605.1.f.a |
\(2\) |
\(0.302\) |
\(\Q(\sqrt{-1}) \) |
\(\Q(\sqrt{-11}) \) |
None |
\(0\) |
\(2\) |
\(0\) |
\(0\) |
|
\(q+(1+i)q^{3}+iq^{4}-iq^{5}+iq^{9}+(-1+\cdots)q^{12}+\cdots\)
|
605.1.h.a |
\(4\) |
\(0.302\) |
\(\Q(\zeta_{10})\) |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-55}) \) |
\(\Q(\sqrt{5}) \) |
\(0\) |
\(0\) |
\(1\) |
\(0\) |
|
\(q+\zeta_{10}^{3}q^{4}+\zeta_{10}q^{5}+\zeta_{10}^{4}q^{9}-\zeta_{10}q^{16}+\cdots\)
|
605.1.l.a |
\(8\) |
\(0.302\) |
\(\Q(\zeta_{20})\) |
\(\Q(\sqrt{-11}) \) |
None |
\(0\) |
\(-2\) |
\(0\) |
\(0\) |
|
\(q+(-\zeta_{20}-\zeta_{20}^{6})q^{3}-\zeta_{20}^{9}q^{4}-\zeta_{20}^{3}q^{5}+\cdots\)
|
605.2.a.a |
\(1\) |
\(4.831\) |
\(\Q\) |
None |
None |
\(-1\) |
\(-3\) |
\(1\) |
\(-3\) |
\(+\) |
\(q-q^{2}-3q^{3}-q^{4}+q^{5}+3q^{6}-3q^{7}+\cdots\)
|
605.2.a.b |
\(1\) |
\(4.831\) |
\(\Q\) |
None |
None |
\(-1\) |
\(0\) |
\(1\) |
\(0\) |
\(+\) |
\(q-q^{2}-q^{4}+q^{5}+3q^{8}-3q^{9}-q^{10}+\cdots\)
|
605.2.a.c |
\(1\) |
\(4.831\) |
\(\Q\) |
None |
None |
\(1\) |
\(-3\) |
\(1\) |
\(3\) |
\(+\) |
\(q+q^{2}-3q^{3}-q^{4}+q^{5}-3q^{6}+3q^{7}+\cdots\)
|
605.2.a.d |
\(2\) |
\(4.831\) |
\(\Q(\sqrt{2}) \) |
None |
None |
\(-2\) |
\(0\) |
\(-2\) |
\(4\) |
\(-\) |
\(q+(-1+\beta )q^{2}+2\beta q^{3}+(1-2\beta )q^{4}+\cdots\)
|
605.2.a.e |
\(2\) |
\(4.831\) |
\(\Q(\sqrt{3}) \) |
None |
None |
\(0\) |
\(-2\) |
\(-2\) |
\(0\) |
\(+\) |
\(q+\beta q^{2}-q^{3}+q^{4}-q^{5}-\beta q^{6}-\beta q^{7}+\cdots\)
|
605.2.a.f |
\(2\) |
\(4.831\) |
\(\Q(\sqrt{3}) \) |
None |
None |
\(0\) |
\(4\) |
\(2\) |
\(0\) |
\(-\) |
\(q+\beta q^{2}+2q^{3}+q^{4}+q^{5}+2\beta q^{6}+\cdots\)
|
605.2.a.g |
\(3\) |
\(4.831\) |
3.3.404.1 |
None |
None |
\(-1\) |
\(1\) |
\(-3\) |
\(1\) |
\(-\) |
\(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(3+\beta _{1}-\beta _{2})q^{4}+\cdots\)
|
605.2.a.h |
\(3\) |
\(4.831\) |
3.3.404.1 |
None |
None |
\(1\) |
\(1\) |
\(-3\) |
\(-1\) |
\(-\) |
\(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(3+\beta _{1}-\beta _{2})q^{4}+\cdots\)
|
605.2.a.i |
\(4\) |
\(4.831\) |
4.4.2525.1 |
None |
None |
\(-3\) |
\(-2\) |
\(4\) |
\(-11\) |
\(+\) |
\(q+(-1-\beta _{3})q^{2}-\beta _{1}q^{3}+(1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
|
605.2.a.j |
\(4\) |
\(4.831\) |
4.4.725.1 |
None |
None |
\(-1\) |
\(0\) |
\(-4\) |
\(-3\) |
\(+\) |
\(q-\beta _{1}q^{2}+(-1+\beta _{2}+\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
|
605.2.a.k |
\(4\) |
\(4.831\) |
4.4.725.1 |
None |
None |
\(1\) |
\(0\) |
\(-4\) |
\(3\) |
\(-\) |
\(q+\beta _{1}q^{2}+(-1+\beta _{2}+\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
|
605.2.a.l |
\(4\) |
\(4.831\) |
4.4.2525.1 |
None |
None |
\(3\) |
\(-2\) |
\(4\) |
\(11\) |
\(-\) |
\(q+(1+\beta _{2}-\beta _{3})q^{2}+(-1+\beta _{1})q^{3}+\cdots\)
|
605.2.a.m |
\(6\) |
\(4.831\) |
6.6.27433728.1 |
None |
None |
\(0\) |
\(6\) |
\(6\) |
\(0\) |
\(-\) |
\(q+\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
|
605.2.b.a |
\(2\) |
\(4.831\) |
\(\Q(\sqrt{-11}) \) |
\(\Q(\sqrt{-11}) \) |
None |
\(0\) |
\(0\) |
\(3\) |
\(0\) |
|
\(q+(-1+2\beta )q^{3}+2q^{4}+(1+\beta )q^{5}+\cdots\)
