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Label | Dim | $A$ | Field | CM | RM | Traces | Fricke sign | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
335.1.d.a | $1$ | $0.167$ | \(\Q\) | \(\Q(\sqrt{-335}) \) | None | \(-1\) | \(-1\) | \(1\) | \(-1\) | \(q-q^{2}-q^{3}+q^{5}+q^{6}-q^{7}+q^{8}+\cdots\) | |
335.1.d.b | $1$ | $0.167$ | \(\Q\) | \(\Q(\sqrt{-335}) \) | None | \(1\) | \(1\) | \(-1\) | \(1\) | \(q+q^{2}+q^{3}-q^{5}+q^{6}+q^{7}-q^{8}+\cdots\) | |
335.1.d.c | $3$ | $0.167$ | \(\Q(\zeta_{18})^+\) | \(\Q(\sqrt{-335}) \) | None | \(0\) | \(0\) | \(-3\) | \(0\) | \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\) | |
335.1.d.d | $3$ | $0.167$ | \(\Q(\zeta_{18})^+\) | \(\Q(\sqrt{-335}) \) | None | \(0\) | \(0\) | \(3\) | \(0\) | \(q-\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\) | |
335.2.a.a | $1$ | $2.675$ | \(\Q\) | None | None | \(0\) | \(0\) | \(1\) | \(-2\) | $+$ | \(q-2q^{4}+q^{5}-2q^{7}-3q^{9}-2q^{11}+\cdots\) |
335.2.a.b | $2$ | $2.675$ | \(\Q(\sqrt{2}) \) | None | None | \(0\) | \(0\) | \(-2\) | \(-4\) | $+$ | \(q+\beta q^{2}-\beta q^{3}-q^{5}-2q^{6}-2q^{7}+\cdots\) |
335.2.a.c | $2$ | $2.675$ | \(\Q(\sqrt{5}) \) | None | None | \(1\) | \(0\) | \(-2\) | \(0\) | $-$ | \(q+\beta q^{2}+(-1+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\) |
335.2.a.d | $7$ | $2.675$ | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) | None | None | \(2\) | \(4\) | \(-7\) | \(10\) | $-$ | \(q+(\beta _{2}+\beta _{5})q^{2}+(1-\beta _{4})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots\) |
335.2.a.e | $11$ | $2.675$ | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) | None | None | \(0\) | \(0\) | \(11\) | \(4\) | $-$ | \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\) |
335.2.c.a | $32$ | $2.675$ | None | None | \(0\) | \(0\) | \(0\) | \(0\) | |||
335.2.e.a | $20$ | $2.675$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | None | \(-3\) | \(0\) | \(-20\) | \(-4\) | \(q-\beta _{1}q^{2}-\beta _{7}q^{3}+(\beta _{10}-\beta _{18})q^{4}+\cdots\) | |
335.2.e.b | $24$ | $2.675$ | None | None | \(-3\) | \(0\) | \(24\) | \(-2\) | |||
335.2.f.a | $64$ | $2.675$ | None | None | \(0\) | \(0\) | \(0\) | \(0\) | |||
335.2.i.a | $64$ | $2.675$ | None | None | \(0\) | \(0\) | \(-6\) | \(0\) | |||
335.2.k.a | $110$ | $2.675$ | None | None | \(-3\) | \(-4\) | \(11\) | \(-6\) | |||
335.2.k.b | $130$ | $2.675$ | None | None | \(-3\) | \(-4\) | \(-13\) | \(-10\) | |||
335.2.m.a | $128$ | $2.675$ | None | None | \(-6\) | \(0\) | \(0\) | \(-6\) | |||
335.2.o.a | $320$ | $2.675$ | None | None | \(0\) | \(0\) | \(-11\) | \(0\) | |||
335.2.q.a | $200$ | $2.675$ | None | None | \(3\) | \(0\) | \(20\) | \(4\) | |||
335.2.q.b | $240$ | $2.675$ | None | None | \(3\) | \(0\) | \(-24\) | \(2\) | |||
335.2.s.a | $640$ | $2.675$ | None | None | \(-22\) | \(-22\) | \(-22\) | \(-22\) | |||
335.2.u.a | $640$ | $2.675$ | None | None | \(0\) | \(0\) | \(-16\) | \(0\) | |||
335.2.w.a | $1280$ | $2.675$ | None | None | \(-38\) | \(-44\) | \(-44\) | \(-38\) | |||
