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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1003.n
\(\chi_{1003}(33,\cdot)\) \(\chi_{1003}(50,\cdot)\) \(\chi_{1003}(67,\cdot)\) \(\chi_{1003}(101,\cdot)\) \(\chi_{1003}(152,\cdot)\) \(\chi_{1003}(220,\cdot)\) \(\chi_{1003}(254,\cdot)\) \(\chi_{1003}(288,\cdot)\) \(\chi_{1003}(305,\cdot)\) \(\chi_{1003}(339,\cdot)\) \(\chi_{1003}(356,\cdot)\) \(\chi_{1003}(424,\cdot)\) \(\chi_{1003}(509,\cdot)\) \(\chi_{1003}(526,\cdot)\) \(\chi_{1003}(628,\cdot)\) \(\chi_{1003}(645,\cdot)\) \(\chi_{1003}(662,\cdot)\) \(\chi_{1003}(679,\cdot)\) \(\chi_{1003}(696,\cdot)\) \(\chi_{1003}(747,\cdot)\) \(\chi_{1003}(764,\cdot)\) \(\chi_{1003}(781,\cdot)\) \(\chi_{1003}(798,\cdot)\) \(\chi_{1003}(832,\cdot)\) \(\chi_{1003}(849,\cdot)\) \(\chi_{1003}(866,\cdot)\) \(\chi_{1003}(917,\cdot)\) \(\chi_{1003}(968,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((768,120)\) → \((-1,e\left(\frac{17}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1003 }(33, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{58}\right)\) | \(e\left(\frac{9}{58}\right)\) | \(e\left(\frac{17}{29}\right)\) | \(e\left(\frac{15}{58}\right)\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{45}{58}\right)\) | \(e\left(\frac{51}{58}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{24}{29}\right)\) |