Basic properties
| Modulus: | \(1339\) | |
| Conductor: | \(1339\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(102\) | 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.bp
\(\chi_{1339}(25,\cdot)\) \(\chi_{1339}(38,\cdot)\) \(\chi_{1339}(129,\cdot)\) \(\chi_{1339}(155,\cdot)\) \(\chi_{1339}(194,\cdot)\) \(\chi_{1339}(298,\cdot)\) \(\chi_{1339}(311,\cdot)\) \(\chi_{1339}(324,\cdot)\) \(\chi_{1339}(337,\cdot)\) \(\chi_{1339}(350,\cdot)\) \(\chi_{1339}(428,\cdot)\) \(\chi_{1339}(441,\cdot)\) \(\chi_{1339}(467,\cdot)\) \(\chi_{1339}(480,\cdot)\) \(\chi_{1339}(519,\cdot)\) \(\chi_{1339}(532,\cdot)\) \(\chi_{1339}(597,\cdot)\) \(\chi_{1339}(636,\cdot)\) \(\chi_{1339}(701,\cdot)\) \(\chi_{1339}(740,\cdot)\) \(\chi_{1339}(753,\cdot)\) \(\chi_{1339}(779,\cdot)\) \(\chi_{1339}(818,\cdot)\) \(\chi_{1339}(831,\cdot)\) \(\chi_{1339}(857,\cdot)\) \(\chi_{1339}(883,\cdot)\) \(\chi_{1339}(922,\cdot)\) \(\chi_{1339}(987,\cdot)\) \(\chi_{1339}(1169,\cdot)\) \(\chi_{1339}(1182,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((1237,417)\) → \((-1,e\left(\frac{1}{51}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1339 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{102}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{37}{51}\right)\) | \(e\left(\frac{53}{102}\right)\) | \(e\left(\frac{13}{102}\right)\) | \(e\left(\frac{59}{102}\right)\) | \(e\left(\frac{3}{34}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{71}{102}\right)\) |