Basic properties
Modulus: | \(1339\) | |
Conductor: | \(1339\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(204\) | 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 1339.ch
\(\chi_{1339}(5,\cdot)\) \(\chi_{1339}(21,\cdot)\) \(\chi_{1339}(44,\cdot)\) \(\chi_{1339}(70,\cdot)\) \(\chi_{1339}(86,\cdot)\) \(\chi_{1339}(96,\cdot)\) \(\chi_{1339}(99,\cdot)\) \(\chi_{1339}(109,\cdot)\) \(\chi_{1339}(138,\cdot)\) \(\chi_{1339}(148,\cdot)\) \(\chi_{1339}(151,\cdot)\) \(\chi_{1339}(174,\cdot)\) \(\chi_{1339}(177,\cdot)\) \(\chi_{1339}(187,\cdot)\) \(\chi_{1339}(190,\cdot)\) \(\chi_{1339}(226,\cdot)\) \(\chi_{1339}(268,\cdot)\) \(\chi_{1339}(281,\cdot)\) \(\chi_{1339}(291,\cdot)\) \(\chi_{1339}(294,\cdot)\) \(\chi_{1339}(307,\cdot)\) \(\chi_{1339}(320,\cdot)\) \(\chi_{1339}(330,\cdot)\) \(\chi_{1339}(395,\cdot)\) \(\chi_{1339}(408,\cdot)\) \(\chi_{1339}(424,\cdot)\) \(\chi_{1339}(447,\cdot)\) \(\chi_{1339}(460,\cdot)\) \(\chi_{1339}(463,\cdot)\) \(\chi_{1339}(486,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{204})$ |
Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((1237,417)\) → \((-i,e\left(\frac{83}{102}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1339 }(109, a) \) | \(1\) | \(1\) | \(e\left(\frac{113}{204}\right)\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{11}{102}\right)\) | \(e\left(\frac{115}{204}\right)\) | \(e\left(\frac{59}{204}\right)\) | \(e\left(\frac{103}{204}\right)\) | \(e\left(\frac{45}{68}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{181}{204}\right)\) |