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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1476.1.h.a \(1\) \(0.737\) \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-41}) \) \(\Q(\sqrt{41}) \) \(-1\) \(0\) \(2\) \(0\) \(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+q^{16}+\cdots\)
1476.1.h.b \(2\) \(0.737\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-41}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}-\beta q^{7}+q^{8}+\beta q^{11}-\beta q^{14}+\cdots\)
1476.1.j.a \(2\) \(0.737\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{8}+(1+i)q^{13}+q^{16}+\cdots\)
1476.1.j.b \(2\) \(0.737\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{8}+(1+i)q^{13}+q^{16}+\cdots\)
1476.1.l.a \(4\) \(0.737\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}-\zeta_{8}^{3})q^{5}+\zeta_{8}^{3}q^{11}+\zeta_{8}q^{17}+\cdots\)
1476.1.o.a \(2\) \(0.737\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-41}) \) None \(-1\) \(-2\) \(1\) \(-1\) \(q+\zeta_{6}^{2}q^{2}-q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{6}+\cdots\)
1476.1.o.b \(2\) \(0.737\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-41}) \) None \(-1\) \(2\) \(1\) \(1\) \(q+\zeta_{6}^{2}q^{2}+q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{6}+\cdots\)
1476.1.o.c \(4\) \(0.737\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-41}) \) None \(-2\) \(0\) \(-2\) \(0\) \(q-\zeta_{12}^{2}q^{2}-\zeta_{12}^{3}q^{3}+\zeta_{12}^{4}q^{4}+\cdots\)
1476.1.o.d \(8\) \(0.737\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-41}) \) None \(4\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{4}q^{2}+\zeta_{24}^{9}q^{3}+\zeta_{24}^{8}q^{4}+\cdots\)
1476.1.w.a \(4\) \(0.737\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(-1-\zeta_{8}^{2})q^{5}+\cdots\)
1476.1.w.b \(4\) \(0.737\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(1+\zeta_{8}^{2})q^{5}+\cdots\)
1476.1.z.a \(4\) \(0.737\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-1}) \) None \(1\) \(0\) \(-2\) \(0\) \(q+\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+(-\zeta_{10}^{3}+\zeta_{10}^{4}+\cdots)q^{5}+\cdots\)
1476.1.ba.a \(4\) \(0.737\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-1}) \) None \(1\) \(0\) \(2\) \(0\) \(q-\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}+(-\zeta_{10}^{2}-\zeta_{10}^{4}+\cdots)q^{5}+\cdots\)
1476.1.bo.a \(8\) \(0.737\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}^{9}q^{2}-\zeta_{20}^{8}q^{4}+(-\zeta_{20}^{2}-\zeta_{20}^{4}+\cdots)q^{5}+\cdots\)
1476.1.bo.b \(8\) \(0.737\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}^{9}q^{2}-\zeta_{20}^{8}q^{4}+(\zeta_{20}^{2}+\zeta_{20}^{4}+\cdots)q^{5}+\cdots\)
1476.1.cc.a \(16\) \(0.737\) \(\Q(\zeta_{40})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+\zeta_{40}^{13}q^{2}-\zeta_{40}^{6}q^{4}+(\zeta_{40}^{8}+\zeta_{40}^{14}+\cdots)q^{5}+\cdots\)
1476.1.cc.b \(16\) \(0.737\) \(\Q(\zeta_{40})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q-\zeta_{40}^{13}q^{2}-\zeta_{40}^{6}q^{4}+(-\zeta_{40}^{8}+\cdots)q^{5}+\cdots\)
1476.2.a.a \(1\) \(11.786\) \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) \(+\) \(q-2q^{7}+q^{11}-2q^{13}+q^{17}-4q^{19}+\cdots\)
1476.2.a.b \(1\) \(11.786\) \(\Q\) None None \(0\) \(0\) \(2\) \(-4\) \(-\) \(q+2q^{5}-4q^{7}+5q^{11}+4q^{13}+5q^{17}+\cdots\)
1476.2.a.c \(2\) \(11.786\) \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(-2\) \(2\) \(+\) \(q+(-1+\beta )q^{5}+(1-\beta )q^{7}+(-2-\beta )q^{11}+\cdots\)
1476.2.a.d \(2\) \(11.786\) \(\Q(\sqrt{6}) \) None None \(0\) \(0\) \(4\) \(4\) \(-\) \(q+(2+\beta )q^{5}+(2-\beta )q^{7}+(1-\beta )q^{11}+\cdots\)
1476.2.a.e \(3\) \(11.786\) 3.3.404.1 None None \(0\) \(0\) \(-4\) \(4\) \(+\) \(q+(-1-\beta _{2})q^{5}+(1+\beta _{1})q^{7}+(-2+\cdots)q^{11}+\cdots\)
