Basic properties
| Modulus: | \(944\) | |
| Conductor: | \(59\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(58\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{59}(56,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 944.n
\(\chi_{944}(33,\cdot)\) \(\chi_{944}(65,\cdot)\) \(\chi_{944}(97,\cdot)\) \(\chi_{944}(113,\cdot)\) \(\chi_{944}(129,\cdot)\) \(\chi_{944}(161,\cdot)\) \(\chi_{944}(209,\cdot)\) \(\chi_{944}(273,\cdot)\) \(\chi_{944}(305,\cdot)\) \(\chi_{944}(337,\cdot)\) \(\chi_{944}(385,\cdot)\) \(\chi_{944}(401,\cdot)\) \(\chi_{944}(465,\cdot)\) \(\chi_{944}(545,\cdot)\) \(\chi_{944}(561,\cdot)\) \(\chi_{944}(657,\cdot)\) \(\chi_{944}(673,\cdot)\) \(\chi_{944}(689,\cdot)\) \(\chi_{944}(705,\cdot)\) \(\chi_{944}(721,\cdot)\) \(\chi_{944}(769,\cdot)\) \(\chi_{944}(785,\cdot)\) \(\chi_{944}(801,\cdot)\) \(\chi_{944}(817,\cdot)\) \(\chi_{944}(849,\cdot)\) \(\chi_{944}(865,\cdot)\) \(\chi_{944}(881,\cdot)\) \(\chi_{944}(929,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((591,709,769)\) → \((1,1,e\left(\frac{21}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 944 }(705, a) \) | \(-1\) | \(1\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{15}{29}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{3}{58}\right)\) | \(e\left(\frac{17}{58}\right)\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{14}{29}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{18}{29}\right)\) |