8.3.d.a |
\(1\) |
\(0.218\) |
\(\Q\) |
\(\Q(\sqrt{-2}) \) |
\(-2\) |
\(-2\) |
\(0\) |
\(0\) |
|
\(q-2q^{2}-2q^{3}+4q^{4}+4q^{6}-8q^{8}+\cdots\)
|
8.4.a.a |
\(1\) |
\(0.472\) |
\(\Q\) |
None |
\(0\) |
\(-4\) |
\(-2\) |
\(24\) |
\(+\) |
\(q-4q^{3}-2q^{5}+24q^{7}-11q^{9}-44q^{11}+\cdots\)
|
8.4.b.a |
\(2\) |
\(0.472\) |
\(\Q(\sqrt{-7}) \) |
None |
\(-2\) |
\(0\) |
\(0\) |
\(-16\) |
|
\(q+(-1-\beta )q^{2}+2\beta q^{3}+(-6+2\beta )q^{4}+\cdots\)
|
8.5.d.a |
\(1\) |
\(0.827\) |
\(\Q\) |
\(\Q(\sqrt{-2}) \) |
\(4\) |
\(-14\) |
\(0\) |
\(0\) |
|
\(q+4q^{2}-14q^{3}+2^{4}q^{4}-56q^{6}+2^{6}q^{8}+\cdots\)
|
8.5.d.b |
\(2\) |
\(0.827\) |
\(\Q(\sqrt{-15}) \) |
None |
\(-2\) |
\(12\) |
\(0\) |
\(0\) |
|
\(q+(-1-\beta )q^{2}+6q^{3}+(-14+2\beta )q^{4}+\cdots\)
|
8.6.a.a |
\(1\) |
\(1.283\) |
\(\Q\) |
None |
\(0\) |
\(20\) |
\(-74\) |
\(-24\) |
\(-\) |
\(q+20q^{3}-74q^{5}-24q^{7}+157q^{9}+\cdots\)
|
8.6.b.a |
\(4\) |
\(1.283\) |
4.0.218489.1 |
None |
\(-2\) |
\(0\) |
\(0\) |
\(96\) |
|
\(q+(-1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(5+\cdots)q^{4}+\cdots\)
|
8.7.d.a |
\(1\) |
\(1.840\) |
\(\Q\) |
\(\Q(\sqrt{-2}) \) |
\(-8\) |
\(46\) |
\(0\) |
\(0\) |
|
\(q-8q^{2}+46q^{3}+2^{6}q^{4}-368q^{6}+\cdots\)
|
8.7.d.b |
\(4\) |
\(1.840\) |
4.0.3803625.2 |
None |
\(2\) |
\(-48\) |
\(0\) |
\(0\) |
|
\(q+\beta _{1}q^{2}+(-13+2\beta _{1}+\beta _{2})q^{3}+(-12+\cdots)q^{4}+\cdots\)
|
8.8.a.a |
\(1\) |
\(2.499\) |
\(\Q\) |
None |
\(0\) |
\(-84\) |
\(-82\) |
\(-456\) |
\(-\) |
\(q-84q^{3}-82q^{5}-456q^{7}+4869q^{9}+\cdots\)
|
8.8.a.b |
\(1\) |
\(2.499\) |
\(\Q\) |
None |
\(0\) |
\(44\) |
\(430\) |
\(-1224\) |
\(+\) |
\(q+44q^{3}+430q^{5}-1224q^{7}-251q^{9}+\cdots\)
|
8.8.b.a |
\(6\) |
\(2.499\) |
\(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
None |
\(6\) |
\(0\) |
\(0\) |
\(-688\) |
|
\(q+(1+\beta _{1})q^{2}+\beta _{4}q^{3}+(19+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
|
8.9.d.a |
\(1\) |
\(3.259\) |
\(\Q\) |
\(\Q(\sqrt{-2}) \) |
\(16\) |
\(34\) |
\(0\) |
\(0\) |
|
\(q+2^{4}q^{2}+34q^{3}+2^{8}q^{4}+544q^{6}+\cdots\)
|
8.9.d.b |
\(6\) |
\(3.259\) |
\(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
None |
\(-14\) |
\(-36\) |
\(0\) |
\(0\) |
|
\(q+(-2+\beta _{1})q^{2}+(-6-\beta _{1}-\beta _{2})q^{3}+\cdots\)
|
8.10.a.a |
