Basic properties
| Modulus: | \(5241\) | |
| Conductor: | \(1747\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(873\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1747}(25,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5241.u
\(\chi_{5241}(4,\cdot)\) \(\chi_{5241}(16,\cdot)\) \(\chi_{5241}(22,\cdot)\) \(\chi_{5241}(25,\cdot)\) \(\chi_{5241}(31,\cdot)\) \(\chi_{5241}(40,\cdot)\) \(\chi_{5241}(43,\cdot)\) \(\chi_{5241}(49,\cdot)\) \(\chi_{5241}(55,\cdot)\) \(\chi_{5241}(76,\cdot)\) \(\chi_{5241}(91,\cdot)\) \(\chi_{5241}(97,\cdot)\) \(\chi_{5241}(109,\cdot)\) \(\chi_{5241}(124,\cdot)\) \(\chi_{5241}(160,\cdot)\) \(\chi_{5241}(163,\cdot)\) \(\chi_{5241}(169,\cdot)\) \(\chi_{5241}(178,\cdot)\) \(\chi_{5241}(196,\cdot)\) \(\chi_{5241}(220,\cdot)\) \(\chi_{5241}(223,\cdot)\) \(\chi_{5241}(229,\cdot)\) \(\chi_{5241}(235,\cdot)\) \(\chi_{5241}(238,\cdot)\) \(\chi_{5241}(241,\cdot)\) \(\chi_{5241}(244,\cdot)\) \(\chi_{5241}(250,\cdot)\) \(\chi_{5241}(256,\cdot)\) \(\chi_{5241}(259,\cdot)\) \(\chi_{5241}(262,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{873})$ |
| Fixed field: | Number field defined by a degree 873 polynomial (not computed) |
Values on generators
\((1748,3496)\) → \((1,e\left(\frac{830}{873}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 5241 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{830}{873}\right)\) | \(e\left(\frac{787}{873}\right)\) | \(e\left(\frac{103}{873}\right)\) | \(e\left(\frac{767}{873}\right)\) | \(e\left(\frac{248}{291}\right)\) | \(e\left(\frac{20}{291}\right)\) | \(e\left(\frac{91}{291}\right)\) | \(e\left(\frac{161}{873}\right)\) | \(e\left(\frac{724}{873}\right)\) | \(e\left(\frac{701}{873}\right)\) |