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.cb
\(\chi_{1339}(24,\cdot)\) \(\chi_{1339}(37,\cdot)\) \(\chi_{1339}(80,\cdot)\) \(\chi_{1339}(89,\cdot)\) \(\chi_{1339}(106,\cdot)\) \(\chi_{1339}(145,\cdot)\) \(\chi_{1339}(176,\cdot)\) \(\chi_{1339}(193,\cdot)\) \(\chi_{1339}(197,\cdot)\) \(\chi_{1339}(228,\cdot)\) \(\chi_{1339}(245,\cdot)\) \(\chi_{1339}(275,\cdot)\) \(\chi_{1339}(279,\cdot)\) \(\chi_{1339}(301,\cdot)\) \(\chi_{1339}(319,\cdot)\) \(\chi_{1339}(331,\cdot)\) \(\chi_{1339}(336,\cdot)\) \(\chi_{1339}(340,\cdot)\) \(\chi_{1339}(422,\cdot)\) \(\chi_{1339}(436,\cdot)\) \(\chi_{1339}(449,\cdot)\) \(\chi_{1339}(492,\cdot)\) \(\chi_{1339}(501,\cdot)\) \(\chi_{1339}(518,\cdot)\) \(\chi_{1339}(539,\cdot)\) \(\chi_{1339}(552,\cdot)\) \(\chi_{1339}(557,\cdot)\) \(\chi_{1339}(604,\cdot)\) \(\chi_{1339}(605,\cdot)\) \(\chi_{1339}(609,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{204})$ |
| Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((1237,417)\) → \((e\left(\frac{7}{12}\right),e\left(\frac{31}{34}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1339 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{143}{204}\right)\) | \(e\left(\frac{91}{102}\right)\) | \(e\left(\frac{41}{102}\right)\) | \(e\left(\frac{11}{68}\right)\) | \(e\left(\frac{121}{204}\right)\) | \(e\left(\frac{13}{204}\right)\) | \(e\left(\frac{7}{68}\right)\) | \(e\left(\frac{40}{51}\right)\) | \(e\left(\frac{44}{51}\right)\) | \(e\left(\frac{143}{204}\right)\) |