392.1.g.a |
\(1\) |
\(0.196\) |
\(\Q\) |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-2}) \) |
\(\Q(\sqrt{14}) \) |
\(1\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+q^{2}+q^{4}+q^{8}-q^{9}-2q^{11}+q^{16}+\cdots\)
|
392.1.g.b |
\(2\) |
\(0.196\) |
\(\Q(\sqrt{2}) \) |
\(\Q(\sqrt{-2}) \) |
None |
\(-2\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}-q^{8}+q^{9}+\cdots\)
|
392.1.j.a |
\(2\) |
\(0.196\) |
\(\Q(\sqrt{-3}) \) |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \) |
\(\Q(\sqrt{2}) \) |
\(1\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{8}+\zeta_{6}q^{9}-\zeta_{6}q^{16}+\cdots\)
|
392.1.k.a |
\(2\) |
\(0.196\) |
\(\Q(\sqrt{-3}) \) |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-2}) \) |
\(\Q(\sqrt{14}) \) |
\(-1\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+q^{8}+\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}+\cdots\)
|
392.1.k.b |
\(4\) |
\(0.196\) |
\(\Q(\sqrt{2}, \sqrt{-3})\) |
\(\Q(\sqrt{-2}) \) |
None |
\(2\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{2}q^{2}-\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+\beta _{3}q^{6}+\cdots\)
|
392.2.a.a |
\(1\) |
\(3.130\) |
\(\Q\) |
None |
None |
\(0\) |
\(-3\) |
\(1\) |
\(0\) |
\(+\) |
\(q-3q^{3}+q^{5}+6q^{9}-q^{11}-2q^{13}+\cdots\)
|
392.2.a.b |
\(1\) |
\(3.130\) |
\(\Q\) |
None |
None |
\(0\) |
\(-2\) |
\(4\) |
\(0\) |
\(-\) |
\(q-2q^{3}+4q^{5}+q^{9}-8q^{15}+2q^{17}+\cdots\)
|
392.2.a.c |
\(1\) |
\(3.130\) |
\(\Q\) |
None |
None |
\(0\) |
\(-1\) |
\(-1\) |
\(0\) |
\(+\) |
\(q-q^{3}-q^{5}-2q^{9}+3q^{11}-6q^{13}+\cdots\)
|
392.2.a.d |
\(1\) |
\(3.130\) |
\(\Q\) |
None |
None |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
\(+\) |
\(q-2q^{5}-3q^{9}-4q^{11}-2q^{13}+6q^{17}+\cdots\)
|
392.2.a.e |
\(1\) |
\(3.130\) |
\(\Q\) |
None |
None |
\(0\) |
\(1\) |
\(1\) |
\(0\) |
\(-\) |
\(q+q^{3}+q^{5}-2q^{9}+3q^{11}+6q^{13}+\cdots\)
|
392.2.a.f |
\(1\) |
\(3.130\) |
\(\Q\) |
None |
None |
\(0\) |
\(3\) |
\(-1\) |
\(0\) |
\(-\) |
\(q+3q^{3}-q^{5}+6q^{9}-q^{11}+2q^{13}+\cdots\)
|
392.2.a.g |
\(2\) |
\(3.130\) |
\(\Q(\sqrt{2}) \) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
\(-\) |
\(q+\beta q^{3}+2\beta q^{5}-q^{9}+6q^{11}-4\beta q^{13}+\cdots\)
|
392.2.a.h |
\(2\) |
\(3.130\) |
\(\Q(\sqrt{2}) \) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
\(-\) |
\(q+\beta q^{3}+\beta q^{5}+5q^{9}-4q^{11}-\beta q^{13}+\cdots\)
|
392.2.b.a |
\(2\) |
\(3.130\) |
\(\Q(\sqrt{-7}) \) |
\(\Q(\sqrt{-7}) \) |
None |
\(-1\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta q^{2}+(-2+\beta )q^{4}+(2+\beta )q^{8}+3q^{9}+\cdots\)
|
392.2.b.b |
\(2\) |
\(3.130\) |
\(\Q(\sqrt{-2}) \) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta q^{2}-\beta q^{3}-2q^{4}+\beta q^{5}+2q^{6}+\cdots\)
|
392.2.b.c |
\(4\) |
\(3.130\) |
4.0.2312.1 |
None |
None |
\(-1\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots\)
|
392.2.b.d |
\(4\) |
\(3.130\) |
4.0.7168.1 |
\(\Q(\sqrt{-14}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{3}q^{2}+\beta _{1}q^{3}+2q^{4}-\beta _{2}q^{5}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
|
392.2.b.e |
