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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
416.1.h.a \(1\) \(0.208\) \(\Q\) \(\Q(\sqrt{-26}) \) None \(0\) \(1\) \(-1\) \(1\) \(q+q^{3}-q^{5}+q^{7}+q^{13}-q^{15}-q^{17}+\cdots\)
416.1.h.b \(1\) \(0.208\) \(\Q\) \(\Q(\sqrt{-26}) \) None \(0\) \(1\) \(1\) \(-1\) \(q+q^{3}+q^{5}-q^{7}-q^{13}+q^{15}-q^{17}+\cdots\)
416.1.t.a \(2\) \(0.208\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(1+i)q^{5}-q^{9}+iq^{13}-iq^{17}+\cdots\)
416.1.bb.a \(4\) \(0.208\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}-\zeta_{12}^{5}q^{7}-\zeta_{12}q^{11}+q^{13}+\cdots\)
416.1.bl.a \(4\) \(0.208\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(\zeta_{12}^{4}+\zeta_{12}^{5})q^{5}+\zeta_{12}^{2}q^{9}+\zeta_{12}q^{13}+\cdots\)
416.2.a.a \(1\) \(3.322\) \(\Q\) None None \(0\) \(-1\) \(1\) \(-3\) \(+\) \(q-q^{3}+q^{5}-3q^{7}-2q^{9}-2q^{11}+\cdots\)
416.2.a.b \(1\) \(3.322\) \(\Q\) None None \(0\) \(1\) \(1\) \(3\) \(-\) \(q+q^{3}+q^{5}+3q^{7}-2q^{9}+2q^{11}+\cdots\)
416.2.a.c \(2\) \(3.322\) \(\Q(\sqrt{17}) \) None None \(0\) \(-1\) \(-3\) \(-3\) \(+\) \(q-\beta q^{3}+(-2+\beta )q^{5}+(-2+\beta )q^{7}+\cdots\)
416.2.a.d \(2\) \(3.322\) \(\Q(\sqrt{5}) \) None None \(0\) \(0\) \(6\) \(0\) \(-\) \(q-\beta q^{3}+3q^{5}-\beta q^{7}+2q^{9}+2\beta q^{11}+\cdots\)
416.2.a.e \(2\) \(3.322\) \(\Q(\sqrt{17}) \) None None \(0\) \(1\) \(-3\) \(3\) \(-\) \(q+\beta q^{3}+(-2+\beta )q^{5}+(2-\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
416.2.a.f \(4\) \(3.322\) 4.4.13448.1 None None \(0\) \(0\) \(-2\) \(0\) \(-\) \(q-\beta _{2}q^{3}+\beta _{3}q^{5}+(\beta _{1}-\beta _{2})q^{7}+(3+\cdots)q^{9}+\cdots\)
416.2.b.a \(2\) \(3.322\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-6\) \(q+iq^{3}+3iq^{5}-3q^{7}+2q^{9}+iq^{13}+\cdots\)
416.2.b.b \(4\) \(3.322\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(12\) \(q+2\zeta_{12}q^{3}-2\zeta_{12}^{2}q^{5}+(3-\zeta_{12}^{3})q^{7}+\cdots\)
416.2.b.c \(6\) \(3.322\) 6.0.399424.1 None None \(0\) \(0\) \(0\) \(-2\) \(q+\beta _{5}q^{3}-\beta _{2}q^{5}+\beta _{1}q^{7}+(-2+\beta _{1}+\cdots)q^{9}+\cdots\)
416.2.e.a \(2\) \(3.322\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{3}-q^{5}-3iq^{7}+2q^{9}+2q^{11}+\cdots\)
416.2.e.b \(2\) \(3.322\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(0\) \(q+iq^{3}+q^{5}+3iq^{7}+2q^{9}-2q^{11}+\cdots\)
416.2.e.c \(8\) \(3.322\) 8.0.4521217600.1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+\beta _{4}q^{5}+\beta _{3}q^{7}+(-3-\beta _{5}+\cdots)q^{9}+\cdots\)
416.2.f.a \(2\) \(3.322\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-6\) \(0\) \(0\) \(q-3q^{3}+3iq^{5}-iq^{7}+6q^{9}+4iq^{11}+\cdots\)
416.2.f.b \(2\) \(3.322\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{5}-3q^{9}+(-3+i)q^{13}-2q^{17}+\cdots\)
416.2.f.c \(2\) \(3.322\) \(\Q(\sqrt{-1}) \) None None \(0\) \(6\) \(0\) \(0\) \(q+3q^{3}+3iq^{5}+iq^{7}+6q^{9}-4iq^{11}+\cdots\)
416.2.f.d \(4\) \(3.322\) \(\Q(i, \sqrt{13})\) \(\Q(\sqrt{-13}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{7}-3q^{9}+(\beta _{1}+\beta _{2})q^{11}-\beta _{3}q^{13}+\cdots\)
416.2.f.e \(4\) \(3.322\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}-\beta _{1}q^{5}-\beta _{2}q^{7}+2q^{9}+(2+\cdots)q^{13}+\cdots\)
416.2.i.a \(2\) \(3.322\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(2\) \(0\) \(q+(-2+2\zeta_{6})q^{3}+q^{5}-\zeta_{6}q^{9}+(-4+\cdots)q^{11}+\cdots\)
416.2.i.b \(2\) \(3.322\) \(\Q(\sqrt{-3}) \) None None \(0\) \(2\) \(2\) \(0\) \(q+(2-2\zeta_{6})q^{3}+q^{5}-\zeta_{6}q^{9}+(4-4\zeta_{6})q^{11}+\cdots\)
