## Results (displaying matches 1-50 of 322) Next

Label Dim. $$A$$ Field CM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
50.2.a.a $$1$$ $$0.399$$ $$\Q$$ None $$-1$$ $$1$$ $$0$$ $$2$$ $$-$$ $$q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots$$
50.2.a.b $$1$$ $$0.399$$ $$\Q$$ None $$1$$ $$-1$$ $$0$$ $$-2$$ $$-$$ $$q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots$$
50.2.b.a $$2$$ $$0.399$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}-q^{4}-q^{6}-2iq^{7}+\cdots$$
50.2.d.a $$4$$ $$0.399$$ $$\Q(\zeta_{10})$$ None $$1$$ $$-1$$ $$5$$ $$-12$$ $$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-1+\cdots)q^{3}+\cdots$$
50.2.d.b $$8$$ $$0.399$$ 8.0.58140625.2 None $$-2$$ $$-3$$ $$0$$ $$4$$ $$q+(-1+\beta _{2}+\beta _{3}+\beta _{6})q^{2}+\beta _{4}q^{3}+\cdots$$
50.2.e.a $$8$$ $$0.399$$ $$\Q(\zeta_{20})$$ None $$0$$ $$0$$ $$-10$$ $$0$$ $$q+\zeta_{20}q^{2}+(-1+\zeta_{20}^{2}-\zeta_{20}^{4}+2\zeta_{20}^{6}+\cdots)q^{3}+\cdots$$
50.3.c.a $$2$$ $$1.362$$ $$\Q(\sqrt{-1})$$ None $$-2$$ $$6$$ $$0$$ $$-6$$ $$q+(-1-i)q^{2}+(3-3i)q^{3}+2iq^{4}+\cdots$$
50.3.c.b $$2$$ $$1.362$$ $$\Q(\sqrt{-1})$$ None $$2$$ $$-6$$ $$0$$ $$6$$ $$q+(1+i)q^{2}+(-3+3i)q^{3}+2iq^{4}+\cdots$$
50.3.c.c $$2$$ $$1.362$$ $$\Q(\sqrt{-1})$$ None $$2$$ $$4$$ $$0$$ $$-4$$ $$q+(1+i)q^{2}+(2-2i)q^{3}+2iq^{4}+4q^{6}+\cdots$$
50.3.f.a $$16$$ $$1.362$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$-4$$ $$2$$ $$0$$ $$-2$$ $$q+(\beta _{1}+\beta _{9})q^{2}+(-1+\beta _{2}-\beta _{3}+\beta _{7}+\cdots)q^{3}+\cdots$$
50.3.f.b $$24$$ $$1.362$$ None $$6$$ $$2$$ $$0$$ $$-2$$
50.4.a.a $$1$$ $$2.950$$ $$\Q$$ None $$-2$$ $$-7$$ $$0$$ $$34$$ $$+$$ $$q-2q^{2}-7q^{3}+4q^{4}+14q^{6}+34q^{7}+\cdots$$
50.4.a.b $$1$$ $$2.950$$ $$\Q$$ None $$-2$$ $$-2$$ $$0$$ $$-26$$ $$-$$ $$q-2q^{2}-2q^{3}+4q^{4}+4q^{6}-26q^{7}+\cdots$$
50.4.a.c $$1$$ $$2.950$$ $$\Q$$ None $$-2$$ $$8$$ $$0$$ $$4$$ $$+$$ $$q-2q^{2}+8q^{3}+4q^{4}-2^{4}q^{6}+4q^{7}+\cdots$$
50.4.a.d $$1$$ $$2.950$$ $$\Q$$ None $$2$$ $$2$$ $$0$$ $$26$$ $$+$$ $$q+2q^{2}+2q^{3}+4q^{4}+4q^{6}+26q^{7}+\cdots$$
50.4.a.e $$1$$ $$2.950$$ $$\Q$$ None $$2$$ $$7$$ $$0$$ $$-34$$ $$+$$ $$q+2q^{2}+7q^{3}+4q^{4}+14q^{6}-34q^{7}+\cdots$$
50.4.b.a $$2$$ $$2.950$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+4iq^{3}-4q^{4}-2^{4}q^{6}-2iq^{7}+\cdots$$
50.4.b.b $$2$$ $$2.950$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{2}-7iq^{3}-4q^{4}+14q^{6}-34iq^{7}+\cdots$$
50.4.d.a $$12$$ $$2.950$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$6$$ $$1$$ $$20$$ $$58$$ $$q+2\beta _{5}q^{2}+(-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots$$
50.4.d.b $$16$$ $$2.950$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$-8$$ $$7$$ $$15$$ $$-54$$ $$q+2\beta _{6}q^{2}+(1-\beta _{1}+\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots$$
50.4.e.a $$32$$ $$2.950$$ None $$0$$ $$0$$ $$-30$$ $$0$$
50.5.c.a $$2$$ $$5.168$$ $$\Q(\sqrt{-1})$$ None $$-4$$ $$-2$$ $$0$$ $$38$$ $$q+(-2-2i)q^{2}+(-1+i)q^{3}+8iq^{4}+\cdots$$
50.5.c.b $$2$$ $$5.168$$ $$\Q(\sqrt{-1})$$ None $$4$$ $$-18$$ $$0$$ $$-58$$ $$q+(2+2i)q^{2}+(-9+9i)q^{3}+8iq^{4}+\cdots$$
