Basic properties
| Modulus: | \(8004\) | |
| Conductor: | \(667\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(308\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{667}(37,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8004.do
\(\chi_{8004}(37,\cdot)\) \(\chi_{8004}(61,\cdot)\) \(\chi_{8004}(97,\cdot)\) \(\chi_{8004}(205,\cdot)\) \(\chi_{8004}(217,\cdot)\) \(\chi_{8004}(337,\cdot)\) \(\chi_{8004}(385,\cdot)\) \(\chi_{8004}(421,\cdot)\) \(\chi_{8004}(433,\cdot)\) \(\chi_{8004}(649,\cdot)\) \(\chi_{8004}(733,\cdot)\) \(\chi_{8004}(757,\cdot)\) \(\chi_{8004}(769,\cdot)\) \(\chi_{8004}(793,\cdot)\) \(\chi_{8004}(889,\cdot)\) \(\chi_{8004}(925,\cdot)\) \(\chi_{8004}(1033,\cdot)\) \(\chi_{8004}(1141,\cdot)\) \(\chi_{8004}(1249,\cdot)\) \(\chi_{8004}(1261,\cdot)\) \(\chi_{8004}(1345,\cdot)\) \(\chi_{8004}(1477,\cdot)\) \(\chi_{8004}(1489,\cdot)\) \(\chi_{8004}(1585,\cdot)\) \(\chi_{8004}(1597,\cdot)\) \(\chi_{8004}(1621,\cdot)\) \(\chi_{8004}(1693,\cdot)\) \(\chi_{8004}(1801,\cdot)\) \(\chi_{8004}(1813,\cdot)\) \(\chi_{8004}(1837,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{308})$ |
| Fixed field: | Number field defined by a degree 308 polynomial (not computed) |
Values on generators
\((4003,2669,3133,553)\) → \((1,1,e\left(\frac{21}{22}\right),e\left(\frac{3}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 8004 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{24}{77}\right)\) | \(e\left(\frac{65}{154}\right)\) | \(e\left(\frac{83}{308}\right)\) | \(e\left(\frac{45}{154}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{87}{308}\right)\) | \(e\left(\frac{48}{77}\right)\) | \(e\left(\frac{257}{308}\right)\) | \(e\left(\frac{113}{154}\right)\) | \(e\left(\frac{113}{308}\right)\) |