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 \(\chi_{841}(521,\cdot)\) | 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
\(843\) → \(e\left(\frac{51}{58}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 1682 }(521, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{58}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{18}{29}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{13}{58}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{43}{58}\right)\) | \(e\left(\frac{23}{58}\right)\) | \(e\left(\frac{33}{58}\right)\) | \(e\left(\frac{47}{58}\right)\) |