|
605.2.b.b |
\(4\) |
\(4.831\) |
4.0.4400.1 |
\(\Q(\sqrt{-55}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{2}q^{2}+(-2-\beta _{3})q^{4}+\beta _{3}q^{5}-\beta _{1}q^{7}+\cdots\)
|
605.2.b.c |
\(4\) |
\(4.831\) |
\(\Q(\sqrt{-3}, \sqrt{-11})\) |
None |
None |
\(0\) |
\(0\) |
\(-3\) |
\(0\) |
|
\(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+\cdots\)
|
605.2.b.d |
\(4\) |
\(4.831\) |
\(\Q(\sqrt{-2}, \sqrt{3})\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{1}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
|
605.2.b.e |
\(4\) |
\(4.831\) |
\(\Q(\sqrt{-2}, \sqrt{3})\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
|
605.2.b.f |
\(8\) |
\(4.831\) |
8.0.1480160000.1 |
None |
None |
\(0\) |
\(0\) |
\(4\) |
\(0\) |
|
\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{6}+\beta _{7})q^{3}+\beta _{2}q^{4}+\cdots\)
|
605.2.b.g |
\(8\) |
\(4.831\) |
8.0.1480160000.1 |
None |
None |
\(0\) |
\(0\) |
\(4\) |
\(0\) |
|
\(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{6}-\beta _{7})q^{3}+\beta _{2}q^{4}+\cdots\)
|
605.2.b.h |
\(12\) |
\(4.831\) |
\(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
None |
None |
\(0\) |
\(0\) |
\(-6\) |
\(0\) |
|
\(q+\beta _{9}q^{2}-\beta _{8}q^{3}+(-2-\beta _{6})q^{4}+\beta _{4}q^{5}+\cdots\)
|
605.2.e.a |
\(20\) |
\(4.831\) |
\(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
None |
None |
\(0\) |
\(4\) |
\(4\) |
\(0\) |
|
\(q+\beta _{1}q^{2}-\beta _{12}q^{3}+(-\beta _{4}+\beta _{10}-\beta _{13}+\cdots)q^{4}+\cdots\)
|
605.2.e.b |
\(32\) |
\(4.831\) |
|
None |
None |
\(0\) |
\(-4\) |
\(8\) |
\(0\) |
|
|
605.2.e.c |
\(40\) |
\(4.831\) |
|
None |
None |
\(0\) |
\(8\) |
\(-4\) |
\(0\) |
|
|
605.2.g.a |
\(4\) |
\(4.831\) |
\(\Q(\zeta_{10})\) |
None |
None |
\(-1\) |
\(0\) |
\(-1\) |
\(0\) |
|
\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
|
605.2.g.b |
\(4\) |
\(4.831\) |
\(\Q(\zeta_{10})\) |
None |
None |
\(-1\) |
\(3\) |
\(-1\) |
\(-3\) |
|
\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
|
605.2.g.c |
\(4\) |
\(4.831\) |
\(\Q(\zeta_{10})\) |
None |
None |
\(1\) |
\(0\) |
\(-1\) |
\(0\) |
|
\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{3}q^{4}+\cdots\)
|
605.2.g.d |
\(4\) |
\(4.831\) |
\(\Q(\zeta_{10})\) |
None |
None |
\(1\) |
\(3\) |
\(-1\) |
\(3\) |
|
\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-3\zeta_{10}^{2}q^{3}+\cdots\)
|
605.2.g.e |
\(8\) |
\(4.831\) |
8.0.13140625.1 |
None |
None |
\(-3\) |
\(5\) |
\(2\) |
\(-4\) |
|
\(q-\beta _{2}q^{2}+(1-\beta _{2}+\beta _{5}+\beta _{7})q^{3}+(1+\cdots)q^{4}+\cdots\)
|
605.2.g.f |
\(8\) |
\(4.831\) |
8.0.64000000.2 |
None |
None |
\(-2\) |
\(0\) |
\(2\) |
\(4\) |
|
\(q+(-1-\beta _{2}+\beta _{3}-\beta _{4}-\beta _{6})q^{2}+(2\beta _{1}+\cdots)q^{3}+\cdots\)
|
605.2.g.g |
\(8\) |
\(4.831\) |
8.0.159390625.1 |
None |
None |
\(-1\) |
\(1\) |
\(-2\) |
\(8\) |
|
\(q+(1-\beta _{2}-\beta _{3}-\beta _{5}-\beta _{6})q^{2}+(-\beta _{1}+\cdots)q^{3}+\cdots\)
|
605.2.g.h |
\(8\) |
\(4.831\) |
8.0.324000000.3 |
None |
None |
\(0\) |
\(-4\) |
\(-2\) |
\(0\) |
|
