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Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
71.1.b.a 71.b 71.b $3$ $0.035$ \(\Q(\zeta_{14})^+\) $D_{7}$ \(\Q(\sqrt{-71}) \) None \(-1\) \(-1\) \(-1\) \(0\) \(q-\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
355.1.c.a 355.c 355.c $1$ $0.177$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-71}) \), \(\Q(\sqrt{-355}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(-1\) \(0\) \(q+q^{4}-q^{5}+q^{9}+q^{16}-2q^{19}-q^{20}+\cdots\)
355.1.c.b 355.c 355.c $6$ $0.177$ \(\Q(\zeta_{14})\) $D_{14}$ \(\Q(\sqrt{-71}) \) None \(0\) \(0\) \(1\) \(0\) \(q+(\zeta_{14}^{2}+\zeta_{14}^{5})q^{2}+(-\zeta_{14}-\zeta_{14}^{6}+\cdots)q^{3}+\cdots\)
568.1.b.a 568.b 568.b $1$ $0.283$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-71}) \), \(\Q(\sqrt{-142}) \) \(\Q(\sqrt{2}) \) \(-1\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{18}+\cdots\)
568.1.b.b 568.b 568.b $6$ $0.283$ \(\Q(\zeta_{14})\) $D_{14}$ \(\Q(\sqrt{-71}) \) None \(1\) \(0\) \(0\) \(0\) \(q-\zeta_{14}^{4}q^{2}+(\zeta_{14}^{2}+\zeta_{14}^{5})q^{3}-\zeta_{14}q^{4}+\cdots\)
639.1.d.a 639.d 71.b $3$ $0.319$ \(\Q(\zeta_{14})^+\) $D_{7}$ \(\Q(\sqrt{-71}) \) None \(1\) \(0\) \(1\) \(0\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{2}q^{5}+(1+\beta _{2})q^{8}+\cdots\)
639.1.g.a 639.g 639.g $2$ $0.319$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-71}) \) None \(1\) \(-1\) \(-2\) \(0\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{5}-q^{6}+q^{8}+\cdots\)
639.1.g.b 639.g 639.g $12$ $0.319$ \(\Q(\zeta_{21})\) $D_{21}$ \(\Q(\sqrt{-71}) \) None \(-1\) \(1\) \(2\) \(0\) \(q+(-\zeta_{42}^{3}+\zeta_{42}^{4})q^{2}-\zeta_{42}^{19}q^{3}+\cdots\)
852.1.d.a 852.d 852.d $1$ $0.425$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-71}) \), \(\Q(\sqrt{-213}) \) \(\Q(\sqrt{3}) \) \(-1\) \(1\) \(0\) \(0\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
852.1.d.b 852.d 852.d $1$ $0.425$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-71}) \), \(\Q(\sqrt{-213}) \) \(\Q(\sqrt{3}) \) \(1\) \(-1\) \(0\) \(0\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
852.1.d.c 852.d 852.d $6$ $0.425$ \(\Q(\zeta_{14})\) $D_{14}$ \(\Q(\sqrt{-71}) \) None \(-1\) \(1\) \(0\) \(0\) \(q+\zeta_{14}^{2}q^{2}+\zeta_{14}q^{3}+\zeta_{14}^{4}q^{4}+(-\zeta_{14}^{3}+\cdots)q^{5}+\cdots\)
852.1.d.d 852.d 852.d $6$ $0.425$ \(\Q(\zeta_{14})\) $D_{14}$ \(\Q(\sqrt{-71}) \) None \(1\) \(-1\) \(0\) \(0\) \(q-\zeta_{14}^{4}q^{2}-\zeta_{14}^{5}q^{3}-\zeta_{14}q^{4}+(-\zeta_{14}+\cdots)q^{5}+\cdots\)
