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Label Char Prim Dim $A$ Field CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
647.1.b.a 647.b 647.b $11$ $0.323$ \(\Q(\zeta_{46})^+\) \(\Q(\sqrt{-647}) \) None 647.1.b.a \(-1\) \(-1\) \(0\) \(-1\) \(q-\beta _{3}q^{2}-\beta _{5}q^{3}+(1+\beta _{6})q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots\)
719.1.b.a 719.b 719.b $15$ $0.359$ \(\Q(\zeta_{62})^+\) \(\Q(\sqrt{-719}) \) None 719.1.b.a \(-1\) \(-1\) \(-1\) \(-1\) \(q+\beta _{12}q^{2}+\beta _{10}q^{3}+(1-\beta _{7})q^{4}-\beta _{13}q^{5}+\cdots\)
887.1.b.a 887.b 887.b $14$ $0.443$ \(\Q(\zeta_{58})^+\) \(\Q(\sqrt{-887}) \) None 887.1.b.a \(-1\) \(-1\) \(0\) \(-1\) \(q-\beta _{11}q^{2}-\beta _{5}q^{3}+(1-\beta _{7})q^{4}+(\beta _{6}+\cdots)q^{6}+\cdots\)
911.1.b.a 911.b 911.b $15$ $0.455$ \(\Q(\zeta_{62})^+\) \(\Q(\sqrt{-911}) \) None 911.1.b.a \(-1\) \(-1\) \(-1\) \(0\) \(q+\beta _{12}q^{2}-\beta _{9}q^{3}+(1-\beta _{7})q^{4}+\beta _{8}q^{5}+\cdots\)
955.1.c.b 955.c 955.c $12$ $0.477$ \(\Q(\zeta_{26})\) \(\Q(\sqrt{-191}) \) None 955.1.c.b \(0\) \(0\) \(1\) \(0\) \(q+(\zeta_{26}^{6}+\zeta_{26}^{7})q^{2}+(-\zeta_{26}^{2}-\zeta_{26}^{11}+\cdots)q^{3}+\cdots\)
1031.1.b.c 1031.b 1031.b $12$ $0.515$ \(\Q(\zeta_{35})^+\) \(\Q(\sqrt{-1031}) \) None 1031.1.b.c \(1\) \(-4\) \(1\) \(0\) \(q+\beta _{9}q^{2}+\beta _{5}q^{3}+(-\beta _{3}-\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots\)
1039.1.b.a 1039.b 1039.b $11$ $0.519$ \(\Q(\zeta_{46})^+\) \(\Q(\sqrt{-1039}) \) None 1039.1.b.a \(-1\) \(0\) \(-1\) \(-1\) \(q-\beta _{3}q^{2}+(1+\beta _{6})q^{4}+\beta _{2}q^{5}-\beta _{7}q^{7}+\cdots\)
1103.1.b.a 1103.b 1103.b $11$ $0.550$ \(\Q(\zeta_{46})^+\) \(\Q(\sqrt{-1103}) \) None 1103.1.b.a \(-1\) \(-1\) \(0\) \(0\) \(q-\beta _{3}q^{2}+\beta _{4}q^{3}+(1+\beta _{6})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
1151.1.b.a 1151.b 1151.b $20$ $0.574$ \(\Q(\zeta_{82})^+\) \(\Q(\sqrt{-1151}) \) None 1151.1.b.a \(-1\) \(-1\) \(-1\) \(-1\) \(q+\beta _{10}q^{2}+\beta _{16}q^{3}+(\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
1223.1.b.c 1223.b 1223.b $12$ $0.610$ \(\Q(\zeta_{35})^+\) \(\Q(\sqrt{-1223}) \) None 1223.1.b.c \(1\) \(1\) \(0\) \(1\) \(q+\beta _{9}q^{2}+\beta _{2}q^{3}+(-\beta _{3}-\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots\)
1279.1.b.a 1279.b 1279.b $11$ $0.638$ \(\Q(\zeta_{46})^+\) \(\Q(\sqrt{-1279}) \) None 1279.1.b.a \(-1\) \(0\) \(-1\) \(-1\) \(q-\beta _{3}q^{2}+(1+\beta _{6})q^{4}-\beta _{5}q^{5}-\beta _{7}q^{7}+\cdots\)
1319.1.b.e 1319.b 1319.b $12$ $0.658$ \(\Q(\zeta_{45})^+\) \(\Q(\sqrt{-1319}) \) None 1319.1.b.e \(0\) \(0\) \(0\) \(3\) \(q+\beta _{9}q^{2}+\beta _{7}q^{3}+(1-\beta _{5}-\beta _{9})q^{4}+\cdots\)
