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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
26.2.a.a \(1\) \(0.208\) \(\Q\) None \(-1\) \(1\) \(-3\) \(-1\) \(-\) \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{7}+\cdots\)
26.2.a.b \(1\) \(0.208\) \(\Q\) None \(1\) \(-3\) \(-1\) \(1\) \(-\) \(q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}+q^{7}+\cdots\)
26.2.b.a \(2\) \(0.208\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+iq^{2}-q^{3}-q^{4}-3iq^{5}-iq^{6}+\cdots\)
26.2.c.a \(2\) \(0.208\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-2\) \(-4\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}-4\zeta_{6}q^{7}+\cdots\)
26.3.d.a \(2\) \(0.708\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(-6\) \(4\) \(q+(1+i)q^{2}+2iq^{4}+(-3-3i)q^{5}+\cdots\)
26.3.f.a \(4\) \(0.708\) \(\Q(\zeta_{12})\) None \(2\) \(0\) \(0\) \(-22\) \(q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots\)
26.3.f.b \(8\) \(0.708\) 8.0.\(\cdots\).1 None \(-4\) \(0\) \(6\) \(-2\) \(q+(-\beta _{3}-\beta _{4})q^{2}+(-\beta _{2}+\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)
26.4.a.a \(1\) \(1.534\) \(\Q\) None \(-2\) \(3\) \(11\) \(19\) \(+\) \(q-2q^{2}+3q^{3}+4q^{4}+11q^{5}-6q^{6}+\cdots\)
26.4.a.b \(1\) \(1.534\) \(\Q\) None \(2\) \(-1\) \(17\) \(-35\) \(+\) \(q+2q^{2}-q^{3}+4q^{4}+17q^{5}-2q^{6}+\cdots\)
26.4.a.c \(1\) \(1.534\) \(\Q\) None \(2\) \(4\) \(-18\) \(20\) \(+\) \(q+2q^{2}+4q^{3}+4q^{4}-18q^{5}+8q^{6}+\cdots\)
26.4.b.a \(4\) \(1.534\) \(\Q(i, \sqrt{217})\) None \(0\) \(-6\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(-2+\beta _{3})q^{3}-4q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
26.4.c.a \(2\) \(1.534\) \(\Q(\sqrt{-3}) \) None \(2\) \(3\) \(4\) \(5\) \(q+(2-2\zeta_{6})q^{2}+(3-3\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots\)
26.4.c.b \(4\) \(1.534\) \(\Q(\sqrt{-3}, \sqrt{217})\) None \(-4\) \(3\) \(-14\) \(45\) \(q-2\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-4+4\beta _{2}+\cdots)q^{4}+\cdots\)
26.4.e.a \(8\) \(1.534\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(-6\) \(0\) \(18\) \(q-\beta _{3}q^{2}+(-2+2\beta _{1}+\beta _{4}-\beta _{7})q^{3}+\cdots\)
26.5.d.a \(6\) \(2.688\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(-12\) \(0\) \(18\) \(-42\) \(q+(-2-2\beta _{2})q^{2}+\beta _{3}q^{3}+8\beta _{2}q^{4}+\cdots\)
26.5.d.b \(6\) \(2.688\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(12\) \(0\) \(-30\) \(-90\) \(q+(2+2\beta _{2})q^{2}-\beta _{3}q^{3}+8\beta _{2}q^{4}+(-5+\cdots)q^{5}+\cdots\)
26.5.f.a \(8\) \(2.688\) 8.0.\(\cdots\).3 None \(-8\) \(0\) \(30\) \(-92\) \(q+(-2\beta _{4}-2\beta _{5}-2\beta _{6})q^{2}+(-1-\beta _{1}+\cdots)q^{3}+\cdots\)
