Basic properties
Modulus: | \(1339\) | |
Conductor: | \(1339\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(204\) | 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 1339.cd
\(\chi_{1339}(6,\cdot)\) \(\chi_{1339}(11,\cdot)\) \(\chi_{1339}(20,\cdot)\) \(\chi_{1339}(67,\cdot)\) \(\chi_{1339}(84,\cdot)\) \(\chi_{1339}(85,\cdot)\) \(\chi_{1339}(115,\cdot)\) \(\chi_{1339}(123,\cdot)\) \(\chi_{1339}(154,\cdot)\) \(\chi_{1339}(188,\cdot)\) \(\chi_{1339}(241,\cdot)\) \(\chi_{1339}(254,\cdot)\) \(\chi_{1339}(271,\cdot)\) \(\chi_{1339}(280,\cdot)\) \(\chi_{1339}(293,\cdot)\) \(\chi_{1339}(314,\cdot)\) \(\chi_{1339}(344,\cdot)\) \(\chi_{1339}(349,\cdot)\) \(\chi_{1339}(357,\cdot)\) \(\chi_{1339}(362,\cdot)\) \(\chi_{1339}(371,\cdot)\) \(\chi_{1339}(379,\cdot)\) \(\chi_{1339}(383,\cdot)\) \(\chi_{1339}(384,\cdot)\) \(\chi_{1339}(396,\cdot)\) \(\chi_{1339}(405,\cdot)\) \(\chi_{1339}(410,\cdot)\) \(\chi_{1339}(457,\cdot)\) \(\chi_{1339}(474,\cdot)\) \(\chi_{1339}(479,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{204})$ |
Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((1237,417)\) → \((e\left(\frac{5}{12}\right),e\left(\frac{83}{102}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1339 }(6, a) \) | \(1\) | \(1\) | \(e\left(\frac{15}{68}\right)\) | \(e\left(\frac{41}{102}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{115}{204}\right)\) | \(e\left(\frac{127}{204}\right)\) | \(e\left(\frac{57}{68}\right)\) | \(e\left(\frac{45}{68}\right)\) | \(e\left(\frac{41}{51}\right)\) | \(e\left(\frac{40}{51}\right)\) | \(e\left(\frac{113}{204}\right)\) |