\cdots\)
2016.1.f.a 2016.f 7.b $4$ $1.006$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-21}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{7}+(-\zeta_{8}+\cdots)q^{11}+\cdots\)
2016.1.l.a 2016.l 56.h $1$ $1.006$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(1\) \(q+q^{7}+2q^{23}-q^{25}+q^{49}-2q^{71}+\cdots\)
2016.1.l.b 2016.l 56.h $2$ $1.006$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{42}) \) \(0\) \(0\) \(0\) \(-2\) \(q-q^{7}-iq^{11}-q^{25}-iq^{29}+q^{49}+\cdots\)
2016.1.bi.a 2016.bi 504.aa $4$ $1.006$ \(\Q(\zeta_{12})\) $A_{4}$ None None \(0\) \(-2\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{3}-\zeta_{12}^{3}q^{5}+\zeta_{12}q^{7}+\zeta_{12}^{4}q^{9}+\cdots\)
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