26.5.f.b \(8\) \(2.688\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(0\) \(-18\) \(4\) \(q+(2\beta _{3}-2\beta _{6})q^{2}+(\beta _{1}+3\beta _{5}-\beta _{6}+\cdots)q^{3}+\cdots\)
26.6.a.a \(1\) \(4.170\) \(\Q\) None \(-4\) \(0\) \(-14\) \(-170\) \(+\) \(q-4q^{2}+2^{4}q^{4}-14q^{5}-170q^{7}+\cdots\)
26.6.a.b \(2\) \(4.170\) \(\Q(\sqrt{2785}) \) None \(-8\) \(9\) \(-37\) \(327\) \(-\) \(q-4q^{2}+(5-\beta )q^{3}+2^{4}q^{4}+(-19+\cdots)q^{5}+\cdots\)
26.6.a.c \(2\) \(4.170\) \(\Q(\sqrt{849}) \) None \(8\) \(9\) \(73\) \(155\) \(-\) \(q+4q^{2}+(5-\beta )q^{3}+2^{4}q^{4}+(35+3\beta )q^{5}+\cdots\)
26.6.b.a \(2\) \(4.170\) \(\Q(\sqrt{-1}) \) None \(0\) \(-26\) \(0\) \(0\) \(q+4iq^{2}-13q^{3}-2^{4}q^{4}-51iq^{5}+\cdots\)
26.6.b.b \(2\) \(4.170\) \(\Q(\sqrt{-1}) \) None \(0\) \(8\) \(0\) \(0\) \(q+2iq^{2}+4q^{3}-2^{4}q^{4}+34iq^{5}+\cdots\)
26.6.c.a \(6\) \(4.170\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(-12\) \(0\) \(2\) \(-202\) \(q-4\beta _{1}q^{2}+\beta _{3}q^{3}+(-2^{4}+2^{4}\beta _{1}+\cdots)q^{4}+\cdots\)
26.6.c.b \(8\) \(4.170\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(16\) \(0\) \(-24\) \(126\) \(q+(4+4\beta _{2})q^{2}-\beta _{1}q^{3}+2^{4}\beta _{2}q^{4}+\cdots\)
26.6.e.a \(12\) \(4.170\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(360\) \(q-\beta _{4}q^{2}-\beta _{3}q^{3}+2^{4}\beta _{7}q^{4}+(5+\beta _{3}+\cdots)q^{5}+\cdots\)
26.7.d.a \(6\) \(5.981\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(24\) \(0\) \(-150\) \(150\) \(q+(4+4\beta _{2})q^{2}+\beta _{3}q^{3}+2^{5}\beta _{2}q^{4}+\cdots\)
26.7.d.b \(8\) \(5.981\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(-32\) \(0\) \(84\) \(-230\) \(q+(-4+4\beta _{3})q^{2}-\beta _{2}q^{3}-2^{5}\beta _{3}q^{4}+\cdots\)
26.7.f.a \(12\) \(5.981\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-24\) \(0\) \(150\) \(-1026\) \(q+(-4+4\beta _{2}+4\beta _{3})q^{2}+(-\beta _{7}-\beta _{11})q^{3}+\cdots\)
26.7.f.b \(16\) \(5.981\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(32\) \(0\) \(-84\) \(-334\) \(q+(4-4\beta _{3}+4\beta _{4})q^{2}-\beta _{1}q^{3}+(2^{5}\beta _{4}+\cdots)q^{4}+\cdots\)
26.8.a.a \(1\) \(8.122\) \(\Q\) None \(-8\) \(-39\) \(385\) \(-293\) \(-\) \(q-8q^{2}-39q^{3}+2^{6}q^{4}+385q^{5}+\cdots\)
26.8.a.b \(1\) \(8.122\) \(\Q\) None \(8\) \(-87\) \(321\) \(-181\) \(+\) \(q+8q^{2}-87q^{3}+2^{6}q^{4}+321q^{5}+\cdots\)
26.8.a.c \(1\) \(8.122\) \(\Q\) None \(8\) \(-27\) \(-245\) \(-587\) \(-\) \(q+8q^{2}-3^{3}q^{3}+2^{6}q^{4}-245q^{5}+\cdots\)
26.8.a.d \(2\) \(8.122\) \(\Q(\sqrt{105}) \) None \(-16\) \(-12\) \(-146\) \(-1780\) \(+\) \(q-8q^{2}+(-6-7\beta )q^{3}+2^{6}q^{4}+(-73+\cdots)q^{5}+\cdots\)
26.8.a.e \(2\) \(8.122\) \(\Q(\sqrt{2305}) \) None \(16\) \(87\) \(215\) \(705\) \(+\) \(q+8q^{2}+(44-\beta )q^{3}+2^{6}q^{4}+(110+\cdots)q^{5}+\cdots\)
