Basic properties
| Modulus: | \(38025\) | |
| Conductor: | \(4225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(780\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4225}(46,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 38025.ov
\(\chi_{38025}(46,\cdot)\) \(\chi_{38025}(136,\cdot)\) \(\chi_{38025}(271,\cdot)\) \(\chi_{38025}(496,\cdot)\) \(\chi_{38025}(631,\cdot)\) \(\chi_{38025}(721,\cdot)\) \(\chi_{38025}(856,\cdot)\) \(\chi_{38025}(1081,\cdot)\) \(\chi_{38025}(1216,\cdot)\) \(\chi_{38025}(1306,\cdot)\) \(\chi_{38025}(1666,\cdot)\) \(\chi_{38025}(1891,\cdot)\) \(\chi_{38025}(2386,\cdot)\) \(\chi_{38025}(2611,\cdot)\) \(\chi_{38025}(2836,\cdot)\) \(\chi_{38025}(2971,\cdot)\) \(\chi_{38025}(3196,\cdot)\) \(\chi_{38025}(3421,\cdot)\) \(\chi_{38025}(3556,\cdot)\) \(\chi_{38025}(3646,\cdot)\) \(\chi_{38025}(3781,\cdot)\) \(\chi_{38025}(4006,\cdot)\) \(\chi_{38025}(4141,\cdot)\) \(\chi_{38025}(4231,\cdot)\) \(\chi_{38025}(4366,\cdot)\) \(\chi_{38025}(4591,\cdot)\) \(\chi_{38025}(4816,\cdot)\) \(\chi_{38025}(5311,\cdot)\) \(\chi_{38025}(5536,\cdot)\) \(\chi_{38025}(5761,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{780})$ |
| Fixed field: | Number field defined by a degree 780 polynomial (not computed) |
Values on generators
\((29576,9127,37351)\) → \((1,e\left(\frac{3}{5}\right),e\left(\frac{131}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 38025 }(46, a) \) | \(-1\) | \(1\) | \(e\left(\frac{343}{780}\right)\) | \(e\left(\frac{343}{390}\right)\) | \(e\left(\frac{133}{156}\right)\) | \(e\left(\frac{83}{260}\right)\) | \(e\left(\frac{73}{780}\right)\) | \(e\left(\frac{19}{65}\right)\) | \(e\left(\frac{148}{195}\right)\) | \(e\left(\frac{157}{390}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{8}{15}\right)\) |