\(6\) |
\(3.130\) |
6.0.1142512.1 |
None |
None |
\(2\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{4}q^{2}+\beta _{3}q^{3}-\beta _{2}q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
|
392.2.b.f |
\(6\) |
\(3.130\) |
6.0.1142512.1 |
None |
None |
\(2\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{4}q^{2}-\beta _{3}q^{3}-\beta _{2}q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
|
392.2.b.g |
\(12\) |
\(3.130\) |
\(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
None |
None |
\(-2\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{4}q^{2}-\beta _{9}q^{3}-\beta _{1}q^{4}+(\beta _{7}-\beta _{8}+\cdots)q^{5}+\cdots\)
|
392.2.e.a |
\(4\) |
\(3.130\) |
4.0.2048.2 |
\(\Q(\sqrt{-2}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{2}q^{2}-\beta _{3}q^{3}+2q^{4}-\beta _{1}q^{6}-2\beta _{2}q^{8}+\cdots\)
|
392.2.e.b |
\(4\) |
\(3.130\) |
4.0.2048.2 |
\(\Q(\sqrt{-2}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{2}q^{2}+\beta _{1}q^{3}+2q^{4}+(-\beta _{1}+\beta _{3})q^{6}+\cdots\)
|
392.2.e.c |
\(8\) |
\(3.130\) |
8.0.339738624.1 |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{5}q^{2}+(\beta _{4}+\beta _{7})q^{3}+(-1+\beta _{6}+\cdots)q^{4}+\cdots\)
|
392.2.e.d |
\(8\) |
\(3.130\) |
8.0.\(\cdots\).10 |
None |
None |
\(4\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(1-\beta _{5})q^{2}-\beta _{2}q^{3}+(\beta _{3}-\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots\)
|
392.2.e.e |
\(12\) |
\(3.130\) |
12.0.\(\cdots\).2 |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{5}q^{2}-\beta _{10}q^{3}+\beta _{1}q^{4}-\beta _{9}q^{5}+\cdots\)
|
392.2.i.a |
\(2\) |
\(3.130\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(0\) |
\(-2\) |
\(4\) |
\(0\) |
|
\(q+(-2+2\zeta_{6})q^{3}+4\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
|
392.2.i.b |
\(2\) |
\(3.130\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(0\) |
\(-1\) |
\(-1\) |
\(0\) |
|
\(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots\)
|
392.2.i.c |
\(2\) |
\(3.130\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
|
\(q-2\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(4-4\zeta_{6})q^{11}+\cdots\)
|
392.2.i.d |
\(2\) |
\(3.130\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(0\) |
\(0\) |
\(2\) |
\(0\) |
|
\(q+2\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(4-4\zeta_{6})q^{11}+\cdots\)
|
392.2.i.e |
\(2\) |
\(3.130\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(0\) |
\(2\) |
\(-4\) |
\(0\) |
|
\(q+(2-2\zeta_{6})q^{3}-4\zeta_{6}q^{5}-\zeta_{6}q^{9}-8q^{15}+\cdots\)
|
392.2.i.f |
\(2\) |
\(3.130\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(0\) |
\(3\) |
\(-1\) |
\(0\) |
|
\(q+(3-3\zeta_{6})q^{3}-\zeta_{6}q^{5}-6\zeta_{6}q^{9}+(1+\cdots)q^{11}+\cdots\)
|
392.2.i.g |
\(4\) |
\(3.130\) |
\(\Q(\sqrt{2}, \sqrt{-3})\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+5\beta _{2}q^{9}+\cdots\)
|
392.2.i.h |
\(4\) |
\(3.130\) |
\(\Q(\sqrt{2}, \sqrt{-3})\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{1}q^{3}+(-2\beta _{1}-2\beta _{3})q^{5}-\beta _{2}q^{9}+\cdots\)
|
392.2.m.a |
\(4\) |