84.2.e.a 84.e 12.b $12$ $0.671$ 12.0.\(\cdots\).2 None None 84.2.e.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}-\beta _{9}q^{3}+(-\beta _{2}-\beta _{3})q^{4}+\cdots\)
1439.1.b.c 1439.b 1439.b $12$ $0.718$ \(\Q(\zeta_{39})^+\) \(\Q(\sqrt{-1439}) \) None 1439.1.b.c \(-2\) \(1\) \(1\) \(0\) \(q+\beta _{3}q^{2}+\beta _{4}q^{3}+(1+\beta _{6})q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots\)
1447.1.b.a 1447.b 1447.b $11$ $0.722$ \(\Q(\zeta_{46})^+\) \(\Q(\sqrt{-1447}) \) None 1447.1.b.a \(-1\) \(0\) \(0\) \(-1\) \(q-\beta _{3}q^{2}+(1+\beta _{6})q^{4}-\beta _{7}q^{7}+(-\beta _{3}+\cdots)q^{8}+\cdots\)
1471.1.b.a 1471.b 1471.b $11$ $0.734$ \(\Q(\zeta_{46})^+\) \(\Q(\sqrt{-1471}) \) None 1471.1.b.a \(-1\) \(0\) \(-1\) \(0\) \(q-\beta _{3}q^{2}+(1+\beta _{6})q^{4}+\beta _{2}q^{5}+(-\beta _{3}+\cdots)q^{8}+\cdots\)
1487.1.b.a 1487.b 1487.b $18$ $0.742$ \(\Q(\zeta_{74})^+\) \(\Q(\sqrt{-1487}) \) None 1487.1.b.a \(-1\) \(-1\) \(0\) \(-1\) \(q+\beta _{8}q^{2}+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
1528.1.b.c 1528.b 1528.b $12$ $0.763$ \(\Q(\zeta_{26})\) \(\Q(\sqrt{-191}) \) None 1528.1.b.c \(-1\) \(0\) \(0\) \(0\) \(q+\zeta_{26}^{10}q^{2}+(\zeta_{26}+\zeta_{26}^{12})q^{3}-\zeta_{26}^{7}q^{4}+\cdots\)
1555.1.b.b 1555.b 1555.b $18$ $0.776$ \(\Q(\zeta_{38})\) \(\Q(\sqrt{-311}) \) None 1555.1.b.b \(0\) \(0\) \(1\) \(0\) \(q+(-\zeta_{38}^{3}-\zeta_{38}^{16})q^{2}+(-\zeta_{38}^{2}+\cdots)q^{3}+\cdots\)
1559.1.b.c 1559.b 1559.b $16$ $0.778$ \(\Q(\zeta_{51})^+\) \(\Q(\sqrt{-1559}) \) None 1559.1.b.c \(-2\) \(1\) \(1\) \(-2\) \(q+\beta _{6}q^{2}+(-\beta _{8}-\beta _{9})q^{3}+(1+\beta _{12}+\cdots)q^{4}+\cdots\)
1679.1.d.e 1679.d 1679.d $12$ $0.838$ \(\Q(\zeta_{52})^+\) \(\Q(\sqrt{-1679}) \) None 1679.1.d.e \(2\) \(-2\) \(0\) \(0\) \(q+\beta _{10}q^{2}+\beta _{4}q^{3}+(1-\beta _{6})q^{4}-\beta _{1}q^{5}+\cdots\)
1720.1.g.g 1720.g 1720.g $12$ $0.858$ \(\Q(\zeta_{28})\) \(\Q(\sqrt{-215}) \) None 1720.1.g.g \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{28}^{9}q^{2}+(-\zeta_{28}^{3}-\zeta_{28}^{11})q^{3}+\cdots\)
1795.1.c.c 1795.c 1795.c $18$ $0.896$ \(\Q(\zeta_{38})\) \(\Q(\sqrt{-359}) \) None 1795.1.c.c \(0\) \(0\) \(-1\) \(0\) \(q+(-\zeta_{38}^{3}-\zeta_{38}^{16})q^{2}+(-\zeta_{38}^{4}+\cdots)q^{3}+\cdots\)
1811.1.b.a 1811.b 1811.b $11$ $0.904$ \(\Q(\zeta_{46})^+\) \(\Q(\sqrt{-1811}) \) None 1811.1.b.a \(0\) \(-1\) \(-1\) \(-1\) \(q-\beta _{3}q^{3}+q^{4}-\beta _{5}q^{5}-\beta _{7}q^{7}+(1+\cdots)q^{9}+\cdots\)
1823.1.b.f 1823.b 1823.b $12$ $0.910$ \(\Q(\zeta_{45})^+\) \(\Q(\sqrt{-1823}) \) None 1823.1.b.f \(0\) \(0\) \(0\) \(-6\) \(q+\beta _{9}q^{2}+\beta _{7}q^{3}+(1-\beta _{5}-\beta _{9})q^{4}+\cdots\)
