Basic properties
| Modulus: | \(40310\) | |
| Conductor: | \(20155\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(644\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{20155}(39,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 40310.fc
\(\chi_{40310}(39,\cdot)\) \(\chi_{40310}(479,\cdot)\) \(\chi_{40310}(659,\cdot)\) \(\chi_{40310}(769,\cdot)\) \(\chi_{40310}(909,\cdot)\) \(\chi_{40310}(939,\cdot)\) \(\chi_{40310}(1139,\cdot)\) \(\chi_{40310}(1199,\cdot)\) \(\chi_{40310}(1429,\cdot)\) \(\chi_{40310}(1539,\cdot)\) \(\chi_{40310}(1969,\cdot)\) \(\chi_{40310}(2049,\cdot)\) \(\chi_{40310}(2099,\cdot)\) \(\chi_{40310}(2299,\cdot)\) \(\chi_{40310}(2439,\cdot)\) \(\chi_{40310}(2589,\cdot)\) \(\chi_{40310}(2649,\cdot)\) \(\chi_{40310}(2689,\cdot)\) \(\chi_{40310}(2839,\cdot)\) \(\chi_{40310}(2979,\cdot)\) \(\chi_{40310}(3259,\cdot)\) \(\chi_{40310}(3279,\cdot)\) \(\chi_{40310}(3469,\cdot)\) \(\chi_{40310}(3549,\cdot)\) \(\chi_{40310}(3559,\cdot)\) \(\chi_{40310}(3569,\cdot)\) \(\chi_{40310}(3709,\cdot)\) \(\chi_{40310}(4039,\cdot)\) \(\chi_{40310}(4079,\cdot)\) \(\chi_{40310}(4319,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{644})$ |
| Fixed field: | Number field defined by a degree 644 polynomial (not computed) |
Values on generators
\((24187,19461,16821)\) → \((-1,e\left(\frac{23}{28}\right),e\left(\frac{35}{46}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 40310 }(39, a) \) | \(1\) | \(1\) | \(e\left(\frac{517}{644}\right)\) | \(e\left(\frac{129}{322}\right)\) | \(e\left(\frac{195}{322}\right)\) | \(e\left(\frac{233}{644}\right)\) | \(e\left(\frac{158}{161}\right)\) | \(e\left(\frac{15}{92}\right)\) | \(e\left(\frac{519}{644}\right)\) | \(e\left(\frac{131}{644}\right)\) | \(e\left(\frac{76}{161}\right)\) | \(e\left(\frac{263}{644}\right)\) |