Basic properties
| Modulus: | \(916\) | |
| Conductor: | \(229\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(57\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{229}(9,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 916.q
\(\chi_{916}(9,\cdot)\) \(\chi_{916}(25,\cdot)\) \(\chi_{916}(37,\cdot)\) \(\chi_{916}(81,\cdot)\) \(\chi_{916}(129,\cdot)\) \(\chi_{916}(149,\cdot)\) \(\chi_{916}(153,\cdot)\) \(\chi_{916}(173,\cdot)\) \(\chi_{916}(193,\cdot)\) \(\chi_{916}(217,\cdot)\) \(\chi_{916}(249,\cdot)\) \(\chi_{916}(277,\cdot)\) \(\chi_{916}(361,\cdot)\) \(\chi_{916}(373,\cdot)\) \(\chi_{916}(409,\cdot)\) \(\chi_{916}(413,\cdot)\) \(\chi_{916}(425,\cdot)\) \(\chi_{916}(453,\cdot)\) \(\chi_{916}(461,\cdot)\) \(\chi_{916}(477,\cdot)\) \(\chi_{916}(509,\cdot)\) \(\chi_{916}(513,\cdot)\) \(\chi_{916}(533,\cdot)\) \(\chi_{916}(541,\cdot)\) \(\chi_{916}(549,\cdot)\) \(\chi_{916}(569,\cdot)\) \(\chi_{916}(609,\cdot)\) \(\chi_{916}(617,\cdot)\) \(\chi_{916}(625,\cdot)\) \(\chi_{916}(629,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 57 polynomial |
Values on generators
\((459,693)\) → \((1,e\left(\frac{47}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 916 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{1}{57}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{6}{19}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{49}{57}\right)\) | \(e\left(\frac{14}{19}\right)\) |