Basic properties
| Modulus: | \(40310\) | |
| Conductor: | \(20155\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(276\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{20155}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 40310.ep
\(\chi_{40310}(17,\cdot)\) \(\chi_{40310}(273,\cdot)\) \(\chi_{40310}(853,\cdot)\) \(\chi_{40310}(887,\cdot)\) \(\chi_{40310}(2047,\cdot)\) \(\chi_{40310}(3173,\cdot)\) \(\chi_{40310}(3497,\cdot)\) \(\chi_{40310}(4043,\cdot)\) \(\chi_{40310}(4367,\cdot)\) \(\chi_{40310}(4657,\cdot)\) \(\chi_{40310}(5493,\cdot)\) \(\chi_{40310}(6107,\cdot)\) \(\chi_{40310}(6363,\cdot)\) \(\chi_{40310}(6397,\cdot)\) \(\chi_{40310}(6687,\cdot)\) \(\chi_{40310}(6943,\cdot)\) \(\chi_{40310}(7523,\cdot)\) \(\chi_{40310}(8393,\cdot)\) \(\chi_{40310}(9007,\cdot)\) \(\chi_{40310}(9297,\cdot)\) \(\chi_{40310}(9553,\cdot)\) \(\chi_{40310}(9587,\cdot)\) \(\chi_{40310}(10457,\cdot)\) \(\chi_{40310}(11003,\cdot)\) \(\chi_{40310}(11037,\cdot)\) \(\chi_{40310}(11327,\cdot)\) \(\chi_{40310}(11873,\cdot)\) \(\chi_{40310}(11907,\cdot)\) \(\chi_{40310}(12163,\cdot)\) \(\chi_{40310}(12197,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{276})$ |
| Fixed field: | Number field defined by a degree 276 polynomial (not computed) |
Values on generators
\((24187,19461,16821)\) → \((i,-i,e\left(\frac{107}{138}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 40310 }(17, a) \) | \(-1\) | \(1\) | \(e\left(\frac{20}{69}\right)\) | \(e\left(\frac{5}{276}\right)\) | \(e\left(\frac{40}{69}\right)\) | \(e\left(\frac{187}{276}\right)\) | \(e\left(\frac{241}{276}\right)\) | \(e\left(\frac{133}{138}\right)\) | \(e\left(\frac{151}{276}\right)\) | \(e\left(\frac{85}{276}\right)\) | \(e\left(\frac{63}{92}\right)\) | \(e\left(\frac{20}{23}\right)\) |