1065.1.l.a 1065.l 1065.l $2$ $0.532$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-71}) \) None \(-2\) \(2\) \(0\) \(0\) \(q+(-1-i)q^{2}+q^{3}+iq^{4}-iq^{5}+\cdots\)
1065.1.l.b 1065.l 1065.l $2$ $0.532$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-71}) \) None \(2\) \(0\) \(0\) \(0\) \(q+(1+i)q^{2}+iq^{3}+iq^{4}+iq^{5}+(-1+\cdots)q^{6}+\cdots\)
1065.1.l.c 1065.l 1065.l $12$ $0.532$ \(\Q(\zeta_{28})\) $D_{28}$ \(\Q(\sqrt{-71}) \) None \(-2\) \(0\) \(0\) \(0\) \(q+(\zeta_{28}^{9}+\zeta_{28}^{12})q^{2}+\zeta_{28}q^{3}+(-\zeta_{28}^{4}+\cdots)q^{4}+\cdots\)
1065.1.l.d 1065.l 1065.l $12$ $0.532$ \(\Q(\zeta_{28})\) $D_{28}$ \(\Q(\sqrt{-71}) \) None \(2\) \(-2\) \(0\) \(0\) \(q+(\zeta_{28}^{9}-\zeta_{28}^{12})q^{2}-\zeta_{28}^{6}q^{3}+(-\zeta_{28}^{4}+\cdots)q^{4}+\cdots\)
1136.1.h.a 1136.h 71.b $3$ $0.567$ \(\Q(\zeta_{14})^+\) $D_{7}$ \(\Q(\sqrt{-71}) \) None \(0\) \(1\) \(-1\) \(0\) \(q+\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(1+\beta _{2})q^{9}+\cdots\)
1136.1.l.a 1136.l 1136.l $2$ $0.567$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-71}) \) None \(0\) \(-2\) \(2\) \(0\) \(q-iq^{2}+(-1+i)q^{3}-q^{4}+(1+i+\cdots)q^{5}+\cdots\)
1136.1.l.b 1136.l 1136.l $12$ $0.567$ \(\Q(\zeta_{28})\) $D_{28}$ \(\Q(\sqrt{-71}) \) None \(0\) \(2\) \(-2\) \(0\) \(q+\zeta_{28}^{3}q^{2}+(\zeta_{28}^{9}-\zeta_{28}^{12})q^{3}+\zeta_{28}^{6}q^{4}+\cdots\)
1349.1.g.a 1349.g 1349.g $2$ $0.673$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-71}) \) None \(-2\) \(1\) \(1\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-3\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots\)
1349.1.g.b 1349.g 1349.g $12$ $0.673$ \(\Q(\zeta_{21})\) $D_{21}$ \(\Q(\sqrt{-71}) \) None \(2\) \(-1\) \(-1\) \(0\) \(q+(\zeta_{42}^{8}+\zeta_{42}^{20})q^{2}+(-\zeta_{42}^{3}+\zeta_{42}^{4}+\cdots)q^{3}+\cdots\)
1349.1.t.a 1349.t 1349.t $6$ $0.673$ \(\Q(\zeta_{18})\) $D_{9}$ \(\Q(\sqrt{-71}) \) None \(0\) \(6\) \(-3\) \(0\) \(q-\zeta_{18}^{4}q^{2}+(1-\zeta_{18}^{5})q^{3}+(-\zeta_{18}^{3}+\cdots)q^{5}+\cdots\)
1349.1.t.b 1349.t 1349.t $36$ $0.673$ \(\Q(\zeta_{63})\) $D_{63}$ \(\Q(\sqrt{-71}) \) None \(0\) \(-6\) \(3\) \(0\) \(q+(\zeta_{126}^{2}-\zeta_{126}^{5})q^{2}+(\zeta_{126}^{36}-\zeta_{126}^{55}+\cdots)q^{3}+\cdots\)
1420.1.l.a 1420.l 1420.l $2$ $0.709$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-71}) \) None \(-2\) \(-2\) \(0\) \(0\) \(q-q^{2}+(-1-i)q^{3}+q^{4}+iq^{5}+(1+\cdots)q^{6}+\cdots\)
1420.1.l.b 1420.l 1420.l $2$ $0.709$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-71}) \) None \(0\) \(2\) \(0\) \(0\) \(q-iq^{2}+(1+i)q^{3}-q^{4}+iq^{5}+(1+\cdots)q^{6}+\cdots\)
