15.2.a.a |
\(1\) |
\(0.120\) |
\(\Q\) |
None |
\(-1\) |
\(-1\) |
\(1\) |
\(0\) |
\(-\) |
\(q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+3q^{8}+\cdots\)
|
15.3.c.a |
\(2\) |
\(0.409\) |
\(\Q(\sqrt{-5}) \) |
None |
\(0\) |
\(-4\) |
\(0\) |
\(-12\) |
|
\(q+\beta q^{2}+(-2-\beta )q^{3}-q^{4}-\beta q^{5}+\cdots\)
|
15.3.d.a |
\(1\) |
\(0.409\) |
\(\Q\) |
\(\Q(\sqrt{-15}) \) |
\(-1\) |
\(3\) |
\(-5\) |
\(0\) |
|
\(q-q^{2}+3q^{3}-3q^{4}-5q^{5}-3q^{6}+\cdots\)
|
15.3.d.b |
\(1\) |
\(0.409\) |
\(\Q\) |
\(\Q(\sqrt{-15}) \) |
\(1\) |
\(-3\) |
\(5\) |
\(0\) |
|
\(q+q^{2}-3q^{3}-3q^{4}+5q^{5}-3q^{6}+\cdots\)
|
15.3.f.a |
\(4\) |
\(0.409\) |
\(\Q(i, \sqrt{6})\) |
None |
\(-4\) |
\(0\) |
\(-4\) |
\(4\) |
|
\(q+(-1+\beta _{1}-\beta _{2})q^{2}+\beta _{3}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
|
15.4.a.a |
\(1\) |
\(0.885\) |
\(\Q\) |
None |
\(1\) |
\(3\) |
\(5\) |
\(-24\) |
\(+\) |
\(q+q^{2}+3q^{3}-7q^{4}+5q^{5}+3q^{6}+\cdots\)
|
15.4.a.b |
\(1\) |
\(0.885\) |
\(\Q\) |
None |
\(3\) |
\(-3\) |
\(-5\) |
\(20\) |
\(+\) |
\(q+3q^{2}-3q^{3}+q^{4}-5q^{5}-9q^{6}+\cdots\)
|
15.4.b.a |
\(4\) |
\(0.885\) |
\(\Q(i, \sqrt{41})\) |
None |
\(0\) |
\(0\) |
\(6\) |
\(0\) |
|
\(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(-5+\beta _{3})q^{4}+(2+\cdots)q^{5}+\cdots\)
|
15.4.e.a |
\(8\) |
\(0.885\) |
8.0.\(\cdots\).8 |
None |
\(0\) |
\(-6\) |
\(0\) |
\(-16\) |
|
\(q-\beta _{3}q^{2}+(-1-\beta _{2}+\beta _{5})q^{3}+(\beta _{2}+\cdots)q^{4}+\cdots\)
|
15.5.c.a |
\(6\) |
\(1.551\) |
\(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
None |
\(0\) |
\(8\) |
\(0\) |
\(76\) |
|
\(q+\beta _{1}q^{2}+(1-\beta _{2})q^{3}+(-8+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
|
15.5.d.a |
\(1\) |
\(1.551\) |
\(\Q\) |
\(\Q(\sqrt{-15}) \) |
\(-7\) |
\(9\) |
\(25\) |
\(0\) |
|
\(q-7q^{2}+9q^{3}+33q^{4}+5^{2}q^{5}-63q^{6}+\cdots\)
|
15.5.d.b |
\(1\) |
\(1.551\) |
\(\Q\) |
\(\Q(\sqrt{-15}) \) |
\(7\) |
\(-9\) |
\(-25\) |
\(0\) |
|
\(q+7q^{2}-9q^{3}+33q^{4}-5^{2}q^{5}-63q^{6}+\cdots\)
|
15.5.d.c |
\(4\) |
\(1.551\) |
\(\Q(\sqrt{10}, \sqrt{-26})\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}-6q^{4}+(2\beta _{2}+\cdots)q^{5}+\cdots\)
|
15.5.f.a |
\(8\) |
\(1.551\) |
\(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
None |
\(0\) |
\(0\) |
\(-84\) |
\(20\) |
|
\(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-\beta _{1}-12\beta _{2}-2\beta _{3}+\cdots)q^{4}+\cdots\)
|
15.6.a.a |
\(1\) |
\(2.406\) |
\(\Q\) |
None |
\(-2\) |
\(-9\) |
\(-25\) |
\(-132\) |
\(+\) |
\(q-2q^{2}-9q^{3}-28q^{4}-5^{2}q^{5}+18q^{6}+\cdots\)
|
15.6.a.b |
\(1\) |
\(2.406\) |
\(\Q\) |
None |
\(7\) |
\(9\) |
\(-25\) |
\(12\) |
\(-\) |
\(q+7q^{2}+9q^{3}+17q^{4}-5^{2}q^{5}+63q^{6}+\cdots\)
|
15.6.a.c |
\(2\) |
\(2.406\) |
\(\Q(\sqrt{409}) \) |
None |
\(-1\) |
\(-18\) |
\(50\) |
\(-112\) |
\(-\) |
\(q-\beta q^{2}-9q^{3}+(70+\beta )q^{4}+5^{2}q^{5}+\cdots\)
|
15.6.b.a |
