Basic properties
| Modulus: | \(4009\) | |
| Conductor: | \(4009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(63\) | 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 4009.da
\(\chi_{4009}(54,\cdot)\) \(\chi_{4009}(384,\cdot)\) \(\chi_{4009}(396,\cdot)\) \(\chi_{4009}(465,\cdot)\) \(\chi_{4009}(595,\cdot)\) \(\chi_{4009}(750,\cdot)\) \(\chi_{4009}(878,\cdot)\) \(\chi_{4009}(898,\cdot)\) \(\chi_{4009}(1005,\cdot)\) \(\chi_{4009}(1024,\cdot)\) \(\chi_{4009}(1089,\cdot)\) \(\chi_{4009}(1156,\cdot)\) \(\chi_{4009}(1233,\cdot)\) \(\chi_{4009}(1240,\cdot)\) \(\chi_{4009}(1339,\cdot)\) \(\chi_{4009}(1942,\cdot)\) \(\chi_{4009}(2000,\cdot)\) \(\chi_{4009}(2153,\cdot)\) \(\chi_{4009}(2164,\cdot)\) \(\chi_{4009}(2227,\cdot)\) \(\chi_{4009}(2289,\cdot)\) \(\chi_{4009}(2438,\cdot)\) \(\chi_{4009}(2506,\cdot)\) \(\chi_{4009}(2816,\cdot)\) \(\chi_{4009}(2904,\cdot)\) \(\chi_{4009}(2916,\cdot)\) \(\chi_{4009}(2923,\cdot)\) \(\chi_{4009}(3027,\cdot)\) \(\chi_{4009}(3132,\cdot)\) \(\chi_{4009}(3266,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((2111,1901)\) → \((e\left(\frac{2}{9}\right),e\left(\frac{13}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4009 }(54, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{17}{63}\right)\) | \(e\left(\frac{22}{63}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{20}{21}\right)\) |