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Label Char Prim Dim $A$ Field CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
164.1.d.a 164.d 164.d $1$ $0.082$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-41}) \) \(\Q(\sqrt{41}) \) \(1\) \(0\) \(-2\) \(0\) \(q+q^{2}+q^{4}-2q^{5}+q^{8}-q^{9}-2q^{10}+\cdots\)
164.1.d.b 164.d 164.d $2$ $0.082$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-41}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}+\beta q^{7}-q^{8}+\cdots\)
656.1.h.a 656.h 164.d $4$ $0.327$ \(\Q(\zeta_{16})^+\) \(\Q(\sqrt{-41}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}-\beta _{2}q^{5}-\beta _{3}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
820.1.e.c 820.e 820.e $8$ $0.409$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-41}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{4}q^{2}+(-\zeta_{16}-\zeta_{16}^{7})q^{3}-q^{4}+\cdots\)
1148.1.o.a 1148.o 1148.o $2$ $0.573$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-41}) \) None \(-1\) \(-1\) \(1\) \(1\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+\cdots\)
1148.1.o.b 1148.o 1148.o $2$ $0.573$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-41}) \) None \(-1\) \(1\) \(1\) \(-1\) \(q-\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+\cdots\)
1148.1.o.c 1148.o 1148.o $4$ $0.573$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-41}) \) None \(-2\) \(0\) \(-2\) \(0\) \(q+\zeta_{12}^{4}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
1148.1.o.d 1148.o 1148.o $8$ $0.573$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-41}) \) None \(4\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{8}q^{2}+(-\zeta_{24}^{9}+\zeta_{24}^{11})q^{3}+\cdots\)
1476.1.h.a 1476.h 164.d $1$ $0.737$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-41}) \) \(\Q(\sqrt{41}) \) \(-1\) \(0\) \(2\) \(0\) \(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+q^{16}+\cdots\)
1476.1.h.b 1476.h 164.d $2$ $0.737$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-41}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}-\beta q^{7}+q^{8}+\beta q^{11}-\beta q^{14}+\cdots\)
1476.1.o.a 1476.o 1476.o $2$ $0.737$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-41}) \) None \(-1\) \(-2\) \(1\) \(-1\) \(q+\zeta_{6}^{2}q^{2}-q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{6}+\cdots\)
1476.1.o.b 1476.o 1476.o $2$ $0.737$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-41}) \) None \(-1\) \(2\) \(1\) \(1\) \(q+\zeta_{6}^{2}q^{2}+q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{6}+\cdots\)
1476.1.o.c 1476.o 1476.o $4$ $0.737$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-41}) \) None \(-2\) \(0\) \(-2\) \(0\) \(q-\zeta_{12}^{2}q^{2}-\zeta_{12}^{3}q^{3}+\zeta_{12}^{4}q^{4}+\cdots\)
1476.1.o.d 1476.o 1476.o $8$ $0.737$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-41}) \) None \(4\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{4}q^{2}+\zeta_{24}^{9}q^{3}+\zeta_{24}^{8}q^{4}+\cdots\)
1804.1.be.a 1804.be 1804.ae $4$ $0.900$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-41}) \) None \(-1\) \(-2\) \(3\) \(3\) \(q+\zeta_{10}^{2}q^{2}-\zeta_{10}q^{3}+\zeta_{10}^{4}q^{4}+(1+\cdots)q^{5}+\cdots\)
1804.1.be.b 1804.be 1804.ae $4$ $0.900$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-41}) \) None \(-1\) \(2\) \(3\) \(-3\) \(q+\zeta_{10}^{2}q^{2}+\zeta_{10}q^{3}+\zeta_{10}^{4}q^{4}+(1+\cdots)q^{5}+\cdots\)
