## Results (1-50 of 38787 matches)

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1001.1.r.a $$4$$ $$0.500$$ $$\Q(\zeta_{12})$$ $$A_{4}$$ None None $$0$$ $$0$$ $$2$$ $$0$$ $$q-\zeta_{12}^{3}q^{2}+\zeta_{12}^{2}q^{5}-\zeta_{12}q^{7}-\zeta_{12}^{3}q^{8}+\cdots$$
1001.1.y.a $$2$$ $$0.500$$ $$\Q(\sqrt{-3})$$ $$D_{3}$$ $$\Q(\sqrt{-143})$$ None $$-1$$ $$1$$ $$0$$ $$1$$ $$q+\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-q^{6}+\zeta_{6}q^{7}-q^{8}+\cdots$$
1001.1.y.b $$2$$ $$0.500$$ $$\Q(\sqrt{-3})$$ $$D_{3}$$ $$\Q(\sqrt{-143})$$ None $$1$$ $$1$$ $$0$$ $$-1$$ $$q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}+q^{6}-\zeta_{6}q^{7}+q^{8}+\cdots$$
1001.1.y.c $$8$$ $$0.500$$ $$\Q(\zeta_{15})$$ $$D_{15}$$ $$\Q(\sqrt{-143})$$ None $$-1$$ $$-1$$ $$0$$ $$1$$ $$q+(\zeta_{30}^{4}+\zeta_{30}^{6})q^{2}+(\zeta_{30}^{6}+\zeta_{30}^{14}+\cdots)q^{3}+\cdots$$
1001.1.y.d $$8$$ $$0.500$$ $$\Q(\zeta_{15})$$ $$D_{15}$$ $$\Q(\sqrt{-143})$$ None $$1$$ $$-1$$ $$0$$ $$-1$$ $$q+(-\zeta_{30}^{4}-\zeta_{30}^{6})q^{2}+(\zeta_{30}^{6}+\zeta_{30}^{14}+\cdots)q^{3}+\cdots$$
1001.1.bo.a $$4$$ $$0.500$$ $$\Q(\zeta_{12})$$ $$A_{4}$$ None None $$0$$ $$0$$ $$2$$ $$0$$ $$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{5}+\zeta_{12}^{3}q^{7}+\cdots$$
1003.1.b.a $$1$$ $$0.501$$ $$\Q$$ $$D_{2}$$ $$\Q(\sqrt{-59})$$, $$\Q(\sqrt{-1003})$$ $$\Q(\sqrt{17})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+q^{4}+q^{9}+q^{16}-q^{17}-2q^{19}+\cdots$$
1003.1.b.b $$2$$ $$0.501$$ $$\Q(\sqrt{-3})$$ $$D_{6}$$ $$\Q(\sqrt{-59})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{6}+\zeta_{6}^{2})q^{3}+q^{4}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{5}+\cdots$$
1003.1.f.a $$2$$ $$0.501$$ $$\Q(\sqrt{-1})$$ $$D_{4}$$ $$\Q(\sqrt{-59})$$ None $$0$$ $$-2$$ $$-2$$ $$-2$$ $$q+(-1+i)q^{3}-q^{4}+(-1+i)q^{5}+\cdots$$
1003.1.f.b $$4$$ $$0.501$$ $$\Q(\zeta_{12})$$ $$D_{12}$$ $$\Q(\sqrt{-59})$$ None $$0$$ $$2$$ $$2$$ $$2$$ $$q+(-\zeta_{12}+\zeta_{12}^{2})q^{3}-q^{4}+(-\zeta_{12}^{4}+\cdots)q^{5}+\cdots$$
1003.1.h.a $$4$$ $$0.501$$ $$\Q(\zeta_{8})$$ $$D_{8}$$ $$\Q(\sqrt{-59})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\cdots)q^{5}+\cdots$$
1003.1.h.b $$8$$ $$0.501$$ $$\Q(\zeta_{24})$$ $$D_{24}$$ $$\Q(\sqrt{-59})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{24}-\zeta_{24}^{2})q^{3}-\zeta_{24}^{6}q^{4}+(\zeta_{24}^{5}+\cdots)q^{5}+\cdots$$
