190.2.a.a |
\(1\) |
\(1.517\) |
\(\Q\) |
None |
\(-1\) |
\(-1\) |
\(-1\) |
\(-1\) |
\(+\) |
\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
|
190.2.a.b |
\(1\) |
\(1.517\) |
\(\Q\) |
None |
\(1\) |
\(-3\) |
\(-1\) |
\(-5\) |
\(+\) |
\(q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}-5q^{7}+\cdots\)
|
190.2.a.c |
\(1\) |
\(1.517\) |
\(\Q\) |
None |
\(1\) |
\(1\) |
\(1\) |
\(-1\) |
\(-\) |
\(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
|
190.2.a.d |
\(2\) |
\(1.517\) |
\(\Q(\sqrt{17}) \) |
None |
\(-2\) |
\(-1\) |
\(2\) |
\(-1\) |
\(-\) |
\(q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}-\beta q^{7}+\cdots\)
|
190.2.b.a |
\(4\) |
\(1.517\) |
\(\Q(\zeta_{8})\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\zeta_{8}^{2}q^{2}+(\zeta_{8}-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}-q^{4}+\cdots\)
|
190.2.b.b |
\(6\) |
\(1.517\) |
6.0.5161984.1 |
None |
\(0\) |
\(0\) |
\(2\) |
\(0\) |
|
\(q-\beta _{4}q^{2}+(\beta _{4}+\beta _{5})q^{3}-q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
|
190.2.e.a |
\(2\) |
\(1.517\) |
\(\Q(\sqrt{-3}) \) |
None |
\(-1\) |
\(0\) |
\(1\) |
\(2\) |
|
\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
|
190.2.e.b |
\(2\) |
\(1.517\) |
\(\Q(\sqrt{-3}) \) |
None |
\(1\) |
\(1\) |
\(1\) |
\(4\) |
|
\(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
|
190.2.e.c |
\(4\) |
\(1.517\) |
\(\Q(\sqrt{-3}, \sqrt{17})\) |
None |
\(2\) |
\(1\) |
\(-2\) |
\(10\) |
|
\(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(-1+\beta _{2})q^{4}-\beta _{2}q^{5}+\cdots\)
|
190.2.f.a |
\(4\) |
\(1.517\) |
\(\Q(\zeta_{8})\) |
None |
\(0\) |
\(0\) |
\(-4\) |
\(-4\) |
|
\(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-1+2\zeta_{8}^{2})q^{5}+\cdots\)
|
190.2.f.b |
\(16\) |
\(1.517\) |
\(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(8\) |
|
\(q-\beta _{8}q^{2}+(\beta _{1}-\beta _{7}+\beta _{10}+\beta _{12})q^{3}+\cdots\)
|
190.2.i.a |
\(20\) |
\(1.517\) |
\(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
None |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
|
\(q+(-\beta _{2}-\beta _{13})q^{2}-\beta _{1}q^{3}+(1-\beta _{3}+\cdots)q^{4}+\cdots\)
|
190.2.k.a |
\(6\) |
\(1.517\) |
\(\Q(\zeta_{18})\) |
None |
\(0\) |
\(3\) |
\(0\) |
\(0\) |
|
\(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{3}+\cdots)q^{3}+\cdots\)
|
190.2.k.b |
\(12\) |
\(1.517\) |
\(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(6\) |
|
\(q+(-\beta _{7}+\beta _{8})q^{2}+(-\beta _{1}+\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots\)
|
190.2.k.c |
\(12\) |
\(1.517\) |
\(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
None |
\(0\) |
\(3\) |
\(0\) |
\(-6\) |
|
