7.3.b.a |
\(1\) |
\(0.191\) |
\(\Q\) |
\(\Q(\sqrt{-7}) \) |
\(-3\) |
\(0\) |
\(0\) |
\(-7\) |
\(q-3q^{2}+5q^{4}-7q^{7}-3q^{8}+9q^{9}+\cdots\)
|
8.3.d.a |
\(1\) |
\(0.218\) |
\(\Q\) |
\(\Q(\sqrt{-2}) \) |
\(-2\) |
\(-2\) |
\(0\) |
\(0\) |
\(q-2q^{2}-2q^{3}+4q^{4}+4q^{6}-8q^{8}+\cdots\)
|
9.3.d.a |
\(2\) |
\(0.245\) |
\(\Q(\sqrt{-3}) \) |
None |
\(-3\) |
\(-3\) |
\(6\) |
\(-2\) |
\(q+(-1-\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
|
10.3.c.a |
\(2\) |
\(0.272\) |
\(\Q(\sqrt{-1}) \) |
None |
\(-2\) |
\(-4\) |
\(0\) |
\(4\) |
\(q+(-1-i)q^{2}+(-2+2i)q^{3}+2iq^{4}+\cdots\)
|
11.3.b.a |
\(1\) |
\(0.300\) |
\(\Q\) |
\(\Q(\sqrt{-11}) \) |
\(0\) |
\(-5\) |
\(-1\) |
\(0\) |
\(q-5q^{3}+4q^{4}-q^{5}+2^{4}q^{9}-11q^{11}+\cdots\)
|
11.3.d.a |
\(4\) |
\(0.300\) |
\(\Q(\zeta_{10})\) |
None |
\(-5\) |
\(0\) |
\(-4\) |
\(10\) |
\(q+(-2\zeta_{10}+2\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-2+\cdots)q^{3}+\cdots\)
|
12.3.c.a |
\(1\) |
\(0.327\) |
\(\Q\) |
\(\Q(\sqrt{-3}) \) |
\(0\) |
\(-3\) |
\(0\) |
\(2\) |
\(q-3q^{3}+2q^{7}+9q^{9}-22q^{13}+26q^{19}+\cdots\)
|
12.3.d.a |
\(2\) |
\(0.327\) |
\(\Q(\sqrt{-3}) \) |
None |
\(-2\) |
\(0\) |
\(-4\) |
\(0\) |
\(q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
|
13.3.d.a |
\(4\) |
\(0.354\) |
\(\Q(i, \sqrt{10})\) |
None |
\(-4\) |
\(-4\) |
\(8\) |
\(-12\) |
\(q+(-1+\beta _{1}-\beta _{2})q^{2}+(-1-\beta _{1}+\beta _{3})q^{3}+\cdots\)
|
13.3.f.a |
\(4\) |
\(0.354\) |
\(\Q(\zeta_{12})\) |
None |
\(-2\) |
\(-2\) |
\(-14\) |
\(16\) |
\(q+(-1+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
|
14.3.d.a |
\(4\) |
\(0.381\) |
\(\Q(\sqrt{2}, \sqrt{-3})\) |
None |
\(0\) |
\(-6\) |
\(-6\) |
\(8\) |
\(q+\beta _{1}q^{2}+(-2-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+\cdots\)
|
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 |
\(-4\) |
\(0\) |
\(-4\) |
\(4\) |
\(q+(-1+\beta _{1}-\beta _{2})q^{2}+\beta _{3}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
|
16.3.c.a |
\(1\) |
\(0.436\) |
\(\Q\) |
\(\Q(\sqrt{-1}) \) |
\(0\) |
\(0\) |
\(-6\) |
\(0\) |
\(q-6q^{5}+9q^{9}+10q^{13}-30q^{17}+\cdots\)
|
16.3.f.a |
\(6\) |
\(0.436\) |
6.0.399424.1 |
None |
\(-2\) |
\(-2\) |
\(-2\) |
\(-4\) |
\(q+\beta _{2}q^{2}+(-1-\beta _{2}+\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots\)
|
17.3.e.a |
\(8\) |
\(0.463\) |
\(\Q(\zeta_{16})\) |
None |
\(-8\) |
\(-8\) |
\(16\) |
\(8\) |
\(q+(-1+\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
|
17.3.e.b |
\(8\) |
\(0.463\) |
\(\Q(\zeta_{16})\) |
None |
\(0\) |
\(0\) |
\(-24\) |
\(-16\) |
\(q+(-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(2\zeta_{16}^{2}+\cdots)q^{3}+\cdots\)
