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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
164.1.d.a \(1\) \(0.082\) \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-41}) \) \(\Q(\sqrt{41}) \) \(1\) \(0\) \(-2\) \(0\) \(q+q^{2}+q^{4}-2q^{5}+q^{8}-q^{9}-2q^{10}+\cdots\)
164.1.d.b \(2\) \(0.082\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-41}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}+\beta q^{7}-q^{8}+\cdots\)
164.1.j.a \(4\) \(0.082\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-1}) \) None \(-1\) \(0\) \(-2\) \(0\) \(q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{5}+\cdots\)
164.1.l.a \(4\) \(0.082\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-1}) \) None \(-1\) \(0\) \(2\) \(0\) \(q+\zeta_{10}^{2}q^{2}+\zeta_{10}^{4}q^{4}+(\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{5}+\cdots\)
164.2.a.a \(4\) \(1.310\) 4.4.25808.1 None None \(0\) \(2\) \(4\) \(0\) \(-\) \(q+(-\beta _{1}+\beta _{2})q^{3}+(2-\beta _{2}+\beta _{3})q^{5}+\cdots\)
164.2.b.a \(4\) \(1.310\) 4.0.25088.1 None None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{1}q^{3}+(-1+\beta _{2})q^{5}-\beta _{3}q^{7}+\beta _{2}q^{9}+\cdots\)
164.2.f.a \(6\) \(1.310\) 6.0.5089536.1 None None \(0\) \(2\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(-\beta _{4}+\beta _{5})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
164.2.g.a \(16\) \(1.310\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(-2\) \(-4\) \(0\) \(q+\beta _{2}q^{3}+(\beta _{3}+\beta _{4}-\beta _{6}+\beta _{7}-\beta _{9}+\cdots)q^{5}+\cdots\)
164.2.i.a \(4\) \(1.310\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(4\) \(0\) \(0\) \(0\) \(q+(1+\zeta_{8}^{2})q^{2}+2\zeta_{8}^{2}q^{4}+4\zeta_{8}^{3}q^{5}+\cdots\)
164.2.i.b \(72\) \(1.310\) None None \(-8\) \(0\) \(-8\) \(0\)
164.2.k.a \(16\) \(1.310\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(4\) \(0\) \(q-\beta _{1}q^{3}-\beta _{12}q^{5}+(-\beta _{9}+\beta _{14})q^{7}+\cdots\)
164.2.m.a \(24\) \(1.310\) None None \(0\) \(-2\) \(0\) \(0\)
164.2.o.a \(16\) \(1.310\) \(\Q(\zeta_{40})\) \(\Q(\sqrt{-1}) \) None \(-4\) \(0\) \(0\) \(0\) \(q+(\zeta_{40}^{2}-\zeta_{40}^{6}+\zeta_{40}^{8}+\zeta_{40}^{10}+\cdots)q^{2}+\cdots\)
164.2.o.b \(288\) \(1.310\) None None \(-12\) \(0\) \(-32\) \(0\)
164.3.c.a \(40\) \(4.469\) None None \(-2\) \(0\) \(0\) \(0\)
164.3.d.a \(4\) \(4.469\) 4.4.3442688.1 \(\Q(\sqrt{-41}) \) None \(-8\) \(0\) \(0\) \(0\) \(q-2q^{2}-\beta _{2}q^{3}+4q^{4}+\beta _{3}q^{5}+2\beta _{2}q^{6}+\cdots\)
164.3.d.b \(4\) \(4.469\) 4.4.83968.1 \(\Q(\sqrt{-41}) \) None \(8\) \(0\) \(0\) \(0\) \(q+2q^{2}-\beta _{3}q^{3}+4q^{4}+3\beta _{2}q^{5}-2\beta _{3}q^{6}+\cdots\)
164.3.d.c \(32\) \(4.469\) None None \(-2\) \(0\) \(-8\) \(0\)
164.3.e.a \(2\) \(4.469\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-2iq^{2}-4q^{4}-6iq^{5}+8iq^{8}-9iq^{9}+\cdots\)
164.3.e.b \(2\) \(4.469\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}-4q^{4}-6iq^{5}-8iq^{8}-9iq^{9}+\cdots\)
164.3.e.c \(76\) \(4.469\) None None \(0\) \(0\) \(0\) \(0\)
164.3.h.a \(28\) \(4.469\) None None \(0\) \(-8\) \(0\) \(0\)
164.3.j.a \(160\) \(4.469\) None None \(-3\) \(0\) \(-10\) \(0\)
164.3.l.a \(160\) \(4.469\) None None \(-3\) \(0\) \(-2\) \(0\)