\(q-\beta _{8}q^{2}+(1+\beta _{4}+\beta _{7}+\beta _{10}-\beta _{11})q^{3}+\cdots\)
|
190.2.k.d |
\(18\) |
\(1.517\) |
\(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{9}q^{2}-\beta _{7}q^{3}-\beta _{11}q^{4}+\beta _{10}q^{5}+\cdots\)
|
190.2.m.a |
\(8\) |
\(1.517\) |
\(\Q(\zeta_{24})\) |
None |
\(0\) |
\(12\) |
\(4\) |
\(-16\) |
|
\(q+\zeta_{24}^{7}q^{2}+(2+\zeta_{24}^{2}-\zeta_{24}^{4}+\zeta_{24}^{6}+\cdots)q^{3}+\cdots\)
|
190.2.m.b |
\(32\) |
\(1.517\) |
|
None |
\(0\) |
\(-12\) |
\(0\) |
\(24\) |
|
|
190.2.p.a |
\(60\) |
\(1.517\) |
|
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
|
190.2.r.a |
\(120\) |
\(1.517\) |
|
None |
\(0\) |
\(0\) |
\(0\) |
\(-12\) |
|
|
190.3.c.a |
\(16\) |
\(5.177\) |
\(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(-8\) |
|
\(q+\beta _{9}q^{2}-\beta _{1}q^{3}-2q^{4}-\beta _{5}q^{5}+(1+\cdots)q^{6}+\cdots\)
|
190.3.d.a |
\(20\) |
\(5.177\) |
\(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
None |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
|
\(q+\beta _{2}q^{2}-\beta _{4}q^{3}+2q^{4}-\beta _{3}q^{5}+\beta _{6}q^{6}+\cdots\)
|
190.3.g.a |
\(16\) |
\(5.177\) |
\(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
None |
\(-16\) |
\(8\) |
\(2\) |
\(-10\) |
|
\(q+(-1-\beta _{5})q^{2}+(-\beta _{2}-\beta _{5})q^{3}+2\beta _{5}q^{4}+\cdots\)
|
190.3.g.b |
\(20\) |
\(5.177\) |
\(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
None |
\(20\) |
\(0\) |
\(2\) |
\(14\) |
|
\(q+(1+\beta _{3})q^{2}-\beta _{2}q^{3}+2\beta _{3}q^{4}+\beta _{16}q^{5}+\cdots\)
|
190.3.h.a |
\(4\) |
\(5.177\) |
\(\Q(\sqrt{2}, \sqrt{-3})\) |
None |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
|
\(q+\beta _{1}q^{2}+2\beta _{1}q^{3}+2\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
|
190.3.h.b |
\(36\) |
\(5.177\) |
|
None |
\(0\) |
\(0\) |
\(4\) |
\(0\) |
|
|
190.3.j.a |
\(32\) |
\(5.177\) |
|
None |
\(0\) |
\(-12\) |
\(0\) |
\(8\) |
|
|
190.3.l.a |
\(4\) |
\(5.177\) |
\(\Q(\zeta_{12})\) |
None |
\(-2\) |
\(-6\) |
\(8\) |
\(32\) |
|
\(q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-3\zeta_{12}+\cdots)q^{3}+\cdots\)
|
190.3.l.b |
\(4\) |
\(5.177\) |
\(\Q(\zeta_{12})\) |
None |
\(2\) |
\(6\) |
\(10\) |
\(8\) |
|
\(q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(3\zeta_{12}+\cdots)q^{3}+\cdots\)
|
190.3.l.c |
\(36\) |
\(5.177\) |
|
None |
\(-18\) |
\(6\) |
\(-10\) |
\(-28\) |
|
|
190.3.l.d |
\(36\) |
\(5.177\) |
|
None |
\(18\) |
\(-6\) |
\(-12\) |
\(12\) |
|
|
190.3.n.a |
\(72\) |
\(5.177\) |
|
None |
\(0\) |
\(12\) |
\(0\) |
\(0\) |
|
|
190.3.o.a |
\(120\) |
\(5.177\) |
|
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
|
190.3.q.a |
\(120\) |
\(5.177\) |
|
None |
\(0\) |
\(0\) |
\(0\) |
\(-18\) |
|
|
