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 \(\chi_{297}(83,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3267.bg
\(\chi_{3267}(239,\cdot)\) \(\chi_{3267}(524,\cdot)\) \(\chi_{3267}(578,\cdot)\) \(\chi_{3267}(596,\cdot)\) \(\chi_{3267}(887,\cdot)\) \(\chi_{3267}(941,\cdot)\) \(\chi_{3267}(959,\cdot)\) \(\chi_{3267}(965,\cdot)\) \(\chi_{3267}(1328,\cdot)\) \(\chi_{3267}(1613,\cdot)\) \(\chi_{3267}(1667,\cdot)\) \(\chi_{3267}(1685,\cdot)\) \(\chi_{3267}(1976,\cdot)\) \(\chi_{3267}(2030,\cdot)\) \(\chi_{3267}(2048,\cdot)\) \(\chi_{3267}(2054,\cdot)\) \(\chi_{3267}(2417,\cdot)\) \(\chi_{3267}(2702,\cdot)\) \(\chi_{3267}(2756,\cdot)\) \(\chi_{3267}(2774,\cdot)\) \(\chi_{3267}(3065,\cdot)\) \(\chi_{3267}(3119,\cdot)\) \(\chi_{3267}(3137,\cdot)\) \(\chi_{3267}(3143,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((3026,244)\) → \((e\left(\frac{1}{18}\right),e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 3267 }(2756, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{17}{90}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{13}{90}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{14}{15}\right)\) |