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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
13.2.e.a $2$ $0.104$ \(\Q(\sqrt{-3}) \) None \(-3\) \(-2\) \(0\) \(0\) $-$ \(q+(-1-\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
13.3.d.a $4$ $0.354$ \(\Q(i, \sqrt{10})\) None \(-4\) \(-4\) \(8\) \(-12\) $-$ \(q+(-1+\beta _{1}-\beta _{2})q^{2}+(-1-\beta _{1}+\beta _{3})q^{3}+\cdots\)
13.3.f.a $4$ $0.354$ \(\Q(\zeta_{12})\) None \(-2\) \(-2\) \(-14\) \(16\) $-$ \(q+(-1+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
13.4.a.a $1$ $0.767$ \(\Q\) None \(-5\) \(-7\) \(-7\) \(-13\) $-$ \(q-5q^{2}-7q^{3}+17q^{4}-7q^{5}+35q^{6}+\cdots\)
13.4.a.b $2$ $0.767$ \(\Q(\sqrt{17}) \) None \(1\) \(5\) \(-3\) \(-9\) $+$ \(q+\beta q^{2}+(4-3\beta )q^{3}+(-4+\beta )q^{4}+\cdots\)
13.4.b.a $2$ $0.767$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $-$ \(q+iq^{2}-q^{3}-q^{4}-3iq^{5}-iq^{6}+\cdots\)
13.4.c.a $2$ $0.767$ \(\Q(\sqrt{-3}) \) None \(-4\) \(-2\) \(34\) \(-20\) $-$ \(q+(-4+4\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}+\cdots\)
13.4.c.b $4$ $0.767$ \(\Q(\sqrt{-3}, \sqrt{17})\) None \(5\) \(-5\) \(-30\) \(-15\) $-$ \(q+(2-\beta _{1}-2\beta _{2}-\beta _{3})q^{2}+(-1+3\beta _{1}+\cdots)q^{3}+\cdots\)
13.4.e.a $2$ $0.767$ \(\Q(\sqrt{-3}) \) None \(-6\) \(7\) \(0\) \(39\) $-$ \(q+(-2-2\zeta_{6})q^{2}+(7-7\zeta_{6})q^{3}+4\zeta_{6}q^{4}+\cdots\)
13.4.e.b $2$ $0.767$ \(\Q(\sqrt{-3}) \) None \(3\) \(-2\) \(0\) \(-24\) $-$ \(q+(1+\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}-5\zeta_{6}q^{4}+\cdots\)
13.5.d.a $6$ $1.344$ 6.0.\(\cdots\).1 None \(-2\) \(-4\) \(-14\) \(48\) $-$ \(q-\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
13.5.f.a $16$ $1.344$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(-4\) \(-2\) \(8\) \(56\) $-$ \(q-\beta _{12}q^{2}+(-1-\beta _{8}+\beta _{9}+\beta _{12}+\cdots)q^{3}+\cdots\)
13.6.a.a $2$ $2.085$ \(\Q(\sqrt{17}) \) None \(-5\) \(-28\) \(-42\) \(-36\) $+$ \(q+(-2-\beta )q^{2}+(-17+6\beta )q^{3}+(-24+\cdots)q^{4}+\cdots\)
13.6.a.b $3$ $2.085$ 3.3.168897.1 None \(7\) \(8\) \(56\) \(-60\) $-$ \(q+(2+\beta _{1})q^{2}+(3-\beta _{1}-\beta _{2})q^{3}+(40+\cdots)q^{4}+\cdots\)
13.6.b.a $6$ $2.085$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(16\) \(0\) \(0\) $-$ \(q+\beta _{1}q^{2}+(3+\beta _{2})q^{3}+(-22-\beta _{2}+\cdots)q^{4}+\cdots\)
13.6.c.a $8$ $2.085$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-5\) \(8\) \(-20\) \(68\) $-$ \(q+(-1-\beta _{1}+\beta _{3})q^{2}+(2-2\beta _{3}-\beta _{5}+\cdots)q^{3}+\cdots\)
13.6.e.a $10$ $2.085$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-3\) \(-10\) \(0\) \(-276\) $-$ \(q-\beta _{3}q^{2}+(-2-2\beta _{2}-\beta _{5}-\beta _{6})q^{3}+\cdots\)
13.7.d.a $12$ $2.991$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(6\) \(-4\) \(108\) \(398\) $-$ \(q-\beta _{2}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3}-\beta _{7})q^{3}+\cdots\)
13.7.f.a $24$ $2.991$ None \(-12\) \(-2\) \(-114\) \(316\) $-$
13.8.a.a $1$ $4.061$ \(\Q\) None \(10\) \(-73\) \(-295\) \(1373\) $-$ \(q+10q^{2}-73q^{3}-28q^{4}-295q^{5}+\cdots\)
13.8.a.b $2$ $4.061$ \(\Q(\sqrt{337}) \) None \(-19\) \(45\) \(-353\) \(-2009\) $-$ \(q+(-9-\beta )q^{2}+(21+3\beta )q^{3}+(37+19\beta )q^{4}+\cdots\)
13.8.a.c $4$ $4.061$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(15\) \(80\) \(258\) \(1692\) $+$ \(q+(4-\beta _{1})q^{2}+(21-2\beta _{1}+\beta _{2})q^{3}+\cdots\)
13.8.b.a $6$ $4.061$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(-56\) \(0\) \(0\) $-$ \(q+\beta _{1}q^{2}+(-9-\beta _{2})q^{3}+(-22-\beta _{4}+\cdots)q^{4}+\cdots\)
13.8.c.a $16$ $4.061$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-9\) \(-28\) \(384\) \(196\) $-$ \(q+(-1-\beta _{1}-\beta _{2})q^{2}+(-4-4\beta _{2}+\cdots)q^{3}+\cdots\)
