Basic properties
| Modulus: | \(1682\) | |
| Conductor: | \(841\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(29\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{841}(59,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1682.g
\(\chi_{1682}(59,\cdot)\) \(\chi_{1682}(117,\cdot)\) \(\chi_{1682}(175,\cdot)\) \(\chi_{1682}(233,\cdot)\) \(\chi_{1682}(291,\cdot)\) \(\chi_{1682}(349,\cdot)\) \(\chi_{1682}(407,\cdot)\) \(\chi_{1682}(465,\cdot)\) \(\chi_{1682}(523,\cdot)\) \(\chi_{1682}(581,\cdot)\) \(\chi_{1682}(639,\cdot)\) \(\chi_{1682}(697,\cdot)\) \(\chi_{1682}(755,\cdot)\) \(\chi_{1682}(813,\cdot)\) \(\chi_{1682}(871,\cdot)\) \(\chi_{1682}(929,\cdot)\) \(\chi_{1682}(987,\cdot)\) \(\chi_{1682}(1045,\cdot)\) \(\chi_{1682}(1103,\cdot)\) \(\chi_{1682}(1161,\cdot)\) \(\chi_{1682}(1219,\cdot)\) \(\chi_{1682}(1277,\cdot)\) \(\chi_{1682}(1335,\cdot)\) \(\chi_{1682}(1393,\cdot)\) \(\chi_{1682}(1451,\cdot)\) \(\chi_{1682}(1509,\cdot)\) \(\chi_{1682}(1567,\cdot)\) \(\chi_{1682}(1625,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 29 polynomial |
Values on generators
\(843\) → \(e\left(\frac{2}{29}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1682 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{17}{29}\right)\) | \(e\left(\frac{19}{29}\right)\) | \(e\left(\frac{25}{29}\right)\) | \(e\left(\frac{10}{29}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{28}{29}\right)\) |