|
18.3.b.a |
\(2\) |
\(0.490\) |
\(\Q(\sqrt{-2}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(-8\) |
\(q+\beta q^{2}-2q^{4}-3\beta q^{5}-4q^{7}-2\beta q^{8}+\cdots\)
|
18.3.d.a |
\(4\) |
\(0.490\) |
\(\Q(\sqrt{-2}, \sqrt{-3})\) |
None |
\(0\) |
\(0\) |
\(-18\) |
\(2\) |
\(q+\beta _{1}q^{2}+(1-2\beta _{1}-2\beta _{2}+\beta _{3})q^{3}+\cdots\)
|
19.3.b.a |
\(1\) |
\(0.518\) |
\(\Q\) |
\(\Q(\sqrt{-19}) \) |
\(0\) |
\(0\) |
\(-9\) |
\(-5\) |
\(q+4q^{4}-9q^{5}-5q^{7}+9q^{9}+3q^{11}+\cdots\)
|
19.3.b.b |
\(2\) |
\(0.518\) |
\(\Q(\sqrt{-13}) \) |
None |
\(0\) |
\(0\) |
\(8\) |
\(-10\) |
\(q+\beta q^{2}-\beta q^{3}-9q^{4}+4q^{5}+13q^{6}+\cdots\)
|
19.3.d.a |
\(6\) |
\(0.518\) |
6.0.6967728.1 |
None |
\(-3\) |
\(-9\) |
\(-2\) |
\(0\) |
\(q+(-1-\beta _{5})q^{2}+(\beta _{1}+2\beta _{2}+\beta _{3}+\beta _{5})q^{3}+\cdots\)
|
19.3.f.a |
\(12\) |
\(0.518\) |
\(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
None |
\(-6\) |
\(0\) |
\(-6\) |
\(6\) |
\(q+\beta _{10}q^{2}+(\beta _{1}-\beta _{4}-\beta _{5}+\beta _{6}-\beta _{7}+\cdots)q^{3}+\cdots\)
|
20.3.b.a |
\(4\) |
\(0.545\) |
\(\Q(\zeta_{10})\) |
None |
\(-2\) |
\(0\) |
\(0\) |
\(0\) |
\(q-\zeta_{10}^{2}q^{2}+\zeta_{10}^{3}q^{3}+(-2-\zeta_{10}+\cdots)q^{4}+\cdots\)
|
20.3.d.a |
\(1\) |
\(0.545\) |
\(\Q\) |
\(\Q(\sqrt{-5}) \) |
\(-2\) |
\(4\) |
\(-5\) |
\(-4\) |
\(q-2q^{2}+4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots\)
|
20.3.d.b |
\(1\) |
\(0.545\) |
\(\Q\) |
\(\Q(\sqrt{-5}) \) |
\(2\) |
\(-4\) |
\(-5\) |
\(4\) |
\(q+2q^{2}-4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots\)
|
20.3.d.c |
\(2\) |
\(0.545\) |
\(\Q(\sqrt{-1}) \) |
\(\Q(\sqrt{-1}) \) |
\(0\) |
\(0\) |
\(6\) |
\(0\) |
\(q+iq^{2}-4q^{4}+(3-2i)q^{5}-4iq^{8}+\cdots\)
|
20.3.f.a |
\(2\) |
\(0.545\) |
\(\Q(\sqrt{-1}) \) |
None |
\(0\) |
\(2\) |
\(-6\) |
\(-14\) |
\(q+(1-i)q^{3}+(-3+4i)q^{5}+(-7-7i)q^{7}+\cdots\)
|
21.3.b.a |
\(4\) |
\(0.572\) |
4.0.65856.1 |
None |
\(0\) |
\(-2\) |
\(0\) |
\(0\) |
\(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(-3+\cdots)q^{4}+\cdots\)
|
21.3.d.a |
\(2\) |
\(0.572\) |
\(\Q(\sqrt{-3}) \) |
None |
\(2\) |
\(0\) |
\(0\) |
\(2\) |
\(q+q^{2}+\zeta_{6}q^{3}-3q^{4}-4\zeta_{6}q^{5}+\zeta_{6}q^{6}+\cdots\)
|
21.3.f.a |
\(2\) |
\(0.572\) |
\(\Q(\sqrt{-3}) \) |
None |
\(-3\) |
\(-3\) |
\(9\) |
\(13\) |
\(q-3\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(-5+5\zeta_{6})q^{4}+\cdots\)
|
21.3.f.b |
\(2\) |
\(0.572\) |
\(\Q(\sqrt{-3}) \) |
None |
\(-1\) |
\(3\) |
\(-9\) |
\(-7\) |
\(q-\zeta_{6}q^{2}+(1+\zeta_{6})q^{3}+(3-3\zeta_{6})q^{4}+\cdots\)
