Basic properties
| Modulus: | \(8325\) | |
| Conductor: | \(8325\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8325.lp
\(\chi_{8325}(488,\cdot)\) \(\chi_{8325}(527,\cdot)\) \(\chi_{8325}(608,\cdot)\) \(\chi_{8325}(752,\cdot)\) \(\chi_{8325}(848,\cdot)\) \(\chi_{8325}(1217,\cdot)\) \(\chi_{8325}(1487,\cdot)\) \(\chi_{8325}(1847,\cdot)\) \(\chi_{8325}(1883,\cdot)\) \(\chi_{8325}(2153,\cdot)\) \(\chi_{8325}(2192,\cdot)\) \(\chi_{8325}(2273,\cdot)\) \(\chi_{8325}(2417,\cdot)\) \(\chi_{8325}(2513,\cdot)\) \(\chi_{8325}(2858,\cdot)\) \(\chi_{8325}(3083,\cdot)\) \(\chi_{8325}(3152,\cdot)\) \(\chi_{8325}(3272,\cdot)\) \(\chi_{8325}(3512,\cdot)\) \(\chi_{8325}(3548,\cdot)\) \(\chi_{8325}(3938,\cdot)\) \(\chi_{8325}(4178,\cdot)\) \(\chi_{8325}(4523,\cdot)\) \(\chi_{8325}(4547,\cdot)\) \(\chi_{8325}(4748,\cdot)\) \(\chi_{8325}(4817,\cdot)\) \(\chi_{8325}(4937,\cdot)\) \(\chi_{8325}(5177,\cdot)\) \(\chi_{8325}(5213,\cdot)\) \(\chi_{8325}(5483,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((3701,7327,5626)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{9}{20}\right),e\left(\frac{8}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 8325 }(1487, a) \) | \(1\) | \(1\) | \(e\left(\frac{91}{180}\right)\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{119}{180}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{103}{180}\right)\) | \(e\left(\frac{19}{90}\right)\) |