Label |
Level |
Weight |
Char |
Prim |
Char order |
Dim |
Rel. Dim |
$A$ |
Field |
Image |
CM |
RM |
Self-dual |
Inner twists |
Rank* |
Traces |
Coefficient ring index |
Sato-Tate |
$q$-expansion |
$a_{2}$ |
$a_{3}$ |
$a_{5}$ |
$a_{7}$ |
300.1.l.a |
$300$ |
$1$ |
300.l |
60.l |
$4$ |
$4$ |
$2$ |
$0.150$ |
\(\Q(\zeta_{8})\) |
$D_{2}$ |
\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-5}) \) |
\(\Q(\sqrt{3}) \) |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{8}q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}-q^{6}+\cdots\) |
363.1.h.a |
$363$ |
$1$ |
363.h |
33.h |
$10$ |
$4$ |
$1$ |
$0.181$ |
\(\Q(\zeta_{10})\) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-11}) \) |
\(\Q(\sqrt{33}) \) |
|
$16$ |
$0$ |
\(0\) |
\(1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{10}^{4}q^{3}-\zeta_{10}q^{4}-\zeta_{10}^{3}q^{9}-q^{12}+\cdots\) |
525.1.k.a |
$525$ |
$1$ |
525.k |
105.k |
$4$ |
$4$ |
$2$ |
$0.262$ |
\(\Q(\zeta_{8})\) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-35}) \) |
\(\Q(\sqrt{105}) \) |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{9}+\cdots\) |
525.1.be.a |
$525$ |
$1$ |
525.be |
105.w |
$12$ |
$8$ |
$2$ |
$0.262$ |
\(\Q(\zeta_{24})\) |
$D_{6}$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{24}^{5}q^{3}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{11}q^{7}+\cdots\) |
600.1.q.a |
$600$ |
$1$ |
600.q |
120.q |
$4$ |
$4$ |
$2$ |
$0.299$ |
\(\Q(\zeta_{8})\) |
$D_{2}$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-15}) \) |
\(\Q(\sqrt{30}) \) |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{8}^{3}q^{2}-\zeta_{8}q^{3}-\zeta_{8}^{2}q^{4}+q^{6}+\cdots\) |
600.1.q.b |
$600$ |
$1$ |
600.q |
120.q |
$4$ |
$8$ |
$4$ |
$0.299$ |
\(\Q(\zeta_{24})\) |
$D_{6}$ |
\(\Q(\sqrt{-2}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{24}^{3}q^{2}-\zeta_{24}q^{3}+\zeta_{24}^{6}q^{4}-\zeta_{24}^{4}q^{6}+\cdots\) |
605.1.h.a |
$605$ |
$1$ |
605.h |
55.h |
$10$ |
$4$ |
$1$ |
$0.302$ |
\(\Q(\zeta_{10})\) |
$D_{2}$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-55}) \) |
\(\Q(\sqrt{5}) \) |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(1\) |
\(0\) |
$1$ |
|
\(q+\zeta_{10}^{3}q^{4}+\zeta_{10}q^{5}+\zeta_{10}^{4}q^{9}-\zeta_{10}q^{16}+\cdots\) |
605.1.l.a |
$605$ |
$1$ |
605.l |
55.k |
$20$ |
$8$ |
$1$ |
$0.302$ |
\(\Q(\zeta_{20})\) |
$D_{4}$ |
\(\Q(\sqrt{-11}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(-2\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+(-\zeta_{20}-\zeta_{20}^{6})q^{3}-\zeta_{20}^{9}q^{4}-\zeta_{20}^{3}q^{5}+\cdots\) |
700.1.j.a |
$700$ |
$1$ |
700.j |
140.j |
$4$ |
$4$ |
$2$ |
$0.349$ |
\(\Q(\zeta_{8})\) |
