31.1.b.a |
\(1\) |
\(0.015\) |
\(\Q\) |
\(\Q(\sqrt{-31}) \) |
None |
\(-1\) |
\(0\) |
\(-1\) |
\(-1\) |
|
\(q-q^{2}-q^{5}-q^{7}+q^{8}+q^{9}+q^{10}+\cdots\)
|
31.2.a.a |
\(2\) |
\(0.248\) |
\(\Q(\sqrt{5}) \) |
None |
None |
\(1\) |
\(-2\) |
\(2\) |
\(-4\) |
\(-\) |
\(q+\beta q^{2}-2\beta q^{3}+(-1+\beta )q^{4}+q^{5}+\cdots\)
|
31.2.c.a |
\(4\) |
\(0.248\) |
\(\Q(\sqrt{2}, \sqrt{-3})\) |
None |
None |
\(-4\) |
\(2\) |
\(-2\) |
\(-2\) |
|
\(q+(-1+\beta _{3})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+\cdots\)
|
31.2.d.a |
\(4\) |
\(0.248\) |
\(\Q(\zeta_{10})\) |
None |
None |
\(-3\) |
\(1\) |
\(-6\) |
\(-3\) |
|
\(q+(-1-\zeta_{10}^{2})q^{2}+(1-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)
|
31.2.g.a |
\(16\) |
\(0.248\) |
\(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
None |
None |
\(-6\) |
\(-12\) |
\(-3\) |
\(2\) |
|
\(q+(-1-\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots\)
|
31.3.b.a |
\(2\) |
\(0.845\) |
\(\Q(\sqrt{-26}) \) |
None |
None |
\(-2\) |
\(0\) |
\(4\) |
\(16\) |
|
\(q-q^{2}+\beta q^{3}-3q^{4}+2q^{5}-\beta q^{6}+\cdots\)
|
31.3.b.b |
\(3\) |
\(0.845\) |
3.3.837.1 |
\(\Q(\sqrt{-31}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{2}q^{2}+(4+\beta _{1}-2\beta _{2})q^{4}+(-3\beta _{1}+\cdots)q^{5}+\cdots\)
|
31.3.e.a |
\(2\) |
\(0.845\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(-6\) |
\(3\) |
\(9\) |
\(1\) |
|
\(q-3q^{2}+(1+\zeta_{6})q^{3}+5q^{4}+9\zeta_{6}q^{5}+\cdots\)
|
31.3.e.b |
\(6\) |
\(0.845\) |
6.0.954288.1 |
None |
None |
\(2\) |
\(-3\) |
\(-7\) |
\(-9\) |
|
\(q+(-\beta _{2}+\beta _{4})q^{2}+(-\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{3}+\cdots\)
|
31.3.f.a |
\(20\) |
\(0.845\) |
\(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
None |
None |
\(-3\) |
\(-5\) |
\(-14\) |
\(-1\) |
|
\(q-\beta _{10}q^{2}-\beta _{13}q^{3}+(3\beta _{11}+\beta _{19})q^{4}+\cdots\)
|
31.3.h.a |
\(32\) |
\(0.845\) |
|
None |
None |
\(-6\) |
\(-10\) |
\(-7\) |
\(-22\) |
|
|
31.4.a.a |
\(2\) |
\(1.829\) |
\(\Q(\sqrt{17}) \) |
None |
None |
\(-5\) |
\(-2\) |
\(-25\) |
\(-19\) |
\(-\) |
\(q+(-2-\beta )q^{2}+(-2+2\beta )q^{3}+5\beta q^{4}+\cdots\)
|
31.4.a.b |
\(5\) |
\(1.829\) |
\(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
None |
None |
\(3\) |
\(4\) |
\(15\) |
\(9\) |
\(+\) |
\(q+(1-\beta _{1})q^{2}+(-\beta _{2}+\beta _{3}-\beta _{4})q^{3}+\cdots\)
|
31.4.c.a |
\(14\) |
\(1.829\) |
\(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
None |
None |
\(-4\) |
\(-11\) |
\(-5\) |
\(31\) |
|
\(q+(-\beta _{1}+\beta _{4})q^{2}+(-2+2\beta _{3}-\beta _{8}+\cdots)q^{3}+\cdots\)
