1155.1.e.a |
\(2\) |
\(0.576\) |
\(\Q(\sqrt{-1}) \) |
\(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-231}) \) |
\(\Q(\sqrt{165}) \) |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-iq^{3}+q^{4}-iq^{5}+iq^{7}-q^{9}-q^{11}+\cdots\)
|
1155.1.e.b |
\(2\) |
\(0.576\) |
\(\Q(\sqrt{-1}) \) |
\(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-231}) \) |
\(\Q(\sqrt{165}) \) |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-iq^{3}+q^{4}-iq^{5}-iq^{7}-q^{9}+q^{11}+\cdots\)
|
1155.1.e.c |
\(4\) |
\(0.576\) |
\(\Q(\zeta_{12})\) |
\(\Q(\sqrt{-231}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(\zeta_{12}^{2}+\zeta_{12}^{4})q^{2}+\zeta_{12}^{3}q^{3}+(-1+\cdots)q^{4}+\cdots\)
|
1155.1.e.d |
\(4\) |
\(0.576\) |
\(\Q(\zeta_{12})\) |
\(\Q(\sqrt{-231}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{2}+\zeta_{12}^{3}q^{3}+\cdots\)
|
1155.1.ca.a |
\(8\) |
\(0.576\) |
\(\Q(\zeta_{20})\) |
\(\Q(\sqrt{-35}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\zeta_{20}^{5}q^{3}+\zeta_{20}^{4}q^{4}-\zeta_{20}^{3}q^{5}+\cdots\)
|
1155.1.ca.b |
\(8\) |
\(0.576\) |
\(\Q(\zeta_{20})\) |
\(\Q(\sqrt{-35}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\zeta_{20}^{7}q^{3}+\zeta_{20}^{4}q^{4}-\zeta_{20}^{3}q^{5}+\cdots\)
|
1155.2.a.a |
\(1\) |
\(9.223\) |
\(\Q\) |
None |
None |
\(-2\) |
\(-1\) |
\(1\) |
\(1\) |
\(+\) |
\(q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}+q^{7}+\cdots\)
|
1155.2.a.b |
\(1\) |
\(9.223\) |
\(\Q\) |
None |
None |
\(-2\) |
\(1\) |
\(-1\) |
\(-1\) |
\(+\) |
\(q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}-q^{7}+\cdots\)
|
1155.2.a.c |
\(1\) |
\(9.223\) |
\(\Q\) |
None |
None |
\(-2\) |
\(1\) |
\(1\) |
\(1\) |
\(+\) |
\(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}+q^{7}+\cdots\)
|
1155.2.a.d |
\(1\) |
\(9.223\) |
\(\Q\) |
None |
None |
\(-1\) |
\(-1\) |
\(-1\) |
\(-1\) |
\(+\) |
\(q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
|
1155.2.a.e |
\(1\) |
\(9.223\) |
\(\Q\) |
None |
None |
\(-1\) |
\(-1\) |
\(1\) |
\(-1\) |
\(+\) |
\(q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
|
1155.2.a.f |
\(1\) |
\(9.223\) |
\(\Q\) |
None |
None |
\(-1\) |
\(1\) |
\(1\) |
\(1\) |
\(-\) |
\(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
|
1155.2.a.g |
\(1\) |
\(9.223\) |
\(\Q\) |
None |
None |
\(0\) |
\(-1\) |
\(-1\) |
\(1\) |
\(+\) |
\(q-q^{3}-2q^{4}-q^{5}+q^{7}+q^{9}+q^{11}+\cdots\)
|
1155.2.a.h |
\(1\) |
\(9.223\) |
\(\Q\) |
None |
None |
\(0\) |
\(1\) |
\(-1\) |
\(1\) |
\(+\) |
\(q+q^{3}-2q^{4}-q^{5}+q^{7}+q^{9}-q^{11}+\cdots\)
|
1155.2.a.i |
\(1\) |
\(9.223\) |
\(\Q\) |
None |
None |
\(0\) |
\(1\) |
\(1\) |
\(-1\) |
\(+\) |
\(q+q^{3}-2q^{4}+q^{5}-q^{7}+q^{9}-q^{11}+\cdots\)
|
1155.2.a.j |
\(1\) |
\(9.223\) |
\(\Q\) |
None |
None |
\(1\) |
\(-1\) |
\(-1\) |
\(1\) |
\(-\) |
\(q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