1004.1.d.a $$1$$ $$0.501$$ $$\Q$$ $$D_{3}$$ $$\Q(\sqrt{-251})$$ None $$0$$ $$2$$ $$-1$$ $$-1$$ $$q+2q^{3}-q^{5}-q^{7}+3q^{9}+2q^{13}+\cdots$$
1004.1.d.b $$6$$ $$0.501$$ $$\Q(\zeta_{21})^+$$ $$D_{21}$$ $$\Q(\sqrt{-251})$$ None $$0$$ $$-2$$ $$1$$ $$1$$ $$q+(-1-\beta _{3}+\beta _{5})q^{3}+\beta _{4}q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$$
1005.1.p.a $$4$$ $$0.502$$ $$\Q(\zeta_{12})$$ $$A_{4}$$ None None $$-2$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}^{2}q^{2}-\zeta_{12}^{3}q^{3}+\zeta_{12}^{3}q^{5}+\cdots$$
1005.1.p.b $$4$$ $$0.502$$ $$\Q(\zeta_{12})$$ $$A_{4}$$ None None $$2$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}^{2}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{3}q^{5}+\cdots$$
1007.1.d.a $$1$$ $$0.503$$ $$\Q$$ $$D_{3}$$ $$\Q(\sqrt{-1007})$$ None $$-1$$ $$-1$$ $$0$$ $$2$$ $$q-q^{2}-q^{3}+q^{6}+2q^{7}+q^{8}-q^{11}+\cdots$$
1007.1.d.b $$1$$ $$0.503$$ $$\Q$$ $$D_{3}$$ $$\Q(\sqrt{-1007})$$ None $$1$$ $$1$$ $$0$$ $$2$$ $$q+q^{2}+q^{3}+q^{6}+2q^{7}-q^{8}-q^{11}+\cdots$$
1007.1.d.c $$2$$ $$0.503$$ $$\Q(\sqrt{5})$$ $$D_{5}$$ $$\Q(\sqrt{-1007})$$ None $$-1$$ $$-1$$ $$0$$ $$-1$$ $$q+(-1+\beta )q^{2}-\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots$$
1007.1.d.d $$2$$ $$0.503$$ $$\Q(\sqrt{5})$$ $$D_{5}$$ $$\Q(\sqrt{-1007})$$ None $$1$$ $$1$$ $$0$$ $$-1$$ $$q+(1-\beta )q^{2}+\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots$$
1007.1.d.e $$4$$ $$0.503$$ $$\Q(\zeta_{15})^+$$ $$D_{15}$$ $$\Q(\sqrt{-1007})$$ None $$-1$$ $$-1$$ $$0$$ $$-2$$ $$q-\beta _{1}q^{2}+(\beta _{2}+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots$$
1007.1.d.f $$4$$ $$0.503$$ $$\Q(\zeta_{15})^+$$ $$D_{15}$$ $$\Q(\sqrt{-1007})$$ None $$1$$ $$1$$ $$0$$ $$-2$$ $$q+\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$$
1008.1.f.a $$1$$ $$0.503$$ $$\Q$$ $$D_{2}$$ $$\Q(\sqrt{-3})$$, $$\Q(\sqrt{-7})$$ $$\Q(\sqrt{21})$$ $$0$$ $$0$$ $$0$$ $$1$$ $$q+q^{7}+q^{25}-2q^{37}+2q^{43}+q^{49}+\cdots$$
1008.1.u.a $$2$$ $$0.503$$ $$\Q(\sqrt{-1})$$ $$D_{4}$$ $$\Q(\sqrt{-7})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}+q^{4}+iq^{7}-q^{8}+(1-i)q^{11}+\cdots$$
