Basic properties
| Modulus: | \(5312\) | |
| Conductor: | \(2656\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(328\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2656}(2333,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5312.bi
\(\chi_{5312}(9,\cdot)\) \(\chi_{5312}(25,\cdot)\) \(\chi_{5312}(41,\cdot)\) \(\chi_{5312}(121,\cdot)\) \(\chi_{5312}(153,\cdot)\) \(\chi_{5312}(169,\cdot)\) \(\chi_{5312}(217,\cdot)\) \(\chi_{5312}(265,\cdot)\) \(\chi_{5312}(297,\cdot)\) \(\chi_{5312}(313,\cdot)\) \(\chi_{5312}(361,\cdot)\) \(\chi_{5312}(393,\cdot)\) \(\chi_{5312}(409,\cdot)\) \(\chi_{5312}(425,\cdot)\) \(\chi_{5312}(441,\cdot)\) \(\chi_{5312}(505,\cdot)\) \(\chi_{5312}(521,\cdot)\) \(\chi_{5312}(585,\cdot)\) \(\chi_{5312}(617,\cdot)\) \(\chi_{5312}(649,\cdot)\) \(\chi_{5312}(681,\cdot)\) \(\chi_{5312}(697,\cdot)\) \(\chi_{5312}(713,\cdot)\) \(\chi_{5312}(729,\cdot)\) \(\chi_{5312}(745,\cdot)\) \(\chi_{5312}(777,\cdot)\) \(\chi_{5312}(825,\cdot)\) \(\chi_{5312}(841,\cdot)\) \(\chi_{5312}(857,\cdot)\) \(\chi_{5312}(889,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{328})$ |
| Fixed field: | Number field defined by a degree 328 polynomial (not computed) |
Values on generators
\((831,3653,3073)\) → \((1,e\left(\frac{3}{8}\right),e\left(\frac{31}{41}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 5312 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{185}{328}\right)\) | \(e\left(\frac{259}{328}\right)\) | \(e\left(\frac{131}{164}\right)\) | \(e\left(\frac{21}{164}\right)\) | \(e\left(\frac{7}{328}\right)\) | \(e\left(\frac{277}{328}\right)\) | \(e\left(\frac{29}{82}\right)\) | \(e\left(\frac{69}{82}\right)\) | \(e\left(\frac{53}{328}\right)\) | \(e\left(\frac{119}{328}\right)\) |