\(4\) |
\(2.406\) |
\(\Q(i, \sqrt{89})\) |
None |
\(0\) |
\(0\) |
\(120\) |
\(0\) |
|
\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-11+\beta _{3})q^{4}+\cdots\)
|
15.6.e.a |
\(16\) |
\(2.406\) |
\(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(-80\) |
|
\(q-\beta _{7}q^{2}-\beta _{4}q^{3}+(-13\beta _{3}-\beta _{6})q^{4}+\cdots\)
|
15.7.c.a |
\(8\) |
\(3.451\) |
\(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
None |
\(0\) |
\(20\) |
\(0\) |
\(160\) |
|
\(q-\beta _{2}q^{2}+(2-\beta _{5})q^{3}+(-41-\beta _{3}+\cdots)q^{4}+\cdots\)
|
15.7.d.a |
\(1\) |
\(3.451\) |
\(\Q\) |
\(\Q(\sqrt{-15}) \) |
\(-11\) |
\(-27\) |
\(125\) |
\(0\) |
|
\(q-11q^{2}-3^{3}q^{3}+57q^{4}+5^{3}q^{5}+\cdots\)
|
15.7.d.b |
\(1\) |
\(3.451\) |
\(\Q\) |
\(\Q(\sqrt{-15}) \) |
\(11\) |
\(27\) |
\(-125\) |
\(0\) |
|
\(q+11q^{2}+3^{3}q^{3}+57q^{4}-5^{3}q^{5}+\cdots\)
|
15.7.d.c |
\(8\) |
\(3.451\) |
\(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{5}q^{2}+(\beta _{1}+\beta _{3}+\beta _{5})q^{3}+(9+\beta _{2}+\cdots)q^{4}+\cdots\)
|
15.7.f.a |
\(12\) |
\(3.451\) |
\(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
None |
\(16\) |
\(0\) |
\(136\) |
\(-696\) |
|
\(q+(1+\beta _{1}-\beta _{4})q^{2}-\beta _{6}q^{3}+(18\beta _{1}+\cdots)q^{4}+\cdots\)
|
15.8.a.a |
\(1\) |
\(4.686\) |
\(\Q\) |
None |
\(-22\) |
\(27\) |
\(-125\) |
\(-420\) |
\(-\) |
\(q-22q^{2}+3^{3}q^{3}+356q^{4}-5^{3}q^{5}+\cdots\)
|
15.8.a.b |
\(1\) |
\(4.686\) |
\(\Q\) |
None |
\(-13\) |
\(-27\) |
\(-125\) |
\(1380\) |
\(+\) |
\(q-13q^{2}-3^{3}q^{3}+41q^{4}-5^{3}q^{5}+\cdots\)
|
15.8.a.c |
\(2\) |
\(4.686\) |
\(\Q(\sqrt{601}) \) |
None |
\(7\) |
\(54\) |
\(250\) |
\(1304\) |
\(+\) |
\(q+(4-\beta )q^{2}+3^{3}q^{3}+(38-7\beta )q^{4}+\cdots\)
|
15.8.b.a |
\(8\) |
\(4.686\) |
\(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
None |
\(0\) |
\(0\) |
\(-444\) |
\(0\) |
|
\(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(-83-\beta _{4})q^{4}+\cdots\)
|
15.8.e.a |
\(24\) |
\(4.686\) |
|
None |
\(0\) |
\(24\) |
\(0\) |
\(1344\) |
|
|
15.9.c.a |
\(10\) |
\(6.111\) |
\(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
None |
\(0\) |
\(-112\) |
\(0\) |
\(7156\) |
|
\(q-\beta _{1}q^{2}+(-11-2\beta _{1}-\beta _{2})q^{3}+(-79+\cdots)q^{4}+\cdots\)
|
15.9.d.a |
\(1\) |
\(6.111\) |
\(\Q\) |
\(\Q(\sqrt{-15}) \) |
\(-17\) |
\(-81\) |
\(-625\) |
\(0\) |
|
\(q-17q^{2}-3^{4}q^{3}+33q^{4}-5^{4}q^{5}+\cdots\)
|
15.9.d.b |
\(1\) |
\(6.111\) |
\(\Q\) |
\(\Q(\sqrt{-15}) \) |
\(17\) |
\(81\) |
\(625\) |
\(0\) |
|
\(q+17q^{2}+3^{4}q^{3}+33q^{4}+5^{4}q^{5}+\cdots\)
|
15.9.d.c |
\(12\) |
\(6.111\) |
\(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{2}q^{2}+(\beta _{2}-\beta _{3})q^{3}+(142-\beta _{1}+\cdots)q^{4}+\cdots\)
|
15.9.f.a |
\(16\) |
\(6.111\) |
\(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
None |
\(0\) |
\(0\) |
\(-444\) |
\(4540\) |
|
