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Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 7 13
3822.2.a.a \(1\) \(30.519\) \(\Q\) None \(-1\) \(-1\) \(-3\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{8}+\cdots\)
3822.2.a.b \(1\) \(30.519\) \(\Q\) None \(-1\) \(-1\) \(-2\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots\)
3822.2.a.c \(1\) \(30.519\) \(\Q\) None \(-1\) \(-1\) \(-2\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots\)
3822.2.a.d \(1\) \(30.519\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
3822.2.a.e \(1\) \(30.519\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
3822.2.a.f \(1\) \(30.519\) \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
3822.2.a.g \(1\) \(30.519\) \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
3822.2.a.h \(1\) \(30.519\) \(\Q\) None \(-1\) \(-1\) \(2\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\cdots\)
3822.2.a.i \(1\) \(30.519\) \(\Q\) None \(-1\) \(-1\) \(2\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\cdots\)
3822.2.a.j \(1\) \(30.519\) \(\Q\) None \(-1\) \(1\) \(-2\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{8}+\cdots\)
3822.2.a.k \(1\) \(30.519\) \(\Q\) None \(-1\) \(1\) \(-2\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{8}+\cdots\)
3822.2.a.l \(1\) \(30.519\) \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
3822.2.a.m \(1\) \(30.519\) \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
3822.2.a.n \(1\) \(30.519\) \(\Q\) None \(-1\) \(1\) \(1\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
3822.2.a.o \(1\) \(30.519\) \(\Q\) None \(-1\) \(1\) \(1\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
3822.2.a.p \(1\) \(30.519\) \(\Q\) None \(-1\) \(1\) \(2\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
3822.2.a.q \(1\) \(30.519\) \(\Q\) None \(-1\) \(1\) \(2\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
3822.2.a.r \(1\) \(30.519\) \(\Q\) None \(1\) \(-1\) \(-3\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+q^{8}+\cdots\)
3822.2.a.s \(1\) \(30.519\) \(\Q\) None \(1\) \(-1\) \(-3\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+q^{8}+\cdots\)
3822.2.a.t \(1\) \(30.519\) \(\Q\) None \(1\) \(-1\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{8}+\cdots\)
3822.2.a.u \(1\) \(30.519\) \(\Q\) None \(1\) \(-1\) \(0\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
3822.2.a.v \(1\) \(30.519\) \(\Q\) None \(1\) \(-1\) \(1\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
3822.2.a.w \(1\) \(30.519\) \(\Q\) None \(1\) \(-1\) \(1\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
3822.2.a.x \(1\) \(30.519\) \(\Q\) None \(1\) \(-1\) \(2\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots\)
3822.2.a.y \(1\) \(30.519\) \(\Q\) None \(1\) \(-1\) \(3\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}+q^{8}+\cdots\)
3822.2.a.z \(1\) \(30.519\) \(\Q\) None \(1\) \(-1\) \(4\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}+q^{8}+\cdots\)
3822.2.a.ba \(1\) \(30.519\) \(\Q\) None \(1\) \(1\) \(-4\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}-4q^{5}+q^{6}+q^{8}+\cdots\)
3822.2.a.bb \(1\) \(30.519\) \(\Q\) None \(1\) \(1\) \(-3\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{8}+\cdots\)
3822.2.a.bc \(1\) \(30.519\) \(\Q\) None \(1\) \(1\) \(-3\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{8}+\cdots\)
3822.2.a.bd \(1\) \(30.519\) \(\Q\) None \(1\) \(1\) \(-2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{8}+\cdots\)
3822.2.a.be \(1\) \(30.519\) \(\Q\) None \(1\) \(1\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
3822.2.a.bf \(1\) \(30.519\) \(\Q\) None \(1\) \(1\) \(0\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
3822.2.a.bg \(1\) \(30.519\) \(\Q\) None \(1\) \(1\) \(3\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+q^{8}+\cdots\)
3822.2.a.bh \(1\) \(30.519\) \(\Q\) None \(1\) \(1\) \(3\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+q^{8}+\cdots\)
3822.2.a.bi \(2\) \(30.519\) \(\Q(\sqrt{7}) \) None \(-2\) \(-2\) \(2\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
3822.2.a.bj \(2\) \(30.519\) \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(2\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
3822.2.a.bk \(2\) \(30.519\) \(\Q(\sqrt{7}) \) None \(-2\) \(2\) \(-2\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}+(-1+\beta )q^{5}-q^{6}+\cdots\)
3822.2.a.bl \(2\) \(30.519\) \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(-2\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
3822.2.a.bm \(2\) \(30.519\) \(\Q(\sqrt{57}) \) None \(-2\) \(2\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}-q^{8}+\cdots\)
3822.2.a.bn \(2\) \(30.519\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(-4\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+(-2+\beta )q^{5}-q^{6}+\cdots\)
3822.2.a.bo \(2\) \(30.519\) \(\Q(\sqrt{17}) \) None \(2\) \(-2\) \(-3\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
3822.2.a.bp \(2\) \(30.519\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(0\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+\beta q^{5}-q^{6}+q^{8}+\cdots\)
3822.2.a.bq \(2\) \(30.519\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(2\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
3822.2.a.br \(2\) \(30.519\) \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
3822.2.a.bs \(2\) \(30.519\) \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(0\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+\beta q^{5}+q^{6}+q^{8}+\cdots\)
3822.2.a.bt \(2\) \(30.519\) \(\Q(\sqrt{41}) \) None \(2\) \(2\) \(1\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+\beta q^{5}+q^{6}+q^{8}+\cdots\)
3822.2.a.bu \(2\) \(30.519\) \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(4\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+(2+\beta )q^{5}+q^{6}+\cdots\)
3822.2.a.bv \(3\) \(30.519\) 3.3.2700.1 None \(-3\) \(-3\) \(3\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+(1-\beta _{1})q^{5}+q^{6}+\cdots\)
3822.2.a.bw \(3\) \(30.519\) 3.3.2700.1 None \(-3\) \(3\) \(-3\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+(-1+\beta _{1})q^{5}-q^{6}+\cdots\)
3822.2.a.bx \(4\) \(30.519\) 4.4.10304.1 None \(-4\) \(-4\) \(-6\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+(-2+\beta _{1})q^{5}+q^{6}+\cdots\)
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