270.2.a.a |
\(1\) |
\(2.156\) |
\(\Q\) |
None |
\(-1\) |
\(0\) |
\(-1\) |
\(2\) |
\(-\) |
\(q-q^{2}+q^{4}-q^{5}+2q^{7}-q^{8}+q^{10}+\cdots\)
|
270.2.a.b |
\(1\) |
\(2.156\) |
\(\Q\) |
None |
\(-1\) |
\(0\) |
\(1\) |
\(2\) |
\(-\) |
\(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots\)
|
270.2.a.c |
\(1\) |
\(2.156\) |
\(\Q\) |
None |
\(1\) |
\(0\) |
\(-1\) |
\(2\) |
\(-\) |
\(q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots\)
|
270.2.a.d |
\(1\) |
\(2.156\) |
\(\Q\) |
None |
\(1\) |
\(0\) |
\(1\) |
\(2\) |
\(-\) |
\(q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots\)
|
270.2.c.a |
\(2\) |
\(2.156\) |
\(\Q(\sqrt{-1}) \) |
None |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
|
\(q+iq^{2}-q^{4}+(-1-2i)q^{5}-4iq^{7}+\cdots\)
|
270.2.c.b |
\(2\) |
\(2.156\) |
\(\Q(\sqrt{-1}) \) |
None |
\(0\) |
\(0\) |
\(2\) |
\(0\) |
|
\(q+iq^{2}-q^{4}+(1-2i)q^{5}+4iq^{7}+\cdots\)
|
270.2.c.c |
\(4\) |
\(2.156\) |
\(\Q(i, \sqrt{19})\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{2}q^{2}-q^{4}+\beta _{1}q^{5}+(1+2\beta _{3})q^{7}+\cdots\)
|
270.2.e.a |
\(2\) |
\(2.156\) |
\(\Q(\sqrt{-3}) \) |
None |
\(-1\) |
\(0\) |
\(1\) |
\(4\) |
|
\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(4+\cdots)q^{7}+\cdots\)
|
270.2.e.b |
\(2\) |
\(2.156\) |
\(\Q(\sqrt{-3}) \) |
None |
\(1\) |
\(0\) |
\(-1\) |
\(1\) |
|
\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots\)
|
270.2.e.c |
\(4\) |
\(2.156\) |
\(\Q(\sqrt{-3}, \sqrt{-11})\) |
None |
\(-2\) |
\(0\) |
\(-2\) |
\(-1\) |
|
\(q-\beta _{1}q^{2}+(-1+\beta _{1})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
|
270.2.f.a |
\(8\) |
\(2.156\) |
\(\Q(\zeta_{24})\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(-8\) |
|
\(q+\zeta_{24}^{5}q^{2}-\zeta_{24}^{3}q^{4}+(\zeta_{24}-\zeta_{24}^{4}+\cdots)q^{5}+\cdots\)
|
270.2.f.b |
\(8\) |
\(2.156\) |
\(\Q(\zeta_{24})\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(4\) |
|
\(q+(\zeta_{24}-\zeta_{24}^{5})q^{2}-\zeta_{24}^{6}q^{4}+(2\zeta_{24}+\cdots)q^{5}+\cdots\)
|
270.2.i.a |
\(4\) |
\(2.156\) |
\(\Q(\zeta_{12})\) |
None |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
|
\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(2\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
|
270.2.i.b |
\(8\) |
\(2.156\) |
\(\Q(\zeta_{24})\) |
None |
\(0\) |
\(0\) |
\(4\) |
\(0\) |
|
\(q+(\zeta_{24}-\zeta_{24}^{4})q^{2}+(1-\zeta_{24}^{2})q^{4}+\cdots\)
|
270.2.k.a |
\(6\) |
\(2.156\) |
\(\Q(\zeta_{18})\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(6\) |
|
\(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+(\zeta_{18}-2\zeta_{18}^{4}+\cdots)q^{3}+\cdots\)
|
270.2.k.b |
\(12\) |