\(q+\beta _{2}q^{2}-\beta _{6}q^{3}+(158\beta _{1}-3\beta _{2}+3\beta _{3}+\cdots)q^{4}+\cdots\)
|
15.10.a.a |
\(1\) |
\(7.726\) |
\(\Q\) |
None |
\(-4\) |
\(81\) |
\(625\) |
\(-7680\) |
\(+\) |
\(q-4q^{2}+3^{4}q^{3}-496q^{4}+5^{4}q^{5}+\cdots\)
|
15.10.a.b |
\(1\) |
\(7.726\) |
\(\Q\) |
None |
\(22\) |
\(-81\) |
\(-625\) |
\(-5988\) |
\(+\) |
\(q+22q^{2}-3^{4}q^{3}-28q^{4}-5^{4}q^{5}+\cdots\)
|
15.10.a.c |
\(2\) |
\(7.726\) |
\(\Q(\sqrt{4729}) \) |
None |
\(19\) |
\(162\) |
\(-1250\) |
\(-11872\) |
\(-\) |
\(q+(10-\beta )q^{2}+3^{4}q^{3}+(770-19\beta )q^{4}+\cdots\)
|
15.10.a.d |
\(2\) |
\(7.726\) |
\(\Q(\sqrt{241}) \) |
None |
\(31\) |
\(-162\) |
\(1250\) |
\(14112\) |
\(-\) |
\(q+(15-\beta )q^{2}-3^{4}q^{3}+(255-31\beta )q^{4}+\cdots\)
|
15.10.b.a |
\(8\) |
\(7.726\) |
\(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
None |
\(0\) |
\(0\) |
\(-690\) |
\(0\) |
|
\(q-\beta _{3}q^{2}+\beta _{4}q^{3}+(-149-\beta _{1})q^{4}+\cdots\)
|
15.10.e.a |
\(32\) |
\(7.726\) |
|
None |
\(0\) |
\(-150\) |
\(0\) |
\(-9760\) |
|
|
15.11.c.a |
\(14\) |
\(9.530\) |
\(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
None |
\(0\) |
\(44\) |
\(0\) |
\(-50548\) |
|
\(q-\beta _{2}q^{2}+(3+\beta _{2}-\beta _{3})q^{3}+(-629+\cdots)q^{4}+\cdots\)
|
15.11.d.a |
\(1\) |
\(9.530\) |
\(\Q\) |
\(\Q(\sqrt{-15}) \) |
\(-61\) |
\(243\) |
\(-3125\) |
\(0\) |
|
\(q-61q^{2}+3^{5}q^{3}+2697q^{4}-5^{5}q^{5}+\cdots\)
|
15.11.d.b |
\(1\) |
\(9.530\) |
\(\Q\) |
\(\Q(\sqrt{-15}) \) |
\(61\) |
\(-243\) |
\(3125\) |
\(0\) |
|
\(q+61q^{2}-3^{5}q^{3}+2697q^{4}+5^{5}q^{5}+\cdots\)
|
15.11.d.c |
\(16\) |
\(9.530\) |
\(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{6}q^{2}+(-\beta _{6}+\beta _{7})q^{3}+(137-\beta _{2}+\cdots)q^{4}+\cdots\)
|
15.11.f.a |
\(20\) |
\(9.530\) |
\(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
None |
\(-64\) |
\(0\) |
\(10676\) |
\(10604\) |
|
\(q+(-3-3\beta _{2}-\beta _{3})q^{2}+\beta _{6}q^{3}+(451\beta _{2}+\cdots)q^{4}+\cdots\)
|
15.12.a.a |
\(1\) |
\(11.525\) |
\(\Q\) |
None |
\(-56\) |
\(-243\) |
\(3125\) |
\(27984\) |
\(-\) |
\(q-56q^{2}-3^{5}q^{3}+1088q^{4}+5^{5}q^{5}+\cdots\)
|
15.12.a.b |
\(2\) |
\(11.525\) |
\(\Q(\sqrt{1609}) \) |
None |
\(-22\) |
\(486\) |
\(-6250\) |
\(-10864\) |
\(-\) |
\(q+(-11-\beta )q^{2}+3^{5}q^{3}+(-318+22\beta )q^{4}+\cdots\)
|
15.12.a.c |
\(2\) |
\(11.525\) |
\(\Q(\sqrt{1801}) \) |
None |
\(-13\) |
\(-486\) |
\(-6250\) |
\(7784\) |
\(+\) |
\(q+(-6-\beta )q^{2}-3^{5}q^{3}+(-1562+13\beta )q^{4}+\cdots\)
|
15.12.a.d |
\(3\) |
\(11.525\) |
\(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
None |
\(-1\) |
\(729\) |
\(9375\) |
\(-14608\) |
\(+\) |
\(q-\beta _{1}q^{2}+3^{5}q^{3}+(1585+3\beta _{1}+\beta _{2})q^{4}+\cdots\)
|
15.12.b.a |
\(12\) |
\(11.525\) |
\(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
None |
\(0\) |
\(0\) |
\(2556\) |
\(0\) |
|
\(q+\beta _{3}q^{2}-\beta _{4}q^{3}+(-1359+\beta _{1})q^{4}+\cdots\)
|