Basic properties
| Modulus: | \(3009\) | |
| Conductor: | \(177\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(58\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{177}(11,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3009.w
\(\chi_{3009}(188,\cdot)\) \(\chi_{3009}(290,\cdot)\) \(\chi_{3009}(392,\cdot)\) \(\chi_{3009}(443,\cdot)\) \(\chi_{3009}(545,\cdot)\) \(\chi_{3009}(596,\cdot)\) \(\chi_{3009}(800,\cdot)\) \(\chi_{3009}(1055,\cdot)\) \(\chi_{3009}(1106,\cdot)\) \(\chi_{3009}(1412,\cdot)\) \(\chi_{3009}(1463,\cdot)\) \(\chi_{3009}(1514,\cdot)\) \(\chi_{3009}(1565,\cdot)\) \(\chi_{3009}(1616,\cdot)\) \(\chi_{3009}(1820,\cdot)\) \(\chi_{3009}(1871,\cdot)\) \(\chi_{3009}(1922,\cdot)\) \(\chi_{3009}(2024,\cdot)\) \(\chi_{3009}(2075,\cdot)\) \(\chi_{3009}(2126,\cdot)\) \(\chi_{3009}(2279,\cdot)\) \(\chi_{3009}(2432,\cdot)\) \(\chi_{3009}(2534,\cdot)\) \(\chi_{3009}(2636,\cdot)\) \(\chi_{3009}(2687,\cdot)\) \(\chi_{3009}(2738,\cdot)\) \(\chi_{3009}(2840,\cdot)\) \(\chi_{3009}(2993,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((1004,1771,1123)\) → \((-1,1,e\left(\frac{25}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 3009 }(188, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{25}{29}\right)\) | \(e\left(\frac{5}{58}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{1}{58}\right)\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{23}{58}\right)\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{21}{29}\right)\) |