Basic properties
| Modulus: | \(1682\) | |
| Conductor: | \(841\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(58\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{841}(28,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1682.h
\(\chi_{1682}(57,\cdot)\) \(\chi_{1682}(115,\cdot)\) \(\chi_{1682}(173,\cdot)\) \(\chi_{1682}(231,\cdot)\) \(\chi_{1682}(289,\cdot)\) \(\chi_{1682}(347,\cdot)\) \(\chi_{1682}(405,\cdot)\) \(\chi_{1682}(463,\cdot)\) \(\chi_{1682}(521,\cdot)\) \(\chi_{1682}(579,\cdot)\) \(\chi_{1682}(637,\cdot)\) \(\chi_{1682}(695,\cdot)\) \(\chi_{1682}(753,\cdot)\) \(\chi_{1682}(811,\cdot)\) \(\chi_{1682}(869,\cdot)\) \(\chi_{1682}(927,\cdot)\) \(\chi_{1682}(985,\cdot)\) \(\chi_{1682}(1043,\cdot)\) \(\chi_{1682}(1101,\cdot)\) \(\chi_{1682}(1159,\cdot)\) \(\chi_{1682}(1217,\cdot)\) \(\chi_{1682}(1275,\cdot)\) \(\chi_{1682}(1333,\cdot)\) \(\chi_{1682}(1391,\cdot)\) \(\chi_{1682}(1449,\cdot)\) \(\chi_{1682}(1507,\cdot)\) \(\chi_{1682}(1565,\cdot)\) \(\chi_{1682}(1623,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\(843\) → \(e\left(\frac{27}{58}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1682 }(869, a) \) | \(1\) | \(1\) | \(e\left(\frac{57}{58}\right)\) | \(e\left(\frac{17}{29}\right)\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{41}{58}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{33}{58}\right)\) | \(e\left(\frac{19}{58}\right)\) | \(e\left(\frac{55}{58}\right)\) | \(e\left(\frac{1}{58}\right)\) |