| Orbit label |
Conrey labels |
Modulus |
Conductor |
Order |
Kernel field |
Value field |
Parity |
Real |
Primitive |
Minimal |
| 1600.a |
\(\chi_{1600}(1, \cdot)\)
|
$1600$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
|
| 1600.b |
\(\chi_{1600}(1151, \cdot)\)
|
$1600$ |
$4$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
\(\Q\) |
odd |
✓ |
|
|
| 1600.c |
\(\chi_{1600}(449, \cdot)\)
|
$1600$ |
$5$ |
$2$ |
\(\Q(\sqrt{5}) \) |
\(\Q\) |
even |
✓ |
|
|
| 1600.d |
\(\chi_{1600}(801, \cdot)\)
|
$1600$ |
$8$ |
$2$ |
\(\Q(\sqrt{2}) \) |
\(\Q\) |
even |
✓ |
|
✓ |
| 1600.e |
\(\chi_{1600}(799, \cdot)\)
|
$1600$ |
$40$ |
$2$ |
\(\Q(\sqrt{-10}) \) |
\(\Q\) |
odd |
✓ |
|
|
| 1600.f |
\(\chi_{1600}(1249, \cdot)\)
|
$1600$ |
$40$ |
$2$ |
\(\Q(\sqrt{10}) \) |
\(\Q\) |
even |
✓ |
|
|
| 1600.g |
\(\chi_{1600}(351, \cdot)\)
|
$1600$ |
$8$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 1600.h |
\(\chi_{1600}(1599, \cdot)\)
|
$1600$ |
$20$ |
$2$ |
\(\Q(\sqrt{-5}) \) |
\(\Q\) |
odd |
✓ |
|
|
| 1600.i |
\(\chi_{1600}(593, \cdot)\)$,$ \(\chi_{1600}(1457, \cdot)\)
|
$1600$ |
$80$ |
$4$ |
4.0.256000.4 |
\(\mathbb{Q}(i)\) |
odd |
|
|
|
| 1600.j |
\(\chi_{1600}(143, \cdot)\)$,$ \(\chi_{1600}(1007, \cdot)\)
|
$1600$ |
$80$ |
$4$ |
4.4.256000.2 |
\(\mathbb{Q}(i)\) |
even |
|
|
|
| 1600.k |
\(\chi_{1600}(399, \cdot)\)$,$ \(\chi_{1600}(1199, \cdot)\)
|
$1600$ |
$80$ |
$4$ |
4.0.51200.2 |
\(\mathbb{Q}(i)\) |
odd |
|
|
|
| 1600.l |
\(\chi_{1600}(401, \cdot)\)$,$ \(\chi_{1600}(1201, \cdot)\)
|
$1600$ |
$16$ |
$4$ |
\(\Q(\zeta_{16})^+\) |
\(\mathbb{Q}(i)\) |
even |
|
|
|
| 1600.m |
\(\chi_{1600}(993, \cdot)\)$,$ \(\chi_{1600}(1057, \cdot)\)
|
$1600$ |
$40$ |
$4$ |
4.0.8000.2 |
\(\mathbb{Q}(i)\) |
odd |
|
|
✓ |
| 1600.n |
\(\chi_{1600}(1343, \cdot)\)$,$ \(\chi_{1600}(1407, \cdot)\)
|
$1600$ |
$20$ |
$4$ |
\(\Q(\zeta_{20})^+\) |
\(\mathbb{Q}(i)\) |
even |
|
|
|
| 1600.o |
\(\chi_{1600}(543, \cdot)\)$,$ \(\chi_{1600}(607, \cdot)\)
|
$1600$ |
$40$ |
$4$ |
4.4.8000.1 |
\(\mathbb{Q}(i)\) |
even |
|
|
✓ |
| 1600.p |
\(\chi_{1600}(193, \cdot)\)$,$ \(\chi_{1600}(257, \cdot)\)
|
$1600$ |
$5$ |
$4$ |
\(\Q(\zeta_{5})\) |
\(\mathbb{Q}(i)\) |
odd |
|
|
|
| 1600.q |
\(\chi_{1600}(49, \cdot)\)$,$ \(\chi_{1600}(849, \cdot)\)
|
$1600$ |
$80$ |
$4$ |
4.4.51200.1 |
\(\mathbb{Q}(i)\) |
even |
|
|
|
| 1600.r |
\(\chi_{1600}(751, \cdot)\)$,$ \(\chi_{1600}(1551, \cdot)\)
|
$1600$ |
$16$ |
$4$ |
4.0.2048.2 |
\(\mathbb{Q}(i)\) |
odd |
|
|
|
| 1600.s |
\(\chi_{1600}(207, \cdot)\)$,$ \(\chi_{1600}(943, \cdot)\)