1008.1.u.b $$2$$ $$0.503$$ $$\Q(\sqrt{-1})$$ $$D_{4}$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-q^{4}-iq^{7}-iq^{8}+(1-i+\cdots)q^{11}+\cdots$$
1008.1.u.c $$2$$ $$0.503$$ $$\Q(\sqrt{-1})$$ $$D_{4}$$ $$\Q(\sqrt{-7})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}+q^{4}+iq^{7}+q^{8}+(-1+i+\cdots)q^{11}+\cdots$$
1008.1.y.a $$4$$ $$0.503$$ $$\Q(\zeta_{8})$$ $$D_{4}$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-q^{7}-\zeta_{8}^{3}q^{8}+\cdots$$
1008.1.y.b $$4$$ $$0.503$$ $$\Q(\zeta_{8})$$ $$D_{4}$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+q^{7}-\zeta_{8}q^{8}+\cdots$$
1008.1.bw.a $$4$$ $$0.503$$ $$\Q(\zeta_{12})$$ $$A_{4}$$ None None $$0$$ $$0$$ $$2$$ $$0$$ $$q-\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}+\cdots$$
1008.1.cd.a $$2$$ $$0.503$$ $$\Q(\sqrt{-3})$$ $$D_{6}$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-1$$ $$q+\zeta_{6}^{2}q^{7}+q^{13}+(1+\zeta_{6})q^{19}+\zeta_{6}q^{25}+\cdots$$
1008.1.cd.b $$2$$ $$0.503$$ $$\Q(\sqrt{-3})$$ $$D_{6}$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$1$$ $$q-\zeta_{6}^{2}q^{7}+q^{13}+(-1-\zeta_{6})q^{19}+\cdots$$
1008.1.cg.a $$2$$ $$0.503$$ $$\Q(\sqrt{-3})$$ $$D_{6}$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-1$$ $$q-\zeta_{6}q^{7}+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+(1-\zeta_{6}^{2}+\cdots)q^{19}+\cdots$$
1008.1.dc.a $$4$$ $$0.503$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ $$S_{4}$$ None None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+\beta _{1}q^{5}+(-1+\beta _{2})q^{7}+(\beta _{1}-\beta _{3})q^{11}+\cdots$$
1008.1.dd.a $$4$$ $$0.503$$ $$\Q(\zeta_{12})$$ $$A_{4}$$ None None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+\zeta_{12}^{5}q^{3}-q^{5}+\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}+\cdots$$
1008.1.dt.a $$8$$ $$0.503$$ $$\Q(\zeta_{24})$$ $$S_{4}$$ None None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-\zeta_{24}^{11}q^{2}-\zeta_{24}^{10}q^{4}+\zeta_{24}^{11}q^{5}+\cdots$$
1008.1.ed.a $$8$$ $$0.503$$ $$\Q(\zeta_{24})$$ $$S_{4}$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}q^{5}+\zeta_{24}^{2}q^{7}+\cdots$$
1011.1.c.a $$1$$ $$0.505$$ $$\Q$$ $$D_{2}$$ $$\Q(\sqrt{-3})$$, $$\Q(\sqrt{-1011})$$ $$\Q(\sqrt{337})$$ $$0$$ $$-1$$ $$0$$ $$2$$ $$q-q^{3}+q^{4}+2q^{7}+q^{9}-q^{12}-2q^{13}+\cdots$$
