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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1776.1.n.a \(1\) \(0.886\) \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-111}) \) \(\Q(\sqrt{37}) \) \(0\) \(-1\) \(0\) \(2\) \(q-q^{3}+2q^{7}+q^{9}-2q^{21}-q^{25}+\cdots\)
1776.1.n.b \(2\) \(0.886\) \(\Q(\sqrt{-3}) \) None \(\Q(\sqrt{37}) \) \(0\) \(1\) \(0\) \(-2\) \(q-\zeta_{6}^{2}q^{3}-q^{7}-\zeta_{6}q^{9}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{11}+\cdots\)
1776.1.n.c \(2\) \(0.886\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-111}) \) None \(0\) \(2\) \(0\) \(0\) \(q+q^{3}-\beta q^{5}+q^{9}-\beta q^{15}+\beta q^{17}+\cdots\)
1776.1.w.a \(2\) \(0.886\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}-iq^{7}+q^{9}+(-1-i)q^{13}+\cdots\)
1776.1.w.b \(2\) \(0.886\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(0\) \(q+q^{3}+iq^{7}+q^{9}+(-1-i)q^{13}+\cdots\)
1776.1.z.a \(4\) \(0.886\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(-4\) \(0\) \(q+\zeta_{8}^{2}q^{2}-\zeta_{8}^{3}q^{3}-q^{4}+(-1+\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
1776.1.z.b \(4\) \(0.886\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(4\) \(0\) \(q-\zeta_{8}^{2}q^{2}-\zeta_{8}^{3}q^{3}-q^{4}+(1-\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
1776.1.z.c \(16\) \(0.886\) \(\Q(\zeta_{32})\) \(\Q(\sqrt{-111}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{32}^{3}q^{2}+\zeta_{32}^{4}q^{3}+\zeta_{32}^{6}q^{4}+\cdots\)
1776.1.bq.a \(2\) \(0.886\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(1\) \(q-\zeta_{6}^{2}q^{3}-\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+(-1+\cdots)q^{13}+\cdots\)
1776.1.bw.a \(2\) \(0.886\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-1\) \(q+\zeta_{6}q^{3}-\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{13}+\cdots\)
1776.1.cr.a \(4\) \(0.886\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+\zeta_{12}^{4}q^{3}+\zeta_{12}q^{7}-\zeta_{12}^{2}q^{9}+(\zeta_{12}^{2}+\cdots)q^{13}+\cdots\)
1776.1.cr.b \(4\) \(0.886\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(0\) \(q-\zeta_{12}^{4}q^{3}-\zeta_{12}q^{7}-\zeta_{12}^{2}q^{9}+(\zeta_{12}^{2}+\cdots)q^{13}+\cdots\)
1776.1.dk.a \(6\) \(0.886\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-3\) \(q+\zeta_{18}^{7}q^{3}+(-\zeta_{18}^{5}+\zeta_{18}^{6})q^{7}+\cdots\)
1776.1.dr.a \(6\) \(0.886\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(3\) \(q+\zeta_{18}q^{3}+(-\zeta_{18}^{2}-\zeta_{18}^{6})q^{7}+\zeta_{18}^{2}q^{9}+\cdots\)
1776.1.em.a \(12\) \(0.886\) \(\Q(\zeta_{36})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{36}^{16}q^{3}+(-\zeta_{36}^{5}+\zeta_{36}^{15})q^{7}+\cdots\)
1776.1.em.b \(12\) \(0.886\) \(\Q(\zeta_{36})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{36}^{16}q^{3}+(\zeta_{36}^{5}-\zeta_{36}^{15})q^{7}+\cdots\)
1776.2.a.a \(1\) \(14.181\) \(\Q\) None None \(0\) \(-1\) \(-2\) \(0\) \(-\) \(q-q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
1776.2.a.b \(1\) \(14.181\) \(\Q\) None None \(0\) \(-1\) \(-2\) \(4\) \(-\) \(q-q^{3}-2q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots\)
1776.2.a.c \(1\) \(14.181\) \(\Q\) None None \(0\) \(-1\) \(0\) \(1\) \(+\) \(q-q^{3}+q^{7}+q^{9}-3q^{11}-q^{13}-3q^{17}+\cdots\)
1776.2.a.d \(1\) \(14.181\) \(\Q\) None None \(0\) \(-1\) \(4\) \(0\) \(-\) \(q-q^{3}+4q^{5}+q^{9}+2q^{13}-4q^{15}+\cdots\)
1776.2.a.e \(1\) \(14.181\) \(\Q\) None None \(0\) \(-1\) \(4\) \(1\) \(-\) \(q-q^{3}+4q^{5}+q^{7}+q^{9}+q^{11}-3q^{13}+\cdots\)
1776.2.a.f \(1\) \(14.181\) \(\Q\) None None \(0\) \(1\) \(-4\) \(-3\) \(-\) \(q+q^{3}-4q^{5}-3q^{7}+q^{9}-5q^{11}+\cdots\)
1776.2.a.g \(1\) \(14.181\) \(\Q\) None None \(0\) \(1\) \(-4\) \(1\) \(+\) \(q+q^{3}-4q^{5}+q^{7}+q^{9}+3q^{11}-5q^{13}+\cdots\)
1776.2.a.h \(1\) \(14.181\) \(\Q\) None None \(0\) \(1\) \(0\) \(-3\) \(+\) \(q+q^{3}-3q^{7}+q^{9}-q^{11}+q^{13}-3q^{17}+\cdots\)
