Basic properties
Modulus: | \(6003\) | |
Conductor: | \(6003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(924\) | 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 6003.do
\(\chi_{6003}(2,\cdot)\) \(\chi_{6003}(32,\cdot)\) \(\chi_{6003}(50,\cdot)\) \(\chi_{6003}(77,\cdot)\) \(\chi_{6003}(95,\cdot)\) \(\chi_{6003}(101,\cdot)\) \(\chi_{6003}(119,\cdot)\) \(\chi_{6003}(131,\cdot)\) \(\chi_{6003}(164,\cdot)\) \(\chi_{6003}(200,\cdot)\) \(\chi_{6003}(308,\cdot)\) \(\chi_{6003}(311,\cdot)\) \(\chi_{6003}(317,\cdot)\) \(\chi_{6003}(338,\cdot)\) \(\chi_{6003}(374,\cdot)\) \(\chi_{6003}(380,\cdot)\) \(\chi_{6003}(416,\cdot)\) \(\chi_{6003}(443,\cdot)\) \(\chi_{6003}(446,\cdot)\) \(\chi_{6003}(491,\cdot)\) \(\chi_{6003}(524,\cdot)\) \(\chi_{6003}(533,\cdot)\) \(\chi_{6003}(554,\cdot)\) \(\chi_{6003}(578,\cdot)\) \(\chi_{6003}(623,\cdot)\) \(\chi_{6003}(653,\cdot)\) \(\chi_{6003}(698,\cdot)\) \(\chi_{6003}(722,\cdot)\) \(\chi_{6003}(740,\cdot)\) \(\chi_{6003}(752,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{924})$ |
Fixed field: | Number field defined by a degree 924 polynomial (not computed) |
Values on generators
\((668,3133,4555)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{6}{11}\right),e\left(\frac{5}{28}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 6003 }(1076, a) \) | \(1\) | \(1\) | \(e\left(\frac{95}{924}\right)\) | \(e\left(\frac{95}{462}\right)\) | \(e\left(\frac{148}{231}\right)\) | \(e\left(\frac{194}{231}\right)\) | \(e\left(\frac{95}{308}\right)\) | \(e\left(\frac{229}{308}\right)\) | \(e\left(\frac{191}{924}\right)\) | \(e\left(\frac{239}{462}\right)\) | \(e\left(\frac{871}{924}\right)\) | \(e\left(\frac{95}{231}\right)\) |