$D_{2}$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-5}) \) |
\(\Q(\sqrt{35}) \) |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}-\zeta_{8}q^{8}+\cdots\) |
700.1.j.b |
$700$ |
$1$ |
700.j |
140.j |
$4$ |
$8$ |
$4$ |
$0.349$ |
\(\Q(\zeta_{24})\) |
$D_{6}$ |
\(\Q(\sqrt{-7}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{3}q^{7}+\cdots\) |
700.1.bf.a |
$700$ |
$1$ |
700.bf |
140.x |
$12$ |
$8$ |
$2$ |
$0.349$ |
\(\Q(\zeta_{24})\) |
$D_{6}$ |
\(\Q(\sqrt{-5}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{24}^{11}q^{2}+(\zeta_{24}^{5}+\zeta_{24}^{9})q^{3}-\zeta_{24}^{10}q^{4}+\cdots\) |
867.1.g.a |
$867$ |
$1$ |
867.g |
51.g |
$8$ |
$8$ |
$2$ |
$0.433$ |
\(\Q(\zeta_{16})\) |
$D_{3}$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{16}^{7}q^{3}+\zeta_{16}^{4}q^{4}-\zeta_{16}^{5}q^{7}+\cdots\) |
900.1.bd.a |
$900$ |
$1$ |
900.bd |
180.v |
$12$ |
$8$ |
$2$ |
$0.449$ |
\(\Q(\zeta_{24})\) |
$D_{6}$ |
\(\Q(\sqrt{-5}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{24}^{11}q^{2}-\zeta_{24}q^{3}-\zeta_{24}^{10}q^{4}+\cdots\) |
961.1.h.a |
$961$ |
$1$ |
961.h |
31.h |
$30$ |
$8$ |
$1$ |
$0.480$ |
\(\Q(\zeta_{15})\) |
$D_{3}$ |
\(\Q(\sqrt{-31}) \) |
None |
|
$16$ |
$0$ |
\(2\) |
\(0\) |
\(4\) |
\(-1\) |
$1$ |
|
\(q+\zeta_{30}^{3}q^{2}-\zeta_{30}^{10}q^{5}+\zeta_{30}^{11}q^{7}+\cdots\) |
980.1.p.c |
$980$ |
$1$ |
980.p |
140.p |
$6$ |
$8$ |
$4$ |
$0.489$ |
\(\Q(\zeta_{24})\) |
$D_{4}$ |
\(\Q(\sqrt{-1}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{24}^{10}q^{2}-\zeta_{24}^{8}q^{4}-\zeta_{24}^{7}q^{5}+\cdots\) |
980.1.y.a |
$980$ |
$1$ |
980.y |
140.x |
$12$ |
$16$ |
$4$ |
$0.489$ |
\(\Q(\zeta_{48})\) |
$D_{8}$ |
\(\Q(\sqrt{-1}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{48}^{2}q^{2}+\zeta_{48}^{4}q^{4}+\zeta_{48}^{5}q^{5}+\cdots\) |
1089.1.k.a |
$1089$ |
$1$ |
1089.k |
11.d |
$10$ |
$8$ |
$2$ |
$0.543$ |
8.0.64000000.1 |
$D_{4}$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\beta _{2}q^{4}-\beta _{7}q^{7}-\beta _{1}q^{13}+\beta _{4}q^{16}+\cdots\) |
1089.1.r.a |
$1089$ |
$1$ |
1089.r |
99.n |
$30$ |
$8$ |
$1$ |
$0.543$ |
\(\Q(\zeta_{15})\) |
$D_{6}$ |
\(\Q(\sqrt{-11}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(-1\) |
\(-3\) |
\(0\) |
$1$ |
|
\(q+\zeta_{30}^{7}q^{3}-\zeta_{30}^{13}q^{4}+(\zeta_{30}^{6}+\zeta_{30}^{11}+\cdots)q^{5}+\cdots\) |
1089.1.s.a |
$1089$ |
$1$ |
1089.s |
99.o |
$30$ |
$8$ |
$1$ |
$0.543$ |
\(\Q(\zeta_{15})\) |
$D_{3}$ |
\(\Q(\sqrt{-11}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(1\) |
\(-1\) |
\(0\) |
$1$ |
|
\(q-\zeta_{30}^{7}q^{3}-\zeta_{30}^{13}q^{4}+\zeta_{30}q^{5}+\cdots\) |
1089.1.s.b |
$1089$ |
$1$ |
1089.s |
99.o |
$30$ |
$16$ |
$2$ |
