Basic properties
| Modulus: | \(3009\) | |
| Conductor: | \(3009\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3009.bf
\(\chi_{3009}(38,\cdot)\) \(\chi_{3009}(47,\cdot)\) \(\chi_{3009}(89,\cdot)\) \(\chi_{3009}(98,\cdot)\) \(\chi_{3009}(149,\cdot)\) \(\chi_{3009}(191,\cdot)\) \(\chi_{3009}(200,\cdot)\) \(\chi_{3009}(242,\cdot)\) \(\chi_{3009}(404,\cdot)\) \(\chi_{3009}(446,\cdot)\) \(\chi_{3009}(455,\cdot)\) \(\chi_{3009}(506,\cdot)\) \(\chi_{3009}(608,\cdot)\) \(\chi_{3009}(659,\cdot)\) \(\chi_{3009}(701,\cdot)\) \(\chi_{3009}(710,\cdot)\) \(\chi_{3009}(752,\cdot)\) \(\chi_{3009}(863,\cdot)\) \(\chi_{3009}(1016,\cdot)\) \(\chi_{3009}(1058,\cdot)\) \(\chi_{3009}(1109,\cdot)\) \(\chi_{3009}(1118,\cdot)\) \(\chi_{3009}(1160,\cdot)\) \(\chi_{3009}(1211,\cdot)\) \(\chi_{3009}(1220,\cdot)\) \(\chi_{3009}(1262,\cdot)\) \(\chi_{3009}(1271,\cdot)\) \(\chi_{3009}(1322,\cdot)\) \(\chi_{3009}(1424,\cdot)\) \(\chi_{3009}(1466,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{116})$ |
| Fixed field: | Number field defined by a degree 116 polynomial (not computed) |
Values on generators
\((1004,1771,1123)\) → \((-1,-i,e\left(\frac{39}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 3009 }(38, a) \) | \(1\) | \(1\) | \(e\left(\frac{39}{58}\right)\) | \(e\left(\frac{10}{29}\right)\) | \(e\left(\frac{33}{116}\right)\) | \(e\left(\frac{41}{116}\right)\) | \(e\left(\frac{1}{58}\right)\) | \(e\left(\frac{111}{116}\right)\) | \(e\left(\frac{65}{116}\right)\) | \(e\left(\frac{15}{58}\right)\) | \(e\left(\frac{3}{116}\right)\) | \(e\left(\frac{20}{29}\right)\) |