Basic properties
| Modulus: | \(3267\) | |
| Conductor: | \(297\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{297}(292,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3267.bf
\(\chi_{3267}(40,\cdot)\) \(\chi_{3267}(94,\cdot)\) \(\chi_{3267}(112,\cdot)\) \(\chi_{3267}(403,\cdot)\) \(\chi_{3267}(457,\cdot)\) \(\chi_{3267}(475,\cdot)\) \(\chi_{3267}(481,\cdot)\) \(\chi_{3267}(844,\cdot)\) \(\chi_{3267}(1129,\cdot)\) \(\chi_{3267}(1183,\cdot)\) \(\chi_{3267}(1201,\cdot)\) \(\chi_{3267}(1492,\cdot)\) \(\chi_{3267}(1546,\cdot)\) \(\chi_{3267}(1564,\cdot)\) \(\chi_{3267}(1570,\cdot)\) \(\chi_{3267}(1933,\cdot)\) \(\chi_{3267}(2218,\cdot)\) \(\chi_{3267}(2272,\cdot)\) \(\chi_{3267}(2290,\cdot)\) \(\chi_{3267}(2581,\cdot)\) \(\chi_{3267}(2635,\cdot)\) \(\chi_{3267}(2653,\cdot)\) \(\chi_{3267}(2659,\cdot)\) \(\chi_{3267}(3022,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((3026,244)\) → \((e\left(\frac{7}{9}\right),e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 3267 }(1183, a) \) | \(-1\) | \(1\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{90}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{23}{30}\right)\) |