Basic properties
| Modulus: | \(5241\) | |
| Conductor: | \(1747\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(291\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1747}(19,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5241.q
\(\chi_{5241}(10,\cdot)\) \(\chi_{5241}(19,\cdot)\) \(\chi_{5241}(64,\cdot)\) \(\chi_{5241}(67,\cdot)\) \(\chi_{5241}(100,\cdot)\) \(\chi_{5241}(106,\cdot)\) \(\chi_{5241}(118,\cdot)\) \(\chi_{5241}(121,\cdot)\) \(\chi_{5241}(166,\cdot)\) \(\chi_{5241}(172,\cdot)\) \(\chi_{5241}(190,\cdot)\) \(\chi_{5241}(298,\cdot)\) \(\chi_{5241}(322,\cdot)\) \(\chi_{5241}(361,\cdot)\) \(\chi_{5241}(388,\cdot)\) \(\chi_{5241}(391,\cdot)\) \(\chi_{5241}(421,\cdot)\) \(\chi_{5241}(436,\cdot)\) \(\chi_{5241}(445,\cdot)\) \(\chi_{5241}(457,\cdot)\) \(\chi_{5241}(496,\cdot)\) \(\chi_{5241}(502,\cdot)\) \(\chi_{5241}(523,\cdot)\) \(\chi_{5241}(610,\cdot)\) \(\chi_{5241}(655,\cdot)\) \(\chi_{5241}(739,\cdot)\) \(\chi_{5241}(754,\cdot)\) \(\chi_{5241}(775,\cdot)\) \(\chi_{5241}(784,\cdot)\) \(\chi_{5241}(835,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{291})$ |
| Fixed field: | Number field defined by a degree 291 polynomial (not computed) |
Values on generators
\((1748,3496)\) → \((1,e\left(\frac{236}{291}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 5241 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{236}{291}\right)\) | \(e\left(\frac{181}{291}\right)\) | \(e\left(\frac{37}{291}\right)\) | \(e\left(\frac{284}{291}\right)\) | \(e\left(\frac{42}{97}\right)\) | \(e\left(\frac{91}{97}\right)\) | \(e\left(\frac{60}{97}\right)\) | \(e\left(\frac{233}{291}\right)\) | \(e\left(\frac{229}{291}\right)\) | \(e\left(\frac{71}{291}\right)\) |