|
1155.2.a.k |
\(1\) |
\(9.223\) |
\(\Q\) |
None |
None |
\(1\) |
\(-1\) |
\(1\) |
\(1\) |
\(+\) |
\(q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
|
1155.2.a.l |
\(1\) |
\(9.223\) |
\(\Q\) |
None |
None |
\(1\) |
\(1\) |
\(-1\) |
\(-1\) |
\(+\) |
\(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
|
1155.2.a.m |
\(1\) |
\(9.223\) |
\(\Q\) |
None |
None |
\(1\) |
\(1\) |
\(1\) |
\(1\) |
\(-\) |
\(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
|
1155.2.a.n |
\(1\) |
\(9.223\) |
\(\Q\) |
None |
None |
\(2\) |
\(-1\) |
\(-1\) |
\(-1\) |
\(+\) |
\(q+2q^{2}-q^{3}+2q^{4}-q^{5}-2q^{6}-q^{7}+\cdots\)
|
1155.2.a.o |
\(2\) |
\(9.223\) |
\(\Q(\sqrt{17}) \) |
None |
None |
\(-1\) |
\(-2\) |
\(2\) |
\(-2\) |
\(+\) |
\(q-\beta q^{2}-q^{3}+(2+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots\)
|
1155.2.a.p |
\(2\) |
\(9.223\) |
\(\Q(\sqrt{2}) \) |
None |
None |
\(0\) |
\(-2\) |
\(-2\) |
\(-2\) |
\(-\) |
\(q+\beta q^{2}-q^{3}-q^{5}-\beta q^{6}-q^{7}-2\beta q^{8}+\cdots\)
|
1155.2.a.q |
\(2\) |
\(9.223\) |
\(\Q(\sqrt{6}) \) |
None |
None |
\(0\) |
\(2\) |
\(2\) |
\(2\) |
\(-\) |
\(q+\beta q^{2}+q^{3}+4q^{4}+q^{5}+\beta q^{6}+q^{7}+\cdots\)
|
1155.2.a.r |
\(2\) |
\(9.223\) |
\(\Q(\sqrt{3}) \) |
None |
None |
\(2\) |
\(-2\) |
\(-2\) |
\(2\) |
\(-\) |
\(q+(1+\beta )q^{2}-q^{3}+(2+2\beta )q^{4}-q^{5}+\cdots\)
|
1155.2.a.s |
\(3\) |
\(9.223\) |
3.3.316.1 |
None |
None |
\(1\) |
\(-3\) |
\(3\) |
\(-3\) |
\(-\) |
\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
|
1155.2.a.t |
\(3\) |
\(9.223\) |
3.3.316.1 |
None |
None |
\(1\) |
\(3\) |
\(3\) |
\(-3\) |
\(-\) |
\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
|
1155.2.a.u |
\(4\) |
\(9.223\) |
4.4.13448.1 |
None |
None |
\(0\) |
\(4\) |
\(-4\) |
\(-4\) |
\(-\) |
\(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
|
1155.2.a.v |
\(4\) |
\(9.223\) |
4.4.7232.1 |
None |
None |
\(2\) |
\(-4\) |
\(4\) |
\(4\) |
\(-\) |
\(q-\beta _{2}q^{2}-q^{3}+(1-\beta _{2}-\beta _{3})q^{4}+q^{5}+\cdots\)
|
1155.2.a.w |
\(5\) |
\(9.223\) |
5.5.352076.1 |
None |
None |
\(1\) |
\(5\) |
\(-5\) |
\(5\) |
\(-\) |
\(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
|
1155.2.c.a |
\(2\) |
\(9.223\) |
\(\Q(\sqrt{-1}) \) |
None |
None |
\(0\) |
\(0\) |
\(-4\) |
\(0\) |
|
\(q+iq^{2}+iq^{3}+q^{4}+(-2+i)q^{5}+\cdots\)
|
1155.2.c.b |
\(2\) |
\(9.223\) |
\(\Q(\sqrt{-1}) \) |
None |
None |
\(0\) |
\(0\) |
\(-4\) |
\(0\) |
|
\(q+iq^{2}+iq^{3}+q^{4}+(-2-i)q^{5}+\cdots\)
|
1155.2.c.c |
\(6\) |
\(9.223\) |
6.0.350464.1 |
None |
None |
\(0\) |
\(0\) |
\(2\) |
\(0\) |
|
\(q-\beta _{5}q^{2}-\beta _{3}q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
|
1155.2.c.d |
\(6\) |
\(9.223\) |
6.0.350464.1 |
None |
None |
\(0\) |
\(0\) |
\(2\) |
\(0\) |
|
\(q-\beta _{5}q^{2}-\beta _{3}q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
|
