360.1.p.a |
\(1\) |
\(0.180\) |
\(\Q\) |
\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-10}) \) |
\(\Q(\sqrt{6}) \) |
\(-1\) |
\(0\) |
\(1\) |
\(0\) |
|
\(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+q^{16}+\cdots\)
|
360.1.p.b |
\(1\) |
\(0.180\) |
\(\Q\) |
\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-10}) \) |
\(\Q(\sqrt{6}) \) |
\(1\) |
\(0\) |
\(-1\) |
\(0\) |
|
\(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+q^{16}+\cdots\)
|
360.1.u.a |
\(4\) |
\(0.180\) |
\(\Q(\zeta_{8})\) |
\(\Q(\sqrt{-6}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(-4\) |
|
\(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{5}+(-1+\cdots)q^{7}+\cdots\)
|
360.2.a.a |
\(1\) |
\(2.875\) |
\(\Q\) |
None |
None |
\(0\) |
\(0\) |
\(-1\) |
\(-4\) |
\(+\) |
\(q-q^{5}-4q^{7}-4q^{11}-2q^{13}-2q^{17}+\cdots\)
|
360.2.a.b |
\(1\) |
\(2.875\) |
\(\Q\) |
None |
None |
\(0\) |
\(0\) |
\(-1\) |
\(0\) |
\(-\) |
\(q-q^{5}+4q^{11}+6q^{13}+6q^{17}-4q^{19}+\cdots\)
|
360.2.a.c |
\(1\) |
\(2.875\) |
\(\Q\) |
None |
None |
\(0\) |
\(0\) |
\(-1\) |
\(2\) |
\(-\) |
\(q-q^{5}+2q^{7}+2q^{11}+4q^{13}-2q^{17}+\cdots\)
|
360.2.a.d |
\(1\) |
\(2.875\) |
\(\Q\) |
None |
None |
\(0\) |
\(0\) |
\(1\) |
\(2\) |
\(-\) |
\(q+q^{5}+2q^{7}-2q^{11}+4q^{13}+2q^{17}+\cdots\)
|
360.2.a.e |
\(1\) |
\(2.875\) |
\(\Q\) |
None |
None |
\(0\) |
\(0\) |
\(1\) |
\(4\) |
\(-\) |
\(q+q^{5}+4q^{7}-6q^{13}+2q^{17}+4q^{19}+\cdots\)
|
360.2.b.a |
\(2\) |
\(2.875\) |
\(\Q(\sqrt{-2}) \) |
None |
None |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
|
\(q+\beta q^{2}-2q^{4}-q^{5}-3\beta q^{7}-2\beta q^{8}+\cdots\)
|
360.2.b.b |
\(2\) |
\(2.875\) |
\(\Q(\sqrt{-2}) \) |
None |
None |
\(0\) |
\(0\) |
\(2\) |
\(0\) |
|
\(q+\beta q^{2}-2q^{4}+q^{5}+3\beta q^{7}-2\beta q^{8}+\cdots\)
|
360.2.b.c |
\(6\) |
\(2.875\) |
6.0.2580992.1 |
None |
None |
\(-2\) |
\(0\) |
\(-6\) |
\(0\) |
|
\(q+\beta _{4}q^{2}+(\beta _{2}+\beta _{5})q^{4}-q^{5}+\beta _{2}q^{7}+\cdots\)
|
360.2.b.d |
\(6\) |
\(2.875\) |
6.0.2580992.1 |
None |
None |
\(2\) |
\(0\) |
\(6\) |
\(0\) |
|
\(q-\beta _{4}q^{2}+(\beta _{2}+\beta _{5})q^{4}+q^{5}+\beta _{2}q^{7}+\cdots\)
|
360.2.d.a |
\(4\) |
\(2.875\) |
\(\Q(\sqrt{-2}, \sqrt{-5})\) |
\(\Q(\sqrt{-30}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+2\beta _{1}q^{8}+\cdots\)
|
360.2.d.b |
\(4\) |
\(2.875\) |
\(\Q(\sqrt{2}, \sqrt{-3})\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{1}q^{2}+(-1+\beta _{3})q^{4}+(-\beta _{2}+\beta _{3})q^{5}+\cdots\)
|
360.2.d.c |
\(4\) |
\(2.875\) |
\(\Q(\sqrt{-3}, \sqrt{5})\) |
\(\Q(\sqrt{-15}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{2}q^{2}+\beta _{3}q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots\)
|
360.2.d.d |
\(4\) |
\(2.875\) |
\(\Q(\sqrt{2}, \sqrt{-3})\) |
\(\Q(\sqrt{-6}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{1}q^{2}+2q^{4}+(\beta _{1}+\beta _{2})q^{5}+2\beta _{3}q^{7}+\cdots\)
|
360.2.d.e |
