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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
840.1.bp.a \(4\) \(0.419\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{8}^{3}q^{2}+\zeta_{8}^{3}q^{3}-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{5}+\cdots\)
840.1.bp.b \(4\) \(0.419\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{3}q^{3}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{5}+\cdots\)
840.1.bp.c \(8\) \(0.419\) \(\Q(\zeta_{16})\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{2}q^{2}+\zeta_{16}^{5}q^{3}+\zeta_{16}^{4}q^{4}+\cdots\)
840.1.bp.d \(8\) \(0.419\) \(\Q(\zeta_{16})\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{2}q^{2}+\zeta_{16}^{3}q^{3}+\zeta_{16}^{4}q^{4}+\cdots\)
840.1.cg.a \(4\) \(0.419\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-\zeta_{12}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{5}+\cdots\)
840.1.cg.b \(4\) \(0.419\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(2\) \(q-\zeta_{12}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}+\cdots\)
840.1.dh.a \(8\) \(0.419\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{5}q^{2}+\zeta_{24}q^{3}+\zeta_{24}^{10}q^{4}+\cdots\)
840.1.dh.b \(8\) \(0.419\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(4\) \(q+\zeta_{24}^{5}q^{2}+\zeta_{24}q^{3}+\zeta_{24}^{10}q^{4}+\cdots\)
840.2.a.a \(1\) \(6.707\) \(\Q\) None None \(0\) \(-1\) \(-1\) \(-1\) \(+\) \(q-q^{3}-q^{5}-q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
840.2.a.b \(1\) \(6.707\) \(\Q\) None None \(0\) \(-1\) \(-1\) \(1\) \(+\) \(q-q^{3}-q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
840.2.a.c \(1\) \(6.707\) \(\Q\) None None \(0\) \(-1\) \(-1\) \(1\) \(-\) \(q-q^{3}-q^{5}+q^{7}+q^{9}-2q^{13}+q^{15}+\cdots\)
840.2.a.d \(1\) \(6.707\) \(\Q\) None None \(0\) \(-1\) \(1\) \(-1\) \(+\) \(q-q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
840.2.a.e \(1\) \(6.707\) \(\Q\) None None \(0\) \(-1\) \(1\) \(-1\) \(-\) \(q-q^{3}+q^{5}-q^{7}+q^{9}+2q^{13}-q^{15}+\cdots\)
840.2.a.f \(1\) \(6.707\) \(\Q\) None None \(0\) \(-1\) \(1\) \(1\) \(-\) \(q-q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
840.2.a.g \(1\) \(6.707\) \(\Q\) None None \(0\) \(1\) \(-1\) \(-1\) \(+\) \(q+q^{3}-q^{5}-q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
840.2.a.h \(1\) \(6.707\) \(\Q\) None None \(0\) \(1\) \(-1\) \(-1\) \(-\) \(q+q^{3}-q^{5}-q^{7}+q^{9}+6q^{13}-q^{15}+\cdots\)
840.2.a.i \(1\) \(6.707\) \(\Q\) None None \(0\) \(1\) \(-1\) \(1\) \(-\) \(q+q^{3}-q^{5}+q^{7}+q^{9}+2q^{13}-q^{15}+\cdots\)
840.2.a.j \(1\) \(6.707\) \(\Q\) None None \(0\) \(1\) \(1\) \(-1\) \(-\) \(q+q^{3}+q^{5}-q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
840.2.a.k \(2\) \(6.707\) \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(2\) \(2\) \(-\) \(q+q^{3}+q^{5}+q^{7}+q^{9}+\beta q^{11}+2q^{13}+\cdots\)
840.2.e.a \(4\) \(6.707\) \(\Q(\zeta_{8})\) None None \(-4\) \(-4\) \(-4\) \(0\) \(q+(-1+\zeta_{8})q^{2}+(-1+\zeta_{8}^{2})q^{3}-2\zeta_{8}q^{4}+\cdots\)
840.2.e.b \(4\) \(6.707\) \(\Q(\zeta_{8})\) None None \(4\) \(-4\) \(4\) \(0\) \(q+(1+\zeta_{8})q^{2}+(-1+\zeta_{8}^{2})q^{3}+2\zeta_{8}q^{4}+\cdots\)
840.2.e.c \(44\) \(6.707\) None None \(-2\) \(4\) \(44\) \(0\)
840.2.e.d \(44\) \(6.707\) None None \(2\) \(4\) \(-44\) \(0\)
840.2.f.a \(16\) \(6.707\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(-16\) \(2\) \(q+\beta _{2}q^{3}-q^{5}+\beta _{4}q^{7}-\beta _{1}q^{9}+\beta _{8}q^{11}+\cdots\)