1420.1.l.c 1420.l 1420.l $12$ $0.709$ \(\Q(\zeta_{28})\) $D_{28}$ \(\Q(\sqrt{-71}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+\zeta_{28}^{3}q^{2}+(-\zeta_{28}^{2}+\zeta_{28}^{5})q^{3}+\cdots\)
1420.1.l.d 1420.l 1420.l $12$ $0.709$ \(\Q(\zeta_{28})\) $D_{28}$ \(\Q(\sqrt{-71}) \) None \(2\) \(2\) \(0\) \(0\) \(q+\zeta_{28}^{6}q^{2}+(\zeta_{28}^{10}+\zeta_{28}^{11})q^{3}+\cdots\)
1704.1.p.a 1704.p 1704.p $1$ $0.850$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-71}) \), \(\Q(\sqrt{-426}) \) \(\Q(\sqrt{6}) \) \(-1\) \(-1\) \(2\) \(0\) \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\cdots\)
1704.1.p.d 1704.p 1704.p $1$ $0.850$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-71}) \), \(\Q(\sqrt{-426}) \) \(\Q(\sqrt{6}) \) \(1\) \(-1\) \(-2\) \(0\) \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{8}+\cdots\)
1704.1.p.i 1704.p 1704.p $6$ $0.850$ \(\Q(\zeta_{14})\) $D_{14}$ \(\Q(\sqrt{-71}) \) None \(-1\) \(1\) \(2\) \(0\) \(q+\zeta_{14}^{2}q^{2}-\zeta_{14}^{6}q^{3}+\zeta_{14}^{4}q^{4}+\cdots\)
1704.1.p.j 1704.p 1704.p $6$ $0.850$ \(\Q(\zeta_{14})\) $D_{14}$ \(\Q(\sqrt{-71}) \) None \(1\) \(1\) \(-2\) \(0\) \(q-\zeta_{14}^{4}q^{2}-\zeta_{14}^{2}q^{3}-\zeta_{14}q^{4}+(-\zeta_{14}+\cdots)q^{5}+\cdots\)
1775.1.c.a 1775.c 355.c $6$ $0.886$ 6.0.153664.1 $D_{7}$ \(\Q(\sqrt{-71}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(-1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
1775.1.d.a 1775.d 71.b $1$ $0.886$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-71}) \), \(\Q(\sqrt{-355}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q-q^{4}-q^{9}+q^{16}+2q^{19}+2q^{29}+\cdots\)
1775.1.d.b 1775.d 71.b $3$ $0.886$ \(\Q(\zeta_{14})^+\) $D_{7}$ \(\Q(\sqrt{-71}) \) None \(1\) \(1\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
1775.1.d.c 1775.d 71.b $6$ $0.886$ \(\Q(\zeta_{28})^+\) $D_{14}$ \(\Q(\sqrt{-71}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+(1-2\beta _{2}+\cdots)q^{6}+\cdots\)
1775.1.p.a 1775.p 1775.p $4$ $0.886$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-71}) \) None \(3\) \(-2\) \(-1\) \(0\) \(q+(1-\zeta_{10}^{3})q^{2}+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{3}+\cdots\)
1775.1.p.b 1775.p 1775.p $24$ $0.886$ \(\Q(\zeta_{35})\) $D_{35}$ \(\Q(\sqrt{-71}) \) None \(-3\) \(2\) \(1\) \(0\) \(q+(-\zeta_{70}+\zeta_{70}^{20})q^{2}+(\zeta_{70}^{18}+\zeta_{70}^{24}+\cdots)q^{3}+\cdots\)
1775.1.bb.a 1775.bb 1775.ab $4$ $0.886$ \(\Q(\zeta_{10})\) $D_{10}$ \(\Q(\sqrt{-71}) \) None \(5\) \(0\) \(1\) \(0\) \(q+(1-\zeta_{10}^{4})q^{2}+(-\zeta_{10}-\zeta_{10}^{2})q^{3}+\cdots\)
