Basic properties
Modulus: | \(891\) | |
Conductor: | \(891\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(270\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 891.be
\(\chi_{891}(5,\cdot)\) \(\chi_{891}(14,\cdot)\) \(\chi_{891}(20,\cdot)\) \(\chi_{891}(38,\cdot)\) \(\chi_{891}(47,\cdot)\) \(\chi_{891}(59,\cdot)\) \(\chi_{891}(86,\cdot)\) \(\chi_{891}(92,\cdot)\) \(\chi_{891}(104,\cdot)\) \(\chi_{891}(113,\cdot)\) \(\chi_{891}(119,\cdot)\) \(\chi_{891}(137,\cdot)\) \(\chi_{891}(146,\cdot)\) \(\chi_{891}(158,\cdot)\) \(\chi_{891}(185,\cdot)\) \(\chi_{891}(191,\cdot)\) \(\chi_{891}(203,\cdot)\) \(\chi_{891}(212,\cdot)\) \(\chi_{891}(218,\cdot)\) \(\chi_{891}(236,\cdot)\) \(\chi_{891}(245,\cdot)\) \(\chi_{891}(257,\cdot)\) \(\chi_{891}(284,\cdot)\) \(\chi_{891}(290,\cdot)\) \(\chi_{891}(302,\cdot)\) \(\chi_{891}(311,\cdot)\) \(\chi_{891}(317,\cdot)\) \(\chi_{891}(335,\cdot)\) \(\chi_{891}(344,\cdot)\) \(\chi_{891}(356,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{135})$ |
Fixed field: | Number field defined by a degree 270 polynomial (not computed) |
Values on generators
\((650,244)\) → \((e\left(\frac{23}{54}\right),e\left(\frac{2}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
\( \chi_{ 891 }(5, a) \) | \(-1\) | \(1\) | \(e\left(\frac{223}{270}\right)\) | \(e\left(\frac{88}{135}\right)\) | \(e\left(\frac{107}{270}\right)\) | \(e\left(\frac{83}{135}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{109}{135}\right)\) | \(e\left(\frac{119}{270}\right)\) | \(e\left(\frac{41}{135}\right)\) | \(e\left(\frac{59}{90}\right)\) |