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.bf
\(\chi_{891}(7,\cdot)\) \(\chi_{891}(13,\cdot)\) \(\chi_{891}(40,\cdot)\) \(\chi_{891}(52,\cdot)\) \(\chi_{891}(61,\cdot)\) \(\chi_{891}(79,\cdot)\) \(\chi_{891}(85,\cdot)\) \(\chi_{891}(94,\cdot)\) \(\chi_{891}(106,\cdot)\) \(\chi_{891}(112,\cdot)\) \(\chi_{891}(139,\cdot)\) \(\chi_{891}(151,\cdot)\) \(\chi_{891}(160,\cdot)\) \(\chi_{891}(178,\cdot)\) \(\chi_{891}(184,\cdot)\) \(\chi_{891}(193,\cdot)\) \(\chi_{891}(205,\cdot)\) \(\chi_{891}(211,\cdot)\) \(\chi_{891}(238,\cdot)\) \(\chi_{891}(250,\cdot)\) \(\chi_{891}(259,\cdot)\) \(\chi_{891}(277,\cdot)\) \(\chi_{891}(283,\cdot)\) \(\chi_{891}(292,\cdot)\) \(\chi_{891}(304,\cdot)\) \(\chi_{891}(310,\cdot)\) \(\chi_{891}(337,\cdot)\) \(\chi_{891}(349,\cdot)\) \(\chi_{891}(358,\cdot)\) \(\chi_{891}(376,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{135})$ |
| Fixed field: | Number field defined by a degree 270 polynomial (not computed) |
Values on generators
\((650,244)\) → \((e\left(\frac{8}{27}\right),e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 891 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{269}{270}\right)\) | \(e\left(\frac{134}{135}\right)\) | \(e\left(\frac{83}{135}\right)\) | \(e\left(\frac{173}{270}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{19}{270}\right)\) | \(e\left(\frac{86}{135}\right)\) | \(e\left(\frac{133}{135}\right)\) | \(e\left(\frac{7}{90}\right)\) |