570.2.a.a |
\(1\) |
\(4.551\) |
\(\Q\) |
None |
\(-1\) |
\(-1\) |
\(-1\) |
\(-2\) |
\(-\) |
\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots\)
|
570.2.a.b |
\(1\) |
\(4.551\) |
\(\Q\) |
None |
\(-1\) |
\(-1\) |
\(-1\) |
\(2\) |
\(+\) |
\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\)
|
570.2.a.c |
\(1\) |
\(4.551\) |
\(\Q\) |
None |
\(-1\) |
\(-1\) |
\(1\) |
\(-2\) |
\(+\) |
\(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
|
570.2.a.d |
\(1\) |
\(4.551\) |
\(\Q\) |
None |
\(-1\) |
\(1\) |
\(-1\) |
\(4\) |
\(-\) |
\(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+4q^{7}+\cdots\)
|
570.2.a.e |
\(1\) |
\(4.551\) |
\(\Q\) |
None |
\(-1\) |
\(1\) |
\(1\) |
\(-4\) |
\(+\) |
\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-4q^{7}+\cdots\)
|
570.2.a.f |
\(1\) |
\(4.551\) |
\(\Q\) |
None |
\(-1\) |
\(1\) |
\(1\) |
\(2\) |
\(-\) |
\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots\)
|
570.2.a.g |
\(1\) |
\(4.551\) |
\(\Q\) |
None |
\(1\) |
\(-1\) |
\(-1\) |
\(0\) |
\(-\) |
\(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\)
|
570.2.a.h |
\(1\) |
\(4.551\) |
\(\Q\) |
None |
\(1\) |
\(-1\) |
\(1\) |
\(-2\) |
\(-\) |
\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
|
570.2.a.i |
\(1\) |
\(4.551\) |
\(\Q\) |
None |
\(1\) |
\(-1\) |
\(1\) |
\(4\) |
\(-\) |
\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+4q^{7}+\cdots\)
|
570.2.a.j |
\(1\) |
\(4.551\) |
\(\Q\) |
None |
\(1\) |
\(1\) |
\(-1\) |
\(2\) |
\(-\) |
\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\)
|
570.2.a.k |
\(1\) |
\(4.551\) |
\(\Q\) |
None |
\(1\) |
\(1\) |
\(-1\) |
\(2\) |
\(-\) |
\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\)
|
570.2.a.l |
\(1\) |
\(4.551\) |
\(\Q\) |
None |
\(1\) |
\(1\) |
\(1\) |
\(-2\) |
\(-\) |
\(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
|
570.2.a.m |
\(1\) |
\(4.551\) |
\(\Q\) |
None |
\(1\) |
\(1\) |
\(1\) |
\(4\) |
\(-\) |
\(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots\)
|
570.2.c.a |
\(4\) |
\(4.551\) |
\(\Q(\zeta_{8})\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots\)
|
570.2.c.b |
\(4\) |
\(4.551\) |
\(\Q(\zeta_{8})\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots\)
|
570.2.c.c |
\(8\) |
\(4.551\) |
8.0.1499238400.2 |
None |
\(0\) |
\(-4\) |
\(0\) |
\(0\) |
|
\(q+\beta _{6}q^{2}+(-1-\beta _{3}+\beta _{4}+\beta _{6}+\beta _{7})q^{3}+\cdots\)
|
570.2.c.d |
\(8\) |
\(4.551\) |
\(\Q(\zeta_{24})\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\zeta_{24}q^{2}-\zeta_{24}^{4}q^{3}-q^{4}+(-\zeta_{24}^{2}+\cdots)q^{5}+\cdots\)