\(2.156\) |
12.0.\(\cdots\).1 |
None |
\(0\) |
\(3\) |
\(0\) |
\(-12\) |
|
\(q-\beta _{7}q^{2}+(1-\beta _{5}-\beta _{7}-\beta _{11})q^{3}+\cdots\)
|
270.2.k.c |
\(12\) |
\(2.156\) |
12.0.\(\cdots\).1 |
None |
\(0\) |
\(3\) |
\(0\) |
\(6\) |
|
\(q+(-\beta _{7}-\beta _{10})q^{2}+(-\beta _{1}+\beta _{4}-\beta _{7}+\cdots)q^{3}+\cdots\)
|
270.2.k.d |
\(18\) |
\(2.156\) |
\(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
None |
\(0\) |
\(-3\) |
\(0\) |
\(-3\) |
|
\(q+\beta _{2}q^{2}-\beta _{7}q^{3}+\beta _{3}q^{4}+(\beta _{3}-\beta _{8}+\cdots)q^{5}+\cdots\)
|
270.2.k.e |
\(24\) |
\(2.156\) |
|
None |
\(0\) |
\(-3\) |
\(0\) |
\(3\) |
|
|
270.2.m.a |
\(8\) |
\(2.156\) |
\(\Q(\zeta_{24})\) |
None |
\(0\) |
\(0\) |
\(-12\) |
\(-8\) |
|
\(q+\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-1+\zeta_{24}^{3}+\cdots)q^{5}+\cdots\)
|
270.2.m.b |
\(16\) |
\(2.156\) |
16.0.\(\cdots\).9 |
None |
\(0\) |
\(0\) |
\(12\) |
\(8\) |
|
\(q+\beta _{5}q^{2}-\beta _{6}q^{4}+(-\beta _{2}+\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots\)
|
270.2.p.a |
\(108\) |
\(2.156\) |
|
None |
\(0\) |
\(0\) |
\(6\) |
\(0\) |
|
|
270.2.r.a |
\(216\) |
\(2.156\) |
|
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
|
270.3.b.a |
\(4\) |
\(7.357\) |
4.0.31744.1 |
None |
\(0\) |
\(0\) |
\(-12\) |
\(0\) |
|
\(q-\beta _{2}q^{2}+2q^{4}+(-3-\beta _{1}-\beta _{2})q^{5}+\cdots\)
|
270.3.b.b |
\(4\) |
\(7.357\) |
\(\Q(\zeta_{8})\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+2q^{4}+(3\zeta_{8}-4\zeta_{8}^{3})q^{5}+\cdots\)
|
270.3.b.c |
\(4\) |
\(7.357\) |
\(\Q(\zeta_{8})\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+2q^{4}+5\zeta_{8}q^{5}+5\zeta_{8}^{2}q^{7}+\cdots\)
|
270.3.b.d |
\(4\) |
\(7.357\) |
4.0.31744.1 |
None |
\(0\) |
\(0\) |
\(12\) |
\(0\) |
|
\(q+\beta _{2}q^{2}+2q^{4}+(3-\beta _{1}+\beta _{2})q^{5}+\cdots\)
|
270.3.d.a |
\(4\) |
\(7.357\) |
\(\Q(\sqrt{-2}, \sqrt{-5})\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(-4\) |
|
\(q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}-q^{7}+2\beta _{1}q^{8}+\cdots\)
|
270.3.d.b |
\(8\) |
\(7.357\) |
8.0.40960000.1 |
None |
\(0\) |
\(0\) |
\(0\) |
\(-8\) |
|
\(q+\beta _{2}q^{2}-2q^{4}-\beta _{1}q^{5}+(-1+\beta _{5}+\cdots)q^{7}+\cdots\)
|
270.3.g.a |
\(4\) |
\(7.357\) |
\(\Q(i, \sqrt{6})\) |
None |
\(-4\) |
\(0\) |
\(-12\) |
\(8\) |
|
\(q+(-1-\beta _{2})q^{2}+2\beta _{2}q^{4}+(-3-2\beta _{1}+\cdots)q^{5}+\cdots\)
|
270.3.g.b |
\(4\) |
\(7.357\) |
\(\Q(i, \sqrt{6})\) |
None |
\(-4\) |
\(0\) |
\(12\) |
\(-4\) |
|
\(q+(-1+\beta _{2})q^{2}-2\beta _{2}q^{4}+(3+2\beta _{1}+\cdots)q^{5}+\cdots\)
|
270.3.g.c |
\(4\) |
\(7.357\) |
\(\Q(i, \sqrt{6})\) |
None |
\(4\) |
