Basic properties
Modulus: | \(6003\) | |
Conductor: | \(6003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(231\) | 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
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6003.dc
\(\chi_{6003}(16,\cdot)\) \(\chi_{6003}(25,\cdot)\) \(\chi_{6003}(49,\cdot)\) \(\chi_{6003}(52,\cdot)\) \(\chi_{6003}(94,\cdot)\) \(\chi_{6003}(169,\cdot)\) \(\chi_{6003}(223,\cdot)\) \(\chi_{6003}(256,\cdot)\) \(\chi_{6003}(400,\cdot)\) \(\chi_{6003}(430,\cdot)\) \(\chi_{6003}(538,\cdot)\) \(\chi_{6003}(547,\cdot)\) \(\chi_{6003}(616,\cdot)\) \(\chi_{6003}(625,\cdot)\) \(\chi_{6003}(634,\cdot)\) \(\chi_{6003}(745,\cdot)\) \(\chi_{6003}(790,\cdot)\) \(\chi_{6003}(808,\cdot)\) \(\chi_{6003}(832,\cdot)\) \(\chi_{6003}(877,\cdot)\) \(\chi_{6003}(886,\cdot)\) \(\chi_{6003}(922,\cdot)\) \(\chi_{6003}(952,\cdot)\) \(\chi_{6003}(1039,\cdot)\) \(\chi_{6003}(1051,\cdot)\) \(\chi_{6003}(1060,\cdot)\) \(\chi_{6003}(1093,\cdot)\) \(\chi_{6003}(1156,\cdot)\) \(\chi_{6003}(1267,\cdot)\) \(\chi_{6003}(1300,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{231})$ |
Fixed field: | Number field defined by a degree 231 polynomial (not computed) |
Values on generators
\((668,3133,4555)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{2}{11}\right),e\left(\frac{2}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 6003 }(1039, a) \) | \(1\) | \(1\) | \(e\left(\frac{227}{231}\right)\) | \(e\left(\frac{223}{231}\right)\) | \(e\left(\frac{31}{231}\right)\) | \(e\left(\frac{50}{231}\right)\) | \(e\left(\frac{73}{77}\right)\) | \(e\left(\frac{9}{77}\right)\) | \(e\left(\frac{26}{231}\right)\) | \(e\left(\frac{82}{231}\right)\) | \(e\left(\frac{46}{231}\right)\) | \(e\left(\frac{215}{231}\right)\) |