Basic properties
Modulus: | \(891\) | |
Conductor: | \(891\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(135\) | 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 891.bc
\(\chi_{891}(4,\cdot)\) \(\chi_{891}(16,\cdot)\) \(\chi_{891}(25,\cdot)\) \(\chi_{891}(31,\cdot)\) \(\chi_{891}(49,\cdot)\) \(\chi_{891}(58,\cdot)\) \(\chi_{891}(70,\cdot)\) \(\chi_{891}(97,\cdot)\) \(\chi_{891}(103,\cdot)\) \(\chi_{891}(115,\cdot)\) \(\chi_{891}(124,\cdot)\) \(\chi_{891}(130,\cdot)\) \(\chi_{891}(148,\cdot)\) \(\chi_{891}(157,\cdot)\) \(\chi_{891}(169,\cdot)\) \(\chi_{891}(196,\cdot)\) \(\chi_{891}(202,\cdot)\) \(\chi_{891}(214,\cdot)\) \(\chi_{891}(223,\cdot)\) \(\chi_{891}(229,\cdot)\) \(\chi_{891}(247,\cdot)\) \(\chi_{891}(256,\cdot)\) \(\chi_{891}(268,\cdot)\) \(\chi_{891}(295,\cdot)\) \(\chi_{891}(301,\cdot)\) \(\chi_{891}(313,\cdot)\) \(\chi_{891}(322,\cdot)\) \(\chi_{891}(328,\cdot)\) \(\chi_{891}(346,\cdot)\) \(\chi_{891}(355,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{135})$ |
Fixed field: | Number field defined by a degree 135 polynomial (not computed) |
Values on generators
\((650,244)\) → \((e\left(\frac{1}{27}\right),e\left(\frac{1}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
\( \chi_{ 891 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{135}\right)\) | \(e\left(\frac{64}{135}\right)\) | \(e\left(\frac{88}{135}\right)\) | \(e\left(\frac{134}{135}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{67}{135}\right)\) | \(e\left(\frac{31}{135}\right)\) | \(e\left(\frac{128}{135}\right)\) | \(e\left(\frac{1}{45}\right)\) |