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 \(\chi_{297}(185,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3267.be
\(\chi_{3267}(245,\cdot)\) \(\chi_{3267}(608,\cdot)\) \(\chi_{3267}(614,\cdot)\) \(\chi_{3267}(632,\cdot)\) \(\chi_{3267}(686,\cdot)\) \(\chi_{3267}(977,\cdot)\) \(\chi_{3267}(995,\cdot)\) \(\chi_{3267}(1049,\cdot)\) \(\chi_{3267}(1334,\cdot)\) \(\chi_{3267}(1697,\cdot)\) \(\chi_{3267}(1703,\cdot)\) \(\chi_{3267}(1721,\cdot)\) \(\chi_{3267}(1775,\cdot)\) \(\chi_{3267}(2066,\cdot)\) \(\chi_{3267}(2084,\cdot)\) \(\chi_{3267}(2138,\cdot)\) \(\chi_{3267}(2423,\cdot)\) \(\chi_{3267}(2786,\cdot)\) \(\chi_{3267}(2792,\cdot)\) \(\chi_{3267}(2810,\cdot)\) \(\chi_{3267}(2864,\cdot)\) \(\chi_{3267}(3155,\cdot)\) \(\chi_{3267}(3173,\cdot)\) \(\chi_{3267}(3227,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((3026,244)\) → \((e\left(\frac{11}{18}\right),e\left(\frac{3}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 3267 }(3155, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{41}{90}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{17}{90}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{17}{30}\right)\) |