\(1\) |
\(4.120\) |
\(\Q\) |
None |
\(0\) |
\(-60\) |
\(-2074\) |
\(-4344\) |
\(+\) |
\(q-60q^{3}-2074q^{5}-4344q^{7}-16083q^{9}+\cdots\)
|
8.10.a.b |
\(1\) |
\(4.120\) |
\(\Q\) |
None |
\(0\) |
\(68\) |
\(1510\) |
\(10248\) |
\(-\) |
\(q+68q^{3}+1510q^{5}+10248q^{7}-15059q^{9}+\cdots\)
|
8.10.b.a |
\(8\) |
\(4.120\) |
\(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
None |
\(-18\) |
\(0\) |
\(0\) |
\(4800\) |
|
\(q+(-2-\beta _{1})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(-54+\cdots)q^{4}+\cdots\)
|
8.11.d.a |
\(1\) |
\(5.083\) |
\(\Q\) |
\(\Q(\sqrt{-2}) \) |
\(-32\) |
\(-482\) |
\(0\) |
\(0\) |
|
\(q-2^{5}q^{2}-482q^{3}+2^{10}q^{4}+15424q^{6}+\cdots\)
|
8.11.d.b |
\(8\) |
\(5.083\) |
\(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
None |
\(42\) |
\(480\) |
\(0\) |
\(0\) |
|
\(q+(5-\beta _{1})q^{2}+(60+\beta _{1}+\beta _{2})q^{3}+(5^{2}+\cdots)q^{4}+\cdots\)
|
8.12.a.a |
\(1\) |
\(6.147\) |
\(\Q\) |
None |
\(0\) |
\(-36\) |
\(-3490\) |
\(-55464\) |
\(-\) |
\(q-6^{2}q^{3}-3490q^{5}-55464q^{7}-175851q^{9}+\cdots\)
|
8.12.a.b |
\(2\) |
\(6.147\) |
\(\Q(\sqrt{109}) \) |
None |
\(0\) |
\(56\) |
\(7868\) |
\(91056\) |
\(+\) |
\(q+(28+\beta )q^{3}+(3934-12\beta )q^{5}+(45528+\cdots)q^{7}+\cdots\)
|
8.12.b.a |
\(10\) |
\(6.147\) |
\(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
None |
\(22\) |
\(0\) |
\(0\) |
\(-33616\) |
|
\(q+(2+\beta _{1})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(43+2\beta _{1}+\cdots)q^{4}+\cdots\)
|
8.13.d.a |
\(1\) |
\(7.312\) |
\(\Q\) |
\(\Q(\sqrt{-2}) \) |
\(64\) |
\(658\) |
\(0\) |
\(0\) |
|
\(q+2^{6}q^{2}+658q^{3}+2^{12}q^{4}+42112q^{6}+\cdots\)
|
8.13.d.b |
\(10\) |
\(7.312\) |
\(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
None |
\(-110\) |
\(-660\) |
\(0\) |
\(0\) |
|
\(q+(-11-\beta _{1})q^{2}+(-66+3\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
|
8.14.a.a |
\(1\) |
\(8.578\) |
\(\Q\) |
None |
\(0\) |
\(-12\) |
\(-4330\) |
\(-139992\) |
\(+\) |
\(q-12q^{3}-4330q^{5}-139992q^{7}+\cdots\)
|
8.14.a.b |
\(2\) |
\(8.578\) |
\(\Q(\sqrt{781}) \) |
None |
\(0\) |
\(872\) |
\(18476\) |
\(110928\) |
\(-\) |
\(q+(436-\beta )q^{3}+(9238-12\beta )q^{5}+(55464+\cdots)q^{7}+\cdots\)
|
8.14.b.a |
\(2\) |
\(8.578\) |
\(\Q(\sqrt{-79}) \) |
None |
\(-112\) |