|
570.2.c.e |
\(8\) |
\(4.551\) |
\(\Q(\zeta_{24})\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\zeta_{24}q^{2}+(-\zeta_{24}-\zeta_{24}^{6})q^{3}-q^{4}+\cdots\)
|
570.2.c.f |
\(8\) |
\(4.551\) |
8.0.1499238400.2 |
None |
\(0\) |
\(4\) |
\(0\) |
\(0\) |
|
\(q+\beta _{6}q^{2}+(-\beta _{3}+\beta _{4}+\beta _{6}+\beta _{7})q^{3}+\cdots\)
|
570.2.d.a |
\(2\) |
\(4.551\) |
\(\Q(\sqrt{-1}) \) |
None |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
|
\(q+iq^{2}+iq^{3}-q^{4}+(-1-2i)q^{5}+\cdots\)
|
570.2.d.b |
\(2\) |
\(4.551\) |
\(\Q(\sqrt{-1}) \) |
None |
\(0\) |
\(0\) |
\(4\) |
\(0\) |
|
\(q+iq^{2}+iq^{3}-q^{4}+(2+i)q^{5}-q^{6}+\cdots\)
|
570.2.d.c |
\(6\) |
\(4.551\) |
6.0.350464.1 |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{3}q^{5}-q^{6}+\cdots\)
|
570.2.d.d |
\(6\) |
\(4.551\) |
6.0.350464.1 |
None |
\(0\) |
\(0\) |
\(2\) |
\(0\) |
|
\(q+\beta _{1}q^{2}-\beta _{1}q^{3}-q^{4}-\beta _{5}q^{5}+q^{6}+\cdots\)
|
570.2.f.a |
\(4\) |
\(4.551\) |
\(\Q(\zeta_{8})\) |
None |
\(-4\) |
\(-4\) |
\(0\) |
\(8\) |
|
\(q-q^{2}+(-1-\zeta_{8}^{2})q^{3}+q^{4}+\zeta_{8}q^{5}+\cdots\)
|
570.2.f.b |
\(4\) |
\(4.551\) |
\(\Q(\zeta_{8})\) |
None |
\(4\) |
\(4\) |
\(0\) |
\(8\) |
|
\(q+q^{2}+(1+\zeta_{8}^{2})q^{3}+q^{4}+\zeta_{8}q^{5}+\cdots\)
|
570.2.f.c |
\(8\) |
\(4.551\) |
8.0.7278137344.1 |
None |
\(-8\) |
\(2\) |
\(0\) |
\(4\) |
|
\(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)
|
570.2.f.d |
\(8\) |
\(4.551\) |
8.0.7278137344.1 |
None |
\(8\) |
\(-2\) |
\(0\) |
\(4\) |
|
\(q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)
|
570.2.i.a |
\(2\) |
\(4.551\) |
\(\Q(\sqrt{-3}) \) |
None |
\(-1\) |
\(-1\) |
\(1\) |
\(-2\) |
|
\(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
|
570.2.i.b |
\(2\) |
\(4.551\) |
\(\Q(\sqrt{-3}) \) |
None |
\(-1\) |
\(-1\) |
\(1\) |
\(-2\) |
|
\(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
|
570.2.i.c |
\(2\) |
\(4.551\) |
\(\Q(\sqrt{-3}) \) |
None |
\(-1\) |
\(1\) |
\(1\) |
\(6\) |
|
\(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
|
570.2.i.d |
\(2\) |
\(4.551\) |
\(\Q(\sqrt{-3}) \) |
None |
\(1\) |
\(-1\) |
\(1\) |
\(-2\) |
|
\(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
|
570.2.i.e |
\(2\) |
\(4.551\) |
\(\Q(\sqrt{-3}) \) |
None |
\(1\) |
\(1\) |
\(-1\) |
\(-10\) |
|
\(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
|
570.2.i.f |
\(4\) |
\(4.551\) |
\(\Q(\sqrt{-2}, \sqrt{-3})\) |
None |
\(-2\) |
\(2\) |
\(-2\) |
\(4\) |
|
\(q+(-1+\beta _{1})q^{2}+(1-\beta _{1})q^{3}-\beta _{1}q^{4}+\cdots\)
|
570.2.i.g |
\(4\) |
\(4.551\) |
