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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
385.1.q.a \(2\) \(0.192\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-55}) \) None \(-1\) \(0\) \(-1\) \(-2\) \(q-\zeta_{6}q^{2}-\zeta_{6}q^{5}-q^{7}-q^{8}-\zeta_{6}q^{9}+\cdots\)
385.1.q.b \(2\) \(0.192\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-55}) \) None \(1\) \(0\) \(-1\) \(2\) \(q+\zeta_{6}q^{2}-\zeta_{6}q^{5}+q^{7}+q^{8}-\zeta_{6}q^{9}+\cdots\)
385.1.q.c \(4\) \(0.192\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{2}+(-1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
385.1.y.a \(4\) \(0.192\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-35}) \) None \(0\) \(-3\) \(1\) \(1\) \(q+(-1+\zeta_{10})q^{3}+\zeta_{10}^{2}q^{4}-\zeta_{10}^{4}q^{5}+\cdots\)
385.1.y.b \(4\) \(0.192\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-35}) \) None \(0\) \(3\) \(-1\) \(-1\) \(q+(1-\zeta_{10})q^{3}+\zeta_{10}^{2}q^{4}+\zeta_{10}^{4}q^{5}+\cdots\)
385.2.a.a \(1\) \(3.074\) \(\Q\) None None \(-1\) \(-2\) \(1\) \(1\) \(+\) \(q-q^{2}-2q^{3}-q^{4}+q^{5}+2q^{6}+q^{7}+\cdots\)
385.2.a.b \(1\) \(3.074\) \(\Q\) None None \(-1\) \(0\) \(1\) \(-1\) \(+\) \(q-q^{2}-q^{4}+q^{5}-q^{7}+3q^{8}-3q^{9}+\cdots\)
385.2.a.c \(2\) \(3.074\) \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(-2\) \(2\) \(-\) \(q+\beta q^{2}+(1+\beta )q^{3}+q^{4}-q^{5}+(3+\beta )q^{6}+\cdots\)
385.2.a.d \(2\) \(3.074\) \(\Q(\sqrt{2}) \) None None \(2\) \(0\) \(-2\) \(-2\) \(-\) \(q+(1+\beta )q^{2}+\beta q^{3}+(1+2\beta )q^{4}-q^{5}+\cdots\)
385.2.a.e \(3\) \(3.074\) 3.3.148.1 None None \(-3\) \(-4\) \(-3\) \(3\) \(+\) \(q+(-1-\beta _{2})q^{2}+(-1-\beta _{1})q^{3}+(2+\cdots)q^{4}+\cdots\)
385.2.a.f \(3\) \(3.074\) 3.3.148.1 None None \(-3\) \(-2\) \(-3\) \(-3\) \(+\) \(q+(-1-\beta _{2})q^{2}+(-1+\beta _{1})q^{3}+(2+\cdots)q^{4}+\cdots\)
385.2.a.g \(3\) \(3.074\) 3.3.148.1 None None \(1\) \(0\) \(3\) \(3\) \(-\) \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
385.2.a.h \(4\) \(3.074\) 4.4.11348.1 None None \(2\) \(2\) \(4\) \(-4\) \(-\) \(q+(1+\beta _{2})q^{2}+(1+\beta _{3})q^{3}+(2+\beta _{2}+\cdots)q^{4}+\cdots\)
385.2.b.a \(2\) \(3.074\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(0\) \(q+iq^{2}-2iq^{3}+q^{4}+(1+2i)q^{5}+\cdots\)
385.2.b.b \(2\) \(3.074\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(0\) \(q+iq^{2}-2iq^{3}+q^{4}+(1-2i)q^{5}+\cdots\)
385.2.b.c \(12\) \(3.074\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(6\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{2}-\beta _{10})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)
385.2.b.d \(16\) \(3.074\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{7}+\beta _{13})q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)
385.2.c.a \(32\) \(3.074\) None None \(0\) \(0\) \(0\) \(0\)
385.2.h.a \(4\) \(3.074\) \(\Q(\sqrt{5}, \sqrt{-7})\) \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{3})q^{3}-2q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)
385.2.h.b \(8\) \(3.074\) 8.0.\(\cdots\).19 \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{2}+(2+\beta _{5})q^{4}+\beta _{1}q^{5}-\beta _{2}q^{7}+\cdots\)
385.2.h.c \(32\) \(3.074\) None None \(0\) \(0\) \(0\) \(0\)
385.2.i.a \(8\) \(3.074\) 8.0.310217769.2 None None \(3\) \(3\) \(-4\) \(1\) \(q+(1+\beta _{1}+\beta _{2}-\beta _{5}-\beta _{7})q^{2}+(-\beta _{2}+\cdots)q^{3}+\cdots\)
