Basic properties
| Modulus: | \(2006\) | |
| Conductor: | \(1003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(58\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1003}(135,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2006.n
\(\chi_{2006}(135,\cdot)\) \(\chi_{2006}(169,\cdot)\) \(\chi_{2006}(203,\cdot)\) \(\chi_{2006}(271,\cdot)\) \(\chi_{2006}(373,\cdot)\) \(\chi_{2006}(407,\cdot)\) \(\chi_{2006}(441,\cdot)\) \(\chi_{2006}(475,\cdot)\) \(\chi_{2006}(543,\cdot)\) \(\chi_{2006}(577,\cdot)\) \(\chi_{2006}(611,\cdot)\) \(\chi_{2006}(713,\cdot)\) \(\chi_{2006}(815,\cdot)\) \(\chi_{2006}(883,\cdot)\) \(\chi_{2006}(951,\cdot)\) \(\chi_{2006}(985,\cdot)\) \(\chi_{2006}(1019,\cdot)\) \(\chi_{2006}(1087,\cdot)\) \(\chi_{2006}(1189,\cdot)\) \(\chi_{2006}(1325,\cdot)\) \(\chi_{2006}(1393,\cdot)\) \(\chi_{2006}(1461,\cdot)\) \(\chi_{2006}(1495,\cdot)\) \(\chi_{2006}(1563,\cdot)\) \(\chi_{2006}(1597,\cdot)\) \(\chi_{2006}(1733,\cdot)\) \(\chi_{2006}(1903,\cdot)\) \(\chi_{2006}(1937,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((1771,1123)\) → \((-1,e\left(\frac{20}{29}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 2006 }(135, a) \) | \(1\) | \(1\) | \(e\left(\frac{57}{58}\right)\) | \(e\left(\frac{37}{58}\right)\) | \(e\left(\frac{53}{58}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{43}{58}\right)\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{18}{29}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{49}{58}\right)\) |