Basic properties
| Modulus: | \(8281\) | |
| Conductor: | \(8281\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(364\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8281.dv
\(\chi_{8281}(8,\cdot)\) \(\chi_{8281}(57,\cdot)\) \(\chi_{8281}(190,\cdot)\) \(\chi_{8281}(281,\cdot)\) \(\chi_{8281}(330,\cdot)\) \(\chi_{8281}(372,\cdot)\) \(\chi_{8281}(421,\cdot)\) \(\chi_{8281}(463,\cdot)\) \(\chi_{8281}(512,\cdot)\) \(\chi_{8281}(554,\cdot)\) \(\chi_{8281}(603,\cdot)\) \(\chi_{8281}(645,\cdot)\) \(\chi_{8281}(694,\cdot)\) \(\chi_{8281}(827,\cdot)\) \(\chi_{8281}(876,\cdot)\) \(\chi_{8281}(918,\cdot)\) \(\chi_{8281}(967,\cdot)\) \(\chi_{8281}(1009,\cdot)\) \(\chi_{8281}(1058,\cdot)\) \(\chi_{8281}(1100,\cdot)\) \(\chi_{8281}(1149,\cdot)\) \(\chi_{8281}(1191,\cdot)\) \(\chi_{8281}(1240,\cdot)\) \(\chi_{8281}(1331,\cdot)\) \(\chi_{8281}(1464,\cdot)\) \(\chi_{8281}(1513,\cdot)\) \(\chi_{8281}(1555,\cdot)\) \(\chi_{8281}(1604,\cdot)\) \(\chi_{8281}(1646,\cdot)\) \(\chi_{8281}(1695,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{364})$ |
| Fixed field: | Number field defined by a degree 364 polynomial (not computed) |
Values on generators
\((1522,3382)\) → \((e\left(\frac{6}{7}\right),e\left(\frac{1}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 8281 }(8, a) \) | \(-1\) | \(1\) | \(e\left(\frac{111}{364}\right)\) | \(e\left(\frac{22}{91}\right)\) | \(e\left(\frac{111}{182}\right)\) | \(e\left(\frac{11}{364}\right)\) | \(e\left(\frac{199}{364}\right)\) | \(e\left(\frac{333}{364}\right)\) | \(e\left(\frac{44}{91}\right)\) | \(e\left(\frac{61}{182}\right)\) | \(e\left(\frac{97}{364}\right)\) | \(e\left(\frac{155}{182}\right)\) |