Basic properties
| Modulus: | \(1009\) | |
| Conductor: | \(1009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(252\) | 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 1009.ba
\(\chi_{1009}(4,\cdot)\) \(\chi_{1009}(6,\cdot)\) \(\chi_{1009}(7,\cdot)\) \(\chi_{1009}(10,\cdot)\) \(\chi_{1009}(15,\cdot)\) \(\chi_{1009}(25,\cdot)\) \(\chi_{1009}(96,\cdot)\) \(\chi_{1009}(101,\cdot)\) \(\chi_{1009}(109,\cdot)\) \(\chi_{1009}(144,\cdot)\) \(\chi_{1009}(168,\cdot)\) \(\chi_{1009}(226,\cdot)\) \(\chi_{1009}(232,\cdot)\) \(\chi_{1009}(252,\cdot)\) \(\chi_{1009}(269,\cdot)\) \(\chi_{1009}(274,\cdot)\) \(\chi_{1009}(286,\cdot)\) \(\chi_{1009}(294,\cdot)\) \(\chi_{1009}(296,\cdot)\) \(\chi_{1009}(324,\cdot)\) \(\chi_{1009}(346,\cdot)\) \(\chi_{1009}(379,\cdot)\) \(\chi_{1009}(402,\cdot)\) \(\chi_{1009}(406,\cdot)\) \(\chi_{1009}(409,\cdot)\) \(\chi_{1009}(411,\cdot)\) \(\chi_{1009}(420,\cdot)\) \(\chi_{1009}(429,\cdot)\) \(\chi_{1009}(441,\cdot)\) \(\chi_{1009}(442,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{252})$ |
| Fixed field: | Number field defined by a degree 252 polynomial (not computed) |
Values on generators
\(11\) → \(e\left(\frac{191}{252}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1009 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{126}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{1}{126}\right)\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{16}{63}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{34}{63}\right)\) | \(e\left(\frac{191}{252}\right)\) |