Orbit label |
Conrey labels |
Modulus |
Conductor |
Order |
Kernel field |
Value field |
Parity |
Real |
Primitive |
Minimal |
416.a |
\(\chi_{416}(1, \cdot)\)
|
$416$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
✓ |
416.b |
\(\chi_{416}(209, \cdot)\)
|
$416$ |
$8$ |
$2$ |
\(\Q(\sqrt{2}) \) |
\(\Q\) |
even |
✓ |
|
|
416.c |
\(\chi_{416}(415, \cdot)\)
|
$416$ |
$52$ |
$2$ |
\(\Q(\sqrt{-13}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
416.d |
\(\chi_{416}(287, \cdot)\)
|
$416$ |
$4$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
416.e |
\(\chi_{416}(337, \cdot)\)
|
$416$ |
$104$ |
$2$ |
\(\Q(\sqrt{26}) \) |
\(\Q\) |
even |
✓ |
|
|
416.f |
\(\chi_{416}(129, \cdot)\)
|
$416$ |
$13$ |
$2$ |
\(\Q(\sqrt{13}) \) |
\(\Q\) |
even |
✓ |
|
✓ |
416.g |
\(\chi_{416}(79, \cdot)\)
|
$416$ |
$8$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
\(\Q\) |
odd |
✓ |
|
|
416.h |
\(\chi_{416}(207, \cdot)\)
|
$416$ |
$104$ |
$2$ |
\(\Q(\sqrt{-26}) \) |
\(\Q\) |
odd |
✓ |
|
|
416.i |
\(\chi_{416}(289, \cdot)\)$,$ \(\chi_{416}(321, \cdot)\)
|
$416$ |
$13$ |
$3$ |
3.3.169.1 |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
|
✓ |
416.j |
\(\chi_{416}(177, \cdot)\)$,$ \(\chi_{416}(369, \cdot)\)
|
$416$ |
$104$ |
$4$ |
4.0.140608.2 |
\(\mathbb{Q}(i)\) |
odd |
|
|
|
416.k |
\(\chi_{416}(31, \cdot)\)$,$ \(\chi_{416}(255, \cdot)\)
|
$416$ |
$52$ |
$4$ |
4.4.35152.1 |
\(\mathbb{Q}(i)\) |
even |
|
|
✓ |
416.l |
\(\chi_{416}(343, \cdot)\)$,$ \(\chi_{416}(359, \cdot)\)
|
$416$ |
$208$ |
$4$ |
4.4.4499456.2 |
\(\mathbb{Q}(i)\) |
even |
|
|
|
416.m |
\(\chi_{416}(265, \cdot)\)$,$ \(\chi_{416}(281, \cdot)\)
|
$416$ |
$208$ |
$4$ |
4.0.4499456.2 |
\(\mathbb{Q}(i)\) |
odd |
|
|
|
416.n |
\(\chi_{416}(105, \cdot)\)$,$ \(\chi_{416}(313, \cdot)\)
|
$416$ |
$16$ |
$4$ |
\(\Q(\zeta_{16})^+\) |
\(\mathbb{Q}(i)\) |
even |
|
|
|
416.o |
\(\chi_{416}(103, \cdot)\)$,$ \(\chi_{416}(311, \cdot)\)
|
$416$ |
$208$ |
$4$ |
4.0.346112.2 |
\(\mathbb{Q}(i)\) |
odd |
|
|
|
416.p |
\(\chi_{416}(25, \cdot)\)$,$ \(\chi_{416}(233, \cdot)\)
|
$416$ |
$208$ |
$4$ |
4.4.346112.1 |
\(\mathbb{Q}(i)\) |
even |
|
|
|
416.q |
\(\chi_{416}(183, \cdot)\)$,$ \(\chi_{416}(391, \cdot)\)
|
$416$ |
$16$ |
$4$ |
4.0.2048.2 |
\(\mathbb{Q}(i)\) |
odd |
|
|
|
416.r |
\(\chi_{416}(57, \cdot)\)$,$ \(\chi_{416}(73, \cdot)\)
|
$416$ |
$208$ |
$4$ |
4.0.4499456.1 |
\(\mathbb{Q}(i)\) |
odd |
|
|
|
416.s |
\(\chi_{416}(135, \cdot)\)$,$ \(\chi_{416}(151, \cdot)\)
|
$416$ |
$208$ |
$4$ |
