Basic properties
Modulus: | \(5241\) | |
Conductor: | \(5241\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1746\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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
\((1748,3496)\) → \((-1,e\left(\frac{1703}{1746}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 5241 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{415}{873}\right)\) | \(e\left(\frac{830}{873}\right)\) | \(e\left(\frac{488}{873}\right)\) | \(e\left(\frac{767}{1746}\right)\) | \(e\left(\frac{124}{291}\right)\) | \(e\left(\frac{10}{291}\right)\) | \(e\left(\frac{191}{291}\right)\) | \(e\left(\frac{161}{1746}\right)\) | \(e\left(\frac{1597}{1746}\right)\) | \(e\left(\frac{787}{873}\right)\) |