1476.2.a.f \(3\) \(11.786\) 3.3.404.1 None None \(0\) \(0\) \(4\) \(4\) \(-\) \(q+(1+\beta _{2})q^{5}+(1+\beta _{1})q^{7}+(2+2\beta _{1}+\cdots)q^{11}+\cdots\)
1476.2.a.g \(4\) \(11.786\) 4.4.25808.1 None None \(0\) \(0\) \(-4\) \(0\) \(-\) \(q+(-2+\beta _{2}-\beta _{3})q^{5}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
1476.2.c.a \(80\) \(11.786\) None None \(0\) \(0\) \(0\) \(0\)
1476.2.d.a \(4\) \(11.786\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{2}-2q^{4}-\zeta_{8}^{2}q^{5}+2\zeta_{8}^{2}q^{8}+\cdots\)
1476.2.d.b \(8\) \(11.786\) 8.0.\(\cdots\).5 None None \(-4\) \(0\) \(0\) \(0\) \(q+(-1+\beta _{4})q^{2}+(-1-\beta _{4})q^{4}-2\beta _{6}q^{5}+\cdots\)
1476.2.d.c \(8\) \(11.786\) 8.0.\(\cdots\).5 None None \(4\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{2}+(-2+\beta _{4})q^{4}-2\beta _{6}q^{5}+\cdots\)
1476.2.d.d \(64\) \(11.786\) None None \(0\) \(0\) \(0\) \(0\)
1476.2.f.a \(2\) \(11.786\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-8\) \(0\) \(q-4q^{5}-4iq^{7}-3iq^{11}-4iq^{13}+\cdots\)
1476.2.f.b \(2\) \(11.786\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(8\) \(0\) \(q+4q^{5}-4iq^{7}+3iq^{11}-4iq^{13}+\cdots\)
1476.2.f.c \(4\) \(11.786\) \(\Q(i, \sqrt{41})\) \(\Q(\sqrt{-123}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{11}+(\beta _{1}-2\beta _{2})q^{17}-5q^{25}+\cdots\)
1476.2.f.d \(4\) \(11.786\) 4.0.25088.1 None None \(0\) \(0\) \(4\) \(0\) \(q+(1-\beta _{2})q^{5}+\beta _{3}q^{7}+(2\beta _{1}+\beta _{3})q^{11}+\cdots\)
1476.2.f.e \(6\) \(11.786\) 6.0.5089536.1 None None \(0\) \(0\) \(-4\) \(0\) \(q+(-1-\beta _{1})q^{5}+(-\beta _{2}+\beta _{5})q^{7}+(\beta _{2}+\cdots)q^{11}+\cdots\)
1476.2.i.a \(2\) \(11.786\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(-5\) \(q+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-5+5\zeta_{6})q^{7}+\cdots\)
1476.2.i.b \(32\) \(11.786\) None None \(0\) \(-1\) \(1\) \(-1\)
1476.2.i.c \(46\) \(11.786\) None None \(0\) \(-1\) \(2\) \(4\)
1476.2.k.a \(6\) \(11.786\) 6.0.5089536.1 None None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{4}-\beta _{5})q^{5}+(\beta _{1}+\beta _{2}-\beta _{5})q^{7}+\cdots\)
1476.2.k.b \(12\) \(11.786\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{5}+(-\beta _{1}-\beta _{3}-\beta _{10})q^{7}+\beta _{11}q^{11}+\cdots\)
1476.2.k.c \(16\) \(11.786\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{5}-\beta _{9}q^{7}+(\beta _{3}-\beta _{4}-\beta _{7}-\beta _{10}+\cdots)q^{11}+\cdots\)
1476.2.n.a \(4\) \(11.786\) \(\Q(\zeta_{10})\) None None \(0\) \(0\) \(-7\) \(9\) \(q+(-3+3\zeta_{10}+2\zeta_{10}^{3})q^{5}+(3+3\zeta_{10}^{2}+\cdots)q^{7}+\cdots\)
1476.2.n.b \(4\) \(11.786\) \(\Q(\zeta_{10})\) None None \(0\) \(0\) \(-5\) \(-3\) \(q+(-1+\zeta_{10}-2\zeta_{10}^{3})q^{5}+(-1-\zeta_{10}^{2}+\cdots)q^{7}+\cdots\)
1476.2.n.c \(4\) \(11.786\) \(\Q(\zeta_{10})\) None None \(0\) \(0\) \(-1\) \(-3\) \(q+(-1+\zeta_{10}+2\zeta_{10}^{3})q^{5}+(-1-\zeta_{10}^{2}+\cdots)q^{7}+\cdots\)
1476.2.n.d \(4\) \(11.786\) \(\Q(\zeta_{10})\) None None \(0\) \(0\) \(7\) \(4\) \(q+(2-2\zeta_{10}+\zeta_{10}^{3})q^{5}+(2-2\zeta_{10}+\cdots)q^{7}+\cdots\)
1476.2.n.e \(8\) \(11.786\) 8.0.2127515625.1 None None \(0\) \(0\) \(2\) \(-7\) \(q-\beta _{4}q^{5}+(-2+\beta _{1}+2\beta _{2}-\beta _{3})q^{7}+\cdots\)
1476.2.n.f \(16\) \(11.786\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(4\) \(0\) \(q+(1+\beta _{3}+\beta _{4}-\beta _{6}-\beta _{9})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1476.2.n.g \(32\) \(11.786\) None None \(0\) \(0\) \(0\) \(0\)
1476.2.q.a \(8\) \(11.786\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}-\zeta_{24}^{5}-2\zeta_{24}^{6}+\zeta_{24}^{7})q^{3}+\cdots\)
1476.2.q.b \(76\) \(11.786\) None None \(0\) \(0\) \(4\) \(0\)
1476.2.x.a \(28\) \(11.786\) None None \(0\) \(0\) \(-4\) \(0\)
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