## Results (displaying matches 1-50 of 51992) Next

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2001.1.i.a $$2$$ $$0.999$$ $$\Q(\sqrt{-1})$$ $$D_{4}$$ $$\Q(\sqrt{-23})$$ None $$-2$$ $$2$$ $$0$$ $$0$$ $$q+(-1+i)q^{2}+q^{3}-iq^{4}+(-1+i+\cdots)q^{6}+\cdots$$
2001.1.i.b $$2$$ $$0.999$$ $$\Q(\sqrt{-1})$$ $$D_{4}$$ $$\Q(\sqrt{-23})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+(1-i)q^{2}+iq^{3}-iq^{4}+(1+i)q^{6}+\cdots$$
2001.1.i.c $$4$$ $$0.999$$ $$\Q(\zeta_{12})$$ $$D_{12}$$ $$\Q(\sqrt{-23})$$ 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 $$4$$ $$0.999$$ $$\Q(\zeta_{12})$$ $$D_{12}$$ $$\Q(\sqrt{-23})$$ 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 $$12$$ $$0.999$$ $$\Q(\zeta_{28})$$ $$D_{28}$$ $$\Q(\sqrt{-23})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{28}^{7}-\zeta_{28}^{10})q^{2}-\zeta_{28}^{9}q^{3}+\cdots$$
2001.1.bf.b $$12$$ $$0.999$$ $$\Q(\zeta_{28})$$ $$D_{28}$$ $$\Q(\sqrt{-23})$$ 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 $$24$$ $$0.999$$ $$\Q(\zeta_{84})$$ $$D_{84}$$ $$\Q(\sqrt{-23})$$ None $$-2$$ $$2$$ $$0$$ $$0$$ $$q+(-\zeta_{84}^{7}-\zeta_{84}^{20})q^{2}-\zeta_{84}^{26}q^{3}+\cdots$$
2001.1.bf.d $$24$$ $$0.999$$ $$\Q(\zeta_{84})$$ $$D_{84}$$ $$\Q(\sqrt{-23})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{84}^{7}+\zeta_{84}^{20})q^{2}+\zeta_{84}^{25}q^{3}+\cdots$$
2003.1.b.a $$1$$ $$1.000$$ $$\Q$$ $$D_{3}$$ $$\Q(\sqrt{-2003})$$ None $$0$$ $$-1$$ $$0$$ $$0$$ $$q-q^{3}+q^{4}-q^{12}-q^{13}+q^{16}+2q^{19}+\cdots$$
2003.1.b.b $$3$$ $$1.000$$ $$\Q(\zeta_{18})^+$$ $$D_{9}$$ $$\Q(\sqrt{-2003})$$ 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 $$1$$ $$1.000$$ $$\Q$$ $$D_{2}$$ $$\Q(\sqrt{-167})$$, $$\Q(\sqrt{-501})$$ $$\Q(\sqrt{3})$$ $$-1$$ $$-1$$ $$0$$ $$0$$ $$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$$
2004.1.g.b $$1$$ $$1.000$$ $$\Q$$ $$D_{2}$$ $$\Q(\sqrt{-167})$$, $$\Q(\sqrt{-501})$$ $$\Q(\sqrt{3})$$ $$1$$ $$1$$ $$0$$ $$0$$ $$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$$
2004.1.g.c $$2$$ $$1.000$$ $$\Q(\sqrt{2})$$ $$D_{4}$$ $$\Q(\sqrt{-501})$$ None $$-2$$ $$2$$ $$0$$ $$0$$ $$q-q^{2}+q^{3}+q^{4}-\beta q^{5}-q^{6}-q^{8}+\cdots$$
2004.1.g.d $$2$$ $$1.000$$ $$\Q(\sqrt{2})$$ $$D_{4}$$ $$\Q(\sqrt{-501})$$ None $$2$$ $$-2$$ $$0$$ $$0$$ $$q+q^{2}-q^{3}+q^{4}-\beta q^{5}-q^{6}+q^{8}+\cdots$$
2004.1.g.e $$10$$ $$1.000$$ $$\Q(\zeta_{22})$$ $$D_{22}$$ $$\Q(\sqrt{-167})$$ 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 $$10$$ $$1.000$$ $$\Q(\zeta_{22})$$ $$D_{22}$$ $$\Q(\sqrt{-167})$$ 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 $$2$$ $$1.001$$ $$\Q(\sqrt{-1})$$ $$D_{4}$$ 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 $$8$$ $$1.001$$ $$\Q(\zeta_{20})$$ $$D_{20}$$ 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 $$1$$ $$1.002$$ $$\Q$$ $$D_{2}$$ $$\Q(\sqrt{-3})$$, $$\Q(\sqrt{-223})$$ $$\Q(\sqrt{669})$$ $$0$$ $$0$$ $$0$$ $$-2$$ $$q-q^{4}-2q^{7}+q^{16}+2q^{19}+q^{25}+\cdots$$
2007.1.d.b $$3$$ $$1.002$$ $$\Q(\zeta_{14})^+$$ $$D_{7}$$ $$\Q(\sqrt{-223})$$ 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 $$6$$ $$1.002$$ $$\Q(\zeta_{28})^+$$ $$D_{14}$$ $$\Q(\sqrt{-223})$$ 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 $$36$$ $$1.002$$ $$\Q(\zeta_{74})$$ $$D_{74}$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q-\zeta_{74}^{20}q^{4}+(\zeta_{74}^{21}+\zeta_{74}^{27})q^{7}+\cdots$$
