Basic properties
| Modulus: | \(1337\) | |
| Conductor: | \(1337\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(114\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1337.x
\(\chi_{1337}(5,\cdot)\) \(\chi_{1337}(52,\cdot)\) \(\chi_{1337}(136,\cdot)\) \(\chi_{1337}(150,\cdot)\) \(\chi_{1337}(180,\cdot)\) \(\chi_{1337}(227,\cdot)\) \(\chi_{1337}(243,\cdot)\) \(\chi_{1337}(327,\cdot)\) \(\chi_{1337}(341,\cdot)\) \(\chi_{1337}(388,\cdot)\) \(\chi_{1337}(418,\cdot)\) \(\chi_{1337}(451,\cdot)\) \(\chi_{1337}(507,\cdot)\) \(\chi_{1337}(535,\cdot)\) \(\chi_{1337}(542,\cdot)\) \(\chi_{1337}(579,\cdot)\) \(\chi_{1337}(598,\cdot)\) \(\chi_{1337}(605,\cdot)\) \(\chi_{1337}(642,\cdot)\) \(\chi_{1337}(698,\cdot)\) \(\chi_{1337}(726,\cdot)\) \(\chi_{1337}(733,\cdot)\) \(\chi_{1337}(789,\cdot)\) \(\chi_{1337}(794,\cdot)\) \(\chi_{1337}(796,\cdot)\) \(\chi_{1337}(871,\cdot)\) \(\chi_{1337}(885,\cdot)\) \(\chi_{1337}(941,\cdot)\) \(\chi_{1337}(985,\cdot)\) \(\chi_{1337}(1062,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((192,974)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{13}{19}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1337 }(418, a) \) | \(-1\) | \(1\) | \(e\left(\frac{44}{57}\right)\) | \(e\left(\frac{23}{114}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{43}{114}\right)\) | \(e\left(\frac{37}{38}\right)\) | \(e\left(\frac{6}{19}\right)\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{17}{114}\right)\) | \(e\left(\frac{28}{57}\right)\) | \(e\left(\frac{85}{114}\right)\) |