26.8.b.a \(10\) \(8.122\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(54\) \(0\) \(0\) \(q+\beta _{6}q^{2}+(5-\beta _{2})q^{3}-2^{6}q^{4}+(2\beta _{6}+\cdots)q^{5}+\cdots\)
26.8.c.a \(6\) \(8.122\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(-24\) \(0\) \(-666\) \(1160\) \(q+(-8-8\beta _{3})q^{2}-\beta _{1}q^{3}+2^{6}\beta _{3}q^{4}+\cdots\)
26.8.c.b \(8\) \(8.122\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(32\) \(0\) \(556\) \(-548\) \(q-8\beta _{1}q^{2}+\beta _{3}q^{3}+(-2^{6}-2^{6}\beta _{1}+\cdots)q^{4}+\cdots\)
26.8.e.a \(16\) \(8.122\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(2520\) \(q+(-\beta _{7}-\beta _{9})q^{2}+\beta _{3}q^{3}+2^{6}\beta _{1}q^{4}+\cdots\)
26.9.d.a \(8\) \(10.592\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-64\) \(0\) \(420\) \(-2702\) \(q+(-8+8\beta _{1})q^{2}+\beta _{5}q^{3}-2^{7}\beta _{1}q^{4}+\cdots\)
26.9.d.b \(8\) \(10.592\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(64\) \(0\) \(-252\) \(-4910\) \(q+(8+8\beta _{2})q^{2}-\beta _{1}q^{3}+2^{7}\beta _{2}q^{4}+\cdots\)
26.9.f.a \(20\) \(10.592\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(-80\) \(0\) \(252\) \(6844\) \(q+(-8-8\beta _{1}-8\beta _{5})q^{2}+(5\beta _{1}+11\beta _{2}+\cdots)q^{3}+\cdots\)
26.9.f.b \(20\) \(10.592\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(80\) \(0\) \(-420\) \(-4292\) \(q+(-8\beta _{1}+8\beta _{3})q^{2}+(5\beta _{1}+11\beta _{2}+\cdots)q^{3}+\cdots\)
26.10.a.a \(1\) \(13.391\) \(\Q\) None \(-16\) \(-273\) \(1015\) \(3955\) \(+\) \(q-2^{4}q^{2}-273q^{3}+2^{8}q^{4}+1015q^{5}+\cdots\)
26.10.a.b \(1\) \(13.391\) \(\Q\) None \(-16\) \(192\) \(-1310\) \(-5810\) \(+\) \(q-2^{4}q^{2}+192q^{3}+2^{8}q^{4}-1310q^{5}+\cdots\)
26.10.a.c \(1\) \(13.391\) \(\Q\) None \(16\) \(75\) \(-1979\) \(-10115\) \(+\) \(q+2^{4}q^{2}+75q^{3}+2^{8}q^{4}-1979q^{5}+\cdots\)
26.10.a.d \(3\) \(13.391\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-48\) \(0\) \(248\) \(-2956\) \(-\) \(q-2^{4}q^{2}-\beta _{2}q^{3}+2^{8}q^{4}+(79-11\beta _{1}+\cdots)q^{5}+\cdots\)
26.10.a.e \(3\) \(13.391\) 3.3.2119705.1 None \(48\) \(156\) \(-1272\) \(17058\) \(-\) \(q+2^{4}q^{2}+(52-\beta _{1}-\beta _{2})q^{3}+2^{8}q^{4}+\cdots\)
26.10.b.a \(10\) \(13.391\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(162\) \(0\) \(0\) \(q-\beta _{5}q^{2}+(2^{4}-\beta _{1})q^{3}-2^{8}q^{4}+(-15\beta _{5}+\cdots)q^{5}+\cdots\)
26.10.c.a \(10\) \(13.391\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(80\) \(-81\) \(-1828\) \(3323\) \(q+(2^{4}-2^{4}\beta _{2})q^{2}+(-2^{4}-\beta _{1}+2^{4}\beta _{2}+\cdots)q^{3}+\cdots\)
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