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
\((1237,417)\) → \((-i,e\left(\frac{1}{102}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1339 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{204}\right)\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{37}{102}\right)\) | \(e\left(\frac{155}{204}\right)\) | \(e\left(\frac{115}{204}\right)\) | \(e\left(\frac{59}{204}\right)\) | \(e\left(\frac{37}{68}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{173}{204}\right)\) |