9.3.d.a |
\(2\) |
\(0.245\) |
\(\Q(\sqrt{-3}) \) |
None |
\(-3\) |
\(-3\) |
\(6\) |
\(-2\) |
|
\(q+(-1-\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
|
9.4.a.a |
\(1\) |
\(0.531\) |
\(\Q\) |
\(\Q(\sqrt{-3}) \) |
\(0\) |
\(0\) |
\(0\) |
\(20\) |
\(+\) |
\(q-8q^{4}+20q^{7}-70q^{13}+2^{6}q^{16}+\cdots\)
|
9.4.c.a |
\(4\) |
\(0.531\) |
\(\Q(\sqrt{-3}, \sqrt{-11})\) |
None |
\(-3\) |
\(-3\) |
\(-15\) |
\(-7\) |
|
\(q+(-\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
|
9.5.b.a |
\(2\) |
\(0.930\) |
\(\Q(\sqrt{-2}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(-56\) |
|
\(q+\beta q^{2}-2q^{4}-7\beta q^{5}-28q^{7}+14\beta q^{8}+\cdots\)
|
9.5.d.a |
\(6\) |
\(0.930\) |
6.0.39400128.1 |
None |
\(-3\) |
\(-3\) |
\(-12\) |
\(12\) |
|
\(q+\beta _{2}q^{2}+(-3+\beta _{1}-3\beta _{3}+\beta _{4})q^{3}+\cdots\)
|
9.6.a.a |
\(1\) |
\(1.443\) |
\(\Q\) |
None |
\(6\) |
\(0\) |
\(-6\) |
\(-40\) |
\(-\) |
\(q+6q^{2}+4q^{4}-6q^{5}-40q^{7}-168q^{8}+\cdots\)
|
9.6.c.a |
\(8\) |
\(1.443\) |
\(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
None |
\(3\) |
\(-12\) |
\(78\) |
\(28\) |
|
\(q+(1-\beta _{1}+\beta _{4}+\beta _{5})q^{2}+(-3+3\beta _{1}+\cdots)q^{3}+\cdots\)
|
9.7.b.a |
\(2\) |
\(2.070\) |
\(\Q(\sqrt{-2}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(1048\) |
|
\(q+\beta q^{2}-98q^{4}+5\beta q^{5}+524q^{7}+\cdots\)
|
9.7.d.a |
\(10\) |
\(2.070\) |
\(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
None |
\(-3\) |
\(24\) |
\(-219\) |
\(-121\) |
|
\(q-\beta _{1}q^{2}+(2+\beta _{1}-\beta _{2}+\beta _{3}+\beta _{6}+\cdots)q^{3}+\cdots\)
|
9.8.a.a |
\(1\) |
\(2.811\) |
\(\Q\) |
None |
\(-6\) |
\(0\) |
\(-390\) |
\(-64\) |
\(-\) |
\(q-6q^{2}-92q^{4}-390q^{5}-2^{6}q^{7}+\cdots\)
|
9.8.a.b |
\(2\) |
\(2.811\) |
\(\Q(\sqrt{10}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(520\) |
\(+\) |
\(q+\beta q^{2}+232q^{4}-2^{4}\beta q^{5}+260q^{7}+\cdots\)
|
9.8.c.a |
\(12\) |
\(2.811\) |
\(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
None |
\(-9\) |
\(24\) |
\(-180\) |
\(-84\) |
|
\(q+(-\beta _{2}-\beta _{3})q^{2}+(1-\beta _{1}-\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots\)
|
9.9.b.a |
\(2\) |
\(3.666\) |
\(\Q(\sqrt{-2}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(3304\) |
|
\(q+\beta q^{2}+238q^{4}+233\beta q^{5}+1652q^{7}+\cdots\)
|
9.9.d.a |
\(14\) |
\(3.666\) |
\(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
None |
\(-3\) |
\(-93\) |
\(438\) |
\(922\) |
|
\(q-\beta _{1}q^{2}+(-5-3\beta _{3}+\beta _{4}+\beta _{6})q^{3}+\cdots\)
|
9.10.a.a |
\(1\) |
\(4.635\) |
\(\Q\) |
None |
\(-18\) |
\(0\) |
\(1530\) |
\(9128\) |
\(-\) |
\(q-18q^{2}-188q^{4}+1530q^{5}+9128q^{7}+\cdots\)
|
9.10.a.b |
\(1\) |
\(4.635\) |
\(\Q\) |
\(\Q(\sqrt{-3}) \) |
\(0\) |
\(0\) |
\(0\) |