|
$1600$ |
$80$ |
$4$ |
4.4.256000.1 |
\(\mathbb{Q}(i)\) |
even |
|
|
|
| 1600.t |
\(\chi_{1600}(657, \cdot)\)$,$ \(\chi_{1600}(1393, \cdot)\)
|
$1600$ |
$80$ |
$4$ |
4.0.256000.2 |
\(\mathbb{Q}(i)\) |
odd |
|
|
|
| 1600.u |
\(\chi_{1600}(321, \cdot)\)$, \cdots ,$\(\chi_{1600}(1281, \cdot)\)
|
$1600$ |
$25$ |
$5$ |
5.5.390625.1 |
\(\Q(\zeta_{5})\) |
even |
|
|
|
| 1600.v |
\(\chi_{1600}(407, \cdot)\)$, \cdots ,$\(\chi_{1600}(1543, \cdot)\)
|
$1600$ |
$160$ |
$8$ |
8.8.33554432000000.2 |
\(\Q(\zeta_{8})\) |
even |
|
|
|
| 1600.w |
\(\chi_{1600}(57, \cdot)\)$, \cdots ,$\(\chi_{1600}(1193, \cdot)\)
|
$1600$ |
$160$ |
$8$ |
8.0.33554432000000.1 |
\(\Q(\zeta_{8})\) |
odd |
|
|
|
| 1600.x |
\(\chi_{1600}(151, \cdot)\)$, \cdots ,$\(\chi_{1600}(1351, \cdot)\)
|
$1600$ |
$32$ |
$8$ |
8.0.2147483648.1 |
\(\Q(\zeta_{8})\) |
odd |
|
|
|
| 1600.y |
\(\chi_{1600}(201, \cdot)\)$, \cdots ,$\(\chi_{1600}(1401, \cdot)\)
|
$1600$ |
$32$ |
$8$ |
\(\Q(\zeta_{32})^+\) |
\(\Q(\zeta_{8})\) |
even |
|
|
|
| 1600.z |
\(\chi_{1600}(199, \cdot)\)$, \cdots ,$\(\chi_{1600}(1399, \cdot)\)
|
$1600$ |
$160$ |
$8$ |
8.0.1342177280000.1 |
\(\Q(\zeta_{8})\) |
odd |
|
|
|
| 1600.ba |
\(\chi_{1600}(249, \cdot)\)$, \cdots ,$\(\chi_{1600}(1449, \cdot)\)
|
$1600$ |
$160$ |
$8$ |
8.8.1342177280000.1 |
\(\Q(\zeta_{8})\) |
even |
|
|
|
| 1600.bb |
\(\chi_{1600}(7, \cdot)\)$, \cdots ,$\(\chi_{1600}(1143, \cdot)\)
|
$1600$ |
$160$ |
$8$ |
8.8.33554432000000.1 |
\(\Q(\zeta_{8})\) |
even |
|
|
|
| 1600.bc |
\(\chi_{1600}(457, \cdot)\)$, \cdots ,$\(\chi_{1600}(1593, \cdot)\)
|
$1600$ |
$160$ |
$8$ |
8.0.33554432000000.2 |
\(\Q(\zeta_{8})\) |
odd |
|
|
|
| 1600.bd |
\(\chi_{1600}(31, \cdot)\)$, \cdots ,$\(\chi_{1600}(1311, \cdot)\)
|
$1600$ |
$200$ |
$10$ |
10.0.5000000000000000.1 |
\(\Q(\zeta_{5})\) |
odd |
|
|
✓ |
| 1600.be |
\(\chi_{1600}(289, \cdot)\)$, \cdots ,$\(\chi_{1600}(1569, \cdot)\)
|
$1600$ |
$200$ |
$10$ |
10.10.25000000000000000.1 |
\(\Q(\zeta_{5})\) |
even |
|
|
✓ |
| 1600.bf |
\(\chi_{1600}(319, \cdot)\)$, \cdots ,$\(\chi_{1600}(1279, \cdot)\)
|
$1600$ |
$100$ |
$10$ |
10.0.781250000000000.1 |
\(\Q(\zeta_{5})\) |
odd |
|
|
|
| 1600.bg |
\(\chi_{1600}(129, \cdot)\)$, \cdots ,$\(\chi_{1600}(1409, \cdot)\)
|
$1600$ |
$25$ |
$10$ |
\(\Q(\zeta_{25})^+\) |
\(\Q(\zeta_{5})\) |
even |
|
|
|
| 1600.bh |
\(\chi_{1600}(191, \cdot)\)$, \cdots ,$\(\chi_{1600}(1471, \cdot)\)
|
$1600$ |
$100$ |
$10$ |
10.0.156250000000000.1 |
\(\Q(\zeta_{5})\) |
odd |
|
|
|
| 1600.bi |
\(\chi_{1600}(159, \cdot)\)$, \cdots ,$\(\chi_{1600}(1439, \cdot)\)