|
21.3.f.c |
\(2\) |
\(0.572\) |
\(\Q(\sqrt{-3}) \) |
None |
\(2\) |
\(-3\) |
\(-6\) |
\(-7\) |
\(q+2\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+\cdots\)
|
21.3.h.a |
\(2\) |
\(0.572\) |
\(\Q(\sqrt{-3}) \) |
\(\Q(\sqrt{-3}) \) |
\(0\) |
\(3\) |
\(0\) |
\(-13\) |
\(q+3\zeta_{6}q^{3}-4\zeta_{6}q^{4}+(-5-3\zeta_{6})q^{7}+\cdots\)
|
21.3.h.b |
\(4\) |
\(0.572\) |
\(\Q(\sqrt{-3}, \sqrt{-5})\) |
None |
\(0\) |
\(-4\) |
\(0\) |
\(14\) |
\(q+\beta _{1}q^{2}+(-\beta _{1}-2\beta _{2}+\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots\)
|
22.3.b.a |
\(2\) |
\(0.599\) |
\(\Q(\sqrt{-2}) \) |
None |
\(0\) |
\(2\) |
\(-2\) |
\(0\) |
\(q+\beta q^{2}+q^{3}-2q^{4}-q^{5}+\beta q^{6}-6\beta q^{7}+\cdots\)
|
22.3.d.a |
\(8\) |
\(0.599\) |
8.0.64000000.1 |
None |
\(0\) |
\(-2\) |
\(2\) |
\(-30\) |
\(q+\beta _{1}q^{2}+(1-\beta _{1}-2\beta _{2}+\beta _{3}+2\beta _{4}+\cdots)q^{3}+\cdots\)
|
23.3.b.a |
\(3\) |
\(0.627\) |
3.3.621.1 |
\(\Q(\sqrt{-23}) \) |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
\(q+(\beta _{1}+\beta _{2})q^{2}+(-2\beta _{1}-\beta _{2})q^{3}+(4+\cdots)q^{4}+\cdots\)
|
23.3.d.a |
\(30\) |
\(0.627\) |
|
None |
\(-11\) |
\(-11\) |
\(-11\) |
\(-11\) |
|
24.3.b.a |
\(4\) |
\(0.654\) |
4.0.4752.1 |
None |
\(2\) |
\(0\) |
\(0\) |
\(0\) |
\(q+(\beta _{1}-\beta _{2})q^{2}+\beta _{2}q^{3}+(-2-\beta _{2}+\cdots)q^{4}+\cdots\)
|
24.3.e.a |
\(2\) |
\(0.654\) |
\(\Q(\sqrt{-2}) \) |
None |
\(0\) |
\(2\) |
\(0\) |
\(-12\) |
\(q+(1+\beta )q^{3}-2\beta q^{5}-6q^{7}+(-7+2\beta )q^{9}+\cdots\)
|
24.3.h.a |
\(1\) |
\(0.654\) |
\(\Q\) |
\(\Q(\sqrt{-6}) \) |
\(-2\) |
\(3\) |
\(2\) |
\(-10\) |
\(q-2q^{2}+3q^{3}+4q^{4}+2q^{5}-6q^{6}+\cdots\)
|
24.3.h.b |
\(1\) |
\(0.654\) |
\(\Q\) |
\(\Q(\sqrt{-6}) \) |
\(2\) |
\(-3\) |
\(-2\) |
\(-10\) |
\(q+2q^{2}-3q^{3}+4q^{4}-2q^{5}-6q^{6}+\cdots\)
|
24.3.h.c |
\(4\) |
\(0.654\) |
\(\Q(\sqrt{2}, \sqrt{-7})\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(16\) |
\(q+\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(-3+\beta _{3})q^{4}+\cdots\)
|
25.3.c.a |
\(4\) |
\(0.681\) |
\(\Q(i, \sqrt{6})\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
\(q+\beta _{1}q^{2}+\beta _{3}q^{3}-\beta _{2}q^{4}-3q^{6}-4\beta _{1}q^{7}+\cdots\)
|
25.3.f.a |
\(32\) |
\(0.681\) |
|
None |
\(-10\) |
\(-10\) |
\(-10\) |
\(-10\) |
|
26.3.d.a |
\(2\) |
\(0.708\) |
\(\Q(\sqrt{-1}) \) |
None |
\(2\) |
\(0\) |
\(-6\) |
\(4\) |
\(q+(1+i)q^{2}+2iq^{4}+(-3-3i)q^{5}+\cdots\)
|
26.3.f.a |
\(4\) |
\(0.708\) |
\(\Q(\zeta_{12})\) |
None |
\(2\) |
\(0\) |
\(0\) |
\(-22\) |
\(q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots\)
|