Basic properties
| Modulus: | \(8004\) | |
| Conductor: | \(8004\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(308\) | 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 8004.dm
\(\chi_{8004}(11,\cdot)\) \(\chi_{8004}(143,\cdot)\) \(\chi_{8004}(155,\cdot)\) \(\chi_{8004}(251,\cdot)\) \(\chi_{8004}(263,\cdot)\) \(\chi_{8004}(287,\cdot)\) \(\chi_{8004}(359,\cdot)\) \(\chi_{8004}(467,\cdot)\) \(\chi_{8004}(479,\cdot)\) \(\chi_{8004}(503,\cdot)\) \(\chi_{8004}(635,\cdot)\) \(\chi_{8004}(659,\cdot)\) \(\chi_{8004}(707,\cdot)\) \(\chi_{8004}(743,\cdot)\) \(\chi_{8004}(815,\cdot)\) \(\chi_{8004}(839,\cdot)\) \(\chi_{8004}(971,\cdot)\) \(\chi_{8004}(983,\cdot)\) \(\chi_{8004}(1055,\cdot)\) \(\chi_{8004}(1091,\cdot)\) \(\chi_{8004}(1187,\cdot)\) \(\chi_{8004}(1295,\cdot)\) \(\chi_{8004}(1307,\cdot)\) \(\chi_{8004}(1331,\cdot)\) \(\chi_{8004}(1355,\cdot)\) \(\chi_{8004}(1487,\cdot)\) \(\chi_{8004}(1523,\cdot)\) \(\chi_{8004}(1535,\cdot)\) \(\chi_{8004}(1643,\cdot)\) \(\chi_{8004}(1667,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{308})$ |
| Fixed field: | Number field defined by a degree 308 polynomial (not computed) |
Values on generators
\((4003,2669,3133,553)\) → \((-1,-1,e\left(\frac{19}{22}\right),e\left(\frac{5}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 8004 }(467, a) \) | \(1\) | \(1\) | \(e\left(\frac{45}{154}\right)\) | \(e\left(\frac{4}{77}\right)\) | \(e\left(\frac{73}{308}\right)\) | \(e\left(\frac{47}{154}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{19}{308}\right)\) | \(e\left(\frac{45}{77}\right)\) | \(e\left(\frac{265}{308}\right)\) | \(e\left(\frac{53}{154}\right)\) | \(e\left(\frac{207}{308}\right)\) |