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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 38025.or
\(\chi_{38025}(41,\cdot)\) \(\chi_{38025}(371,\cdot)\) \(\chi_{38025}(461,\cdot)\) \(\chi_{38025}(956,\cdot)\) \(\chi_{38025}(986,\cdot)\) \(\chi_{38025}(1046,\cdot)\) \(\chi_{38025}(1211,\cdot)\) \(\chi_{38025}(1541,\cdot)\) \(\chi_{38025}(1571,\cdot)\) \(\chi_{38025}(1631,\cdot)\) \(\chi_{38025}(1796,\cdot)\) \(\chi_{38025}(2156,\cdot)\) \(\chi_{38025}(2381,\cdot)\) \(\chi_{38025}(2711,\cdot)\) \(\chi_{38025}(2741,\cdot)\) \(\chi_{38025}(2966,\cdot)\) \(\chi_{38025}(3296,\cdot)\) \(\chi_{38025}(3386,\cdot)\) \(\chi_{38025}(3881,\cdot)\) \(\chi_{38025}(3911,\cdot)\) \(\chi_{38025}(3971,\cdot)\) \(\chi_{38025}(4466,\cdot)\) \(\chi_{38025}(4496,\cdot)\) \(\chi_{38025}(4556,\cdot)\) \(\chi_{38025}(4721,\cdot)\) \(\chi_{38025}(5081,\cdot)\) \(\chi_{38025}(5141,\cdot)\) \(\chi_{38025}(5306,\cdot)\) \(\chi_{38025}(5636,\cdot)\) \(\chi_{38025}(5891,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{780})$ |
| Fixed field: | Number field defined by a degree 780 polynomial (not computed) |
Values on generators
\((29576,9127,37351)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{1}{5}\right),e\left(\frac{85}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 38025 }(41, a) \) | \(1\) | \(1\) | \(e\left(\frac{451}{780}\right)\) | \(e\left(\frac{61}{390}\right)\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{191}{260}\right)\) | \(e\left(\frac{121}{780}\right)\) | \(e\left(\frac{83}{390}\right)\) | \(e\left(\frac{61}{195}\right)\) | \(e\left(\frac{127}{195}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{11}{15}\right)\) |