\(3.130\) |
\(\Q(\sqrt{-3}, \sqrt{-7})\) |
\(\Q(\sqrt{-7}) \) |
None |
\(-1\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{3}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(-3+\beta _{1}+\cdots)q^{8}+\cdots\)
|
392.2.m.b |
\(8\) |
\(3.130\) |
8.0.339738624.1 |
\(\Q(\sqrt{-2}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{6}q^{2}+\beta _{3}q^{3}+(-2-2\beta _{4})q^{4}+\cdots\)
|
392.2.m.c |
\(8\) |
\(3.130\) |
8.0.339738624.1 |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{6}q^{2}+(-\beta _{3}+\beta _{5}-\beta _{7})q^{3}+(-2+\cdots)q^{4}+\cdots\)
|
392.2.m.d |
\(8\) |
\(3.130\) |
8.0.339738624.1 |
\(\Q(\sqrt{-2}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{5}q^{2}-\beta _{1}q^{3}+(-2-2\beta _{4})q^{4}+\cdots\)
|
392.2.m.e |
\(8\) |
\(3.130\) |
8.0.339738624.1 |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{2}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+2q^{4}+(2\beta _{1}+\cdots)q^{5}+\cdots\)
|
392.2.m.f |
\(8\) |
\(3.130\) |
\(\Q(\zeta_{24})\) |
None |
None |
\(4\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(1+\zeta_{24}-\zeta_{24}^{2})q^{2}+(-\zeta_{24}^{4}+\zeta_{24}^{7})q^{3}+\cdots\)
|
392.2.m.g |
\(12\) |
\(3.130\) |
12.0.\(\cdots\).2 |
None |
None |
\(0\) |
\(6\) |
\(0\) |
\(0\) |
|
\(q+(\beta _{1}-\beta _{8})q^{2}+(1+\beta _{10})q^{3}+(\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)
|
392.2.m.h |
\(16\) |
\(3.130\) |
\(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
None |
None |
\(-4\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(\beta _{5}+\beta _{14})q^{2}-\beta _{15}q^{3}+(1+\beta _{5}+\cdots)q^{4}+\cdots\)
|
392.2.p.a |
\(4\) |
\(3.130\) |
\(\Q(\sqrt{-2}, \sqrt{-3})\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+2\beta _{2}q^{4}+\cdots\)
|
392.2.p.b |
\(4\) |
\(3.130\) |
\(\Q(\sqrt{-2}, \sqrt{-3})\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+2\beta _{2}q^{4}+\beta _{1}q^{5}+\cdots\)
|
392.2.p.c |
\(4\) |
\(3.130\) |
\(\Q(\sqrt{-3}, \sqrt{-7})\) |
\(\Q(\sqrt{-7}) \) |
None |
\(1\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{3}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(3-\beta _{1}+\cdots)q^{8}+\cdots\)
|
392.2.p.d |
\(8\) |
\(3.130\) |
8.0.\(\cdots\).10 |
\(\Q(\sqrt{-14}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{5}q^{2}-\beta _{6}q^{3}+(-2+2\beta _{2})q^{4}+\cdots\)
|
392.2.p.e |
\(8\) |
\(3.130\) |
8.0.432972864.2 |
None |
None |
\(1\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(-\beta _{1}-\beta _{6})q^{2}+(\beta _{5}+\beta _{6})q^{3}+\beta _{5}q^{4}+\cdots\)
|
392.2.p.f |
\(8\) |
\(3.130\) |
8.0.432972864.2 |
None |
None |
\(1\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(-\beta _{1}-\beta _{6})q^{2}+(-\beta _{5}-\beta _{6})q^{3}+\cdots\)
|
392.2.p.g |
\(12\) |
\(3.130\) |
12.0.\(\cdots\).1 |
None |
None |
\(-2\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(-\beta _{1}+\beta _{5})q^{2}-\beta _{6}q^{3}-\beta _{3}q^{4}+\cdots\)
|
392.2.p.h |
\(24\) |
\(3.130\) |
|
None |
None |
\(2\) |
\(0\) |
\(0\) |
\(0\) |
|
|
392.2.q.a |
\(42\) |
\(3.130\) |
|
None |
None |
\(0\) |
\(-7\) |
\(-2\) |
\(1\) |
|
|