4.4.4499456.1 |
\(\mathbb{Q}(i)\) |
even |
|
|
|
416.t |
\(\chi_{416}(161, \cdot)\)$,$ \(\chi_{416}(385, \cdot)\)
|
$416$ |
$13$ |
$4$ |
4.0.2197.1 |
\(\mathbb{Q}(i)\) |
odd |
|
|
✓ |
416.u |
\(\chi_{416}(47, \cdot)\)$,$ \(\chi_{416}(239, \cdot)\)
|
$416$ |
$104$ |
$4$ |
4.4.140608.1 |
\(\mathbb{Q}(i)\) |
even |
|
|
|
416.v |
\(\chi_{416}(367, \cdot)\)$,$ \(\chi_{416}(399, \cdot)\)
|
$416$ |
$104$ |
$6$ |
6.0.14623232.1 |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
|
|
416.w |
\(\chi_{416}(225, \cdot)\)$,$ \(\chi_{416}(257, \cdot)\)
|
$416$ |
$13$ |
$6$ |
\(\Q(\zeta_{13})^+\) |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
|
✓ |
416.x |
\(\chi_{416}(303, \cdot)\)$,$ \(\chi_{416}(335, \cdot)\)
|
$416$ |
$104$ |
$6$ |
6.0.190102016.1 |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
|
|
416.y |
\(\chi_{416}(95, \cdot)\)$,$ \(\chi_{416}(127, \cdot)\)
|
$416$ |
$52$ |
$6$ |
6.0.23762752.1 |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
|
✓ |
416.z |
\(\chi_{416}(81, \cdot)\)$,$ \(\chi_{416}(113, \cdot)\)
|
$416$ |
$104$ |
$6$ |
6.6.14623232.1 |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
|
|
416.ba |
\(\chi_{416}(17, \cdot)\)$,$ \(\chi_{416}(49, \cdot)\)
|
$416$ |
$104$ |
$6$ |
6.6.190102016.1 |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
|
|
416.bb |
\(\chi_{416}(159, \cdot)\)$,$ \(\chi_{416}(191, \cdot)\)
|
$416$ |
$52$ |
$6$ |
6.0.1827904.1 |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
|
✓ |
416.bc |
\(\chi_{416}(5, \cdot)\)$, \cdots ,$\(\chi_{416}(333, \cdot)\)
|
$416$ |
$416$ |
$8$ |
8.0.10365493399519232.5 |
\(\Q(\zeta_{8})\) |
odd |
|
✓ |
✓ |
416.bd |
\(\chi_{416}(83, \cdot)\)$, \cdots ,$\(\chi_{416}(411, \cdot)\)
|
$416$ |
$416$ |
$8$ |
8.8.10365493399519232.1 |
\(\Q(\zeta_{8})\) |
even |
|
✓ |
✓ |
416.be |
\(\chi_{416}(51, \cdot)\)$, \cdots ,$\(\chi_{416}(363, \cdot)\)
|
$416$ |
$416$ |
$8$ |
8.0.61334280470528.11 |
\(\Q(\zeta_{8})\) |
odd |
|
✓ |
✓ |
416.bf |
\(\chi_{416}(53, \cdot)\)$, \cdots ,$\(\chi_{416}(365, \cdot)\)
|
$416$ |
$32$ |
$8$ |
\(\Q(\zeta_{32})^+\) |
\(\Q(\zeta_{8})\) |
even |
|
|
✓ |
416.bg |
\(\chi_{416}(77, \cdot)\)$, \cdots ,$\(\chi_{416}(389, \cdot)\)
|
$416$ |
$416$ |
$8$ |
8.8.61334280470528.1 |
\(\Q(\zeta_{8})\) |
even |
|
✓ |
✓ |
416.bh |
\(\chi_{416}(27, \cdot)\)$, \cdots ,$\(\chi_{416}(339, \cdot)\)
|
$416$ |
$32$ |
$8$ |
8.0.2147483648.1 |
\(\Q(\zeta_{8})\) |
odd |
|
|
✓ |
416.bi |
\(\chi_{416}(99, \cdot)\)$, \cdots ,$\(\chi_{416}(395, \cdot)\)
|
$416$ |
