Basic properties
Modulus: | \(3009\) | |
Conductor: | \(59\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(29\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{59}(36,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3009.u
\(\chi_{3009}(154,\cdot)\) \(\chi_{3009}(205,\cdot)\) \(\chi_{3009}(256,\cdot)\) \(\chi_{3009}(307,\cdot)\) \(\chi_{3009}(358,\cdot)\) \(\chi_{3009}(664,\cdot)\) \(\chi_{3009}(715,\cdot)\) \(\chi_{3009}(970,\cdot)\) \(\chi_{3009}(1174,\cdot)\) \(\chi_{3009}(1225,\cdot)\) \(\chi_{3009}(1327,\cdot)\) \(\chi_{3009}(1378,\cdot)\) \(\chi_{3009}(1480,\cdot)\) \(\chi_{3009}(1582,\cdot)\) \(\chi_{3009}(1786,\cdot)\) \(\chi_{3009}(1939,\cdot)\) \(\chi_{3009}(2041,\cdot)\) \(\chi_{3009}(2092,\cdot)\) \(\chi_{3009}(2143,\cdot)\) \(\chi_{3009}(2245,\cdot)\) \(\chi_{3009}(2347,\cdot)\) \(\chi_{3009}(2500,\cdot)\) \(\chi_{3009}(2653,\cdot)\) \(\chi_{3009}(2704,\cdot)\) \(\chi_{3009}(2755,\cdot)\) \(\chi_{3009}(2857,\cdot)\) \(\chi_{3009}(2908,\cdot)\) \(\chi_{3009}(2959,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{29})$ |
Fixed field: | Number field defined by a degree 29 polynomial |
Values on generators
\((1004,1771,1123)\) → \((1,1,e\left(\frac{22}{29}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 3009 }(154, a) \) | \(1\) | \(1\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{15}{29}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{19}{29}\right)\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{4}{29}\right)\) | \(e\left(\frac{12}{29}\right)\) | \(e\left(\frac{1}{29}\right)\) |