840.2.f.b \(16\) \(6.707\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(16\) \(2\) \(q-\beta _{2}q^{3}+q^{5}+\beta _{9}q^{7}-\beta _{1}q^{9}+\beta _{8}q^{11}+\cdots\)
840.2.g.a \(8\) \(6.707\) \(\Q(\zeta_{16})\) None None \(0\) \(0\) \(0\) \(8\) \(q+\zeta_{16}^{5}q^{2}+\zeta_{16}^{2}q^{3}-\zeta_{16}q^{4}+\zeta_{16}^{2}q^{5}+\cdots\)
840.2.g.b \(12\) \(6.707\) 12.0.\(\cdots\).1 None None \(-2\) \(0\) \(0\) \(-12\) \(q+\beta _{2}q^{2}-\beta _{4}q^{3}-\beta _{7}q^{4}-\beta _{4}q^{5}+\cdots\)
840.2.g.c \(12\) \(6.707\) 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(12\) \(q+\beta _{5}q^{2}+\beta _{4}q^{3}+\beta _{7}q^{4}-\beta _{4}q^{5}+\cdots\)
840.2.g.d \(16\) \(6.707\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-2\) \(0\) \(0\) \(-16\) \(q-\beta _{4}q^{2}-\beta _{5}q^{3}-\beta _{2}q^{4}+\beta _{5}q^{5}+\cdots\)
840.2.j.a \(2\) \(6.707\) \(\Q(\sqrt{-1}) \) None None \(-2\) \(-2\) \(-4\) \(0\) \(q+(-1-i)q^{2}-q^{3}+2iq^{4}+(-2+\cdots)q^{5}+\cdots\)
840.2.j.b \(2\) \(6.707\) \(\Q(\sqrt{-1}) \) None None \(-2\) \(2\) \(-4\) \(0\) \(q+(-1+i)q^{2}+q^{3}-2iq^{4}+(-2+\cdots)q^{5}+\cdots\)
840.2.j.c \(2\) \(6.707\) \(\Q(\sqrt{-1}) \) None None \(2\) \(-2\) \(4\) \(0\) \(q+(1+i)q^{2}-q^{3}+2iq^{4}+(2+i)q^{5}+\cdots\)
840.2.j.d \(2\) \(6.707\) \(\Q(\sqrt{-1}) \) None None \(2\) \(2\) \(4\) \(0\) \(q+(1+i)q^{2}+q^{3}+2iq^{4}+(2+i)q^{5}+\cdots\)
840.2.j.e \(32\) \(6.707\) None None \(-2\) \(-32\) \(0\) \(0\)
840.2.j.f \(32\) \(6.707\) None None \(2\) \(32\) \(0\) \(0\)
840.2.k.a \(24\) \(6.707\) None None \(0\) \(0\) \(0\) \(0\)
840.2.k.b \(24\) \(6.707\) None None \(0\) \(0\) \(0\) \(0\)
840.2.p.a \(72\) \(6.707\) None None \(0\) \(0\) \(0\) \(-72\)
840.2.p.b \(72\) \(6.707\) None None \(0\) \(0\) \(0\) \(72\)
840.2.t.a \(2\) \(6.707\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) \(q-iq^{3}+(-1-2i)q^{5}-iq^{7}-q^{9}+\cdots\)
840.2.t.b \(2\) \(6.707\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) \(q-iq^{3}+(-1+2i)q^{5}-iq^{7}-q^{9}+\cdots\)
840.2.t.c \(4\) \(6.707\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}-\beta _{3}q^{5}-\beta _{1}q^{7}-q^{9}-2q^{11}+\cdots\)
840.2.t.d \(6\) \(6.707\) 6.0.350464.1 None None \(0\) \(0\) \(-2\) \(0\) \(q-\beta _{1}q^{3}-\beta _{2}q^{5}+\beta _{1}q^{7}-q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
840.2.t.e \(6\) \(6.707\) 6.0.350464.1 None None \(0\) \(0\) \(-2\) \(0\) \(q+\beta _{1}q^{3}-\beta _{2}q^{5}-\beta _{1}q^{7}-q^{9}+(\beta _{2}+\cdots)q^{11}+\cdots\)
840.2.u.a \(4\) \(6.707\) \(\Q(\sqrt{-2}, \sqrt{3})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(-4\) \(q-\beta _{1}q^{2}-\beta _{2}q^{3}-2q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
840.2.u.b \(4\) \(6.707\) \(\Q(\sqrt{-2}, \sqrt{3})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(4\) \(q-\beta _{1}q^{2}+\beta _{2}q^{3}-2q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
840.2.u.c \(8\) \(6.707\) 8.0.2517630976.5 \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}-\beta _{2}q^{3}+2q^{4}-\beta _{6}q^{5}+(\beta _{3}+\cdots)q^{6}+\cdots\)
840.2.u.d \(8\) \(6.707\) 8.0.2517630976.5 \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{7}q^{3}+2q^{4}+\beta _{6}q^{5}+(\beta _{2}+\cdots)q^{6}+\cdots\)
840.2.u.e \(160\) \(6.707\) None None \(0\) \(0\) \(0\) \(0\)
840.2.w.a \(48\) \(6.707\) None None \(0\) \(-48\) \(0\) \(0\)
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