Basic properties
| Modulus: | \(1003\) | |
| Conductor: | \(1003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(58\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1003.l
\(\chi_{1003}(16,\cdot)\) \(\chi_{1003}(84,\cdot)\) \(\chi_{1003}(135,\cdot)\) \(\chi_{1003}(169,\cdot)\) \(\chi_{1003}(186,\cdot)\) \(\chi_{1003}(203,\cdot)\) \(\chi_{1003}(271,\cdot)\) \(\chi_{1003}(322,\cdot)\) \(\chi_{1003}(373,\cdot)\) \(\chi_{1003}(390,\cdot)\) \(\chi_{1003}(407,\cdot)\) \(\chi_{1003}(441,\cdot)\) \(\chi_{1003}(458,\cdot)\) \(\chi_{1003}(475,\cdot)\) \(\chi_{1003}(492,\cdot)\) \(\chi_{1003}(543,\cdot)\) \(\chi_{1003}(560,\cdot)\) \(\chi_{1003}(577,\cdot)\) \(\chi_{1003}(594,\cdot)\) \(\chi_{1003}(611,\cdot)\) \(\chi_{1003}(713,\cdot)\) \(\chi_{1003}(730,\cdot)\) \(\chi_{1003}(815,\cdot)\) \(\chi_{1003}(883,\cdot)\) \(\chi_{1003}(900,\cdot)\) \(\chi_{1003}(934,\cdot)\) \(\chi_{1003}(951,\cdot)\) \(\chi_{1003}(985,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((768,120)\) → \((-1,e\left(\frac{2}{29}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1003 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{55}{58}\right)\) | \(e\left(\frac{4}{29}\right)\) | \(e\left(\frac{53}{58}\right)\) | \(e\left(\frac{1}{58}\right)\) | \(e\left(\frac{43}{58}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{57}{58}\right)\) | \(e\left(\frac{13}{58}\right)\) |