Basic properties
| Modulus: | \(5241\) | |
| Conductor: | \(5241\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1746\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5241.x
\(\chi_{5241}(2,\cdot)\) \(\chi_{5241}(5,\cdot)\) \(\chi_{5241}(20,\cdot)\) \(\chi_{5241}(32,\cdot)\) \(\chi_{5241}(38,\cdot)\) \(\chi_{5241}(44,\cdot)\) \(\chi_{5241}(47,\cdot)\) \(\chi_{5241}(50,\cdot)\) \(\chi_{5241}(53,\cdot)\) \(\chi_{5241}(59,\cdot)\) \(\chi_{5241}(71,\cdot)\) \(\chi_{5241}(83,\cdot)\) \(\chi_{5241}(86,\cdot)\) \(\chi_{5241}(89,\cdot)\) \(\chi_{5241}(95,\cdot)\) \(\chi_{5241}(107,\cdot)\) \(\chi_{5241}(122,\cdot)\) \(\chi_{5241}(128,\cdot)\) \(\chi_{5241}(131,\cdot)\) \(\chi_{5241}(134,\cdot)\) \(\chi_{5241}(149,\cdot)\) \(\chi_{5241}(155,\cdot)\) \(\chi_{5241}(161,\cdot)\) \(\chi_{5241}(167,\cdot)\) \(\chi_{5241}(173,\cdot)\) \(\chi_{5241}(176,\cdot)\) \(\chi_{5241}(188,\cdot)\) \(\chi_{5241}(194,\cdot)\) \(\chi_{5241}(200,\cdot)\) \(\chi_{5241}(203,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{873})$ |
| Fixed field: | Number field defined by a degree 1746 polynomial (not computed) |
Values on generators
\((1748,3496)\) → \((-1,e\left(\frac{5}{1746}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 5241 }(32, a) \) | \(1\) | \(1\) | \(e\left(\frac{439}{873}\right)\) | \(e\left(\frac{5}{873}\right)\) | \(e\left(\frac{329}{873}\right)\) | \(e\left(\frac{1535}{1746}\right)\) | \(e\left(\frac{148}{291}\right)\) | \(e\left(\frac{256}{291}\right)\) | \(e\left(\frac{59}{291}\right)\) | \(e\left(\frac{1037}{1746}\right)\) | \(e\left(\frac{667}{1746}\right)\) | \(e\left(\frac{10}{873}\right)\) |