Basic properties
| Modulus: | \(40310\) | |
| Conductor: | \(4031\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1932\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4031}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 40310.fv
\(\chi_{40310}(11,\cdot)\) \(\chi_{40310}(31,\cdot)\) \(\chi_{40310}(391,\cdot)\) \(\chi_{40310}(421,\cdot)\) \(\chi_{40310}(541,\cdot)\) \(\chi_{40310}(561,\cdot)\) \(\chi_{40310}(591,\cdot)\) \(\chi_{40310}(711,\cdot)\) \(\chi_{40310}(781,\cdot)\) \(\chi_{40310}(831,\cdot)\) \(\chi_{40310}(881,\cdot)\) \(\chi_{40310}(901,\cdot)\) \(\chi_{40310}(971,\cdot)\) \(\chi_{40310}(1001,\cdot)\) \(\chi_{40310}(1091,\cdot)\) \(\chi_{40310}(1121,\cdot)\) \(\chi_{40310}(1141,\cdot)\) \(\chi_{40310}(1181,\cdot)\) \(\chi_{40310}(1371,\cdot)\) \(\chi_{40310}(1431,\cdot)\) \(\chi_{40310}(1461,\cdot)\) \(\chi_{40310}(1471,\cdot)\) \(\chi_{40310}(1511,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{1932})$ |
| Fixed field: | Number field defined by a degree 1932 polynomial (not computed) |
Values on generators
\((24187,19461,16821)\) → \((1,e\left(\frac{1}{28}\right),e\left(\frac{28}{69}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 40310 }(31, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1577}{1932}\right)\) | \(e\left(\frac{347}{483}\right)\) | \(e\left(\frac{611}{966}\right)\) | \(e\left(\frac{1417}{1932}\right)\) | \(e\left(\frac{593}{966}\right)\) | \(e\left(\frac{47}{276}\right)\) | \(e\left(\frac{145}{1932}\right)\) | \(e\left(\frac{1033}{1932}\right)\) | \(e\left(\frac{108}{161}\right)\) | \(e\left(\frac{289}{644}\right)\) |