| Orbit label |
Conrey labels |
Modulus |
Conductor |
Order |
Kernel field |
Value field |
Parity |
Real |
Primitive |
Minimal |
| 409600.a |
\(\chi_{409600}(1, \cdot)\)
|
$409600$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
|
| 409600.b |
\(\chi_{409600}(49151, \cdot)\)
|
$409600$ |
$4$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
\(\Q\) |
odd |
✓ |
|
|
| 409600.c |
\(\chi_{409600}(360449, \cdot)\)
|
$409600$ |
$5$ |
$2$ |
\(\Q(\sqrt{5}) \) |
\(\Q\) |
even |
✓ |
|
|
| 409600.d |
\(\chi_{409600}(204801, \cdot)\)
|
$409600$ |
$8$ |
$2$ |
\(\Q(\sqrt{2}) \) |
\(\Q\) |
even |
✓ |
|
|
| 409600.e |
\(\chi_{409600}(204799, \cdot)\)
|
$409600$ |
$40$ |
$2$ |
\(\Q(\sqrt{-10}) \) |
\(\Q\) |
odd |
✓ |
|
|
| 409600.f |
\(\chi_{409600}(155649, \cdot)\)
|
$409600$ |
$40$ |
$2$ |
\(\Q(\sqrt{10}) \) |
\(\Q\) |
even |
✓ |
|
|
| 409600.g |
\(\chi_{409600}(253951, \cdot)\)
|
$409600$ |
$8$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
\(\Q\) |
odd |
✓ |
|
|
| 409600.h |
\(\chi_{409600}(409599, \cdot)\)
|
$409600$ |
$20$ |
$2$ |
\(\Q(\sqrt{-5}) \) |
\(\Q\) |
odd |
✓ |
|
|
| 409600.i |
\(\chi_{409600}(45057, \cdot)\)$,$ \(\chi_{409600}(315393, \cdot)\)
|
$409600$ |
$80$ |
$4$ |
4.0.256000.4 |
\(\mathbb{Q}(i)\) |
odd |
|
|
|
| 409600.j |
\(\chi_{409600}(94207, \cdot)\)$,$ \(\chi_{409600}(364543, \cdot)\)
|
$409600$ |
$80$ |
$4$ |
4.4.256000.2 |
\(\mathbb{Q}(i)\) |
even |
|
|
|
| 409600.k |
\(\chi_{409600}(102399, \cdot)\)$,$ \(\chi_{409600}(307199, \cdot)\)
|
$409600$ |
$80$ |
$4$ |
4.0.51200.2 |
\(\mathbb{Q}(i)\) |
odd |
|
|
|
| 409600.l |
\(\chi_{409600}(102401, \cdot)\)$,$ \(\chi_{409600}(307201, \cdot)\)
|
$409600$ |
$16$ |
$4$ |
\(\Q(\zeta_{16})^+\) |
\(\mathbb{Q}(i)\) |
even |
|
|
|
| 409600.m |
\(\chi_{409600}(8193, \cdot)\)$,$ \(\chi_{409600}(352257, \cdot)\)
|
$409600$ |
$40$ |
$4$ |
4.0.8000.2 |
\(\mathbb{Q}(i)\) |
odd |
|
|
|
| 409600.n |
\(\chi_{409600}(196607, \cdot)\)$,$ \(\chi_{409600}(262143, \cdot)\)
|
$409600$ |
$20$ |
$4$ |
\(\Q(\zeta_{20})^+\) |
\(\mathbb{Q}(i)\) |
even |
|
|
|
| 409600.o |
\(\chi_{409600}(57343, \cdot)\)$,$ \(\chi_{409600}(401407, \cdot)\)
|
$409600$ |
$40$ |
$4$ |
4.4.8000.1 |
\(\mathbb{Q}(i)\) |
even |
|
|
|
| 409600.p |
\(\chi_{409600}(147457, \cdot)\)$,$ \(\chi_{409600}(212993, \cdot)\)
|
$409600$ |
$5$ |
$4$ |
\(\Q(\zeta_{5})\) |
\(\mathbb{Q}(i)\) |
odd |
|
|
|
| 409600.q |
\(\chi_{409600}(53249, \cdot)\)$,$ \(\chi_{409600}(258049, \cdot)\)
|
$409600$ |
$80$ |
$4$ |
4.4.51200.1 |
\(\mathbb{Q}(i)\) |
even |
|
|
|
| 409600.r |
\(\chi_{409600}(151551, \cdot)\)$,$ \(\chi_{409600}(356351, \cdot)\)
|
$409600$ |
$16$ |
$4$ |
4.0.2048.2 |
\(\mathbb{Q}(i)\) |
odd |
|
|
|
| 409600.s |
\(\chi_{409600}(159743, \cdot)\)$,$ \(\chi_{409600}(299007, \cdot)\)