$0.543$ |
16.0.\(\cdots\).1 |
$S_{4}$ |
None |
None |
|
$16$ |
$0$ |
\(0\) |
\(-2\) |
\(-2\) |
\(0\) |
$1$ |
|
\(q+\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}+(\beta _{3}+\beta _{15})q^{5}+\cdots\) |
1156.1.g.a |
$1156$ |
$1$ |
1156.g |
68.g |
$8$ |
$4$ |
$1$ |
$0.577$ |
\(\Q(\zeta_{8})\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-17}) \) |
\(\Q(\sqrt{17}) \) |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{8}-\zeta_{8}q^{9}+\cdots\) |
1156.1.g.b |
$1156$ |
$1$ |
1156.g |
68.g |
$8$ |
$8$ |
$2$ |
$0.577$ |
\(\Q(\zeta_{16})\) |
$D_{4}$ |
\(\Q(\sqrt{-1}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{2}$ |
|
\(q+\zeta_{16}^{6}q^{2}-\zeta_{16}^{4}q^{4}+(-\zeta_{16}^{3}-\zeta_{16}^{7}+\cdots)q^{5}+\cdots\) |
1176.1.s.c |
$1176$ |
$1$ |
1176.s |
168.s |
$6$ |
$8$ |
$4$ |
$0.587$ |
\(\Q(\zeta_{24})\) |
$D_{4}$ |
\(\Q(\sqrt{-14}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{24}^{10}q^{2}-\zeta_{24}^{5}q^{3}-\zeta_{24}^{8}q^{4}+\cdots\) |
1176.1.be.a |
$1176$ |
$1$ |
1176.be |
168.ae |
$6$ |
$16$ |
$8$ |
$0.587$ |
\(\Q(\zeta_{48})\) |
$D_{8}$ |
\(\Q(\sqrt{-2}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{48}^{4}q^{2}+\zeta_{48}^{5}q^{3}+\zeta_{48}^{8}q^{4}+\cdots\) |
1200.1.bj.a |
$1200$ |
$1$ |
1200.bj |
60.l |
$4$ |
$4$ |
$2$ |
$0.599$ |
\(\Q(\zeta_{8})\) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-5}) \) |
\(\Q(\sqrt{15}) \) |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{8}q^{3}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{9}-2q^{21}+\cdots\) |
1200.1.bj.b |
$1200$ |
$1$ |
1200.bj |
60.l |
$4$ |
$8$ |
$4$ |
$0.599$ |
\(\Q(\zeta_{24})\) |
$D_{6}$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{4}$ |
|
\(q-\zeta_{24}^{3}q^{3}+\zeta_{24}^{9}q^{7}+\zeta_{24}^{6}q^{9}+\cdots\) |
1225.1.q.a |
$1225$ |
$1$ |
1225.q |
35.l |
$12$ |
$4$ |
$1$ |
$0.611$ |
\(\Q(\zeta_{12})\) |
$D_{2}$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-35}) \) |
\(\Q(\sqrt{5}) \) |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{12}q^{4}-\zeta_{12}^{5}q^{9}+\zeta_{12}^{4}q^{11}+\cdots\) |
1225.1.q.b |
$1225$ |
$1$ |
1225.q |
35.l |
$12$ |
$8$ |
$2$ |
$0.611$ |
\(\Q(\zeta_{24})\) |
$D_{6}$ |
\(\Q(\sqrt{-7}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$3^{2}$ |
|
\(q+(\zeta_{24}^{5}+\zeta_{24}^{9})q^{2}+(-\zeta_{24}^{2}-\zeta_{24}^{6}+\cdots)q^{4}+\cdots\) |
1400.1.y.a |
$1400$ |
$1$ |
1400.y |
280.y |
$4$ |
$4$ |
$2$ |
$0.699$ |
\(\Q(\zeta_{8})\) |
$D_{2}$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-10}) \) |
\(\Q(\sqrt{70}) \) |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}-\zeta_{8}q^{8}+\cdots\) |
1400.1.y.b |
$1400$ |
$1$ |
1400.y |