1804.1.be.c 1804.be 1804.ae $8$ $0.900$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-41}) \) None \(-2\) \(0\) \(-6\) \(0\) \(q+\zeta_{20}^{4}q^{2}+\zeta_{20}^{8}q^{4}+(-1+\zeta_{20}^{2}+\cdots)q^{5}+\cdots\)
1804.1.be.d 1804.be 1804.ae $16$ $0.900$ \(\Q(\zeta_{40})\) \(\Q(\sqrt{-41}) \) None \(4\) \(0\) \(0\) \(0\) \(q+\zeta_{40}^{12}q^{2}+(-\zeta_{40}+\zeta_{40}^{11})q^{3}+\cdots\)
2460.1.u.a 2460.u 2460.u $16$ $1.228$ \(\Q(\zeta_{32})\) \(\Q(\sqrt{-41}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{32}^{4}q^{2}-\zeta_{32}^{3}q^{3}+\zeta_{32}^{8}q^{4}+\cdots\)
2460.1.u.b 2460.u 2460.u $16$ $1.228$ \(\Q(\zeta_{32})\) \(\Q(\sqrt{-41}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{32}^{12}q^{2}-\zeta_{32}^{3}q^{3}-\zeta_{32}^{8}q^{4}+\cdots\)
2624.1.h.a 2624.h 164.d $1$ $1.310$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-41}) \) \(\Q(\sqrt{41}) \) \(0\) \(0\) \(2\) \(0\) \(q+2q^{5}-q^{9}+3q^{25}+2q^{37}+q^{41}+\cdots\)
2624.1.h.b 2624.h 164.d $2$ $1.310$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-41}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{3}-\beta q^{7}+q^{9}+\beta q^{11}-\beta q^{19}+\cdots\)
2624.1.h.c 2624.h 164.d $4$ $1.310$ \(\Q(\zeta_{16})^+\) \(\Q(\sqrt{-41}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{3}-\beta _{2}q^{5}-\beta _{1}q^{7}+(1-\beta _{2}+\cdots)q^{9}+\cdots\)
3116.1.q.a 3116.q 3116.q $2$ $1.555$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-41}) \) None \(-1\) \(-1\) \(-2\) \(2\) \(q-\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+\cdots\)
3116.1.q.b 3116.q 3116.q $2$ $1.555$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-41}) \) None \(-1\) \(1\) \(-2\) \(-2\) \(q-\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+\cdots\)
3116.1.q.c 3116.q 3116.q $4$ $1.555$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-41}) \) None \(-2\) \(0\) \(4\) \(0\) \(q+\zeta_{12}^{4}q^{2}+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{3}+\cdots\)
3116.1.q.d 3116.q 3116.q $8$ $1.555$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-41}) \) None \(4\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{8}q^{2}+(\zeta_{24}^{7}+\zeta_{24}^{9})q^{3}-\zeta_{24}^{4}q^{4}+\cdots\)
3116.1.bm.a 3116.bm 3116.am $6$ $1.555$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-41}) \) None \(0\) \(-3\) \(0\) \(0\) \(q-\zeta_{18}^{5}q^{2}+(\zeta_{18}^{6}-\zeta_{18}^{7})q^{3}-\zeta_{18}q^{4}+\cdots\)
3116.1.bm.b 3116.bm 3116.am $6$ $1.555$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-41}) \) None \(0\) \(3\) \(0\) \(0\) \(q-\zeta_{18}^{5}q^{2}+(-\zeta_{18}^{6}+\zeta_{18}^{7})q^{3}+\cdots\)
3116.1.bm.c 3116.bm 3116.am $12$ $1.555$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-41}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{36}^{10}q^{2}+(\zeta_{36}^{3}+\zeta_{36}^{5})q^{3}-\zeta_{36}^{2}q^{4}+\cdots\)
3116.1.bm.d 3116.bm 3116.am $24$ $1.555$ \(\Q(\zeta_{72})\) \(\Q(\sqrt{-41}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{72}^{20}q^{2}+(\zeta_{72}+\zeta_{72}^{15})q^{3}-\zeta_{72}^{4}q^{4}+\cdots\)
3280.1.e.a 3280.e 820.e $1$ $1.637$ \(\Q\) \(\Q(\sqrt{-41}) \), \(\Q(\sqrt{-205}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(-1\) \(0\) \(q-q^{5}+q^{9}-2q^{11}+2q^{19}+q^{25}+\cdots\)
3280.1.e.b 3280.e 820.e $1$ $1.637$ \(\Q\) \(\Q(\sqrt{-41}) \), \(\Q(\sqrt{-205}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(-1\) \(0\) \(q-q^{5}+q^{9}+2q^{11}-2q^{19}+q^{25}+\cdots\)
3280.1.e.e 3280.e 820.e $2$ $1.637$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-41}) \) \(\Q(\sqrt{205}) \) \(0\) \(0\) \(2\) \(0\) \(q-iq^{3}+q^{5}-iq^{7}-3q^{9}-2iq^{15}+\cdots\)