164.3.n.a \(8\) \(4.469\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-2\zeta_{20}^{3}q^{2}+4\zeta_{20}^{6}q^{4}+(-4+3\zeta_{20}+\cdots)q^{5}+\cdots\)
164.3.n.b \(8\) \(4.469\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2\zeta_{20}^{3}q^{2}+4\zeta_{20}^{6}q^{4}+(4+3\zeta_{20}+\cdots)q^{5}+\cdots\)
164.3.n.c \(304\) \(4.469\) None None \(-10\) \(0\) \(-20\) \(0\)
164.3.p.a \(112\) \(4.469\) None None \(0\) \(8\) \(0\) \(0\)
164.4.a.a \(3\) \(9.676\) 3.3.4344.1 None None \(0\) \(-2\) \(-10\) \(0\) \(-\) \(q+(-1-\beta _{1})q^{3}+(-3+\beta _{1}-\beta _{2})q^{5}+\cdots\)
164.4.a.b \(7\) \(9.676\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(0\) \(4\) \(10\) \(0\) \(+\) \(q+(1-\beta _{2})q^{3}+(2-\beta _{2}-\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots\)
164.4.b.a \(10\) \(9.676\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{3}-\beta _{3}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
164.4.f.a \(22\) \(9.676\) None None \(0\) \(2\) \(0\) \(0\)
164.4.g.a \(40\) \(9.676\) None None \(0\) \(-2\) \(0\) \(0\)
164.4.i.a \(4\) \(9.676\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(-8\) \(0\) \(0\) \(0\) \(q+(-2-2\zeta_{8}^{2})q^{2}+8\zeta_{8}^{2}q^{4}+4\zeta_{8}^{3}q^{5}+\cdots\)
164.4.i.b \(240\) \(9.676\) None None \(4\) \(0\) \(-8\) \(0\)
164.4.k.a \(40\) \(9.676\) None None \(0\) \(0\) \(0\) \(0\)
164.4.m.a \(88\) \(9.676\) None None \(0\) \(-2\) \(0\) \(0\)
164.4.o.a \(16\) \(9.676\) \(\Q(\zeta_{40})\) \(\Q(\sqrt{-1}) \) None \(8\) \(0\) \(0\) \(0\) \(q+(-2\zeta_{40}^{2}+2\zeta_{40}^{6}-2\zeta_{40}^{8}-2\zeta_{40}^{10}+\cdots)q^{2}+\cdots\)
164.4.o.b \(960\) \(9.676\) None None \(-24\) \(0\) \(-32\) \(0\)
164.5.c.a \(80\) \(16.953\) None None \(6\) \(0\) \(0\) \(0\)
164.5.d.a \(2\) \(16.953\) \(\Q(\sqrt{41}) \) \(\Q(\sqrt{-41}) \) None \(-8\) \(-22\) \(0\) \(138\) \(q-4q^{2}+(-11-\beta )q^{3}+2^{4}q^{4}+6\beta q^{5}+\cdots\)
164.5.d.b \(2\) \(16.953\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(-8\) \(0\) \(28\) \(0\) \(q-4q^{2}+2^{4}q^{4}+14q^{5}-2^{6}q^{8}-3^{4}q^{9}+\cdots\)
164.5.d.c \(2\) \(16.953\) \(\Q(\sqrt{41}) \) \(\Q(\sqrt{-41}) \) None \(-8\) \(22\) \(0\) \(-138\) \(q-4q^{2}+(11-\beta )q^{3}+2^{4}q^{4}-6\beta q^{5}+\cdots\)
164.5.d.d \(2\) \(16.953\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-41}) \) None \(8\) \(0\) \(-64\) \(0\) \(q+4q^{2}+11\beta q^{3}+2^{4}q^{4}-2^{5}q^{5}+\cdots\)
164.5.d.e \(2\) \(16.953\) \(\Q(\sqrt{82}) \) \(\Q(\sqrt{-41}) \) None \(8\) \(0\) \(64\) \(0\) \(q+4q^{2}+\beta q^{3}+2^{4}q^{4}+2^{5}q^{5}+4\beta q^{6}+\cdots\)
164.5.d.f \(72\) \(16.953\) None None \(6\) \(0\) \(-8\) \(0\)
164.5.h.a \(56\) \(16.953\) None None \(0\) \(16\) \(0\) \(0\)
164.6.a.a \(6\) \(26.303\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(0\) \(-8\) \(-68\) \(88\) \(+\) \(q+(-1-\beta _{3})q^{3}+(-11+\beta _{2})q^{5}+(14+\cdots)q^{7}+\cdots\)
164.6.a.b \(10\) \(26.303\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(10\) \(32\) \(88\) \(-\) \(q+(1+\beta _{1})q^{3}+(3+\beta _{3})q^{5}+(9+2\beta _{1}+\cdots)q^{7}+\cdots\)
164.6.b.a \(18\) \(26.303\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None \(0\) \(0\) \(-72\) \(0\) \(q+\beta _{1}q^{3}+(-4-\beta _{3})q^{5}+(\beta _{1}+\beta _{12}+\cdots)q^{7}+\cdots\)
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