2008.1.c.a $$3$$ $$1.002$$ $$\Q(\zeta_{14})^+$$ $$D_{7}$$ $$\Q(\sqrt{-502})$$ 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 $$3$$ $$1.002$$ $$\Q(\zeta_{14})^+$$ $$D_{7}$$ $$\Q(\sqrt{-502})$$ 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 $$4$$ $$1.002$$ $$\Q(\zeta_{10})$$ $$D_{5}$$ $$\Q(\sqrt{-2})$$ 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 $$20$$ $$1.002$$ $$\Q(\zeta_{50})$$ $$D_{25}$$ $$\Q(\sqrt{-2})$$ 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 $$100$$ $$1.002$$ $$\Q(\zeta_{250})$$ $$D_{125}$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{250}^{35}q^{2}+(\zeta_{250}^{14}-\zeta_{250}^{53})q^{3}+\cdots$$
2009.1.i.a $$6$$ $$1.003$$ 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 $$6$$ $$1.003$$ 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 $$3$$ $$1.004$$ $$\Q(\zeta_{14})^+$$ $$D_{7}$$ $$\Q(\sqrt{-2011})$$ 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 $$4$$ $$1.005$$ $$\Q(\zeta_{10})$$ $$D_{5}$$ $$\Q(\sqrt{-183})$$ 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 $$4$$ $$1.005$$ $$\Q(\zeta_{10})$$ $$D_{5}$$ $$\Q(\sqrt{-183})$$ 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 $$8$$ $$1.005$$ $$\Q(\zeta_{20})$$ $$D_{10}$$ $$\Q(\sqrt{-183})$$ 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 $$16$$ $$1.005$$ $$\Q(\zeta_{40})$$ $$D_{20}$$ $$\Q(\sqrt{-183})$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q+(\zeta_{40}^{9}+\zeta_{40}^{15})q^{2}-\zeta_{40}^{16}q^{3}+\cdots$$
2015.1.h.a $$4$$ $$1.006$$ $$\Q(\zeta_{8})$$ $$D_{4}$$ $$\Q(\sqrt{-155})$$ 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 $$6$$ $$1.006$$ $$\Q(\zeta_{26})^+$$ $$D_{13}$$ $$\Q(\sqrt{-2015})$$ 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 $$6$$ $$1.006$$ $$\Q(\zeta_{26})^+$$ $$D_{13}$$ $$\Q(\sqrt{-2015})$$ 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 $$6$$ $$1.006$$ $$\Q(\zeta_{26})^+$$ $$D_{13}$$ $$\Q(\sqrt{-2015})$$ 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 $$6$$ $$1.006$$ $$\Q(\zeta_{26})^+$$ $$D_{13}$$ $$\Q(\sqrt{-2015})$$ 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 $$8$$ $$1.006$$ $$\Q(\zeta_{24})$$ $$D_{12}$$ $$\Q(\sqrt{-155})$$ 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 $$2$$ $$1.006$$ $$\Q(\sqrt{-3})$$ $$D_{3}$$ $$\Q(\sqrt{-155})$$ 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 $$2$$ $$1.006$$ $$\Q(\sqrt{-3})$$ $$D_{3}$$ $$\Q(\sqrt{-155})$$ 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 $$4$$ $$1.006$$ $$\Q(\zeta_{12})$$ $$A_{4}$$ 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 $$4$$ $$1.006$$ $$\Q(\zeta_{12})$$ $$D_{6}$$ $$\Q(\sqrt{-155})$$ 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 $$4$$ $$1.006$$ $$\Q(\zeta_{12})$$ $$A_{4}$$ 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 $$4$$ $$1.006$$ $$\Q(\zeta_{8})$$ $$D_{4}$$ $$\Q(\sqrt{-7})$$ 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 $$4$$ $$1.006$$ $$\Q(\zeta_{8})$$ $$D_{4}$$ $$\Q(\sqrt{-21})$$ 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 $$1$$ $$1.006$$ $$\Q$$ $$D_{2}$$ $$\Q(\sqrt{-7})$$, $$\Q(\sqrt{-14})$$ $$\Q(\sqrt{2})$$ $$0$$ $$0$$ $$0$$ $$1$$ $$q+q^{7}+2q^{23}-q^{25}+q^{49}-2q^{71}+\cdots$$
2016.1.l.b $$2$$ $$1.006$$ $$\Q(\sqrt{-1})$$ $$D_{2}$$ $$\Q(\sqrt{-7})$$, $$\Q(\sqrt{-6})$$ $$\Q(\sqrt{42})$$ $$0$$ $$0$$ $$0$$ $$-2$$ $$q-q^{7}-iq^{11}-q^{25}-iq^{29}+q^{49}+\cdots$$
2016.1.bi.a $$4$$ $$1.006$$ $$\Q(\zeta_{12})$$ $$A_{4}$$ 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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