$416$ |
$8$ |
8.8.10365493399519232.2 |
\(\Q(\zeta_{8})\) |
even |
|
✓ |
✓ |
416.bj |
\(\chi_{416}(21, \cdot)\)$, \cdots ,$\(\chi_{416}(317, \cdot)\)
|
$416$ |
$416$ |
$8$ |
8.0.10365493399519232.3 |
\(\Q(\zeta_{8})\) |
odd |
|
✓ |
✓ |
416.bk |
\(\chi_{416}(15, \cdot)\)$, \cdots ,$\(\chi_{416}(271, \cdot)\)
|
$416$ |
$104$ |
$12$ |
12.12.469804094334435328.1 |
\(\Q(\zeta_{12})\) |
even |
|
|
|
416.bl |
\(\chi_{416}(33, \cdot)\)$, \cdots ,$\(\chi_{416}(353, \cdot)\)
|
$416$ |
$13$ |
$12$ |
\(\Q(\zeta_{13})\) |
\(\Q(\zeta_{12})\) |
odd |
|
|
✓ |
416.bm |
\(\chi_{416}(41, \cdot)\)$, \cdots ,$\(\chi_{416}(345, \cdot)\)
|
$416$ |
$208$ |
$12$ |
12.0.15394540563150776827904.2 |
\(\Q(\zeta_{12})\) |
odd |
|
|
|
416.bn |
\(\chi_{416}(7, \cdot)\)$, \cdots ,$\(\chi_{416}(279, \cdot)\)
|
$416$ |
$208$ |
$12$ |
12.12.15394540563150776827904.2 |
\(\Q(\zeta_{12})\) |
even |
|
|
|
416.bo |
\(\chi_{416}(55, \cdot)\)$, \cdots ,$\(\chi_{416}(295, \cdot)\)
|
$416$ |
$208$ |
$12$ |
12.0.7007073538075000832.1 |
\(\Q(\zeta_{12})\) |
odd |
|
|
|
416.bp |
\(\chi_{416}(121, \cdot)\)$, \cdots ,$\(\chi_{416}(361, \cdot)\)
|
$416$ |
$208$ |
$12$ |
12.12.1184195427934675140608.1 |
\(\Q(\zeta_{12})\) |
even |
|
|
|
416.bq |
\(\chi_{416}(23, \cdot)\)$, \cdots ,$\(\chi_{416}(407, \cdot)\)
|
$416$ |
$208$ |
$12$ |
12.0.1184195427934675140608.1 |
\(\Q(\zeta_{12})\) |
odd |
|
|
|
416.br |
\(\chi_{416}(9, \cdot)\)$, \cdots ,$\(\chi_{416}(393, \cdot)\)
|
$416$ |
$208$ |
$12$ |
12.12.7007073538075000832.1 |
\(\Q(\zeta_{12})\) |
even |
|
|
|
416.bs |
\(\chi_{416}(71, \cdot)\)$, \cdots ,$\(\chi_{416}(375, \cdot)\)
|
$416$ |
$208$ |
$12$ |
12.12.15394540563150776827904.1 |
\(\Q(\zeta_{12})\) |
even |
|
|
|
416.bt |
\(\chi_{416}(137, \cdot)\)$, \cdots ,$\(\chi_{416}(409, \cdot)\)
|
$416$ |
$208$ |
$12$ |
12.0.15394540563150776827904.1 |
\(\Q(\zeta_{12})\) |
odd |
|
|
|
416.bu |
\(\chi_{416}(63, \cdot)\)$, \cdots ,$\(\chi_{416}(383, \cdot)\)
|
$416$ |
$52$ |
$12$ |
\(\Q(\zeta_{52})^+\) |
\(\Q(\zeta_{12})\) |
even |
|
|
✓ |
416.bv |
\(\chi_{416}(145, \cdot)\)$, \cdots ,$\(\chi_{416}(401, \cdot)\)
|
$416$ |
$104$ |
$12$ |
12.0.469804094334435328.1 |
\(\Q(\zeta_{12})\) |
odd |
|
|
|
416.bw |
\(\chi_{416}(37, \cdot)\)$, \cdots ,$\(\chi_{416}(301, \cdot)\)
|
$416$ |
$416$ |
$24$ |
not computed |
\(\Q(\zeta_{24})\) |
odd |
|
✓ |
✓ |
416.bx |
\(\chi_{416}(115, \cdot)\)$, \cdots ,$\(\chi_{416}(379, \cdot)\)
|
$416$ |
$416$ |
$24$ |
not computed |
\(\Q(\zeta_{24})\) |
even |
|
✓ |
✓ |