\(0\) |
\(0\) |
\(-351664\) |
|
\(q+(-56-4\beta )q^{2}+129\beta q^{3}+(-1920+\cdots)q^{4}+\cdots\)
|
8.14.b.b |
\(10\) |
\(8.578\) |
\(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
None |
\(110\) |
\(0\) |
\(0\) |
\(586960\) |
|
\(q+(11+\beta _{1})q^{2}+(3\beta _{1}+\beta _{3})q^{3}+(-472+\cdots)q^{4}+\cdots\)
|
8.15.d.a |
\(1\) |
\(9.946\) |
\(\Q\) |
\(\Q(\sqrt{-2}) \) |
\(-128\) |
\(3022\) |
\(0\) |
\(0\) |
|
\(q-2^{7}q^{2}+3022q^{3}+2^{14}q^{4}-386816q^{6}+\cdots\)
|
8.15.d.b |
\(12\) |
\(9.946\) |
\(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
None |
\(218\) |
\(-3024\) |
\(0\) |
\(0\) |
|
\(q+(18+\beta _{1})q^{2}+(-252+3\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots\)
|
8.16.a.a |
\(1\) |
\(11.415\) |
\(\Q\) |
None |
\(0\) |
\(-3444\) |
\(313358\) |
\(-2324616\) |
\(-\) |
\(q-3444q^{3}+313358q^{5}-2324616q^{7}+\cdots\)
|
8.16.a.b |
\(1\) |
\(11.415\) |
\(\Q\) |
None |
\(0\) |
\(2700\) |
\(-251890\) |
\(1374072\) |
\(-\) |
\(q+2700q^{3}-251890q^{5}+1374072q^{7}+\cdots\)
|
8.16.a.c |
\(2\) |
\(11.415\) |
\(\Q(\sqrt{58}) \) |
None |
\(0\) |
\(-4072\) |
\(-140260\) |
\(126192\) |
\(+\) |
\(q+(-2036+\beta )q^{3}+(-70130+6^{2}\beta )q^{5}+\cdots\)
|
8.16.b.a |
\(14\) |
\(11.415\) |
\(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
None |
\(-90\) |
\(0\) |
\(0\) |
\(-1647088\) |
|
\(q+(-6-\beta _{1})q^{2}+\beta _{2}q^{3}+(3672+5\beta _{1}+\cdots)q^{4}+\cdots\)
|
8.17.d.a |
\(1\) |
\(12.986\) |
\(\Q\) |
\(\Q(\sqrt{-2}) \) |
\(256\) |
\(-11966\) |
\(0\) |
\(0\) |
|
\(q+2^{8}q^{2}-11966q^{3}+2^{16}q^{4}-3063296q^{6}+\cdots\)
|
8.17.d.b |
\(14\) |
\(12.986\) |
\(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
None |
\(-350\) |
\(11964\) |
\(0\) |
\(0\) |
|
\(q+(-5^{2}-\beta _{1})q^{2}+(855-6\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots\)
|
8.18.a.a |
\(2\) |
\(14.658\) |
\(\Q(\sqrt{2146}) \) |
None |
\(0\) |
\(-952\) |
\(-53620\) |
\(-333168\) |
\(-\) |
\(q+(-476+\beta )q^{3}+(-26810+60\beta )q^{5}+\cdots\)
|
8.18.a.b |
\(2\) |
\(14.658\) |
\(\Q(\sqrt{114}) \) |
None |
\(0\) |
\(11592\) |
\(-791924\) |
\(-18932592\) |
\(+\) |
\(q+(5796+\beta )q^{3}+(-395962-68\beta )q^{5}+\cdots\)
|
8.18.b.a |
\(16\) |
\(14.658\) |
\(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