\(-12580\) |
\(+\) |
\(q-2^{9}q^{4}-12580q^{7}+118370q^{13}+\cdots\)
|
9.10.a.c |
\(1\) |
\(4.635\) |
\(\Q\) |
None |
\(36\) |
\(0\) |
\(1314\) |
\(-4480\) |
\(-\) |
\(q+6^{2}q^{2}+28^{2}q^{4}+1314q^{5}-4480q^{7}+\cdots\)
|
9.10.c.a |
\(16\) |
\(4.635\) |
\(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
None |
\(15\) |
\(-3\) |
\(453\) |
\(-343\) |
|
\(q+(2+\beta _{2}-2\beta _{3})q^{2}+(9-18\beta _{3}+\beta _{5}+\cdots)q^{3}+\cdots\)
|
9.11.b.a |
\(4\) |
\(5.718\) |
\(\Q(\sqrt{-2}, \sqrt{385})\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(-44464\) |
|
\(q-\beta _{1}q^{2}+(-1073-\beta _{2})q^{4}+(-35\beta _{1}+\cdots)q^{5}+\cdots\)
|
9.11.d.a |
\(18\) |
\(5.718\) |
\(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
None |
\(-3\) |
\(51\) |
\(4956\) |
\(-6120\) |
|
\(q-\beta _{3}q^{2}+(3-\beta _{1}+\beta _{3}+\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots\)
|
9.12.a.a |
\(1\) |
\(6.915\) |
\(\Q\) |
None |
\(-78\) |
\(0\) |
\(5370\) |
\(-27760\) |
\(-\) |
\(q-78q^{2}+4036q^{4}+5370q^{5}-27760q^{7}+\cdots\)
|
9.12.a.b |
\(1\) |
\(6.915\) |
\(\Q\) |
None |
\(24\) |
\(0\) |
\(-4830\) |
\(-16744\) |
\(-\) |
\(q+24q^{2}-1472q^{4}-4830q^{5}-16744q^{7}+\cdots\)
|
9.12.a.c |
\(2\) |
\(6.915\) |
\(\Q(\sqrt{70}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(116200\) |
\(+\) |
\(q+\beta q^{2}+472q^{4}+224\beta q^{5}+58100q^{7}+\cdots\)
|
9.12.c.a |
\(20\) |
\(6.915\) |
\(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
None |
\(-33\) |
\(-12\) |
\(-7230\) |
\(8512\) |
|
\(q+(\beta _{1}-3\beta _{3})q^{2}+(24-51\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots\)
|
9.13.b.a |
\(2\) |
\(8.226\) |
\(\Q(\sqrt{-2}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(-223736\) |
|
\(q+8\beta q^{2}-6272q^{4}-2291\beta q^{5}-111868q^{7}+\cdots\)
|
9.13.b.b |
\(2\) |
\(8.226\) |
\(\Q(\sqrt{-2}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(232456\) |
|
\(q+\beta q^{2}+2638q^{4}-175\beta q^{5}+116228q^{7}+\cdots\)
|
9.13.d.a |
\(22\) |
\(8.226\) |
|
None |
\(-3\) |
\(618\) |
\(-15987\) |
\(34319\) |
|
|
9.14.a.a |
\(1\) |
\(9.651\) |
\(\Q\) |
None |
\(12\) |
\(0\) |
\(30210\) |
\(235088\) |
\(-\) |
\(q+12q^{2}-8048q^{4}+30210q^{5}+235088q^{7}+\cdots\)
|
9.14.a.b |
\(2\) |
\(9.651\) |
\(\Q(\sqrt{55}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(-266600\) |
\(+\) |
\(q+\beta q^{2}-272q^{4}-520\beta q^{5}-133300q^{7}+\cdots\)
|
9.14.a.c |
\(2\) |
\(9.651\) |
\(\Q(\sqrt{1969}) \) |
None |
\(54\) |
\(0\) |
\(-40716\) |
\(-21008\) |
\(-\) |
\(q+(3^{3}-\beta )q^{2}+(10258-54\beta )q^{4}+(-20358+\cdots)q^{5}+\cdots\)
|
9.14.c.a |
\(24\) |
\(9.651\) |
|
None |
\(63\) |
\(-732\) |
\(52128\) |
\(-93912\) |
|
|
9.15.b.a |
\(4\) |
\(11.190\) |
