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 \(\chi_{1328}(347,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5312.bc
\(\chi_{5312}(15,\cdot)\) \(\chi_{5312}(47,\cdot)\) \(\chi_{5312}(79,\cdot)\) \(\chi_{5312}(143,\cdot)\) \(\chi_{5312}(239,\cdot)\) \(\chi_{5312}(271,\cdot)\) \(\chi_{5312}(303,\cdot)\) \(\chi_{5312}(367,\cdot)\) \(\chi_{5312}(399,\cdot)\) \(\chi_{5312}(495,\cdot)\) \(\chi_{5312}(623,\cdot)\) \(\chi_{5312}(655,\cdot)\) \(\chi_{5312}(719,\cdot)\) \(\chi_{5312}(975,\cdot)\) \(\chi_{5312}(1039,\cdot)\) \(\chi_{5312}(1103,\cdot)\) \(\chi_{5312}(1135,\cdot)\) \(\chi_{5312}(1167,\cdot)\) \(\chi_{5312}(1263,\cdot)\) \(\chi_{5312}(1295,\cdot)\) \(\chi_{5312}(1487,\cdot)\) \(\chi_{5312}(1551,\cdot)\) \(\chi_{5312}(1583,\cdot)\) \(\chi_{5312}(1679,\cdot)\) \(\chi_{5312}(1775,\cdot)\) \(\chi_{5312}(1839,\cdot)\) \(\chi_{5312}(1871,\cdot)\) \(\chi_{5312}(1967,\cdot)\) \(\chi_{5312}(2031,\cdot)\) \(\chi_{5312}(2063,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{164})$ |
| Fixed field: | Number field defined by a degree 164 polynomial (not computed) |
Values on generators
\((831,3653,3073)\) → \((-1,i,e\left(\frac{17}{82}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 5312 }(15, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{164}\right)\) | \(e\left(\frac{139}{164}\right)\) | \(e\left(\frac{27}{41}\right)\) | \(e\left(\frac{29}{82}\right)\) | \(e\left(\frac{119}{164}\right)\) | \(e\left(\frac{117}{164}\right)\) | \(e\left(\frac{1}{41}\right)\) | \(e\left(\frac{25}{41}\right)\) | \(e\left(\frac{163}{164}\right)\) | \(e\left(\frac{137}{164}\right)\) |