385.2.i.b \(12\) \(3.074\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(3\) \(-1\) \(6\) \(-3\) \(q+(-\beta _{1}+\beta _{5})q^{2}-\beta _{9}q^{3}+(-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
385.2.i.c \(16\) \(3.074\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-3\) \(-1\) \(-8\) \(-1\) \(q-\beta _{1}q^{2}+(-\beta _{4}+\beta _{7})q^{3}+(-\beta _{8}+\beta _{11}+\cdots)q^{4}+\cdots\)
385.2.i.d \(20\) \(3.074\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(-3\) \(3\) \(10\) \(-1\) \(q-\beta _{1}q^{2}+(-\beta _{10}+\beta _{17})q^{3}+(-\beta _{3}+\cdots)q^{4}+\cdots\)
385.2.j.a \(4\) \(3.074\) \(\Q(\zeta_{12})\) None None \(-4\) \(-6\) \(-2\) \(-8\) \(q+(-1-\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
385.2.j.b \(4\) \(3.074\) \(\Q(\zeta_{12})\) None None \(-4\) \(6\) \(2\) \(0\) \(q+(-1+\zeta_{12}^{3})q^{2}+(1-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
385.2.j.c \(32\) \(3.074\) None None \(8\) \(0\) \(0\) \(8\)
385.2.j.d \(40\) \(3.074\) None None \(0\) \(0\) \(0\) \(0\)
385.2.k.a \(72\) \(3.074\) None None \(0\) \(4\) \(0\) \(0\)
385.2.n.a \(4\) \(3.074\) \(\Q(\zeta_{10})\) None None \(1\) \(-3\) \(-1\) \(-1\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-\zeta_{10}+\cdots)q^{3}+\cdots\)
385.2.n.b \(4\) \(3.074\) \(\Q(\zeta_{10})\) None None \(5\) \(3\) \(1\) \(1\) \(q+(1+\zeta_{10}-\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(\zeta_{10}+\cdots)q^{3}+\cdots\)
385.2.n.c \(8\) \(3.074\) 8.0.13140625.1 None None \(2\) \(4\) \(-2\) \(-2\) \(q+(-\beta _{3}+\beta _{5}+\beta _{6})q^{2}+(1-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
385.2.n.d \(16\) \(3.074\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-4\) \(4\) \(4\) \(4\) \(q+(-1-\beta _{4}+\beta _{7}-\beta _{8}-\beta _{9}-\beta _{10}+\cdots)q^{2}+\cdots\)
385.2.n.e \(28\) \(3.074\) None None \(3\) \(0\) \(7\) \(-7\)
385.2.n.f \(36\) \(3.074\) None None \(1\) \(0\) \(-9\) \(9\)
385.2.o.a \(16\) \(3.074\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{10}-\beta _{14})q^{2}+(\beta _{1}+2\beta _{5}-\beta _{7}+\cdots)q^{4}+\cdots\)
385.2.o.b \(72\) \(3.074\) None None \(0\) \(0\) \(0\) \(0\)
385.2.t.a \(4\) \(3.074\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-2\) \(0\) \(q+\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
385.2.t.b \(36\) \(3.074\) None None \(0\) \(0\) \(2\) \(0\)
385.2.t.c \(40\) \(3.074\) None None \(0\) \(0\) \(0\) \(0\)
385.2.u.a \(64\) \(3.074\) None None \(0\) \(0\) \(0\) \(0\)
385.2.v.a \(8\) \(3.074\) 8.0.37515625.1 \(\Q(\sqrt{-35}) \) None \(0\) \(-5\) \(-10\) \(0\) \(q+(\beta _{2}+\beta _{5}-\beta _{6}+\beta _{7})q^{3}-2\beta _{3}q^{4}+\cdots\)
385.2.v.b \(8\) \(3.074\) 8.0.37515625.1 \(\Q(\sqrt{-35}) \) None \(0\) \(5\) \(10\) \(0\) \(q+(2-\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5}-2\beta _{6}+\cdots)q^{3}+\cdots\)
385.2.v.c \(160\) \(3.074\) None None \(0\) \(0\) \(0\) \(0\)
385.2.ba.a \(128\) \(3.074\) None None \(0\) \(0\) \(0\) \(0\)
385.2.bb.a \(144\) \(3.074\) None None \(0\) \(0\) \(2\) \(0\)
385.2.bc.a \(176\) \(3.074\) None None \(0\) \(-4\) \(-8\) \(0\)
385.2.bd.a \(80\) \(3.074\) None None \(0\) \(0\) \(0\) \(0\)
385.2.bd.b \(80\) \(3.074\) None None \(0\) \(0\) \(0\) \(0\)
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