\(q+\beta _{7}q^{2}+2\beta _{6}q^{3}+\beta _{4}q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)
|
605.2.g.i |
\(8\) |
\(4.831\) |
8.0.324000000.3 |
None |
None |
\(0\) |
\(2\) |
\(2\) |
\(0\) |
|
\(q+\beta _{7}q^{2}-\beta _{6}q^{3}+\beta _{4}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
|
605.2.g.j |
\(8\) |
\(4.831\) |
8.0.159390625.1 |
None |
None |
\(1\) |
\(1\) |
\(-2\) |
\(-8\) |
|
\(q+(-1+\beta _{2}+\beta _{3}+\beta _{5}+\beta _{6})q^{2}+(-\beta _{1}+\cdots)q^{3}+\cdots\)
|
605.2.g.k |
\(8\) |
\(4.831\) |
8.0.13140625.1 |
None |
None |
\(2\) |
\(-5\) |
\(2\) |
\(1\) |
|
\(q+\beta _{6}q^{2}+(-1+\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)
|
605.2.g.l |
\(8\) |
\(4.831\) |
8.0.64000000.2 |
None |
None |
\(2\) |
\(0\) |
\(2\) |
\(-4\) |
|
\(q+(-\beta _{2}+\beta _{7})q^{2}+2\beta _{1}q^{3}+(2\beta _{1}+2\beta _{3}+\cdots)q^{4}+\cdots\)
|
605.2.g.m |
\(8\) |
\(4.831\) |
8.0.13140625.1 |
None |
None |
\(3\) |
\(5\) |
\(2\) |
\(4\) |
|
\(q+\beta _{2}q^{2}+(1-\beta _{2}+\beta _{5}+\beta _{7})q^{3}+(1+\cdots)q^{4}+\cdots\)
|
605.2.g.n |
\(8\) |
\(4.831\) |
8.0.159390625.1 |
None |
None |
\(4\) |
\(1\) |
\(-2\) |
\(3\) |
|
\(q+(\beta _{1}+\beta _{2}-\beta _{4})q^{2}+\beta _{1}q^{3}+(-2+\cdots)q^{4}+\cdots\)
|
605.2.g.o |
\(12\) |
\(4.831\) |
\(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
None |
None |
\(-1\) |
\(-1\) |
\(3\) |
\(1\) |
|
\(q-\beta _{11}q^{2}+\beta _{8}q^{3}+(-\beta _{1}-3\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
|
605.2.g.p |
\(12\) |
\(4.831\) |
\(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
None |
None |
\(1\) |
\(-1\) |
\(3\) |
\(-1\) |
|
\(q+\beta _{9}q^{2}-\beta _{1}q^{3}+(-3+\beta _{3}+3\beta _{4}+\cdots)q^{4}+\cdots\)
|
605.2.g.q |
\(24\) |
\(4.831\) |
|
None |
None |
\(0\) |
\(-6\) |
\(-6\) |
\(0\) |
|
|
605.2.j.a |
\(8\) |
\(4.831\) |
8.0.484000000.6 |
\(\Q(\sqrt{-55}) \) |
None |
\(0\) |
\(0\) |
\(-10\) |
\(0\) |
|
\(q+(\beta _{1}-\beta _{4})q^{2}+(1+\beta _{2}-3\beta _{3}+3\beta _{5}+\cdots)q^{4}+\cdots\)
|
605.2.j.b |
\(8\) |
\(4.831\) |
8.0.228765625.1 |
\(\Q(\sqrt{-11}) \) |
None |
\(0\) |
\(0\) |
\(-3\) |
\(0\) |
|
\(q+(-\beta _{4}-2\beta _{5})q^{3}+(-2+2\beta _{3}+2\beta _{4}+\cdots)q^{4}+\cdots\)
|
605.2.j.c |
\(8\) |
\(4.831\) |
8.0.484000000.6 |
\(\Q(\sqrt{-55}) \) |
None |
\(0\) |
\(0\) |
\(10\) |
\(0\) |
|
\(q+(\beta _{1}-\beta _{6})q^{2}+(-2\beta _{2}+2\beta _{3}-3\beta _{5}+\cdots)q^{4}+\cdots\)
|
605.2.j.d |
\(16\) |
\(4.831\) |
\(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
None |
None |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
|
\(q+(\beta _{1}-\beta _{12}-\beta _{13})q^{2}+(-\beta _{5}-\beta _{13}+\cdots)q^{3}+\cdots\)
|
605.2.j.e |
\(16\) |
\(4.831\) |
16.0.\(\cdots\).7 |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{12}q^{2}+\beta _{3}q^{3}-\beta _{10}q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
|
605.2.j.f |
\(16\) |
\(4.831\) |
16.0.\(\cdots\).7 |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{12}q^{2}-\beta _{3}q^{3}-\beta _{10}q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
|