190.3.q.b |
\(120\) |
\(5.177\) |
|
None |
\(0\) |
\(0\) |
\(0\) |
\(-18\) |
|
|
190.4.a.a |
\(1\) |
\(11.210\) |
\(\Q\) |
None |
\(-2\) |
\(-2\) |
\(5\) |
\(8\) |
\(+\) |
\(q-2q^{2}-2q^{3}+4q^{4}+5q^{5}+4q^{6}+\cdots\)
|
190.4.a.b |
\(1\) |
\(11.210\) |
\(\Q\) |
None |
\(-2\) |
\(2\) |
\(5\) |
\(-12\) |
\(-\) |
\(q-2q^{2}+2q^{3}+4q^{4}+5q^{5}-4q^{6}+\cdots\)
|
190.4.a.c |
\(1\) |
\(11.210\) |
\(\Q\) |
None |
\(2\) |
\(-4\) |
\(5\) |
\(-20\) |
\(-\) |
\(q+2q^{2}-4q^{3}+4q^{4}+5q^{5}-8q^{6}+\cdots\)
|
190.4.a.d |
\(2\) |
\(11.210\) |
\(\Q(\sqrt{313}) \) |
None |
\(-4\) |
\(1\) |
\(10\) |
\(-27\) |
\(+\) |
\(q-2q^{2}+\beta q^{3}+4q^{4}+5q^{5}-2\beta q^{6}+\cdots\)
|
190.4.a.e |
\(2\) |
\(11.210\) |
\(\Q(\sqrt{3}) \) |
None |
\(-4\) |
\(2\) |
\(-10\) |
\(8\) |
\(+\) |
\(q-2q^{2}+(1+3\beta )q^{3}+4q^{4}-5q^{5}+\cdots\)
|
190.4.a.f |
\(2\) |
\(11.210\) |
\(\Q(\sqrt{34}) \) |
None |
\(4\) |
\(0\) |
\(-10\) |
\(24\) |
\(+\) |
\(q+2q^{2}+\beta q^{3}+4q^{4}-5q^{5}+2\beta q^{6}+\cdots\)
|
190.4.a.g |
\(3\) |
\(11.210\) |
3.3.126168.1 |
None |
\(-6\) |
\(-1\) |
\(-15\) |
\(1\) |
\(-\) |
\(q-2q^{2}-\beta _{1}q^{3}+4q^{4}-5q^{5}+2\beta _{1}q^{6}+\cdots\)
|
190.4.a.h |
\(3\) |
\(11.210\) |
3.3.5468.1 |
None |
\(6\) |
\(-9\) |
\(-15\) |
\(-11\) |
\(-\) |
\(q+2q^{2}+(-3-\beta _{1})q^{3}+4q^{4}-5q^{5}+\cdots\)
|
190.4.a.i |
\(3\) |
\(11.210\) |
3.3.15357.1 |
None |
\(6\) |
\(11\) |
\(15\) |
\(29\) |
\(+\) |
\(q+2q^{2}+(4-\beta _{1})q^{3}+4q^{4}+5q^{5}+\cdots\)
|
190.4.b.a |
\(12\) |
\(11.210\) |
\(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
None |
\(0\) |
\(0\) |
\(20\) |
\(0\) |
|
\(q+\beta _{8}q^{2}+(\beta _{8}-\beta _{9})q^{3}-4q^{4}+(2+\beta _{4}+\cdots)q^{5}+\cdots\)
|
190.4.b.b |
\(14\) |
\(11.210\) |
\(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
None |
\(0\) |
\(0\) |
\(-8\) |
\(0\) |
|
\(q-\beta _{8}q^{2}+\beta _{3}q^{3}-4q^{4}+(-1+\beta _{5}+\cdots)q^{5}+\cdots\)
|
190.4.e.a |
\(2\) |
\(11.210\) |
\(\Q(\sqrt{-3}) \) |
None |
\(2\) |
\(2\) |
\(-5\) |
\(-56\) |
|
\(q+(2-2\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots\)
|
190.4.e.b |
\(2\) |
\(11.210\) |
\(\Q(\sqrt{-3}) \) |
None |
\(2\) |
\(2\) |
\(5\) |
\(64\) |
|
\(q+(2-2\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots\)
|
190.4.e.c |
\(6\) |
\(11.210\) |
\(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
None |
\(6\) |
\(3\) |
\(-15\) |
\(36\) |
|
\(q+2\beta _{2}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-4+4\beta _{2}+\cdots)q^{4}+\cdots\)
|
190.4.e.d |
\(8\) |
\(11.210\) |
\(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
None |
\(8\) |
\(3\) |
\(20\) |
\(-82\) |
|
\(q+(2+2\beta _{1})q^{2}+(1+\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots\)
|