\(\Q(\sqrt{-3}, \sqrt{73})\) |
None |
\(2\) |
\(-2\) |
\(-2\) |
\(-4\) |
|
\(q+(1-\beta _{2})q^{2}+(-1+\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots\)
|
570.2.i.h |
\(4\) |
\(4.551\) |
\(\Q(\sqrt{-3}, \sqrt{19})\) |
None |
\(2\) |
\(-2\) |
\(2\) |
\(0\) |
|
\(q+(1+\beta _{2})q^{2}+(-1-\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots\)
|
570.2.i.i |
\(4\) |
\(4.551\) |
\(\Q(\sqrt{-3}, \sqrt{7})\) |
None |
\(2\) |
\(2\) |
\(2\) |
\(0\) |
|
\(q+(1+\beta _{2})q^{2}+(1+\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots\)
|
570.2.i.j |
\(6\) |
\(4.551\) |
6.0.29654208.1 |
None |
\(-3\) |
\(-3\) |
\(-3\) |
\(2\) |
|
\(q+(-1+\beta _{1})q^{2}+(-1+\beta _{1})q^{3}-\beta _{1}q^{4}+\cdots\)
|
570.2.k.a |
\(36\) |
\(4.551\) |
|
None |
\(0\) |
\(4\) |
\(0\) |
\(-12\) |
|
|
570.2.k.b |
\(36\) |
\(4.551\) |
|
None |
\(0\) |
\(4\) |
\(0\) |
\(20\) |
|
|
570.2.m.a |
\(20\) |
\(4.551\) |
\(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
None |
\(0\) |
\(0\) |
\(-4\) |
\(-4\) |
|
\(q+\beta _{2}q^{2}+\beta _{11}q^{3}+\beta _{4}q^{4}+\beta _{6}q^{5}+\cdots\)
|
570.2.m.b |
\(20\) |
\(4.551\) |
\(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
None |
\(0\) |
\(0\) |
\(12\) |
\(-4\) |
|
\(q+\beta _{7}q^{2}-\beta _{10}q^{3}+\beta _{2}q^{4}+(1+\beta _{6}+\cdots)q^{5}+\cdots\)
|
570.2.n.a |
\(80\) |
\(4.551\) |
|
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
|
570.2.q.a |
\(8\) |
\(4.551\) |
\(\Q(\zeta_{24})\) |
None |
\(0\) |
\(0\) |
\(4\) |
\(0\) |
|
\(q+(\zeta_{24}-\zeta_{24}^{4})q^{2}+(\zeta_{24}-\zeta_{24}^{4})q^{3}+\cdots\)
|
570.2.q.b |
\(12\) |
\(4.551\) |
12.0.\(\cdots\).1 |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(-\beta _{3}-\beta _{4})q^{2}+(-\beta _{3}-\beta _{4})q^{3}+\cdots\)
|
570.2.q.c |
\(20\) |
\(4.551\) |
\(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{11}q^{2}+\beta _{11}q^{3}+(1-\beta _{12})q^{4}+\cdots\)
|
570.2.s.a |
\(24\) |
\(4.551\) |
|
None |
\(-12\) |
\(4\) |
\(0\) |
\(-12\) |
|
|
570.2.s.b |
\(24\) |
\(4.551\) |
|
None |
\(12\) |
\(2\) |
\(0\) |
\(-12\) |
|
|
570.2.u.a |
\(6\) |
\(4.551\) |
\(\Q(\zeta_{18})\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(-6\) |
|
\(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
|
570.2.u.b |
\(6\) |
\(4.551\) |
\(\Q(\zeta_{18})\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(-6\) |
|
\(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
|
570.2.u.c |
\(6\) |
\(4.551\) |
\(\Q(\zeta_{18})\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(-3\) |
|
\(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
|