Basic properties
| Modulus: | \(3267\) | |
| Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(55\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{121}(38,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3267.ba
\(\chi_{3267}(82,\cdot)\) \(\chi_{3267}(136,\cdot)\) \(\chi_{3267}(163,\cdot)\) \(\chi_{3267}(190,\cdot)\) \(\chi_{3267}(379,\cdot)\) \(\chi_{3267}(433,\cdot)\) \(\chi_{3267}(460,\cdot)\) \(\chi_{3267}(676,\cdot)\) \(\chi_{3267}(730,\cdot)\) \(\chi_{3267}(757,\cdot)\) \(\chi_{3267}(784,\cdot)\) \(\chi_{3267}(973,\cdot)\) \(\chi_{3267}(1027,\cdot)\) \(\chi_{3267}(1054,\cdot)\) \(\chi_{3267}(1081,\cdot)\) \(\chi_{3267}(1270,\cdot)\) \(\chi_{3267}(1324,\cdot)\) \(\chi_{3267}(1351,\cdot)\) \(\chi_{3267}(1378,\cdot)\) \(\chi_{3267}(1567,\cdot)\) \(\chi_{3267}(1621,\cdot)\) \(\chi_{3267}(1648,\cdot)\) \(\chi_{3267}(1675,\cdot)\) \(\chi_{3267}(1864,\cdot)\) \(\chi_{3267}(1918,\cdot)\) \(\chi_{3267}(1972,\cdot)\) \(\chi_{3267}(2161,\cdot)\) \(\chi_{3267}(2215,\cdot)\) \(\chi_{3267}(2242,\cdot)\) \(\chi_{3267}(2269,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 55 polynomial |
Values on generators
\((3026,244)\) → \((1,e\left(\frac{42}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 3267 }(2458, a) \) | \(1\) | \(1\) | \(e\left(\frac{42}{55}\right)\) | \(e\left(\frac{29}{55}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{19}{55}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{7}{55}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{23}{55}\right)\) |