None |
\(270\) |
\(0\) |
\(0\) |
\(11529600\) |
|
\(q+(17-\beta _{1})q^{2}+(3\beta _{1}-\beta _{2})q^{3}+(-1712+\cdots)q^{4}+\cdots\)
|
8.19.d.a |
\(1\) |
\(16.431\) |
\(\Q\) |
\(\Q(\sqrt{-2}) \) |
\(-512\) |
\(-3266\) |
\(0\) |
\(0\) |
|
\(q-2^{9}q^{2}-3266q^{3}+2^{18}q^{4}+1672192q^{6}+\cdots\)
|
8.19.d.b |
\(16\) |
\(16.431\) |
\(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
None |
\(426\) |
\(3264\) |
\(0\) |
\(0\) |
|
\(q+(3^{3}+\beta _{1})q^{2}+(203-4\beta _{1}-\beta _{2})q^{3}+\cdots\)
|
8.20.a.a |
\(2\) |
\(18.305\) |
\(\Q(\sqrt{1453}) \) |
None |
\(0\) |
\(-27912\) |
\(1226620\) |
\(88510512\) |
\(-\) |
\(q+(-13956-\beta )q^{3}+(613310+44\beta )q^{5}+\cdots\)
|
8.20.a.b |
\(3\) |
\(18.305\) |
\(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
None |
\(0\) |
\(23732\) |
\(2140218\) |
\(55851720\) |
\(+\) |
\(q+(7911-\beta _{1})q^{3}+(713429-70\beta _{1}+\cdots)q^{5}+\cdots\)
|
8.20.b.a |
\(18\) |
\(18.305\) |
\(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
None |
\(-458\) |
\(0\) |
\(0\) |
\(-80707216\) |
|
\(q+(-5^{2}+\beta _{1})q^{2}+(2+5\beta _{1}-\beta _{2})q^{3}+\cdots\)
|
8.21.d.a |
\(1\) |
\(20.281\) |
\(\Q\) |
\(\Q(\sqrt{-2}) \) |
\(1024\) |
\(114226\) |
\(0\) |
\(0\) |
|
\(q+2^{10}q^{2}+114226q^{3}+2^{20}q^{4}+\cdots\)
|
8.21.d.b |
\(18\) |
\(20.281\) |
\(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
None |
\(-398\) |
\(-114228\) |
\(0\) |
\(0\) |
|
\(q+(-22+\beta _{1})q^{2}+(-6347-5\beta _{1}+\cdots)q^{3}+\cdots\)
|
8.22.a.a |
\(2\) |
\(22.358\) |
\(\Q(\sqrt{358549}) \) |
None |
\(0\) |
\(-105432\) |
\(2108140\) |
\(444771792\) |
\(+\) |
\(q+(-52716-\beta )q^{3}+(1054070+20\beta )q^{5}+\cdots\)
|
8.22.a.b |
\(3\) |
\(22.358\) |
\(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
None |
\(0\) |
\(96764\) |
\(-24111774\) |
\(295988280\) |
\(-\) |
\(q+(32255-\beta _{1})q^{3}+(-8037261+9\beta _{1}+\cdots)q^{5}+\cdots\)
|
8.22.b.a |
\(20\) |
\(22.358\) |
\(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
None |
\(286\) |
\(0\) |
\(0\) |
\(564950496\) |
|
\(q+(14-\beta _{1})q^{2}+(1+3\beta _{1}-\beta _{2})q^{3}+\cdots\)
|
8.23.d.a |
\(1\) |
\(24.537\) |
\(\Q\) |
\(\Q(\sqrt{-2}) \) |
\(-2048\) |
\(-199058\) |
\(0\) |
\(0\) |
|
\(q-2^{11}q^{2}-199058q^{3}+2^{22}q^{4}+\cdots\)
|