Basic properties
| Modulus: | \(3724\) | |
| Conductor: | \(931\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(63\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{931}(9,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3724.ec
\(\chi_{3724}(9,\cdot)\) \(\chi_{3724}(81,\cdot)\) \(\chi_{3724}(289,\cdot)\) \(\chi_{3724}(473,\cdot)\) \(\chi_{3724}(529,\cdot)\) \(\chi_{3724}(541,\cdot)\) \(\chi_{3724}(613,\cdot)\) \(\chi_{3724}(709,\cdot)\) \(\chi_{3724}(821,\cdot)\) \(\chi_{3724}(1005,\cdot)\) \(\chi_{3724}(1061,\cdot)\) \(\chi_{3724}(1073,\cdot)\) \(\chi_{3724}(1241,\cdot)\) \(\chi_{3724}(1593,\cdot)\) \(\chi_{3724}(1605,\cdot)\) \(\chi_{3724}(1677,\cdot)\) \(\chi_{3724}(1773,\cdot)\) \(\chi_{3724}(1885,\cdot)\) \(\chi_{3724}(2069,\cdot)\) \(\chi_{3724}(2209,\cdot)\) \(\chi_{3724}(2305,\cdot)\) \(\chi_{3724}(2417,\cdot)\) \(\chi_{3724}(2601,\cdot)\) \(\chi_{3724}(2657,\cdot)\) \(\chi_{3724}(2669,\cdot)\) \(\chi_{3724}(2741,\cdot)\) \(\chi_{3724}(2837,\cdot)\) \(\chi_{3724}(2949,\cdot)\) \(\chi_{3724}(3133,\cdot)\) \(\chi_{3724}(3189,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((1863,3041,3137)\) → \((1,e\left(\frac{1}{21}\right),e\left(\frac{4}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 3724 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{52}{63}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{40}{63}\right)\) | \(e\left(\frac{44}{63}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{10}{21}\right)\) |