Basic properties
Modulus: | \(3724\) | |
Conductor: | \(3724\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3724.ej
\(\chi_{3724}(167,\cdot)\) \(\chi_{3724}(223,\cdot)\) \(\chi_{3724}(279,\cdot)\) \(\chi_{3724}(307,\cdot)\) \(\chi_{3724}(363,\cdot)\) \(\chi_{3724}(447,\cdot)\) \(\chi_{3724}(699,\cdot)\) \(\chi_{3724}(755,\cdot)\) \(\chi_{3724}(811,\cdot)\) \(\chi_{3724}(839,\cdot)\) \(\chi_{3724}(895,\cdot)\) \(\chi_{3724}(1231,\cdot)\) \(\chi_{3724}(1287,\cdot)\) \(\chi_{3724}(1343,\cdot)\) \(\chi_{3724}(1427,\cdot)\) \(\chi_{3724}(1511,\cdot)\) \(\chi_{3724}(1819,\cdot)\) \(\chi_{3724}(1875,\cdot)\) \(\chi_{3724}(1903,\cdot)\) \(\chi_{3724}(2043,\cdot)\) \(\chi_{3724}(2295,\cdot)\) \(\chi_{3724}(2407,\cdot)\) \(\chi_{3724}(2435,\cdot)\) \(\chi_{3724}(2491,\cdot)\) \(\chi_{3724}(2575,\cdot)\) \(\chi_{3724}(2827,\cdot)\) \(\chi_{3724}(2883,\cdot)\) \(\chi_{3724}(2967,\cdot)\) \(\chi_{3724}(3023,\cdot)\) \(\chi_{3724}(3107,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((1863,3041,3137)\) → \((-1,e\left(\frac{13}{14}\right),e\left(\frac{5}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 3724 }(1343, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{126}\right)\) | \(e\left(\frac{47}{126}\right)\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{2}{63}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{125}{126}\right)\) | \(e\left(\frac{43}{126}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{5}{42}\right)\) |