13.8.e.a $14$ $4.061$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(-3\) \(26\) \(0\) \(-2772\) $-$ \(q+\beta _{2}q^{2}+(4+4\beta _{3}-\beta _{4}-\beta _{6})q^{3}+\cdots\)
13.9.d.a $18$ $5.296$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-2\) \(-4\) \(166\) \(5308\) $-$ \(q-\beta _{3}q^{2}+\beta _{6}q^{3}+(-\beta _{1}-142\beta _{2}+\cdots)q^{4}+\cdots\)
13.9.f.a $32$ $5.296$ None \(-4\) \(-2\) \(-172\) \(-2784\) $-$
13.10.a.a $4$ $6.695$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-33\) \(-163\) \(471\) \(-11241\) $+$ \(q+(-8-\beta _{1})q^{2}+(-41+2\beta _{1}-\beta _{3})q^{3}+\cdots\)
13.10.a.b $5$ $6.695$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(15\) \(161\) \(1803\) \(10099\) $-$ \(q+(3+\beta _{1})q^{2}+(2^{5}+2\beta _{1}-\beta _{2})q^{3}+\cdots\)
13.10.b.a $10$ $6.695$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(-2\) \(0\) \(0\) $-$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(-2^{8}+\beta _{2})q^{4}+\cdots\)
13.10.c.a $18$ $6.695$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(15\) \(161\) \(-2280\) \(-1939\) $-$ \(q+(-2\beta _{2}-\beta _{3})q^{2}+(-18\beta _{2}-\beta _{6}+\cdots)q^{3}+\cdots\)
13.10.e.a $20$ $6.695$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(-3\) \(-163\) \(0\) \(1023\) $-$ \(q+(\beta _{1}-\beta _{2})q^{2}+(2^{4}\beta _{5}-\beta _{6})q^{3}+(2^{8}+\cdots)q^{4}+\cdots\)
13.11.d.a $20$ $8.260$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-34\) \(-4\) \(-7792\) \(-38312\) $-$ \(q+(-2-2\beta _{2}+\beta _{3})q^{2}+(-\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots\)
13.11.f.a $44$ $8.260$ None \(28\) \(-2\) \(7786\) \(30856\) $-$
13.12.a.a $5$ $9.988$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-41\) \(-496\) \(-2542\) \(-36296\) $-$ \(q+(-8-\beta _{1})q^{2}+(-99-2\beta _{1}-\beta _{4})q^{3}+\cdots\)
13.12.a.b $6$ $9.988$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(55\) \(476\) \(3312\) \(-4176\) $+$ \(q+(9+\beta _{1})q^{2}+(80-2\beta _{1}+\beta _{4})q^{3}+\cdots\)
13.12.b.a $12$ $9.988$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(-488\) \(0\) \(0\) $-$ \(q+\beta _{1}q^{2}+(-41-\beta _{2})q^{3}+(-2^{10}+\cdots)q^{4}+\cdots\)
13.12.c.a $24$ $9.988$ None \(31\) \(-244\) \(-10436\) \(-2928\) $-$
13.12.e.a $22$ $9.988$ None \(-3\) \(242\) \(0\) \(128496\) $-$
13.13.d.a $26$ $11.882$ None \(-2\) \(-4\) \(5146\) \(-114402\) $-$
13.13.f.a $52$ $11.882$ None \(-4\) \(-2\) \(-5152\) \(-91524\) $-$
13.14.a.a $6$ $13.940$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-65\) \(-2188\) \(-76752\) \(271440\) $+$ \(q+(-11+\beta _{1})q^{2}+(-365+2\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
13.14.a.b $7$ $13.940$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(127\) \(728\) \(34886\) \(131864\) $-$ \(q+(18+\beta _{1})q^{2}+(104+\beta _{1}+\beta _{2})q^{3}+\cdots\)
13.14.b.a $14$ $13.940$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(1456\) \(0\) \(0\) $-$ \(q+\beta _{1}q^{2}+(104+\beta _{3})q^{3}+(-3511+\cdots)q^{4}+\cdots\)
13.14.c.a $28$ $13.940$ None \(-65\) \(728\) \(41860\) \(-173992\) $-$
13.14.e.a $30$ $13.940$ None \(-3\) \(-730\) \(0\) \(438984\) $-$
13.15.d.a $32$ $16.163$ None \(126\) \(-4\) \(40308\) \(-342172\) $-$
13.15.f.a $60$ $16.163$ None \(-132\) \(-2\) \(-40314\) \(-1557904\) $-$
13.16.a.a $7$ $18.550$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-345\) \(-1027\) \(-169503\) \(-3685093\) $-$ \(q+(-7^{2}-\beta _{1})q^{2}+(-149+7\beta _{1}+\beta _{4}+\cdots)q^{3}+\cdots\)
13.16.a.b $8$ $18.550$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(39\) \(7721\) \(161733\) \(719199\) $+$ \(q+(5-\beta _{1})q^{2}+(966-6\beta _{1}-\beta _{4})q^{3}+\cdots\)
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