|
31.4.d.a |
\(28\) |
\(1.829\) |
|
None |
None |
\(-3\) |
\(-7\) |
\(0\) |
\(35\) |
|
|
31.4.g.a |
\(56\) |
\(1.829\) |
|
None |
None |
\(-6\) |
\(1\) |
\(0\) |
\(-71\) |
|
|
31.5.b.a |
\(3\) |
\(3.204\) |
3.3.837.1 |
\(\Q(\sqrt{-31}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(-\beta _{1}+\beta _{2})q^{2}+(2^{4}-6\beta _{1}+\beta _{2})q^{4}+\cdots\)
|
31.5.b.b |
\(6\) |
\(3.204\) |
\(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
None |
None |
\(-2\) |
\(0\) |
\(-8\) |
\(-132\) |
|
\(q-\beta _{3}q^{2}+\beta _{1}q^{3}+(4+\beta _{3}+\beta _{4})q^{4}+\cdots\)
|
31.5.e.a |
\(20\) |
\(3.204\) |
\(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
None |
None |
\(-4\) |
\(6\) |
\(-4\) |
\(-98\) |
|
\(q-\beta _{3}q^{2}+\beta _{8}q^{3}+(6+\beta _{2})q^{4}+(-\beta _{11}+\cdots)q^{5}+\cdots\)
|
31.5.f.a |
\(36\) |
\(3.204\) |
|
None |
None |
\(-3\) |
\(-5\) |
\(-2\) |
\(-73\) |
|
|
31.5.h.a |
\(80\) |
\(3.204\) |
|
None |
None |
\(-6\) |
\(-16\) |
\(-1\) |
\(288\) |
|
|
31.6.a.a |
\(5\) |
\(4.972\) |
\(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
None |
None |
\(-9\) |
\(-20\) |
\(-72\) |
\(-108\) |
\(+\) |
\(q+(-2+\beta _{1})q^{2}+(-4-\beta _{1}-\beta _{3})q^{3}+\cdots\)
|
31.6.a.b |
\(8\) |
\(4.972\) |
\(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
None |
None |
\(7\) |
\(-2\) |
\(128\) |
\(88\) |
\(-\) |
\(q+(1-\beta _{1})q^{2}+\beta _{6}q^{3}+(19-3\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
|
31.6.c.a |
\(24\) |
\(4.972\) |
|
None |
None |
\(-4\) |
\(10\) |
\(28\) |
\(-134\) |
|
|
31.6.d.a |
\(52\) |
\(4.972\) |
|
None |
None |
\(-3\) |
\(17\) |
\(-66\) |
\(205\) |
|
|
31.6.g.a |
\(96\) |
\(4.972\) |
|
None |
None |
\(-6\) |
\(-20\) |
\(-33\) |
\(-66\) |
|
|
31.7.b.a |
\(1\) |
\(7.132\) |
\(\Q\) |
\(\Q(\sqrt{-31}) \) |
None |
\(-15\) |
\(0\) |
\(-246\) |
\(-430\) |
|
\(q-15q^{2}+161q^{4}-246q^{5}-430q^{7}+\cdots\)
|
31.7.b.b |
\(2\) |
\(7.132\) |
\(\Q(\sqrt{93}) \) |
\(\Q(\sqrt{-31}) \) |
None |
\(15\) |
\(0\) |
\(246\) |
\(430\) |
|
\(q+(8-\beta )q^{2}+(23-15\beta )q^{4}+(127-8\beta )q^{5}+\cdots\)
|
31.7.b.c |
\(12\) |
\(7.132\) |
\(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
None |
None |
\(-2\) |
\(0\) |
\(-146\) |
\(6\) |
|
\(q-\beta _{8}q^{2}-\beta _{1}q^{3}+(10+\beta _{6}-\beta _{8})q^{4}+\cdots\)
|
31.7.e.a |
\(30\) |
\(7.132\) |
|
None |
None |
\(-4\) |
\(-3\) |
\(-73\) |
\(723\) |
|
|
31.7.f.a |
\(60\) |
\(7.132\) |
|
None |
None |
\(-3\) |
\(-5\) |
\(136\) |
\(1009\) |
|
|
31.7.h.a |
\(120\) |
\(7.132\) |
|
None |
None |
\(-6\) |
\(-7\) |
\(68\) |
\(-1753\) |
|
|
31.8.a.a |