|
$409600$ |
$80$ |
$4$ |
4.4.256000.1 |
\(\mathbb{Q}(i)\) |
even |
|
|
|
| 409600.t |
\(\chi_{409600}(110593, \cdot)\)$,$ \(\chi_{409600}(249857, \cdot)\)
|
$409600$ |
$80$ |
$4$ |
4.0.256000.2 |
\(\mathbb{Q}(i)\) |
odd |
|
|
|
| 409600.u |
\(\chi_{409600}(81921, \cdot)\)$, \cdots ,$\(\chi_{409600}(327681, \cdot)\)
|
$409600$ |
$25$ |
$5$ |
5.5.390625.1 |
\(\Q(\zeta_{5})\) |
even |
|
|
|
| 409600.v |
\(\chi_{409600}(108543, \cdot)\)$, \cdots ,$\(\chi_{409600}(350207, \cdot)\)
|
$409600$ |
$160$ |
$8$ |
8.8.33554432000000.2 |
\(\Q(\zeta_{8})\) |
even |
|
|
|
| 409600.w |
\(\chi_{409600}(59393, \cdot)\)$, \cdots ,$\(\chi_{409600}(301057, \cdot)\)
|
$409600$ |
$160$ |
$8$ |
8.0.33554432000000.1 |
\(\Q(\zeta_{8})\) |
odd |
|
|
|
| 409600.x |
\(\chi_{409600}(100351, \cdot)\)$, \cdots ,$\(\chi_{409600}(407551, \cdot)\)
|
$409600$ |
$32$ |
$8$ |
8.0.2147483648.1 |
\(\Q(\zeta_{8})\) |
odd |
|
|
|
| 409600.y |
\(\chi_{409600}(51201, \cdot)\)$, \cdots ,$\(\chi_{409600}(358401, \cdot)\)
|
$409600$ |
$32$ |
$8$ |
\(\Q(\zeta_{32})^+\) |
\(\Q(\zeta_{8})\) |
even |
|
|
|
| 409600.z |
\(\chi_{409600}(51199, \cdot)\)$, \cdots ,$\(\chi_{409600}(358399, \cdot)\)
|
$409600$ |
$160$ |
$8$ |
8.0.1342177280000.1 |
\(\Q(\zeta_{8})\) |
odd |
|
|
|
| 409600.ba |
\(\chi_{409600}(2049, \cdot)\)$, \cdots ,$\(\chi_{409600}(309249, \cdot)\)
|
$409600$ |
$160$ |
$8$ |
8.8.1342177280000.1 |
\(\Q(\zeta_{8})\) |
even |
|
|
|
| 409600.bb |
\(\chi_{409600}(6143, \cdot)\)$, \cdots ,$\(\chi_{409600}(247807, \cdot)\)
|
$409600$ |
$160$ |
$8$ |
8.8.33554432000000.1 |
\(\Q(\zeta_{8})\) |
even |
|
|
|
| 409600.bc |
\(\chi_{409600}(161793, \cdot)\)$, \cdots ,$\(\chi_{409600}(403457, \cdot)\)
|
$409600$ |
$160$ |
$8$ |
8.0.33554432000000.2 |
\(\Q(\zeta_{8})\) |
odd |
|
|
|
| 409600.bd |
\(\chi_{409600}(8191, \cdot)\)$, \cdots ,$\(\chi_{409600}(335871, \cdot)\)
|
$409600$ |
$200$ |
$10$ |
10.0.5000000000000000.1 |
\(\Q(\zeta_{5})\) |
odd |
|
|
|
| 409600.be |
\(\chi_{409600}(73729, \cdot)\)$, \cdots ,$\(\chi_{409600}(401409, \cdot)\)
|
$409600$ |
$200$ |
$10$ |
10.10.25000000000000000.1 |
\(\Q(\zeta_{5})\) |
even |
|
|
|
| 409600.bf |
\(\chi_{409600}(81919, \cdot)\)$, \cdots ,$\(\chi_{409600}(327679, \cdot)\)
|
$409600$ |
$100$ |
$10$ |
10.0.781250000000000.1 |
\(\Q(\zeta_{5})\) |
odd |
|
|
|
| 409600.bg |
\(\chi_{409600}(32769, \cdot)\)$, \cdots ,$\(\chi_{409600}(278529, \cdot)\)
|
$409600$ |
$25$ |
$10$ |
\(\Q(\zeta_{25})^+\) |
\(\Q(\zeta_{5})\) |
even |
|
|
|
| 409600.bh |
\(\chi_{409600}(131071, \cdot)\)$, \cdots ,$\(\chi_{409600}(376831, \cdot)\)
|
$409600$ |
$100$ |
$10$ |
10.0.156250000000000.1 |
\(\Q(\zeta_{5})\) |
odd |
|
|
|
| 409600.bi |
