Basic properties
| Modulus: | \(1003\) | |
| 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 \(\chi_{59}(42,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1003.m
\(\chi_{1003}(18,\cdot)\) \(\chi_{1003}(52,\cdot)\) \(\chi_{1003}(69,\cdot)\) \(\chi_{1003}(103,\cdot)\) \(\chi_{1003}(120,\cdot)\) \(\chi_{1003}(188,\cdot)\) \(\chi_{1003}(273,\cdot)\) \(\chi_{1003}(290,\cdot)\) \(\chi_{1003}(392,\cdot)\) \(\chi_{1003}(409,\cdot)\) \(\chi_{1003}(426,\cdot)\) \(\chi_{1003}(443,\cdot)\) \(\chi_{1003}(460,\cdot)\) \(\chi_{1003}(511,\cdot)\) \(\chi_{1003}(528,\cdot)\) \(\chi_{1003}(545,\cdot)\) \(\chi_{1003}(562,\cdot)\) \(\chi_{1003}(596,\cdot)\) \(\chi_{1003}(613,\cdot)\) \(\chi_{1003}(630,\cdot)\) \(\chi_{1003}(681,\cdot)\) \(\chi_{1003}(732,\cdot)\) \(\chi_{1003}(800,\cdot)\) \(\chi_{1003}(817,\cdot)\) \(\chi_{1003}(834,\cdot)\) \(\chi_{1003}(868,\cdot)\) \(\chi_{1003}(919,\cdot)\) \(\chi_{1003}(987,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((768,120)\) → \((1,e\left(\frac{11}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1003 }(868, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{58}\right)\) | \(e\left(\frac{14}{29}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{4}{29}\right)\) | \(e\left(\frac{39}{58}\right)\) | \(e\left(\frac{12}{29}\right)\) | \(e\left(\frac{33}{58}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{19}{58}\right)\) | \(e\left(\frac{43}{58}\right)\) |