Basic properties
Modulus: | \(6003\) | |
Conductor: | \(6003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(924\) | 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 6003.dp
\(\chi_{6003}(40,\cdot)\) \(\chi_{6003}(43,\cdot)\) \(\chi_{6003}(61,\cdot)\) \(\chi_{6003}(76,\cdot)\) \(\chi_{6003}(79,\cdot)\) \(\chi_{6003}(97,\cdot)\) \(\chi_{6003}(106,\cdot)\) \(\chi_{6003}(130,\cdot)\) \(\chi_{6003}(148,\cdot)\) \(\chi_{6003}(166,\cdot)\) \(\chi_{6003}(205,\cdot)\) \(\chi_{6003}(214,\cdot)\) \(\chi_{6003}(247,\cdot)\) \(\chi_{6003}(250,\cdot)\) \(\chi_{6003}(304,\cdot)\) \(\chi_{6003}(337,\cdot)\) \(\chi_{6003}(385,\cdot)\) \(\chi_{6003}(421,\cdot)\) \(\chi_{6003}(454,\cdot)\) \(\chi_{6003}(475,\cdot)\) \(\chi_{6003}(490,\cdot)\) \(\chi_{6003}(511,\cdot)\) \(\chi_{6003}(520,\cdot)\) \(\chi_{6003}(562,\cdot)\) \(\chi_{6003}(619,\cdot)\) \(\chi_{6003}(628,\cdot)\) \(\chi_{6003}(664,\cdot)\) \(\chi_{6003}(682,\cdot)\) \(\chi_{6003}(688,\cdot)\) \(\chi_{6003}(727,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{924})$ |
Fixed field: | Number field defined by a degree 924 polynomial (not computed) |
Values on generators
\((668,3133,4555)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{15}{22}\right),e\left(\frac{5}{28}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 6003 }(1192, a) \) | \(1\) | \(1\) | \(e\left(\frac{809}{924}\right)\) | \(e\left(\frac{347}{462}\right)\) | \(e\left(\frac{64}{231}\right)\) | \(e\left(\frac{199}{462}\right)\) | \(e\left(\frac{193}{308}\right)\) | \(e\left(\frac{47}{308}\right)\) | \(e\left(\frac{863}{924}\right)\) | \(e\left(\frac{197}{462}\right)\) | \(e\left(\frac{283}{924}\right)\) | \(e\left(\frac{116}{231}\right)\) |