Basic properties
| Modulus: | \(38025\) | |
| Conductor: | \(4225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(130\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4225}(64,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 38025.jx
\(\chi_{38025}(64,\cdot)\) \(\chi_{38025}(1234,\cdot)\) \(\chi_{38025}(1819,\cdot)\) \(\chi_{38025}(2404,\cdot)\) \(\chi_{38025}(2989,\cdot)\) \(\chi_{38025}(4159,\cdot)\) \(\chi_{38025}(4744,\cdot)\) \(\chi_{38025}(5329,\cdot)\) \(\chi_{38025}(7084,\cdot)\) \(\chi_{38025}(7669,\cdot)\) \(\chi_{38025}(8254,\cdot)\) \(\chi_{38025}(8839,\cdot)\) \(\chi_{38025}(10009,\cdot)\) \(\chi_{38025}(10594,\cdot)\) \(\chi_{38025}(11179,\cdot)\) \(\chi_{38025}(11764,\cdot)\) \(\chi_{38025}(12934,\cdot)\) \(\chi_{38025}(14104,\cdot)\) \(\chi_{38025}(14689,\cdot)\) \(\chi_{38025}(15859,\cdot)\) \(\chi_{38025}(16444,\cdot)\) \(\chi_{38025}(17029,\cdot)\) \(\chi_{38025}(17614,\cdot)\) \(\chi_{38025}(18784,\cdot)\) \(\chi_{38025}(19369,\cdot)\) \(\chi_{38025}(19954,\cdot)\) \(\chi_{38025}(20539,\cdot)\) \(\chi_{38025}(21709,\cdot)\) \(\chi_{38025}(22294,\cdot)\) \(\chi_{38025}(22879,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{65})$ |
| Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((29576,9127,37351)\) → \((1,e\left(\frac{3}{10}\right),e\left(\frac{1}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 38025 }(64, a) \) | \(1\) | \(1\) | \(e\left(\frac{22}{65}\right)\) | \(e\left(\frac{44}{65}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{1}{65}\right)\) | \(e\left(\frac{99}{130}\right)\) | \(e\left(\frac{62}{65}\right)\) | \(e\left(\frac{23}{65}\right)\) | \(e\left(\frac{67}{130}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) |