Basic properties
| Modulus: | \(1003\) | |
| Conductor: | \(1003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(116\) | 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.o
\(\chi_{1003}(13,\cdot)\) \(\chi_{1003}(30,\cdot)\) \(\chi_{1003}(38,\cdot)\) \(\chi_{1003}(47,\cdot)\) \(\chi_{1003}(55,\cdot)\) \(\chi_{1003}(72,\cdot)\) \(\chi_{1003}(89,\cdot)\) \(\chi_{1003}(98,\cdot)\) \(\chi_{1003}(106,\cdot)\) \(\chi_{1003}(115,\cdot)\) \(\chi_{1003}(132,\cdot)\) \(\chi_{1003}(149,\cdot)\) \(\chi_{1003}(157,\cdot)\) \(\chi_{1003}(174,\cdot)\) \(\chi_{1003}(183,\cdot)\) \(\chi_{1003}(191,\cdot)\) \(\chi_{1003}(200,\cdot)\) \(\chi_{1003}(208,\cdot)\) \(\chi_{1003}(217,\cdot)\) \(\chi_{1003}(242,\cdot)\) \(\chi_{1003}(259,\cdot)\) \(\chi_{1003}(268,\cdot)\) \(\chi_{1003}(276,\cdot)\) \(\chi_{1003}(319,\cdot)\) \(\chi_{1003}(327,\cdot)\) \(\chi_{1003}(378,\cdot)\) \(\chi_{1003}(387,\cdot)\) \(\chi_{1003}(404,\cdot)\) \(\chi_{1003}(421,\cdot)\) \(\chi_{1003}(446,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{116})$ |
| Fixed field: | Number field defined by a degree 116 polynomial (not computed) |
Values on generators
\((768,120)\) → \((i,e\left(\frac{45}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1003 }(13, a) \) | \(-1\) | \(1\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{5}{116}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{105}{116}\right)\) | \(e\left(\frac{37}{116}\right)\) | \(e\left(\frac{83}{116}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{5}{58}\right)\) | \(e\left(\frac{21}{116}\right)\) | \(e\left(\frac{17}{116}\right)\) |