Basic properties
Modulus: | \(8044\) | |
Conductor: | \(8044\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(402\) | 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 8044.y
\(\chi_{8044}(15,\cdot)\) \(\chi_{8044}(67,\cdot)\) \(\chi_{8044}(91,\cdot)\) \(\chi_{8044}(139,\cdot)\) \(\chi_{8044}(143,\cdot)\) \(\chi_{8044}(163,\cdot)\) \(\chi_{8044}(171,\cdot)\) \(\chi_{8044}(231,\cdot)\) \(\chi_{8044}(243,\cdot)\) \(\chi_{8044}(275,\cdot)\) \(\chi_{8044}(363,\cdot)\) \(\chi_{8044}(527,\cdot)\) \(\chi_{8044}(643,\cdot)\) \(\chi_{8044}(655,\cdot)\) \(\chi_{8044}(707,\cdot)\) \(\chi_{8044}(719,\cdot)\) \(\chi_{8044}(727,\cdot)\) \(\chi_{8044}(827,\cdot)\) \(\chi_{8044}(867,\cdot)\) \(\chi_{8044}(899,\cdot)\) \(\chi_{8044}(987,\cdot)\) \(\chi_{8044}(1111,\cdot)\) \(\chi_{8044}(1167,\cdot)\) \(\chi_{8044}(1175,\cdot)\) \(\chi_{8044}(1191,\cdot)\) \(\chi_{8044}(1239,\cdot)\) \(\chi_{8044}(1255,\cdot)\) \(\chi_{8044}(1283,\cdot)\) \(\chi_{8044}(1475,\cdot)\) \(\chi_{8044}(1479,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{201})$ |
Fixed field: | Number field defined by a degree 402 polynomial (not computed) |
Values on generators
\((4023,4025)\) → \((-1,e\left(\frac{205}{402}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 8044 }(15, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{201}\right)\) | \(e\left(\frac{38}{201}\right)\) | \(e\left(\frac{197}{201}\right)\) | \(e\left(\frac{4}{201}\right)\) | \(e\left(\frac{64}{201}\right)\) | \(e\left(\frac{19}{67}\right)\) | \(e\left(\frac{40}{201}\right)\) | \(e\left(\frac{383}{402}\right)\) | \(e\left(\frac{115}{201}\right)\) | \(e\left(\frac{199}{201}\right)\) |