280.y |
$4$ |
$8$ |
$4$ |
$0.699$ |
\(\Q(\zeta_{24})\) |
$D_{6}$ |
\(\Q(\sqrt{-7}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{3}q^{7}+\cdots\) |
1400.1.cf.a |
$1400$ |
$1$ |
1400.cf |
280.ap |
$12$ |
$8$ |
$2$ |
$0.699$ |
\(\Q(\zeta_{24})\) |
$D_{6}$ |
\(\Q(\sqrt{-10}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{24}^{11}q^{2}-\zeta_{24}^{10}q^{4}-\zeta_{24}^{3}q^{7}+\cdots\) |
1425.1.j.e |
$1425$ |
$1$ |
1425.j |
285.j |
$4$ |
$4$ |
$2$ |
$0.711$ |
\(\Q(\zeta_{8})\) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-95}) \) |
\(\Q(\sqrt{285}) \) |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{2}q^{9}+\zeta_{8}q^{12}+\cdots\) |
1425.1.j.f |
$1425$ |
$1$ |
1425.j |
285.j |
$4$ |
$4$ |
$2$ |
$0.711$ |
\(\Q(\zeta_{8})\) |
$D_{2}$ |
\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-95}) \) |
\(\Q(\sqrt{57}) \) |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{8}^{3}q^{2}+\zeta_{8}q^{3}-3\zeta_{8}^{2}q^{4}+2q^{6}+\cdots\) |
1425.1.j.g |
$1425$ |
$1$ |
1425.j |
285.j |
$4$ |
$8$ |
$4$ |
$0.711$ |
\(\Q(\zeta_{24})\) |
$D_{6}$ |
None |
\(\Q(\sqrt{57}) \) |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{4}$ |
|
\(q-\zeta_{24}^{9}q^{2}-\zeta_{24}^{3}q^{3}-q^{6}+(-\zeta_{24}^{7}+\cdots)q^{7}+\cdots\) |
1425.1.be.a |
$1425$ |
$1$ |
1425.be |
285.w |
$12$ |
$8$ |
$2$ |
$0.711$ |
\(\Q(\zeta_{24})\) |
$D_{6}$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{24}^{7}q^{3}+\zeta_{24}^{2}q^{4}+(-\zeta_{24}-\zeta_{24}^{5}+\cdots)q^{7}+\cdots\) |
1425.1.be.b |
$1425$ |
$1$ |
1425.be |
285.w |
$12$ |
$8$ |
$2$ |
$0.711$ |
\(\Q(\zeta_{24})\) |
$D_{6}$ |
\(\Q(\sqrt{-15}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{24}^{7}q^{2}+\zeta_{24}q^{3}-\zeta_{24}^{8}q^{6}-\zeta_{24}^{9}q^{8}+\cdots\) |
1425.1.cd.a |
$1425$ |
$1$ |
1425.cd |
285.aj |
$36$ |
$24$ |
$2$ |
$0.711$ |
\(\Q(\zeta_{72})\) |
$D_{18}$ |
\(\Q(\sqrt{-15}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+(\zeta_{72}^{3}+\zeta_{72}^{35})q^{2}+\zeta_{72}^{13}q^{3}+\cdots\) |
1425.1.cd.b |
$1425$ |
$1$ |
1425.cd |
285.aj |
$36$ |
$24$ |
$2$ |
$0.711$ |
\(\Q(\zeta_{72})\) |
$D_{18}$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{72}^{31}q^{3}+\zeta_{72}^{2}q^{4}+(\zeta_{72}^{5}+\zeta_{72}^{25}+\cdots)q^{7}+\cdots\) |
1452.1.m.c |
$1452$ |
$1$ |
1452.m |
33.h |
$10$ |
$8$ |
$2$ |
$0.725$ |
\(\Q(\zeta_{15})\) |
$D_{6}$ |
\(\Q(\sqrt{-11}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{30}q^{3}+(\zeta_{30}^{8}+\zeta_{30}^{13})q^{5}+\zeta_{30}^{2}q^{9}+\cdots\) |
1452.1.m.d |
$1452$ |
$1$ |
1452.m |
33.h |
$10$ |
$8$ |
$2$ |
$0.725$ |
8.0.324000000.3 |