1011.1.c.b $$1$$ $$0.505$$ $$\Q$$ $$D_{3}$$ $$\Q(\sqrt{-1011})$$ None $$0$$ $$1$$ $$-1$$ $$-1$$ $$q+q^{3}+q^{4}-q^{5}-q^{7}+q^{9}+2q^{11}+\cdots$$
1011.1.c.c $$1$$ $$0.505$$ $$\Q$$ $$D_{3}$$ $$\Q(\sqrt{-1011})$$ None $$0$$ $$1$$ $$1$$ $$-1$$ $$q+q^{3}+q^{4}+q^{5}-q^{7}+q^{9}-2q^{11}+\cdots$$
1011.1.c.d $$2$$ $$0.505$$ $$\Q(\sqrt{3})$$ $$D_{6}$$ $$\Q(\sqrt{-1011})$$ None $$0$$ $$-2$$ $$0$$ $$-2$$ $$q-q^{3}+q^{4}-\beta q^{5}-q^{7}+q^{9}-q^{12}+\cdots$$
1011.1.f.a $$2$$ $$0.505$$ $$\Q(\sqrt{-1})$$ $$D_{4}$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+q^{4}-q^{9}-iq^{12}+q^{16}+\cdots$$
1011.1.f.b $$4$$ $$0.505$$ $$\Q(\zeta_{8})$$ $$S_{4}$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\cdots$$
1011.1.l.a $$4$$ $$0.505$$ $$\Q(\zeta_{8})$$ $$D_{8}$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-\zeta_{8}^{3}q^{3}+q^{4}+(-1-\zeta_{8}^{2})q^{7}-\zeta_{8}^{2}q^{9}+\cdots$$
1011.1.q.a $$6$$ $$0.505$$ $$\Q(\zeta_{14})$$ $$D_{14}$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$0$$ $$-2$$ $$q-\zeta_{14}^{6}q^{3}+\zeta_{14}^{6}q^{4}+(-\zeta_{14}-\zeta_{14}^{5}+\cdots)q^{7}+\cdots$$
1011.1.r.a $$6$$ $$0.505$$ $$\Q(\zeta_{14})$$ $$D_{7}$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$-2$$ $$q-\zeta_{14}^{3}q^{3}-\zeta_{14}^{3}q^{4}+(\zeta_{14}^{4}+\zeta_{14}^{6}+\cdots)q^{7}+\cdots$$
1011.1.y.a $$12$$ $$0.505$$ $$\Q(\zeta_{28})$$ $$D_{28}$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{28}^{3}q^{3}-\zeta_{28}^{10}q^{4}+(-\zeta_{28}^{4}+\cdots)q^{7}+\cdots$$
1011.1.bf.a $$24$$ $$0.505$$ $$\Q(\zeta_{56})$$ $$D_{56}$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q-\zeta_{56}^{15}q^{3}+\zeta_{56}^{8}q^{4}+(\zeta_{56}^{6}-\zeta_{56}^{16}+\cdots)q^{7}+\cdots$$
1012.1.r.a $$20$$ $$0.505$$ $$\Q(\zeta_{33})$$ $$D_{33}$$ $$\Q(\sqrt{-11})$$ None $$0$$ $$2$$ $$2$$ $$0$$ $$q+(\zeta_{66}^{2}-\zeta_{66}^{19})q^{3}+(-\zeta_{66}^{25}+\zeta_{66}^{32}+\cdots)q^{5}+\cdots$$
1015.1.f.a $$1$$ $$0.507$$ $$\Q$$ $$D_{2}$$ $$\Q(\sqrt{-35})$$, $$\Q(\sqrt{-1015})$$ $$\Q(\sqrt{29})$$ $$0$$ $$0$$ $$-1$$ $$-1$$ $$q-q^{4}-q^{5}-q^{7}+q^{9}+2q^{13}+q^{16}+\cdots$$
1015.1.f.b $$1$$ $$0.507$$ $$\Q$$ $$D_{2}$$ $$\Q(\sqrt{-35})$$, $$\Q(\sqrt{-1015})$$ $$\Q(\sqrt{29})$$ $$0$$ $$0$$ $$1$$ $$1$$ $$q-q^{4}+q^{5}+q^{7}+q^{9}-2q^{13}+q^{16}+\cdots$$