\(0\) |
\(-12\) |
\(-4\) |
|
\(q+(1-\beta _{2})q^{2}-2\beta _{2}q^{4}+(-3+2\beta _{1}+\cdots)q^{5}+\cdots\)
|
270.3.g.d |
\(4\) |
\(7.357\) |
\(\Q(i, \sqrt{6})\) |
None |
\(4\) |
\(0\) |
\(12\) |
\(8\) |
|
\(q+(1+\beta _{2})q^{2}+2\beta _{2}q^{4}+(3+2\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
|
270.3.g.e |
\(8\) |
\(7.357\) |
8.0.\(\cdots\).38 |
None |
\(-8\) |
\(0\) |
\(12\) |
\(-8\) |
|
\(q+(-1-\beta _{1})q^{2}+2\beta _{1}q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\)
|
270.3.g.f |
\(8\) |
\(7.357\) |
8.0.\(\cdots\).38 |
None |
\(8\) |
\(0\) |
\(-12\) |
\(-8\) |
|
\(q+(1+\beta _{1})q^{2}+2\beta _{1}q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots\)
|
270.3.h.a |
\(16\) |
\(7.357\) |
\(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(-4\) |
|
\(q+\beta _{6}q^{2}-2\beta _{10}q^{4}+\beta _{12}q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots\)
|
270.3.j.a |
\(8\) |
\(7.357\) |
\(\Q(\zeta_{24})\) |
None |
\(0\) |
\(0\) |
\(12\) |
\(0\) |
|
\(q+(-\zeta_{24}^{4}+\zeta_{24}^{7})q^{2}-2\zeta_{24}^{2}q^{4}+\cdots\)
|
270.3.j.b |
\(16\) |
\(7.357\) |
\(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
None |
\(0\) |
\(0\) |
\(-30\) |
\(0\) |
|
\(q+\beta _{1}q^{2}+(-2-2\beta _{2})q^{4}+(\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\)
|
270.3.l.a |
\(24\) |
\(7.357\) |
|
None |
\(-12\) |
\(0\) |
\(0\) |
\(6\) |
|
|
270.3.l.b |
\(24\) |
\(7.357\) |
|
None |
\(12\) |
\(0\) |
\(0\) |
\(-6\) |
|
|
270.3.n.a |
\(216\) |
\(7.357\) |
|
None |
\(0\) |
\(0\) |
\(-18\) |
\(0\) |
|
|
270.3.o.a |
\(144\) |
\(7.357\) |
|
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
|
270.3.q.a |
\(216\) |
\(7.357\) |
|
None |
\(0\) |
\(0\) |
\(0\) |
\(18\) |
|
|
270.3.q.b |
\(216\) |
\(7.357\) |
|
None |
\(0\) |
\(0\) |
\(0\) |
\(-18\) |
|
|
270.4.a.a |
\(1\) |
\(15.931\) |
\(\Q\) |
None |
\(-2\) |
\(0\) |
\(-5\) |
\(-34\) |
\(+\) |
\(q-2q^{2}+4q^{4}-5q^{5}-34q^{7}-8q^{8}+\cdots\)
|
270.4.a.b |
\(1\) |
\(15.931\) |
\(\Q\) |
None |
\(-2\) |
\(0\) |
\(-5\) |
\(8\) |
\(-\) |
\(q-2q^{2}+4q^{4}-5q^{5}+8q^{7}-8q^{8}+\cdots\)
|
270.4.a.c |
\(1\) |
\(15.931\) |
\(\Q\) |
None |
\(-2\) |
\(0\) |
\(5\) |
\(-22\) |
\(+\) |
\(q-2q^{2}+4q^{4}+5q^{5}-22q^{7}-8q^{8}+\cdots\)
|
270.4.a.d |
\(1\) |
\(15.931\) |
\(\Q\) |
None |
\(-2\) |
\(0\) |
\(5\) |
\(-13\) |
\(-\) |
\(q-2q^{2}+4q^{4}+5q^{5}-13q^{7}-8q^{8}+\cdots\)
|
270.4.a.e |
\(1\) |
\(15.931\) |
\(\Q\) |
None |
\(-2\) |
\(0\) |
\(5\) |
\(-4\) |
\(-\) |
\(q-2q^{2}+4q^{4}+5q^{5}-4q^{7}-8q^{8}+\cdots\)
|
270.4.a.f |
\(1\) |
\(15.931\) |
\(\Q\) |
None |
\(-2\) |
\(0\) |
\(5\) |
\(14\) |
\(+\) |
\(q-2q^{2}+4q^{4}+5q^{5}+14q^{7}-8q^{8}+\cdots\)
|