\(\chi_{409600}(40959, \cdot)\)$, \cdots ,$\(\chi_{409600}(368639, \cdot)\)
|
$409600$ |
$200$ |
$10$ |
10.0.25000000000000000.1 |
\(\Q(\zeta_{5})\) |
odd |
|
|
|
| 409600.bj |
\(\chi_{409600}(40961, \cdot)\)$, \cdots ,$\(\chi_{409600}(368641, \cdot)\)
|
$409600$ |
$200$ |
$10$ |
10.10.5000000000000000.1 |
\(\Q(\zeta_{5})\) |
even |
|
|
|
| 409600.bk |
\(\chi_{409600}(70657, \cdot)\)$, \cdots ,$\(\chi_{409600}(392193, \cdot)\)
|
$409600$ |
$320$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
odd |
|
|
|
| 409600.bl |
\(\chi_{409600}(68607, \cdot)\)$, \cdots ,$\(\chi_{409600}(390143, \cdot)\)
|
$409600$ |
$320$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
even |
|
|
|
| 409600.bm |
\(\chi_{409600}(25601, \cdot)\)$, \cdots ,$\(\chi_{409600}(384001, \cdot)\)
|
$409600$ |
$64$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
even |
|
|
|
| 409600.bn |
\(\chi_{409600}(27649, \cdot)\)$, \cdots ,$\(\chi_{409600}(386049, \cdot)\)
|
$409600$ |
$320$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
even |
|
|
|
| 409600.bo |
\(\chi_{409600}(23551, \cdot)\)$, \cdots ,$\(\chi_{409600}(381951, \cdot)\)
|
$409600$ |
$64$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
odd |
|
|
|
| 409600.bp |
\(\chi_{409600}(25599, \cdot)\)$, \cdots ,$\(\chi_{409600}(383999, \cdot)\)
|
$409600$ |
$320$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
odd |
|
|
|
| 409600.bq |
\(\chi_{409600}(19457, \cdot)\)$, \cdots ,$\(\chi_{409600}(340993, \cdot)\)
|
$409600$ |
$320$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
odd |
|
|
|
| 409600.br |
\(\chi_{409600}(17407, \cdot)\)$, \cdots ,$\(\chi_{409600}(338943, \cdot)\)
|
$409600$ |
$320$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
even |
|
|
|
| 409600.bs |
\(\chi_{409600}(4097, \cdot)\)$, \cdots ,$\(\chi_{409600}(356353, \cdot)\)
|
$409600$ |
$400$ |
$20$ |
not computed |
\(\Q(\zeta_{20})\) |
odd |
|
|
|
| 409600.bt |
\(\chi_{409600}(53247, \cdot)\)$, \cdots ,$\(\chi_{409600}(405503, \cdot)\)
|
$409600$ |
$400$ |
$20$ |
not computed |
\(\Q(\zeta_{20})\) |
even |
|
|
|
| 409600.bu |
\(\chi_{409600}(20481, \cdot)\)$, \cdots ,$\(\chi_{409600}(389121, \cdot)\)
|
$409600$ |
$400$ |
$20$ |
not computed |
\(\Q(\zeta_{20})\) |
even |
|
|
|
| 409600.bv |
\(\chi_{409600}(20479, \cdot)\)$, \cdots ,$\(\chi_{409600}(389119, \cdot)\)
|
$409600$ |
$400$ |
$20$ |
not computed |
\(\Q(\zeta_{20})\) |
odd |
|
|
|
| 409600.bw |
\(\chi_{409600}(49153, \cdot)\)$, \cdots ,$\(\chi_{409600}(393217, \cdot)\)
|
$409600$ |
$25$ |
$20$ |
not computed |
\(\Q(\zeta_{20})\) |
odd |
|
|
|
| 409600.bx |
\(\chi_{409600}(73727, \cdot)\)$, \cdots ,$\(\chi_{409600}(385023, \cdot)\)
|
$409600$ |
$200$ |
$20$ |
not computed |
\(\Q(\zeta_{20})\) |
even |
|
|
|