416.2.i.c \(4\) \(3.322\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(-2\) \(0\) \(6\) \(q+(-1+\beta _{1}-\beta _{2})q^{3}+2\beta _{3}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
416.2.i.d \(4\) \(3.322\) \(\Q(\sqrt{-3}, \sqrt{11})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{7}+8\beta _{2}q^{9}+\cdots\)
416.2.i.e \(4\) \(3.322\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+(1-2\zeta_{12}+\zeta_{12}^{3})q^{5}+3\zeta_{12}^{2}q^{9}+\cdots\)
416.2.i.f \(4\) \(3.322\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(2\) \(0\) \(-6\) \(q+(1+\beta _{1}+\beta _{2})q^{3}-2\beta _{3}q^{5}+(\beta _{1}+3\beta _{2}+\cdots)q^{7}+\cdots\)
416.2.i.g \(8\) \(3.322\) 8.0.6927565824.3 None None \(0\) \(0\) \(-4\) \(0\) \(q+(-\beta _{2}-\beta _{7})q^{3}+(-1+\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
416.2.k.a \(2\) \(3.322\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(-2\) \(q-2iq^{3}+(-1-i)q^{5}+(-1-i)q^{7}+\cdots\)
416.2.k.b \(2\) \(3.322\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(2\) \(q+2iq^{3}+(-1-i)q^{5}+(1+i)q^{7}+\cdots\)
416.2.k.c \(4\) \(3.322\) \(\Q(i, \sqrt{10})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{3}+\beta _{1}q^{5}-\beta _{1}q^{7}+2q^{9}+(-1+\cdots)q^{11}+\cdots\)
416.2.k.d \(4\) \(3.322\) \(\Q(i, \sqrt{10})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+\beta _{1}q^{5}+\beta _{1}q^{7}+2q^{9}+(1+\cdots)q^{11}+\cdots\)
416.2.k.e \(8\) \(3.322\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(0\) \(0\) \(-2\) \(q-\beta _{4}q^{3}+\beta _{7}q^{5}+(-\beta _{3}+\beta _{7})q^{7}+\cdots\)
416.2.k.f \(8\) \(3.322\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(0\) \(0\) \(2\) \(q-\beta _{4}q^{3}-\beta _{6}q^{5}+(-\beta _{2}+\beta _{6})q^{7}+\cdots\)
416.2.u.a \(4\) \(3.322\) \(\Q(i, \sqrt{26})\) None None \(0\) \(4\) \(0\) \(0\) \(q+q^{3}+\beta _{1}q^{5}-\beta _{3}q^{7}-2q^{9}+(-1+\cdots)q^{11}+\cdots\)
416.2.u.b \(20\) \(3.322\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(4\) \(0\) \(0\) \(q+\beta _{2}q^{3}+\beta _{15}q^{5}+(\beta _{4}-\beta _{9})q^{7}+(1+\cdots)q^{9}+\cdots\)
416.2.w.a \(4\) \(3.322\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(-2+4\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
416.2.w.b \(4\) \(3.322\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-1+2\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+(3-3\zeta_{12}^{2}+\cdots)q^{9}+\cdots\)
416.2.w.c \(8\) \(3.322\) 8.0.56070144.2 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{3}+(-\beta _{4}+\beta _{5})q^{5}+\beta _{3}q^{7}+\cdots\)
416.2.w.d \(12\) \(3.322\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{9}q^{3}+(-2\beta _{4}-\beta _{5}+\beta _{6})q^{5}-\beta _{3}q^{7}+\cdots\)
416.2.z.a \(24\) \(3.322\) None None \(0\) \(0\) \(0\) \(2\)
416.2.ba.a \(4\) \(3.322\) \(\Q(\zeta_{12})\) None None \(0\) \(-6\) \(8\) \(12\) \(q+(-1+\zeta_{12}-\zeta_{12}^{2})q^{3}+(2+2\zeta_{12}+\cdots)q^{5}+\cdots\)
416.2.ba.b \(4\) \(3.322\) \(\Q(\zeta_{12})\) None None \(0\) \(6\) \(-8\) \(12\) \(q+(2-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+(-2+\cdots)q^{5}+\cdots\)
416.2.ba.c \(16\) \(3.322\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(-18\) \(q+(-\beta _{1}+\beta _{8}+\beta _{12})q^{3}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
416.2.bd.a \(216\) \(3.322\) None None \(-4\) \(-8\) \(-4\) \(0\)
416.2.bf.a \(192\) \(3.322\) None None \(0\) \(0\) \(0\) \(0\)
416.2.bg.a \(216\) \(3.322\) None None \(0\) \(-8\) \(0\) \(0\)
416.2.bi.a \(216\) \(3.322\) None None \(-4\) \(-8\) \(-4\) \(-8\)
416.2.bk.a \(48\) \(3.322\) None None \(0\) \(4\) \(0\) \(0\)
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