\(7\) |
\(9.684\) |
\(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
None |
None |
\(-17\) |
\(-14\) |
\(-430\) |
\(-832\) |
\(-\) |
\(q+(-2-\beta _{1})q^{2}+(-2+\beta _{1}+\beta _{3})q^{3}+\cdots\)
|
31.8.a.b |
\(10\) |
\(9.684\) |
\(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
None |
None |
\(15\) |
\(40\) |
\(570\) |
\(540\) |
\(+\) |
\(q+(2-\beta _{1})q^{2}+(4+\beta _{2})q^{3}+(61+\beta _{1}+\cdots)q^{4}+\cdots\)
|
31.8.c.a |
\(36\) |
\(9.684\) |
|
None |
None |
\(-4\) |
\(-2\) |
\(70\) |
\(-2158\) |
|
|
31.8.d.a |
\(68\) |
\(9.684\) |
|
None |
None |
\(-3\) |
\(-31\) |
\(-150\) |
\(-3083\) |
|
|
31.8.g.a |
\(144\) |
\(9.684\) |
|
None |
None |
\(-6\) |
\(-8\) |
\(-75\) |
\(5518\) |
|
|
31.9.b.a |
\(3\) |
\(12.629\) |
3.3.837.1 |
\(\Q(\sqrt{-31}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(-6\beta _{1}+\beta _{2})q^{2}+(2^{8}-\beta _{1}+3^{4}\beta _{2})q^{4}+\cdots\)
|
31.9.b.b |
\(18\) |
\(12.629\) |
\(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
None |
None |
\(-2\) |
\(0\) |
\(292\) |
\(-5472\) |
|
\(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(140+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
|
31.9.e.a |
\(40\) |
\(12.629\) |
|
None |
None |
\(-4\) |
\(-84\) |
\(146\) |
\(272\) |
|
|
31.9.f.a |
\(84\) |
\(12.629\) |
|
None |
None |
\(-3\) |
\(-5\) |
\(-302\) |
\(5067\) |
|
|
31.9.h.a |
\(160\) |
\(12.629\) |
|
None |
None |
\(-6\) |
\(74\) |
\(-151\) |
\(118\) |
|
|
31.10.a.a |
\(10\) |
\(15.966\) |
\(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
None |
None |
\(-33\) |
\(-8\) |
\(-3297\) |
\(-495\) |
\(+\) |
\(q+(-3-\beta _{1})q^{2}+(-1+\beta _{1}-\beta _{3})q^{3}+\cdots\)
|
31.10.a.b |
\(13\) |
\(15.966\) |
\(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
None |
None |
\(31\) |
\(154\) |
\(1703\) |
\(9109\) |
\(-\) |
\(q+(2+\beta _{1})q^{2}+(12+\beta _{3})q^{3}+(300+6\beta _{1}+\cdots)q^{4}+\cdots\)
|
31.10.c.a |
\(46\) |
\(15.966\) |
|
None |
None |
\(-4\) |
\(13\) |
\(-797\) |
\(6359\) |
|
|
31.10.d.a |
\(92\) |
\(15.966\) |
|
None |
None |
\(-3\) |
\(-151\) |
\(1584\) |
\(15771\) |
|
|
31.10.g.a |
\(184\) |
\(15.966\) |
|
None |
None |
\(-6\) |
\(-23\) |
\(792\) |
\(-30759\) |
|
|
31.11.b.a |
\(3\) |
\(19.696\) |
3.3.837.1 |
\(\Q(\sqrt{-31}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(-15\beta _{1}+14\beta _{2})q^{2}+(2^{10}-644\beta _{1}+\cdots)q^{4}+\cdots\)
|
31.11.b.b |
\(22\) |
\(19.696\) |
|
None |
None |
\(-2\) |
\(0\) |
\(3304\) |
\(19916\) |
|
|
31.11.e.a |
\(52\) |
\(19.696\) |
|
None |
None |
\(-4\) |
\(-246\) |
\(1652\) |
\(-19306\) |
|
|