Basic properties
Modulus: | \(3332\) | |
Conductor: | \(833\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{833}(81,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3332.cn
\(\chi_{3332}(81,\cdot)\) \(\chi_{3332}(149,\cdot)\) \(\chi_{3332}(429,\cdot)\) \(\chi_{3332}(625,\cdot)\) \(\chi_{3332}(837,\cdot)\) \(\chi_{3332}(905,\cdot)\) \(\chi_{3332}(1033,\cdot)\) \(\chi_{3332}(1101,\cdot)\) \(\chi_{3332}(1313,\cdot)\) \(\chi_{3332}(1381,\cdot)\) \(\chi_{3332}(1509,\cdot)\) \(\chi_{3332}(1577,\cdot)\) \(\chi_{3332}(1789,\cdot)\) \(\chi_{3332}(1857,\cdot)\) \(\chi_{3332}(1985,\cdot)\) \(\chi_{3332}(2053,\cdot)\) \(\chi_{3332}(2265,\cdot)\) \(\chi_{3332}(2461,\cdot)\) \(\chi_{3332}(2741,\cdot)\) \(\chi_{3332}(2809,\cdot)\) \(\chi_{3332}(2937,\cdot)\) \(\chi_{3332}(3005,\cdot)\) \(\chi_{3332}(3217,\cdot)\) \(\chi_{3332}(3285,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1667,885,785)\) → \((1,e\left(\frac{2}{21}\right),i)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 3332 }(81, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{1}{28}\right)\) |