3280.1.e.f 3280.e 820.e $4$ $1.637$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-41}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{8}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{5}+(\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{7}+\cdots\)
3444.1.l.k 3444.l 3444.l $8$ $1.719$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-41}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{4}q^{2}-\zeta_{16}^{3}q^{3}-q^{4}+(\zeta_{16}^{2}+\cdots)q^{5}+\cdots\)
3444.1.l.l 3444.l 3444.l $8$ $1.719$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-41}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{4}q^{2}-\zeta_{16}^{3}q^{3}-q^{4}+(-\zeta_{16}^{2}+\cdots)q^{5}+\cdots\)
3444.1.bg.a 3444.bg 3444.ag $16$ $1.719$ \(\Q(\zeta_{48})\) \(\Q(\sqrt{-41}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{48}^{20}q^{2}+\zeta_{48}^{5}q^{3}-\zeta_{48}^{16}q^{4}+\cdots\)
3444.1.bg.b 3444.bg 3444.ag $16$ $1.719$ \(\Q(\zeta_{48})\) \(\Q(\sqrt{-41}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{48}^{4}q^{2}-\zeta_{48}^{9}q^{3}+\zeta_{48}^{8}q^{4}+\cdots\)
3936.1.b.a 3936.b 123.b $16$ $1.964$ \(\Q(\zeta_{32})\) \(\Q(\sqrt{-41}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{32}^{3}q^{3}+(\zeta_{32}^{2}+\zeta_{32}^{14})q^{5}+(-\zeta_{32}^{7}+\cdots)q^{7}+\cdots\)
492.2.d.a 492.d 492.d $16$ $3.929$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) \(\Q(\sqrt{-41}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{4}q^{2}+\beta _{14}q^{3}-2q^{4}+\beta _{7}q^{5}+\cdots\)
164.3.d.a 164.d 164.d $4$ $4.469$ 4.4.3442688.1 \(\Q(\sqrt{-41}) \) None \(-8\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{2}-\beta _{2}q^{3}+4q^{4}+\beta _{3}q^{5}+2\beta _{2}q^{6}+\cdots\)
164.3.d.b 164.d 164.d $4$ $4.469$ 4.4.83968.1 \(\Q(\sqrt{-41}) \) None \(8\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{2}-\beta _{3}q^{3}+4q^{4}+3\beta _{2}q^{5}-2\beta _{3}q^{6}+\cdots\)
820.2.r.c 820.r 820.r $16$ $6.548$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) \(\Q(\sqrt{-41}) \) None \(-16\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1+\beta _{2})q^{2}+\beta _{13}q^{3}-2\beta _{2}q^{4}+\cdots\)
820.2.r.d 820.r 820.r $16$ $6.548$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) \(\Q(\sqrt{-41}) \) None \(16\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(1+\beta _{1})q^{2}-\beta _{5}q^{3}+2\beta _{1}q^{4}-\beta _{2}q^{5}+\cdots\)
1312.2.d.d 1312.d 41.b $8$ $10.476$ 8.0.\(\cdots\).9 \(\Q(\sqrt{-41}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{3}q^{3}+\beta _{1}q^{5}+\beta _{6}q^{7}+(-3+\beta _{1}+\cdots)q^{9}+\cdots\)
1312.2.d.e 1312.d 41.b $8$ $10.476$ 8.0.\(\cdots\).5 \(\Q(\sqrt{-41}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{6}q^{3}+\beta _{2}q^{5}-\beta _{7}q^{7}+(-3-\beta _{2}+\cdots)q^{9}+\cdots\)
1968.2.g.e 1968.g 492.d $16$ $15.715$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) \(\Q(\sqrt{-41}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{3}+\beta _{6}q^{5}+\beta _{10}q^{7}+\beta _{2}q^{9}+\cdots\)
164.5.d.a 164.d 164.d $2$ $16.953$ \(\Q(\sqrt{41}) \) \(\Q(\sqrt{-41}) \) None \(-8\) \(-22\) \(0\) \(138\) $\mathrm{U}(1)[D_{2}]$ \(q-4q^{2}+(-11-\beta )q^{3}+2^{4}q^{4}+6\beta q^{5}+\cdots\)
164.5.d.c 164.d 164.d $2$ $16.953$ \(\Q(\sqrt{41}) \) \(\Q(\sqrt{-41}) \) None \(-8\) \(22\) \(0\) \(-138\) $\mathrm{U}(1)[D_{2}]$ \(q-4q^{2}+(11-\beta )q^{3}+2^{4}q^{4}-6\beta q^{5}+\cdots\)
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