1775.1.bb.b 1775.bb 1775.ab $24$ $0.886$ \(\Q(\zeta_{35})\) $D_{70}$ \(\Q(\sqrt{-71}) \) None \(-5\) \(0\) \(-1\) \(0\) \(q+(\zeta_{70}^{17}-\zeta_{70}^{25})q^{2}+(-\zeta_{70}^{23}+\cdots)q^{3}+\cdots\)
1917.1.g.a 1917.g 639.g $2$ $0.957$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-71}) \) None \(-1\) \(0\) \(2\) \(0\) \(q+\zeta_{6}^{2}q^{2}+\zeta_{6}q^{5}-q^{8}-2q^{10}-\zeta_{6}^{2}q^{16}+\cdots\)
1917.1.g.b 1917.g 639.g $12$ $0.957$ \(\Q(\zeta_{21})\) $D_{21}$ \(\Q(\sqrt{-71}) \) None \(1\) \(0\) \(-2\) \(0\) \(q+(\zeta_{42}^{3}-\zeta_{42}^{4})q^{2}+(\zeta_{42}^{6}-\zeta_{42}^{7}+\cdots)q^{4}+\cdots\)
1917.1.s.a 1917.s 1917.s $6$ $0.957$ \(\Q(\zeta_{18})\) $D_{9}$ \(\Q(\sqrt{-71}) \) None \(6\) \(0\) \(0\) \(0\) \(q+(1-\zeta_{18}^{5})q^{2}+\zeta_{18}^{8}q^{3}+(1-\zeta_{18}+\cdots)q^{4}+\cdots\)
1917.1.s.b 1917.s 1917.s $36$ $0.957$ \(\Q(\zeta_{63})\) $D_{63}$ \(\Q(\sqrt{-71}) \) None \(-6\) \(0\) \(0\) \(0\) \(q+(-\zeta_{126}^{5}-\zeta_{126}^{9})q^{2}+\zeta_{126}^{8}q^{3}+\cdots\)
2059.1.b.a 2059.b 2059.b $1$ $1.028$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-71}) \), \(\Q(\sqrt{-2059}) \) \(\Q(\sqrt{29}) \) \(0\) \(0\) \(-2\) \(0\) \(q+q^{4}-2q^{5}+q^{9}+q^{16}-2q^{20}+\cdots\)
2059.1.b.c 2059.b 2059.b $6$ $1.028$ \(\Q(\zeta_{14})\) $D_{14}$ \(\Q(\sqrt{-71}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(\zeta_{14}^{2}+\zeta_{14}^{5})q^{2}+(\zeta_{14}+\zeta_{14}^{6}+\cdots)q^{3}+\cdots\)
2059.1.x.a 2059.x 2059.x $42$ $1.028$ \(\Q(\zeta_{98})\) $D_{49}$ \(\Q(\sqrt{-71}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{98}+\zeta_{98}^{6})q^{2}+(-\zeta_{98}^{11}+\zeta_{98}^{24}+\cdots)q^{3}+\cdots\)
2059.1.bh.a 2059.bh 2059.ah $42$ $1.028$ \(\Q(\zeta_{98})\) $D_{98}$ \(\Q(\sqrt{-71}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{98}+\zeta_{98}^{6})q^{2}+(-\zeta_{98}^{11}-\zeta_{98}^{24}+\cdots)q^{3}+\cdots\)
2272.1.b.a 2272.b 568.b $1$ $1.134$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-71}) \), \(\Q(\sqrt{-142}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(0\) \(q+q^{9}+q^{25}+q^{49}+q^{71}-2q^{73}+\cdots\)
2272.1.b.b 2272.b 568.b $6$ $1.134$ \(\Q(\zeta_{14})\) $D_{14}$ \(\Q(\sqrt{-71}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{14}+\zeta_{14}^{6})q^{3}+(-\zeta_{14}^{3}-\zeta_{14}^{4}+\cdots)q^{5}+\cdots\)
2272.1.p.a 2272.p 2272.p $4$ $1.134$ \(\Q(\zeta_{8})\) $D_{8}$ \(\Q(\sqrt{-71}) \) None \(0\) \(0\) \(4\) \(0\) \(q-\zeta_{8}^{3}q^{2}+(\zeta_{8}-\zeta_{8}^{2})q^{3}-\zeta_{8}^{2}q^{4}+\cdots\)
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