Basic properties
| Modulus: | \(3267\) | |
| Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{121}(2,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3267.bj
\(\chi_{3267}(28,\cdot)\) \(\chi_{3267}(217,\cdot)\) \(\chi_{3267}(244,\cdot)\) \(\chi_{3267}(271,\cdot)\) \(\chi_{3267}(325,\cdot)\) \(\chi_{3267}(514,\cdot)\) \(\chi_{3267}(541,\cdot)\) \(\chi_{3267}(568,\cdot)\) \(\chi_{3267}(622,\cdot)\) \(\chi_{3267}(811,\cdot)\) \(\chi_{3267}(865,\cdot)\) \(\chi_{3267}(919,\cdot)\) \(\chi_{3267}(1108,\cdot)\) \(\chi_{3267}(1135,\cdot)\) \(\chi_{3267}(1162,\cdot)\) \(\chi_{3267}(1216,\cdot)\) \(\chi_{3267}(1405,\cdot)\) \(\chi_{3267}(1432,\cdot)\) \(\chi_{3267}(1459,\cdot)\) \(\chi_{3267}(1513,\cdot)\) \(\chi_{3267}(1702,\cdot)\) \(\chi_{3267}(1729,\cdot)\) \(\chi_{3267}(1756,\cdot)\) \(\chi_{3267}(1810,\cdot)\) \(\chi_{3267}(1999,\cdot)\) \(\chi_{3267}(2026,\cdot)\) \(\chi_{3267}(2053,\cdot)\) \(\chi_{3267}(2107,\cdot)\) \(\chi_{3267}(2323,\cdot)\) \(\chi_{3267}(2350,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((3026,244)\) → \((1,e\left(\frac{1}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 3267 }(244, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{110}\right)\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{7}{110}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{49}{110}\right)\) |