Basic properties
| Modulus: | \(36000\) | |
| Conductor: | \(36000\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(600\) | 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 36000.mt
\(\chi_{36000}(29,\cdot)\) \(\chi_{36000}(389,\cdot)\) \(\chi_{36000}(509,\cdot)\) \(\chi_{36000}(869,\cdot)\) \(\chi_{36000}(1109,\cdot)\) \(\chi_{36000}(1229,\cdot)\) \(\chi_{36000}(1469,\cdot)\) \(\chi_{36000}(1589,\cdot)\) \(\chi_{36000}(1829,\cdot)\) \(\chi_{36000}(2189,\cdot)\) \(\chi_{36000}(2309,\cdot)\) \(\chi_{36000}(2669,\cdot)\) \(\chi_{36000}(2909,\cdot)\) \(\chi_{36000}(3029,\cdot)\) \(\chi_{36000}(3269,\cdot)\) \(\chi_{36000}(3389,\cdot)\) \(\chi_{36000}(3629,\cdot)\) \(\chi_{36000}(3989,\cdot)\) \(\chi_{36000}(4109,\cdot)\) \(\chi_{36000}(4469,\cdot)\) \(\chi_{36000}(4709,\cdot)\) \(\chi_{36000}(4829,\cdot)\) \(\chi_{36000}(5069,\cdot)\) \(\chi_{36000}(5189,\cdot)\) \(\chi_{36000}(5429,\cdot)\) \(\chi_{36000}(5789,\cdot)\) \(\chi_{36000}(5909,\cdot)\) \(\chi_{36000}(6269,\cdot)\) \(\chi_{36000}(6509,\cdot)\) \(\chi_{36000}(6629,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{600})$ |
| Fixed field: | Number field defined by a degree 600 polynomial (not computed) |
Values on generators
\((6751,22501,28001,29377)\) → \((1,e\left(\frac{5}{8}\right),e\left(\frac{5}{6}\right),e\left(\frac{49}{50}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 36000 }(4469, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{263}{600}\right)\) | \(e\left(\frac{157}{600}\right)\) | \(e\left(\frac{27}{50}\right)\) | \(e\left(\frac{3}{200}\right)\) | \(e\left(\frac{89}{300}\right)\) | \(e\left(\frac{281}{600}\right)\) | \(e\left(\frac{53}{75}\right)\) | \(e\left(\frac{9}{200}\right)\) | \(e\left(\frac{11}{300}\right)\) |