Basic properties
| Modulus: | \(1143\) | |
| Conductor: | \(381\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{381}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1143.ck
\(\chi_{1143}(17,\cdot)\) \(\chi_{1143}(26,\cdot)\) \(\chi_{1143}(35,\cdot)\) \(\chi_{1143}(44,\cdot)\) \(\chi_{1143}(62,\cdot)\) \(\chi_{1143}(71,\cdot)\) \(\chi_{1143}(98,\cdot)\) \(\chi_{1143}(161,\cdot)\) \(\chi_{1143}(197,\cdot)\) \(\chi_{1143}(206,\cdot)\) \(\chi_{1143}(215,\cdot)\) \(\chi_{1143}(242,\cdot)\) \(\chi_{1143}(251,\cdot)\) \(\chi_{1143}(269,\cdot)\) \(\chi_{1143}(296,\cdot)\) \(\chi_{1143}(314,\cdot)\) \(\chi_{1143}(323,\cdot)\) \(\chi_{1143}(422,\cdot)\) \(\chi_{1143}(485,\cdot)\) \(\chi_{1143}(494,\cdot)\) \(\chi_{1143}(521,\cdot)\) \(\chi_{1143}(539,\cdot)\) \(\chi_{1143}(557,\cdot)\) \(\chi_{1143}(629,\cdot)\) \(\chi_{1143}(656,\cdot)\) \(\chi_{1143}(665,\cdot)\) \(\chi_{1143}(719,\cdot)\) \(\chi_{1143}(755,\cdot)\) \(\chi_{1143}(773,\cdot)\) \(\chi_{1143}(836,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((128,892)\) → \((-1,e\left(\frac{19}{63}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 1143 }(17, a) \) | \(-1\) | \(1\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{1}{126}\right)\) | \(e\left(\frac{22}{63}\right)\) | \(e\left(\frac{113}{126}\right)\) | \(e\left(\frac{6}{7}\right)\) |