1871.1.b.e 1871.b 1871.b $12$ $0.934$ \(\Q(\zeta_{45})^+\) \(\Q(\sqrt{-1871}) \) None 1871.1.b.e \(0\) \(0\) \(0\) \(0\) \(q+\beta _{7}q^{2}+\beta _{1}q^{3}+(1+\beta _{11})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
120.2.m.b 120.m 120.m $16$ $0.958$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None 120.2.m.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-\beta _{13}q^{3}-\beta _{11}q^{4}+\beta _{7}q^{5}+\cdots\)
1955.1.d.f 1955.d 1955.d $12$ $0.976$ \(\Q(\zeta_{28})\) \(\Q(\sqrt{-391}) \) None 1955.1.d.f \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{28}^{2}-\zeta_{28}^{12})q^{2}+(-1+\zeta_{28}^{4}+\cdots)q^{4}+\cdots\)
1979.1.b.a 1979.b 1979.b $11$ $0.988$ \(\Q(\zeta_{46})^+\) \(\Q(\sqrt{-1979}) \) None 1979.1.b.a \(0\) \(-1\) \(-1\) \(-1\) \(q-\beta _{3}q^{3}+q^{4}+\beta _{4}q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
1991.1.d.f 1991.d 1991.d $12$ $0.994$ \(\Q(\zeta_{56})^+\) \(\Q(\sqrt{-1991}) \) None 1991.1.d.f \(0\) \(-4\) \(0\) \(0\) \(q+\beta _{9}q^{2}+\beta _{8}q^{3}+(1-\beta _{10})q^{4}+\beta _{6}q^{5}+\cdots\)
2020.1.d.e 2020.d 2020.d $12$ $1.008$ \(\Q(\zeta_{28})\) \(\Q(\sqrt{-101}) \) None 2020.1.d.e \(0\) \(0\) \(2\) \(0\) \(q+\zeta_{28}^{7}q^{2}+(-\zeta_{28}^{3}-\zeta_{28}^{11})q^{3}+\cdots\)
2039.1.b.e 2039.b 2039.b $12$ $1.018$ \(\Q(\zeta_{45})^+\) \(\Q(\sqrt{-2039}) \) None 2039.1.b.e \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{2}+\beta _{7}q^{3}+(1+\beta _{9})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
2063.1.b.e 2063.b 2063.b $12$ $1.030$ \(\Q(\zeta_{45})^+\) \(\Q(\sqrt{-2063}) \) None 2063.1.b.e \(0\) \(3\) \(0\) \(0\) \(q+\beta _{7}q^{2}+\beta _{6}q^{3}+(1+\beta _{11})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
129.2.d.a 129.d 129.d $12$ $1.030$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None 129.2.d.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+\beta _{6}q^{3}+\beta _{9}q^{4}+\beta _{11}q^{5}+\cdots\)
2087.1.b.c 2087.b 2087.b $12$ $1.042$ \(\Q(\zeta_{35})^+\) \(\Q(\sqrt{-2087}) \) None 2087.1.b.c \(1\) \(-4\) \(0\) \(0\) \(q+\beta _{9}q^{2}+(-1-\beta _{5}-\beta _{10})q^{3}+(-\beta _{3}+\cdots)q^{4}+\cdots\)
2104.1.d.e 2104.d 2104.d $12$ $1.050$ \(\Q(\zeta_{26})\) \(\Q(\sqrt{-263}) \) None 2104.1.d.e \(1\) \(0\) \(0\) \(0\) \(q-\zeta_{26}^{10}q^{2}+(\zeta_{26}^{2}+\zeta_{26}^{11})q^{3}+\cdots\)
132.2.h.a 132.h 44.c $12$ $1.054$ 12.0.\(\cdots\).2 None None 132.2.h.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(\beta _{2}+\beta _{3})q^{4}+(\beta _{6}+\cdots)q^{5}+\cdots\)
2155.1.c.g 2155.c 2155.c $12$ $1.075$ \(\Q(\zeta_{21})\) \(\Q(\sqrt{-431}) \) None 2155.1.c.g \(0\) \(0\) \(-1\) \(0\) \(q+(-\zeta_{42}^{3}-\zeta_{42}^{18})q^{2}+(\zeta_{42}^{2}+\zeta_{42}^{19}+\cdots)q^{3}+\cdots\)