\(\Q(\sqrt{-2}, \sqrt{3745})\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(-1065904\) |
|
\(q-\beta _{3}q^{2}+(-833-\beta _{2})q^{4}+(-7\beta _{1}+\cdots)q^{5}+\cdots\)
|
9.15.d.a |
\(26\) |
\(11.190\) |
|
None |
\(-3\) |
\(-2199\) |
\(-107994\) |
\(-146330\) |
|
|
9.16.a.a |
\(1\) |
\(12.842\) |
\(\Q\) |
None |
\(-216\) |
\(0\) |
\(-52110\) |
\(2822456\) |
\(-\) |
\(q-6^{3}q^{2}+13888q^{4}-52110q^{5}+\cdots\)
|
9.16.a.b |
\(1\) |
\(12.842\) |
\(\Q\) |
\(\Q(\sqrt{-3}) \) |
\(0\) |
\(0\) |
\(0\) |
\(1244900\) |
\(+\) |
\(q-2^{15}q^{4}+1244900q^{7}+397771850q^{13}+\cdots\)
|
9.16.a.c |
\(1\) |
\(12.842\) |
\(\Q\) |
None |
\(72\) |
\(0\) |
\(221490\) |
\(-2149000\) |
\(-\) |
\(q+72q^{2}-27584q^{4}+221490q^{5}+\cdots\)
|
9.16.a.d |
\(1\) |
\(12.842\) |
\(\Q\) |
None |
\(234\) |
\(0\) |
\(-280710\) |
\(-1373344\) |
\(-\) |
\(q+234q^{2}+21988q^{4}-280710q^{5}+\cdots\)
|
9.16.a.e |
\(2\) |
\(12.842\) |
\(\Q(\sqrt{370}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(-5182520\) |
\(+\) |
\(q+\beta q^{2}+87112q^{4}+464\beta q^{5}-2591260q^{7}+\cdots\)
|
9.16.c.a |
\(28\) |
\(12.842\) |
|
None |
\(-129\) |
\(3345\) |
\(-152655\) |
\(803705\) |
|
|
9.17.b.a |
\(6\) |
\(14.609\) |
\(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(5400696\) |
|
\(q-\beta _{1}q^{2}+(-61382-\beta _{4})q^{4}+(-189\beta _{1}+\cdots)q^{5}+\cdots\)
|
9.17.d.a |
\(30\) |
\(14.609\) |
|
None |
\(-3\) |
\(2049\) |
\(507588\) |
\(220596\) |
|
|
9.18.a.a |
\(1\) |
\(16.490\) |
\(\Q\) |
None |
\(-204\) |
\(0\) |
\(163554\) |
\(-20846560\) |
\(-\) |
\(q-204q^{2}-89456q^{4}+163554q^{5}+\cdots\)
|
9.18.a.b |
\(1\) |
\(16.490\) |
\(\Q\) |
None |
\(528\) |
\(0\) |
\(1025850\) |
\(3225992\) |
\(-\) |
\(q+528q^{2}+147712q^{4}+1025850q^{5}+\cdots\)
|
9.18.a.c |
\(2\) |
\(16.490\) |
\(\Q(\sqrt{14569}) \) |
None |
\(-594\) |
\(0\) |
\(-382860\) |
\(24471568\) |
\(-\) |
\(q+(-297-\beta )q^{2}+(88258+594\beta )q^{4}+\cdots\)
|
9.18.a.d |
\(2\) |
\(16.490\) |
\(\Q(\sqrt{910}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(-392840\) |
\(+\) |
\(q+\beta q^{2}-2^{5}q^{4}-280\beta q^{5}-196420q^{7}+\cdots\)
|
9.18.c.a |
\(32\) |
\(16.490\) |
|
None |
\(255\) |
\(-2280\) |
\(255678\) |
\(-5846540\) |
|
|
9.19.b.a |
\(6\) |
\(18.485\) |
\(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(19180488\) |
|
\(q+\beta _{1}q^{2}+(-42038-\beta _{2})q^{4}+(1082\beta _{1}+\cdots)q^{5}+\cdots\)
|
9.19.d.a |
\(34\) |
\(18.485\) |
|
None |
\(-3\) |
\(3804\) |
\(2192181\) |
\(4302359\) |
|
|
9.20.a.a |
\(1\) |
\(20.594\) |
\(\Q\) |
None |
\(-456\) |
\(0\) |
\(2377410\) |
\(-16917544\) |
\(-\) |
\(q-456q^{2}-316352q^{4}+2377410q^{5}+\cdots\)
|
9.20.a.b |
\(1\) |
\(20.594\) |
\(\Q\) |
None |
\(1104\) |
\(0\) |
\(-3516270\) |
\(-195590584\) |
\(-\) |
\(q+1104q^{2}+694528q^{4}-3516270q^{5}+\cdots\)
|