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.nt
\(\chi_{38025}(47,\cdot)\) \(\chi_{38025}(83,\cdot)\) \(\chi_{38025}(473,\cdot)\) \(\chi_{38025}(1022,\cdot)\) \(\chi_{38025}(1058,\cdot)\) \(\chi_{38025}(1217,\cdot)\) \(\chi_{38025}(1802,\cdot)\) \(\chi_{38025}(1838,\cdot)\) \(\chi_{38025}(2192,\cdot)\) \(\chi_{38025}(2228,\cdot)\) \(\chi_{38025}(2387,\cdot)\) \(\chi_{38025}(2423,\cdot)\) \(\chi_{38025}(2777,\cdot)\) \(\chi_{38025}(2813,\cdot)\) \(\chi_{38025}(3008,\cdot)\) \(\chi_{38025}(3362,\cdot)\) \(\chi_{38025}(3398,\cdot)\) \(\chi_{38025}(3947,\cdot)\) \(\chi_{38025}(3983,\cdot)\) \(\chi_{38025}(4142,\cdot)\) \(\chi_{38025}(4178,\cdot)\) \(\chi_{38025}(4727,\cdot)\) \(\chi_{38025}(4763,\cdot)\) \(\chi_{38025}(5117,\cdot)\) \(\chi_{38025}(5153,\cdot)\) \(\chi_{38025}(5312,\cdot)\) \(\chi_{38025}(5348,\cdot)\) \(\chi_{38025}(5702,\cdot)\) \(\chi_{38025}(5738,\cdot)\) \(\chi_{38025}(5897,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{780})$ |
| Fixed field: | Number field defined by a degree 780 polynomial (not computed) |
Values on generators
\((29576,9127,37351)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{17}{20}\right),e\left(\frac{21}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 38025 }(47, a) \) | \(-1\) | \(1\) | \(e\left(\frac{82}{195}\right)\) | \(e\left(\frac{164}{195}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{17}{65}\right)\) | \(e\left(\frac{283}{780}\right)\) | \(e\left(\frac{107}{195}\right)\) | \(e\left(\frac{133}{195}\right)\) | \(e\left(\frac{133}{260}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{47}{60}\right)\) |