335.3.b.a | $44$ | $9.128$ | None | None | \(0\) | \(0\) | \(0\) | \(0\) | |||
335.3.d.a | $9$ | $9.128$ | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) | \(\Q(\sqrt{-335}) \) | None | \(0\) | \(0\) | \(-45\) | \(0\) | \(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(4+\beta _{6}+\beta _{7})q^{4}+\cdots\) | |
335.3.d.b | $9$ | $9.128$ | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) | \(\Q(\sqrt{-335}) \) | None | \(0\) | \(0\) | \(45\) | \(0\) | \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(4+\beta _{6}+\beta _{7})q^{4}+\cdots\) | |
335.3.d.c | $48$ | $9.128$ | None | None | \(0\) | \(0\) | \(0\) | \(0\) | |||
335.3.g.a | $132$ | $9.128$ | None | None | \(-4\) | \(0\) | \(-4\) | \(-4\) | |||
335.3.h.a | $132$ | $9.128$ | None | None | \(0\) | \(0\) | \(0\) | \(0\) | |||
335.3.j.a | $92$ | $9.128$ | None | None | \(0\) | \(0\) | \(0\) | \(18\) | |||
335.3.l.a | $264$ | $9.128$ | None | None | \(-2\) | \(0\) | \(-8\) | \(-2\) | |||
335.3.n.a | $660$ | $9.128$ | None | None | \(0\) | \(0\) | \(-11\) | \(0\) | |||
335.3.p.a | $440$ | $9.128$ | None | None | \(0\) | \(0\) | \(0\) | \(0\) | |||
335.3.r.a | $1320$ | $9.128$ | None | None | \(-18\) | \(-22\) | \(-18\) | \(-18\) | |||
335.3.t.a | $920$ | $9.128$ | None | None | \(0\) | \(0\) | \(0\) | \(-18\) | |||
335.3.v.a | $1320$ | $9.128$ | None | None | \(0\) | \(0\) | \(-22\) | \(0\) | |||
335.3.x.a | $2640$ | $9.128$ | None | None | \(-42\) | \(-44\) | \(-36\) | \(-42\) | |||
335.4.a.a | $11$ | $19.766$ | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) | None | None | \(-5\) | \(-5\) | \(55\) | \(-48\) | $-$ | \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\) |
335.4.a.b | $13$ | $19.766$ | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) | None | None | \(-1\) | \(-7\) | \(-65\) | \(-50\) | $-$ | \(q-\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(3+\beta _{2})q^{4}+\cdots\) |
335.4.a.c | $20$ | $19.766$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | None | \(5\) | \(5\) | \(-100\) | \(48\) | $+$ | \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(5+\beta _{2})q^{4}-5q^{5}+\cdots\) |
335.4.a.d | $22$ | $19.766$ | None | None | \(1\) | \(7\) | \(110\) | \(50\) | $+$ | ||
335.4.c.a | $100$ | $19.766$ | None | None | \(0\) | \(0\) | \(6\) | \(0\) | |||
335.5.b.a | $92$ | $34.629$ | None | None | \(0\) | \(0\) | \(0\) | \(0\) | |||
335.6.a.a | $22$ | $53.729$ | None | None | \(-7\) | \(-16\) | \(550\) | \(-470\) | $+$ | ||
335.6.a.b | $24$ | $53.729$ | None | None | \(-5\) | \(-20\) | \(-600\) | \(-216\) | $+$ | ||
335.6.a.c | $31$ | $53.729$ | None | None | \(7\) | \(16\) | \(-775\) | \(470\) | $-$ | ||
335.6.a.d | $33$ | $53.729$ | None | None | \(5\) | \(20\) | \(825\) | \(216\) | $-$ | ||
335.8.a.a | $33$ | $104.649$ | None | None | \(5\) | \(-20\) | \(4125\) | \(-1252\) | $-$ | ||
335.8.a.b | $35$ | $104.649$ | None | None | \(-29\) | \(-88\) | \(-4375\) | \(-3550\) | $-$ | ||
335.8.a.c | $42$ | $104.649$ | None | None | \(-5\) | \(20\) | \(-5250\) | \(1252\) | $+$ |