Basic properties
| Modulus: | \(3267\) | |
| Conductor: | \(1089\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(165\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1089}(697,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3267.bl
\(\chi_{3267}(37,\cdot)\) \(\chi_{3267}(64,\cdot)\) \(\chi_{3267}(91,\cdot)\) \(\chi_{3267}(181,\cdot)\) \(\chi_{3267}(235,\cdot)\) \(\chi_{3267}(262,\cdot)\) \(\chi_{3267}(280,\cdot)\) \(\chi_{3267}(289,\cdot)\) \(\chi_{3267}(334,\cdot)\) \(\chi_{3267}(361,\cdot)\) \(\chi_{3267}(388,\cdot)\) \(\chi_{3267}(478,\cdot)\) \(\chi_{3267}(532,\cdot)\) \(\chi_{3267}(559,\cdot)\) \(\chi_{3267}(577,\cdot)\) \(\chi_{3267}(586,\cdot)\) \(\chi_{3267}(631,\cdot)\) \(\chi_{3267}(658,\cdot)\) \(\chi_{3267}(685,\cdot)\) \(\chi_{3267}(775,\cdot)\) \(\chi_{3267}(829,\cdot)\) \(\chi_{3267}(883,\cdot)\) \(\chi_{3267}(955,\cdot)\) \(\chi_{3267}(982,\cdot)\) \(\chi_{3267}(1072,\cdot)\) \(\chi_{3267}(1126,\cdot)\) \(\chi_{3267}(1153,\cdot)\) \(\chi_{3267}(1171,\cdot)\) \(\chi_{3267}(1180,\cdot)\) \(\chi_{3267}(1225,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 165 polynomial (not computed) |
Values on generators
\((3026,244)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{36}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 3267 }(334, a) \) | \(1\) | \(1\) | \(e\left(\frac{163}{165}\right)\) | \(e\left(\frac{161}{165}\right)\) | \(e\left(\frac{17}{165}\right)\) | \(e\left(\frac{151}{165}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{128}{165}\right)\) | \(e\left(\frac{149}{165}\right)\) | \(e\left(\frac{157}{165}\right)\) | \(e\left(\frac{4}{55}\right)\) |