Basic properties
| Modulus: | \(38025\) | |
| Conductor: | \(38025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(780\) | 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 38025.op
\(\chi_{38025}(34,\cdot)\) \(\chi_{38025}(229,\cdot)\) \(\chi_{38025}(304,\cdot)\) \(\chi_{38025}(619,\cdot)\) \(\chi_{38025}(814,\cdot)\) \(\chi_{38025}(889,\cdot)\) \(\chi_{38025}(1204,\cdot)\) \(\chi_{38025}(1669,\cdot)\) \(\chi_{38025}(1984,\cdot)\) \(\chi_{38025}(2059,\cdot)\) \(\chi_{38025}(2254,\cdot)\) \(\chi_{38025}(2569,\cdot)\) \(\chi_{38025}(2644,\cdot)\) \(\chi_{38025}(2839,\cdot)\) \(\chi_{38025}(2959,\cdot)\) \(\chi_{38025}(3154,\cdot)\) \(\chi_{38025}(3229,\cdot)\) \(\chi_{38025}(3544,\cdot)\) \(\chi_{38025}(3739,\cdot)\) \(\chi_{38025}(3814,\cdot)\) \(\chi_{38025}(4009,\cdot)\) \(\chi_{38025}(4129,\cdot)\) \(\chi_{38025}(4594,\cdot)\) \(\chi_{38025}(4714,\cdot)\) \(\chi_{38025}(4909,\cdot)\) \(\chi_{38025}(4984,\cdot)\) \(\chi_{38025}(5179,\cdot)\) \(\chi_{38025}(5494,\cdot)\) \(\chi_{38025}(5569,\cdot)\) \(\chi_{38025}(5764,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{780})$ |
| Fixed field: | Number field defined by a degree 780 polynomial (not computed) |
Values on generators
\((29576,9127,37351)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{7}{10}\right),e\left(\frac{49}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 38025 }(34, a) \) | \(-1\) | \(1\) | \(e\left(\frac{241}{780}\right)\) | \(e\left(\frac{241}{390}\right)\) | \(e\left(\frac{155}{156}\right)\) | \(e\left(\frac{241}{260}\right)\) | \(e\left(\frac{721}{780}\right)\) | \(e\left(\frac{59}{195}\right)\) | \(e\left(\frac{46}{195}\right)\) | \(e\left(\frac{44}{65}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{7}{30}\right)\) |