1776.2.a.i \(1\) \(14.181\) \(\Q\) None None \(0\) \(1\) \(0\) \(0\) \(+\) \(q+q^{3}+q^{9}-4q^{11}-2q^{13}-6q^{19}+\cdots\)
1776.2.a.j \(1\) \(14.181\) \(\Q\) None None \(0\) \(1\) \(0\) \(0\) \(+\) \(q+q^{3}+q^{9}-6q^{13}-4q^{17}-4q^{19}+\cdots\)
1776.2.a.k \(1\) \(14.181\) \(\Q\) None None \(0\) \(1\) \(2\) \(0\) \(-\) \(q+q^{3}+2q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots\)
1776.2.a.l \(2\) \(14.181\) \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(-4\) \(4\) \(+\) \(q-q^{3}+(-2+\beta )q^{5}+(2+2\beta )q^{7}+q^{9}+\cdots\)
1776.2.a.m \(2\) \(14.181\) \(\Q(\sqrt{6}) \) None None \(0\) \(-2\) \(0\) \(-4\) \(+\) \(q-q^{3}+\beta q^{5}-2q^{7}+q^{9}+(2-2\beta )q^{13}+\cdots\)
1776.2.a.n \(2\) \(14.181\) \(\Q(\sqrt{41}) \) None None \(0\) \(-2\) \(0\) \(-3\) \(-\) \(q-q^{3}+(-1-\beta )q^{7}+q^{9}+(-1-\beta )q^{11}+\cdots\)
1776.2.a.o \(2\) \(14.181\) \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(-2\) \(0\) \(-\) \(q+q^{3}+(-1+\beta )q^{5}+2\beta q^{7}+q^{9}+\cdots\)
1776.2.a.p \(2\) \(14.181\) \(\Q(\sqrt{5}) \) None None \(0\) \(2\) \(2\) \(-8\) \(+\) \(q+q^{3}+(1+\beta )q^{5}-4q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
1776.2.a.q \(2\) \(14.181\) \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(2\) \(4\) \(-\) \(q+q^{3}+(1+\beta )q^{5}+2q^{7}+q^{9}+(2+2\beta )q^{11}+\cdots\)
1776.2.a.r \(3\) \(14.181\) 3.3.568.1 None None \(0\) \(-3\) \(0\) \(1\) \(+\) \(q-q^{3}+(\beta _{1}+\beta _{2})q^{5}-\beta _{2}q^{7}+q^{9}+\cdots\)
1776.2.a.s \(3\) \(14.181\) 3.3.316.1 None None \(0\) \(3\) \(2\) \(5\) \(-\) \(q+q^{3}+(1-\beta _{1}-\beta _{2})q^{5}+(1+2\beta _{1}+\cdots)q^{7}+\cdots\)
1776.2.a.t \(3\) \(14.181\) 3.3.148.1 None None \(0\) \(3\) \(4\) \(4\) \(-\) \(q+q^{3}+(1+\beta _{2})q^{5}+(2-\beta _{1}-\beta _{2})q^{7}+\cdots\)
1776.2.a.u \(4\) \(14.181\) 4.4.6224.1 None None \(0\) \(-4\) \(-2\) \(-4\) \(-\) \(q-q^{3}+(-1+\beta _{3})q^{5}+(-2+\beta _{2}+\beta _{3})q^{7}+\cdots\)
1776.2.e.a \(2\) \(14.181\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(0\) \(0\) \(q+(-1-\zeta_{6})q^{3}+(2-4\zeta_{6})q^{5}+(1-2\zeta_{6})q^{7}+\cdots\)
1776.2.e.b \(2\) \(14.181\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{3}-2\zeta_{6}q^{5}-2\zeta_{6}q^{7}-3q^{9}+\cdots\)
1776.2.e.c \(2\) \(14.181\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{6}q^{3}-2\zeta_{6}q^{5}+2\zeta_{6}q^{7}-3q^{9}+\cdots\)
1776.2.e.d \(2\) \(14.181\) \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(0\) \(0\) \(q+(1+\zeta_{6})q^{3}+(2-4\zeta_{6})q^{5}+(-1+2\zeta_{6})q^{7}+\cdots\)
1776.2.e.e \(8\) \(14.181\) 8.0.8275904784.2 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}+(2\beta _{3}-2\beta _{5}-\beta _{6})q^{7}+(-\beta _{2}+\cdots)q^{9}+\cdots\)
1776.2.e.f \(12\) \(14.181\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{10}q^{3}-\beta _{1}q^{5}+(-\beta _{6}-\beta _{10})q^{7}+\cdots\)
1776.2.e.g \(12\) \(14.181\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{8}q^{3}+\beta _{10}q^{5}-\beta _{11}q^{7}+(-\beta _{2}+\cdots)q^{9}+\cdots\)
1776.2.e.h \(16\) \(14.181\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{3}+\beta _{6}q^{5}-\beta _{2}q^{9}+(\beta _{5}+\beta _{12}+\cdots)q^{11}+\cdots\)
1776.2.e.i \(16\) \(14.181\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+\beta _{7}q^{5}+(-\beta _{1}-\beta _{3}-\beta _{13}+\cdots)q^{7}+\cdots\)
1776.2.h.a \(2\) \(14.181\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(0\) \(-6\) \(q-q^{3}+2iq^{5}-3q^{7}+q^{9}+3q^{11}+\cdots\)
1776.2.h.b \(2\) \(14.181\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}+q^{9}-4q^{11}-2iq^{13}+2iq^{17}+\cdots\)
1776.2.h.c \(2\) \(14.181\) \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(0\) \(0\) \(q+q^{3}+iq^{5}+q^{9}+iq^{15}-iq^{17}+\cdots\)
1776.2.h.d \(4\) \(14.181\) 4.0.32448.1 None None \(0\) \(-4\) \(0\) \(4\) \(q-q^{3}+\beta _{1}q^{5}+(1-\beta _{2})q^{7}+q^{9}+2\beta _{1}q^{13}+\cdots\)
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