Basic properties
| Modulus: | \(216000\) | |
| Conductor: | \(36000\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(600\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{36000}(31469,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 216000.vj
\(\chi_{216000}(89,\cdot)\) \(\chi_{216000}(1529,\cdot)\) \(\chi_{216000}(3689,\cdot)\) \(\chi_{216000}(4409,\cdot)\) \(\chi_{216000}(6569,\cdot)\) \(\chi_{216000}(8009,\cdot)\) \(\chi_{216000}(8729,\cdot)\) \(\chi_{216000}(10169,\cdot)\) \(\chi_{216000}(10889,\cdot)\) \(\chi_{216000}(12329,\cdot)\) \(\chi_{216000}(14489,\cdot)\) \(\chi_{216000}(15209,\cdot)\) \(\chi_{216000}(17369,\cdot)\) \(\chi_{216000}(18809,\cdot)\) \(\chi_{216000}(19529,\cdot)\) \(\chi_{216000}(20969,\cdot)\) \(\chi_{216000}(21689,\cdot)\) \(\chi_{216000}(23129,\cdot)\) \(\chi_{216000}(25289,\cdot)\) \(\chi_{216000}(26009,\cdot)\) \(\chi_{216000}(28169,\cdot)\) \(\chi_{216000}(29609,\cdot)\) \(\chi_{216000}(30329,\cdot)\) \(\chi_{216000}(31769,\cdot)\) \(\chi_{216000}(32489,\cdot)\) \(\chi_{216000}(33929,\cdot)\) \(\chi_{216000}(36089,\cdot)\) \(\chi_{216000}(36809,\cdot)\) \(\chi_{216000}(38969,\cdot)\) \(\chi_{216000}(40409,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{600})$ |
| Fixed field: | Number field defined by a degree 600 polynomial (not computed) |
Values on generators
\((114751,202501,136001,29377)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{5}{6}\right),e\left(\frac{49}{50}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 216000 }(20969, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{413}{600}\right)\) | \(e\left(\frac{7}{600}\right)\) | \(e\left(\frac{27}{50}\right)\) | \(e\left(\frac{153}{200}\right)\) | \(e\left(\frac{239}{300}\right)\) | \(e\left(\frac{131}{600}\right)\) | \(e\left(\frac{53}{75}\right)\) | \(e\left(\frac{59}{200}\right)\) | \(e\left(\frac{161}{300}\right)\) |