\(6\) |
\(2.875\) |
6.0.839056.1 |
None |
None |
\(-1\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{3}q^{2}+(-\beta _{1}-\beta _{2})q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
|
360.2.d.f |
\(6\) |
\(2.875\) |
6.0.839056.1 |
None |
None |
\(1\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{2}q^{2}+(\beta _{1}-\beta _{3})q^{4}+(\beta _{2}-\beta _{3})q^{5}+\cdots\)
|
360.2.f.a |
\(2\) |
\(2.875\) |
\(\Q(\sqrt{-1}) \) |
None |
None |
\(0\) |
\(0\) |
\(-4\) |
\(0\) |
|
\(q+(-2+i)q^{5}+2iq^{7}-2q^{11}+2iq^{13}+\cdots\)
|
360.2.f.b |
\(2\) |
\(2.875\) |
\(\Q(\sqrt{-1}) \) |
None |
None |
\(0\) |
\(0\) |
\(-4\) |
\(0\) |
|
\(q+(-2+i)q^{5}-4iq^{7}+4q^{11}-4iq^{13}+\cdots\)
|
360.2.f.c |
\(2\) |
\(2.875\) |
\(\Q(\sqrt{-1}) \) |
None |
None |
\(0\) |
\(0\) |
\(2\) |
\(0\) |
|
\(q+(1+i)q^{5}-iq^{7}+4q^{11}+2iq^{13}+\cdots\)
|
360.2.f.d |
\(2\) |
\(2.875\) |
\(\Q(\sqrt{-1}) \) |
None |
None |
\(0\) |
\(0\) |
\(4\) |
\(0\) |
|
\(q+(2+i)q^{5}+4iq^{7}-4q^{11}+4iq^{13}+\cdots\)
|
360.2.k.a |
\(2\) |
\(2.875\) |
\(\Q(\sqrt{-1}) \) |
None |
None |
\(-2\) |
\(0\) |
\(0\) |
\(-8\) |
|
\(q+(-1+i)q^{2}-2iq^{4}+iq^{5}-4q^{7}+\cdots\)
|
360.2.k.b |
\(2\) |
\(2.875\) |
\(\Q(\sqrt{-1}) \) |
None |
None |
\(-2\) |
\(0\) |
\(0\) |
\(4\) |
|
\(q+(-1+i)q^{2}-2iq^{4}+iq^{5}+2q^{7}+\cdots\)
|
360.2.k.c |
\(2\) |
\(2.875\) |
\(\Q(\sqrt{-1}) \) |
None |
None |
\(2\) |
\(0\) |
\(0\) |
\(-8\) |
|
\(q+(1+i)q^{2}+2iq^{4}+iq^{5}-4q^{7}+\cdots\)
|
360.2.k.d |
\(4\) |
\(2.875\) |
\(\Q(i, \sqrt{7})\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(8\) |
|
\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+2q^{7}+\cdots\)
|
360.2.k.e |
\(4\) |
\(2.875\) |
\(\Q(\zeta_{12})\) |
None |
None |
\(2\) |
\(0\) |
\(0\) |
\(-4\) |
|
\(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{4}+\cdots\)
|
360.2.k.f |
\(6\) |
\(2.875\) |
6.0.399424.1 |
None |
None |
\(-2\) |
\(0\) |
\(0\) |
\(4\) |
|
\(q-\beta _{1}q^{2}+(\beta _{2}-\beta _{3})q^{4}+\beta _{3}q^{5}+(1+\cdots)q^{7}+\cdots\)
|
360.2.m.a |
\(4\) |
\(2.875\) |
\(\Q(\sqrt{-2}, \sqrt{-5})\) |
\(\Q(\sqrt{-10}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(-8\) |
|
\(q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+(-2+\beta _{3})q^{7}+\cdots\)
|
360.2.m.b |
\(4\) |
\(2.875\) |
\(\Q(\sqrt{-2}, \sqrt{-5})\) |
\(\Q(\sqrt{-10}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(8\) |
|
\(q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+(2-\beta _{3})q^{7}+\cdots\)
|
360.2.m.c |
\(16\) |
\(2.875\) |
\(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{1}q^{2}+(1-\beta _{2})q^{4}-\beta _{12}q^{5}+(-\beta _{6}+\cdots)q^{7}+\cdots\)
|
360.2.q.a |
\(2\) |
\(2.875\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(0\) |
\(-3\) |
\(1\) |
\(0\) |
|
\(q+(-1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+3\zeta_{6}q^{9}+\cdots\)
|
360.2.q.b |
\(4\) |
\(2.875\) |
\(\Q(\zeta_{12})\) |
None |
None |