50.5.c.c $$4$$ $$5.168$$ $$\Q(i, \sqrt{6})$$ None $$-8$$ $$-24$$ $$0$$ $$-144$$ $$q+(-2+2\beta _{2})q^{2}+(-6+\beta _{1}-6\beta _{2}+\cdots)q^{3}+\cdots$$
50.5.c.d $$4$$ $$5.168$$ $$\Q(i, \sqrt{6})$$ None $$8$$ $$24$$ $$0$$ $$144$$ $$q+(2-2\beta _{2})q^{2}+(6+\beta _{1}+6\beta _{2})q^{3}+\cdots$$
50.5.f.a $$40$$ $$5.168$$ None $$-20$$ $$-10$$ $$30$$ $$-10$$
50.5.f.b $$40$$ $$5.168$$ None $$20$$ $$-10$$ $$30$$ $$-10$$
50.6.a.a $$1$$ $$8.019$$ $$\Q$$ None $$-4$$ $$-11$$ $$0$$ $$-142$$ $$-$$ $$q-4q^{2}-11q^{3}+2^{4}q^{4}+44q^{6}-142q^{7}+\cdots$$
50.6.a.b $$1$$ $$8.019$$ $$\Q$$ None $$-4$$ $$-6$$ $$0$$ $$118$$ $$+$$ $$q-4q^{2}-6q^{3}+2^{4}q^{4}+24q^{6}+118q^{7}+\cdots$$
50.6.a.c $$1$$ $$8.019$$ $$\Q$$ None $$-4$$ $$14$$ $$0$$ $$158$$ $$-$$ $$q-4q^{2}+14q^{3}+2^{4}q^{4}-56q^{6}+158q^{7}+\cdots$$
50.6.a.d $$1$$ $$8.019$$ $$\Q$$ None $$4$$ $$-24$$ $$0$$ $$172$$ $$-$$ $$q+4q^{2}-24q^{3}+2^{4}q^{4}-96q^{6}+172q^{7}+\cdots$$
50.6.a.e $$1$$ $$8.019$$ $$\Q$$ None $$4$$ $$-14$$ $$0$$ $$-158$$ $$+$$ $$q+4q^{2}-14q^{3}+2^{4}q^{4}-56q^{6}-158q^{7}+\cdots$$
50.6.a.f $$1$$ $$8.019$$ $$\Q$$ None $$4$$ $$11$$ $$0$$ $$142$$ $$-$$ $$q+4q^{2}+11q^{3}+2^{4}q^{4}+44q^{6}+142q^{7}+\cdots$$
50.6.a.g $$1$$ $$8.019$$ $$\Q$$ None $$4$$ $$26$$ $$0$$ $$22$$ $$-$$ $$q+4q^{2}+26q^{3}+2^{4}q^{4}+104q^{6}+\cdots$$
50.6.b.a $$2$$ $$8.019$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{2}+12iq^{3}-2^{4}q^{4}-96q^{6}+\cdots$$
50.6.b.b $$2$$ $$8.019$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{2}-3iq^{3}-2^{4}q^{4}+24q^{6}+\cdots$$
50.6.b.c $$2$$ $$8.019$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+4iq^{2}-11iq^{3}-2^{4}q^{4}+44q^{6}+\cdots$$
50.6.b.d $$2$$ $$8.019$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{2}-13iq^{3}-2^{4}q^{4}+104q^{6}+\cdots$$
50.6.d.a $$24$$ $$8.019$$ None $$-24$$ $$-11$$ $$-120$$ $$548$$
50.6.d.b $$28$$ $$8.019$$ None $$28$$ $$7$$ $$-145$$ $$-236$$
50.6.e.a $$48$$ $$8.019$$ None $$0$$ $$0$$ $$180$$ $$0$$
50.7.c.a $$2$$ $$11.503$$ $$\Q(\sqrt{-1})$$ None $$-8$$ $$-6$$ $$0$$ $$-234$$ $$q+(-4-4i)q^{2}+(-3+3i)q^{3}+2^{5}iq^{4}+\cdots$$
50.7.c.b $$2$$ $$11.503$$ $$\Q(\sqrt{-1})$$ None $$8$$ $$6$$ $$0$$ $$234$$ $$q+(4+4i)q^{2}+(3-3i)q^{3}+2^{5}iq^{4}+\cdots$$
50.7.c.c $$2$$ $$11.503$$ $$\Q(\sqrt{-1})$$ None $$8$$ $$46$$ $$0$$ $$494$$ $$q+(4+4i)q^{2}+(23-23i)q^{3}+2^{5}iq^{4}+\cdots$$
50.7.c.d $$4$$ $$11.503$$ $$\Q(i, \sqrt{129})$$ None $$-16$$ $$18$$ $$0$$ $$202$$ $$q+(-4+4\beta _{1})q^{2}+(5+5\beta _{1}-\beta _{2})q^{3}+\cdots$$
50.7.c.e $$4$$ $$11.503$$ $$\Q(i, \sqrt{6})$$ None $$-16$$ $$48$$ $$0$$ $$672$$ $$q+(-4-4\beta _{2})q^{2}+(12-12\beta _{2}-\beta _{3})q^{3}+\cdots$$
50.7.c.f $$4$$ $$11.503$$ $$\Q(i, \sqrt{6})$$ None $$16$$ $$-48$$ $$0$$ $$-672$$ $$q+(4+4\beta _{2})q^{2}+(-12+12\beta _{2}-\beta _{3})q^{3}+\cdots$$
50.7.f.a $$56$$ $$11.503$$ None $$56$$ $$32$$ $$150$$ $$348$$
50.7.f.b $$64$$ $$11.503$$ None $$-64$$ $$32$$ $$-330$$ $$348$$
50.8.a.a $$1$$ $$15.619$$ $$\Q$$ None $$-8$$ $$-43$$ $$0$$ $$-974$$ $$+$$ $$q-8q^{2}-43q^{3}+2^{6}q^{4}+344q^{6}+\cdots$$
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