1155.2.c.e |
\(20\) |
\(9.223\) |
\(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
None |
None |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
|
\(q+\beta _{1}q^{2}+\beta _{13}q^{3}+(-1+\beta _{2})q^{4}+\cdots\)
|
1155.2.c.f |
\(20\) |
\(9.223\) |
\(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
None |
None |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
|
\(q+\beta _{1}q^{2}-\beta _{11}q^{3}+(-1+\beta _{2})q^{4}+\cdots\)
|
1155.2.i.a |
\(8\) |
\(9.223\) |
8.0.303595776.1 |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(\beta _{1}-\beta _{5})q^{2}+\beta _{4}q^{3}+(-2-\beta _{7})q^{4}+\cdots\)
|
1155.2.i.b |
\(8\) |
\(9.223\) |
\(\Q(\zeta_{24})\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(\zeta_{24}^{4}-\zeta_{24}^{5})q^{2}-\zeta_{24}^{3}q^{3}+(-\zeta_{24}^{2}+\cdots)q^{4}+\cdots\)
|
1155.2.i.c |
\(16\) |
\(9.223\) |
\(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{8}q^{2}+\beta _{9}q^{3}+(-2-\beta _{3})q^{4}-\beta _{9}q^{5}+\cdots\)
|
1155.2.i.d |
\(32\) |
\(9.223\) |
|
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
|
1155.2.k.a |
\(48\) |
\(9.223\) |
|
None |
None |
\(0\) |
\(-48\) |
\(4\) |
\(0\) |
|
|
1155.2.k.b |
\(48\) |
\(9.223\) |
|
None |
None |
\(0\) |
\(48\) |
\(-4\) |
\(0\) |
|
|
1155.2.l.a |
\(4\) |
\(9.223\) |
\(\Q(\zeta_{8})\) |
None |
None |
\(-4\) |
\(4\) |
\(0\) |
\(0\) |
|
\(q+(-1-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}^{2})q^{3}+(1+\cdots)q^{4}+\cdots\)
|
1155.2.l.b |
\(4\) |
\(9.223\) |
\(\Q(\zeta_{8})\) |
None |
None |
\(0\) |
\(4\) |
\(0\) |
\(0\) |
|
\(q+\zeta_{8}^{3}q^{2}+(1-\zeta_{8}^{2})q^{3}-\zeta_{8}q^{5}+(-2\zeta_{8}+\cdots)q^{6}+\cdots\)
|
1155.2.l.c |
\(4\) |
\(9.223\) |
\(\Q(\zeta_{8})\) |
None |
None |
\(0\) |
\(4\) |
\(0\) |
\(0\) |
|
\(q+\zeta_{8}^{3}q^{2}+(1-\zeta_{8}^{2})q^{3}+\zeta_{8}q^{5}+(-2\zeta_{8}+\cdots)q^{6}+\cdots\)
|
1155.2.l.d |
\(4\) |
\(9.223\) |
\(\Q(\zeta_{8})\) |
None |
None |
\(4\) |
\(4\) |
\(0\) |
\(0\) |
|
\(q+(1-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}^{2})q^{3}+(1-2\zeta_{8}^{3})q^{4}+\cdots\)
|
1155.2.l.e |
\(40\) |
\(9.223\) |
|
None |
None |
\(-4\) |
\(-4\) |
\(0\) |
\(0\) |
|
|
1155.2.l.f |
\(40\) |
\(9.223\) |
|
None |
None |
\(4\) |
\(-4\) |
\(0\) |
\(0\) |
|
|
1155.2.q.a |
\(2\) |
\(9.223\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(-2\) |
\(-1\) |
\(-1\) |
\(-1\) |
|
\(q-2\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
|
1155.2.q.b |
\(2\) |
\(9.223\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(0\) |
\(-1\) |
\(-1\) |
\(-5\) |
|
\(q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}-\zeta_{6}q^{5}+\cdots\)
|
1155.2.q.c |
\(2\) |
\(9.223\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(0\) |
\(-1\) |
\(-1\) |
\(5\) |
|
\(q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}-\zeta_{6}q^{5}+\cdots\)
|