\(0\) |
\(0\) |
\(2\) |
\(-4\) |
|
\(q-\zeta_{12}^{2}q^{3}+\zeta_{12}q^{5}+(-2+2\zeta_{12}+\cdots)q^{7}+\cdots\)
|
360.2.q.c |
\(4\) |
\(2.875\) |
\(\Q(\sqrt{-2}, \sqrt{-3})\) |
None |
None |
\(0\) |
\(2\) |
\(2\) |
\(-2\) |
|
\(q+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\beta _{2}q^{5}+(-1+\cdots)q^{7}+\cdots\)
|
360.2.q.d |
\(6\) |
\(2.875\) |
6.0.954288.1 |
None |
None |
\(0\) |
\(-1\) |
\(-3\) |
\(5\) |
|
\(q-\beta _{1}q^{3}+(-1-\beta _{3})q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
|
360.2.q.e |
\(8\) |
\(2.875\) |
8.0.856615824.2 |
None |
None |
\(0\) |
\(0\) |
\(-4\) |
\(1\) |
|
\(q-\beta _{4}q^{3}-\beta _{1}q^{5}+(-\beta _{2}+\beta _{4})q^{7}+\cdots\)
|
360.2.s.a |
\(4\) |
\(2.875\) |
\(\Q(\zeta_{8})\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+(4\zeta_{8}+4\zeta_{8}^{3})q^{11}+\cdots\)
|
360.2.s.b |
\(8\) |
\(2.875\) |
8.0.40960000.1 |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(-8\) |
|
\(q+\beta _{7}q^{5}+(-1-\beta _{2}-\beta _{5})q^{7}+(\beta _{1}+\cdots)q^{11}+\cdots\)
|
360.2.w.a |
\(4\) |
\(2.875\) |
\(\Q(\zeta_{8})\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(4\) |
|
\(q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-2q^{4}+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots\)
|
360.2.w.b |
\(4\) |
\(2.875\) |
\(\Q(\zeta_{8})\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(-4\) |
|
\(q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+2q^{4}+(-2\zeta_{8}+\cdots)q^{5}+\cdots\)
|
360.2.w.c |
\(8\) |
\(2.875\) |
\(\Q(\zeta_{20})\) |
None |
None |
\(2\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\zeta_{20}^{7}q^{2}+\zeta_{20}q^{4}+(1+\zeta_{20}^{2}-\zeta_{20}^{5}+\cdots)q^{5}+\cdots\)
|
360.2.w.d |
\(16\) |
\(2.875\) |
\(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{15}q^{2}-\beta _{2}q^{4}+(\beta _{10}-\beta _{15})q^{5}+\cdots\)
|
360.2.w.e |
\(24\) |
\(2.875\) |
|
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
|
360.2.x.a |
\(48\) |
\(2.875\) |
|
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
|
360.2.bd.a |
\(8\) |
\(2.875\) |
\(\Q(\zeta_{24})\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(-\zeta_{24}+\zeta_{24}^{6})q^{2}+(-\zeta_{24}^{3}+\zeta_{24}^{4}+\cdots)q^{3}+\cdots\)
|
360.2.bd.b |
\(128\) |
\(2.875\) |
|
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
|
360.2.bf.a |
\(4\) |
\(2.875\) |
\(\Q(\zeta_{12})\) |
None |
None |
\(-2\) |
\(0\) |
\(0\) |
\(8\) |
|
\(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots\)
|
360.2.bf.b |
\(92\) |
\(2.875\) |
|
None |
None |
\(2\) |
\(0\) |
\(0\) |
\(-8\) |
|
|
360.2.bi.a |
\(4\) |
\(2.875\) |
\(\Q(\zeta_{12})\) |
None |
None |
\(0\) |
\(0\) |
\(2\) |
\(0\) |
|
\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(-2\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
|
360.2.bi.b |
\(32\) |
\(2.875\) |
|
None |
None |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
|
|