|
$1600$ |
$200$ |
$10$ |
10.0.25000000000000000.1 |
\(\Q(\zeta_{5})\) |
odd |
|
|
✓ |
| 1600.bj |
\(\chi_{1600}(161, \cdot)\)$, \cdots ,$\(\chi_{1600}(1441, \cdot)\)
|
$1600$ |
$200$ |
$10$ |
10.10.5000000000000000.1 |
\(\Q(\zeta_{5})\) |
even |
|
|
✓ |
| 1600.bk |
\(\chi_{1600}(157, \cdot)\)$, \cdots ,$\(\chi_{1600}(1493, \cdot)\)
|
$1600$ |
$320$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
odd |
|
|
✓ |
| 1600.bl |
\(\chi_{1600}(43, \cdot)\)$, \cdots ,$\(\chi_{1600}(1507, \cdot)\)
|
$1600$ |
$320$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
even |
|
|
✓ |
| 1600.bm |
\(\chi_{1600}(101, \cdot)\)$, \cdots ,$\(\chi_{1600}(1501, \cdot)\)
|
$1600$ |
$64$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
even |
|
|
✓ |
| 1600.bn |
\(\chi_{1600}(149, \cdot)\)$, \cdots ,$\(\chi_{1600}(1549, \cdot)\)
|
$1600$ |
$320$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
even |
|
|
|
| 1600.bo |
\(\chi_{1600}(51, \cdot)\)$, \cdots ,$\(\chi_{1600}(1451, \cdot)\)
|
$1600$ |
$64$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
odd |
|
|
✓ |
| 1600.bp |
\(\chi_{1600}(99, \cdot)\)$, \cdots ,$\(\chi_{1600}(1499, \cdot)\)
|
$1600$ |
$320$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
odd |
|
|
|
| 1600.bq |
\(\chi_{1600}(93, \cdot)\)$, \cdots ,$\(\chi_{1600}(1557, \cdot)\)
|
$1600$ |
$320$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
odd |
|
|
✓ |
| 1600.br |
\(\chi_{1600}(107, \cdot)\)$, \cdots ,$\(\chi_{1600}(1443, \cdot)\)
|
$1600$ |
$320$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
even |
|
|
✓ |
| 1600.bs |
\(\chi_{1600}(17, \cdot)\)$, \cdots ,$\(\chi_{1600}(1297, \cdot)\)
|
$1600$ |
$400$ |
$20$ |
not computed |
\(\Q(\zeta_{20})\) |
odd |
|
|
|
| 1600.bt |
\(\chi_{1600}(303, \cdot)\)$, \cdots ,$\(\chi_{1600}(1583, \cdot)\)
|
$1600$ |
$400$ |
$20$ |
not computed |
\(\Q(\zeta_{20})\) |
even |
|
|
|
| 1600.bu |
\(\chi_{1600}(81, \cdot)\)$, \cdots ,$\(\chi_{1600}(1521, \cdot)\)
|
$1600$ |
$400$ |
$20$ |
not computed |
\(\Q(\zeta_{20})\) |
even |
|
|
|
| 1600.bv |
\(\chi_{1600}(79, \cdot)\)$, \cdots ,$\(\chi_{1600}(1519, \cdot)\)
|
$1600$ |
$400$ |
$20$ |
not computed |
\(\Q(\zeta_{20})\) |
odd |
|
|
|
| 1600.bw |
\(\chi_{1600}(513, \cdot)\)$, \cdots ,$\(\chi_{1600}(1537, \cdot)\)
|
$1600$ |
$25$ |
$20$ |
not computed |
\(\Q(\zeta_{20})\) |
odd |
|
|
|
| 1600.bx |
\(\chi_{1600}(223, \cdot)\)$, \cdots ,$\(\chi_{1600}(1567, \cdot)\)
|
$1600$ |
$200$ |
$20$ |
not computed |
\(\Q(\zeta_{20})\) |
even |
|
|
✓ |