$D_{6}$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(2\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+(1+\beta _{2}+\beta _{4}+\beta _{6})q^{3}-\beta _{7}q^{7}+\beta _{6}q^{9}+\cdots\) |
1500.1.l.a |
$1500$ |
$1$ |
1500.l |
60.l |
$4$ |
$16$ |
$8$ |
$0.749$ |
\(\Q(\zeta_{40})\) |
$D_{10}$ |
\(\Q(\sqrt{-5}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{40}^{5}q^{2}-\zeta_{40}^{11}q^{3}+\zeta_{40}^{10}q^{4}+\cdots\) |
1500.1.l.b |
$1500$ |
$1$ |
1500.l |
60.l |
$4$ |
$16$ |
$8$ |
$0.749$ |
\(\Q(\zeta_{40})\) |
$D_{10}$ |
\(\Q(\sqrt{-15}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{40}^{11}q^{2}+\zeta_{40}^{5}q^{3}-\zeta_{40}^{2}q^{4}+\cdots\) |
1575.1.ci.a |
$1575$ |
$1$ |
1575.ci |
35.l |
$12$ |
$8$ |
$2$ |
$0.786$ |
\(\Q(\zeta_{24})\) |
$D_{6}$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{24}^{2}q^{4}-\zeta_{24}^{11}q^{7}+(-\zeta_{24}-\zeta_{24}^{5}+\cdots)q^{13}+\cdots\) |
1575.1.cn.a |
$1575$ |
$1$ |
1575.cn |
315.bf |
$12$ |
$8$ |
$2$ |
$0.786$ |
\(\Q(\zeta_{24})\) |
$D_{6}$ |
\(\Q(\sqrt{-35}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{24}^{9}q^{3}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{7}q^{7}+\cdots\) |
1617.1.k.e |
$1617$ |
$1$ |
1617.k |
231.k |
$6$ |
$16$ |
$8$ |
$0.807$ |
\(\Q(\zeta_{48})\) |
$D_{8}$ |
\(\Q(\sqrt{-11}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{48}^{5}q^{3}+\zeta_{48}^{8}q^{4}+(\zeta_{48}-\zeta_{48}^{7}+\cdots)q^{5}+\cdots\) |
1620.1.p.b |
$1620$ |
$1$ |
1620.p |
180.p |
$6$ |
$4$ |
$2$ |
$0.808$ |
\(\Q(\zeta_{12})\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-15}) \) |
\(\Q(\sqrt{15}) \) |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{5}+\zeta_{12}^{3}q^{8}+\cdots\) |
1620.1.w.b |
$1620$ |
$1$ |
1620.w |
180.v |
$12$ |
$8$ |
$2$ |
$0.808$ |
\(\Q(\zeta_{24})\) |
$D_{4}$ |
\(\Q(\sqrt{-1}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}-\zeta_{24}q^{5}+\cdots\) |
1725.1.l.a |
$1725$ |
$1$ |
1725.l |
345.l |
$4$ |
$4$ |
$2$ |
$0.861$ |
\(\Q(\zeta_{8})\) |
$D_{2}$ |
\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-23}) \) |
\(\Q(\sqrt{345}) \) |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{8}^{3}q^{2}-\zeta_{8}q^{3}-3\zeta_{8}^{2}q^{4}-2q^{6}+\cdots\) |
1725.1.l.b |
$1725$ |
$1$ |
1725.l |
345.l |
$4$ |
$8$ |
$4$ |
$0.861$ |
\(\Q(\zeta_{24})\) |
$D_{6}$ |
\(\Q(\sqrt{-23}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{24}^{3}q^{2}-\zeta_{24}q^{3}-\zeta_{24}^{4}q^{6}-\zeta_{24}^{9}q^{8}+\cdots\) |
1725.1.l.c |
$1725$ |
$1$ |
1725.l |
345.l |
$4$ |
$24$ |
$12$ |
$0.861$ |
\(\Q(\zeta_{72})\) |
$D_{18}$ |
\(\Q(\sqrt{-23}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+(\zeta_{72}^{5}+\zeta_{72}^{13})q^{2}-\zeta_{72}^{19}q^{3}+\cdots\) |