Basic properties
| Modulus: | \(5635\) | |
| Conductor: | \(5635\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(462\) | 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.dm
\(\chi_{5635}(4,\cdot)\) \(\chi_{5635}(9,\cdot)\) \(\chi_{5635}(39,\cdot)\) \(\chi_{5635}(144,\cdot)\) \(\chi_{5635}(179,\cdot)\) \(\chi_{5635}(219,\cdot)\) \(\chi_{5635}(284,\cdot)\) \(\chi_{5635}(289,\cdot)\) \(\chi_{5635}(354,\cdot)\) \(\chi_{5635}(394,\cdot)\) \(\chi_{5635}(464,\cdot)\) \(\chi_{5635}(499,\cdot)\) \(\chi_{5635}(564,\cdot)\) \(\chi_{5635}(604,\cdot)\) \(\chi_{5635}(634,\cdot)\) \(\chi_{5635}(639,\cdot)\) \(\chi_{5635}(669,\cdot)\) \(\chi_{5635}(739,\cdot)\) \(\chi_{5635}(744,\cdot)\) \(\chi_{5635}(809,\cdot)\) \(\chi_{5635}(844,\cdot)\) \(\chi_{5635}(984,\cdot)\) \(\chi_{5635}(1024,\cdot)\) \(\chi_{5635}(1089,\cdot)\) \(\chi_{5635}(1094,\cdot)\) \(\chi_{5635}(1129,\cdot)\) \(\chi_{5635}(1159,\cdot)\) \(\chi_{5635}(1199,\cdot)\) \(\chi_{5635}(1269,\cdot)\) \(\chi_{5635}(1369,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{231})$ |
| Fixed field: | Number field defined by a degree 462 polynomial (not computed) |
Values on generators
\((3382,346,2696)\) → \((-1,e\left(\frac{5}{21}\right),e\left(\frac{2}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 5635 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{462}\right)\) | \(e\left(\frac{299}{462}\right)\) | \(e\left(\frac{25}{231}\right)\) | \(e\left(\frac{54}{77}\right)\) | \(e\left(\frac{25}{154}\right)\) | \(e\left(\frac{68}{231}\right)\) | \(e\left(\frac{37}{231}\right)\) | \(e\left(\frac{349}{462}\right)\) | \(e\left(\frac{139}{154}\right)\) | \(e\left(\frac{50}{231}\right)\) |