Basic properties
| Modulus: | \(5635\) | |
| Conductor: | \(5635\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(924\) | 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 5635.do
\(\chi_{5635}(3,\cdot)\) \(\chi_{5635}(12,\cdot)\) \(\chi_{5635}(52,\cdot)\) \(\chi_{5635}(73,\cdot)\) \(\chi_{5635}(82,\cdot)\) \(\chi_{5635}(87,\cdot)\) \(\chi_{5635}(108,\cdot)\) \(\chi_{5635}(173,\cdot)\) \(\chi_{5635}(187,\cdot)\) \(\chi_{5635}(192,\cdot)\) \(\chi_{5635}(213,\cdot)\) \(\chi_{5635}(243,\cdot)\) \(\chi_{5635}(248,\cdot)\) \(\chi_{5635}(257,\cdot)\) \(\chi_{5635}(262,\cdot)\) \(\chi_{5635}(278,\cdot)\) \(\chi_{5635}(292,\cdot)\) \(\chi_{5635}(348,\cdot)\) \(\chi_{5635}(353,\cdot)\) \(\chi_{5635}(397,\cdot)\) \(\chi_{5635}(418,\cdot)\) \(\chi_{5635}(432,\cdot)\) \(\chi_{5635}(453,\cdot)\) \(\chi_{5635}(537,\cdot)\) \(\chi_{5635}(542,\cdot)\) \(\chi_{5635}(577,\cdot)\) \(\chi_{5635}(593,\cdot)\) \(\chi_{5635}(633,\cdot)\) \(\chi_{5635}(647,\cdot)\) \(\chi_{5635}(698,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{924})$ |
| Fixed field: | Number field defined by a degree 924 polynomial (not computed) |
Values on generators
\((3382,346,2696)\) → \((-i,e\left(\frac{1}{42}\right),e\left(\frac{8}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 5635 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{761}{924}\right)\) | \(e\left(\frac{841}{924}\right)\) | \(e\left(\frac{299}{462}\right)\) | \(e\left(\frac{113}{154}\right)\) | \(e\left(\frac{145}{308}\right)\) | \(e\left(\frac{379}{462}\right)\) | \(e\left(\frac{115}{231}\right)\) | \(e\left(\frac{515}{924}\right)\) | \(e\left(\frac{67}{308}\right)\) | \(e\left(\frac{68}{231}\right)\) |