Basic properties
| Modulus: | \(5312\) | |
| Conductor: | \(1328\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(164\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1328}(349,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5312.be
\(\chi_{5312}(17,\cdot)\) \(\chi_{5312}(49,\cdot)\) \(\chi_{5312}(81,\cdot)\) \(\chi_{5312}(113,\cdot)\) \(\chi_{5312}(177,\cdot)\) \(\chi_{5312}(241,\cdot)\) \(\chi_{5312}(369,\cdot)\) \(\chi_{5312}(401,\cdot)\) \(\chi_{5312}(529,\cdot)\) \(\chi_{5312}(561,\cdot)\) \(\chi_{5312}(593,\cdot)\) \(\chi_{5312}(625,\cdot)\) \(\chi_{5312}(689,\cdot)\) \(\chi_{5312}(785,\cdot)\) \(\chi_{5312}(817,\cdot)\) \(\chi_{5312}(881,\cdot)\) \(\chi_{5312}(977,\cdot)\) \(\chi_{5312}(1073,\cdot)\) \(\chi_{5312}(1105,\cdot)\) \(\chi_{5312}(1169,\cdot)\) \(\chi_{5312}(1361,\cdot)\) \(\chi_{5312}(1393,\cdot)\) \(\chi_{5312}(1489,\cdot)\) \(\chi_{5312}(1521,\cdot)\) \(\chi_{5312}(1553,\cdot)\) \(\chi_{5312}(1617,\cdot)\) \(\chi_{5312}(1681,\cdot)\) \(\chi_{5312}(1937,\cdot)\) \(\chi_{5312}(2001,\cdot)\) \(\chi_{5312}(2033,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{164})$ |
| Fixed field: | Number field defined by a degree 164 polynomial (not computed) |
Values on generators
\((831,3653,3073)\) → \((1,-i,e\left(\frac{28}{41}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 5312 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{69}{164}\right)\) | \(e\left(\frac{31}{164}\right)\) | \(e\left(\frac{79}{82}\right)\) | \(e\left(\frac{69}{82}\right)\) | \(e\left(\frac{23}{164}\right)\) | \(e\left(\frac{137}{164}\right)\) | \(e\left(\frac{25}{41}\right)\) | \(e\left(\frac{10}{41}\right)\) | \(e\left(\frac{57}{164}\right)\) | \(e\left(\frac{63}{164}\right)\) |