136.2.h.a 136.h 136.h $16$ $1.086$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None 136.2.h.a \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}+\beta _{12}q^{3}-\beta _{3}q^{4}-\beta _{6}q^{5}+\cdots\)
2207.1.b.c 2207.b 2207.b $12$ $1.101$ \(\Q(\zeta_{39})^+\) \(\Q(\sqrt{-2207}) \) None 2207.1.b.c \(1\) \(1\) \(0\) \(0\) \(q+\beta _{4}q^{2}+(-\beta _{1}-\beta _{11})q^{3}+(1-\beta _{5}+\cdots)q^{4}+\cdots\)
2231.1.d.a 2231.d 2231.d $14$ $1.113$ \(\Q(\zeta_{58})^+\) \(\Q(\sqrt{-2231}) \) None 2231.1.d.a \(-1\) \(-1\) \(-1\) \(-1\) \(q+\beta _{2}q^{2}-\beta _{13}q^{3}+(1+\beta _{4})q^{4}-\beta _{11}q^{5}+\cdots\)
2231.1.d.b 2231.d 2231.d $14$ $1.113$ \(\Q(\zeta_{58})^+\) \(\Q(\sqrt{-2231}) \) None 2231.1.d.a \(-1\) \(-1\) \(1\) \(1\) \(q+\beta _{2}q^{2}-\beta _{13}q^{3}+(1+\beta _{4})q^{4}+\beta _{11}q^{5}+\cdots\)
2239.1.b.c 2239.b 2239.b $12$ $1.117$ \(\Q(\zeta_{35})^+\) \(\Q(\sqrt{-2239}) \) None 2239.1.b.c \(1\) \(0\) \(-4\) \(1\) \(q+\beta _{9}q^{2}+(-\beta _{3}-\beta _{5}+\beta _{6}-\beta _{7}-\beta _{10}+\cdots)q^{4}+\cdots\)
140.2.c.b 140.c 140.c $16$ $1.118$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None 140.2.c.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}-\beta _{9}q^{3}+(-1+\beta _{6})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
2279.1.d.f 2279.d 2279.d $12$ $1.137$ \(\Q(\zeta_{56})^+\) \(\Q(\sqrt{-2279}) \) None 2279.1.d.f \(0\) \(0\) \(0\) \(0\) \(q+\beta _{9}q^{2}+\beta _{1}q^{3}+(1-\beta _{10})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
2287.1.b.a 2287.b 2287.b $14$ $1.141$ \(\Q(\zeta_{58})^+\) \(\Q(\sqrt{-2287}) \) None 2287.1.b.a \(-1\) \(0\) \(0\) \(-1\) \(q-\beta _{11}q^{2}+(1-\beta _{7})q^{4}-\beta _{5}q^{7}+(\beta _{4}+\cdots)q^{8}+\cdots\)
143.2.b.a 143.b 13.b $12$ $1.142$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None 143.2.b.a \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(-1+\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
2292.1.e.e 2292.e 2292.e $12$ $1.144$ \(\Q(\zeta_{26})\) \(\Q(\sqrt{-191}) \) None 2292.1.e.e \(-1\) \(-1\) \(0\) \(0\) \(q+\zeta_{26}^{10}q^{2}+\zeta_{26}^{12}q^{3}-\zeta_{26}^{7}q^{4}+\cdots\)
2292.1.e.f 2292.e 2292.e $12$ $1.144$ \(\Q(\zeta_{26})\) \(\Q(\sqrt{-191}) \) None 2292.1.e.e \(1\) \(1\) \(0\) \(0\) \(q-\zeta_{26}^{10}q^{2}+\zeta_{26}q^{3}-\zeta_{26}^{7}q^{4}+\cdots\)
2311.1.b.a 2311.b 2311.b $14$ $1.153$ \(\Q(\zeta_{58})^+\) \(\Q(\sqrt{-2311}) \) None 2311.1.b.a \(-1\) \(0\) \(-1\) \(0\) \(q-\beta _{11}q^{2}+(1-\beta _{7})q^{4}-\beta _{1}q^{5}+(\beta _{4}+\cdots)q^{8}+\cdots\)
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