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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3724.em
\(\chi_{3724}(51,\cdot)\) \(\chi_{3724}(219,\cdot)\) \(\chi_{3724}(375,\cdot)\) \(\chi_{3724}(515,\cdot)\) \(\chi_{3724}(583,\cdot)\) \(\chi_{3724}(751,\cdot)\) \(\chi_{3724}(907,\cdot)\) \(\chi_{3724}(991,\cdot)\) \(\chi_{3724}(1003,\cdot)\) \(\chi_{3724}(1115,\cdot)\) \(\chi_{3724}(1283,\cdot)\) \(\chi_{3724}(1523,\cdot)\) \(\chi_{3724}(1535,\cdot)\) \(\chi_{3724}(1579,\cdot)\) \(\chi_{3724}(1815,\cdot)\) \(\chi_{3724}(1971,\cdot)\) \(\chi_{3724}(2055,\cdot)\) \(\chi_{3724}(2067,\cdot)\) \(\chi_{3724}(2111,\cdot)\) \(\chi_{3724}(2179,\cdot)\) \(\chi_{3724}(2347,\cdot)\) \(\chi_{3724}(2503,\cdot)\) \(\chi_{3724}(2587,\cdot)\) \(\chi_{3724}(2599,\cdot)\) \(\chi_{3724}(2643,\cdot)\) \(\chi_{3724}(2711,\cdot)\) \(\chi_{3724}(2879,\cdot)\) \(\chi_{3724}(3035,\cdot)\) \(\chi_{3724}(3119,\cdot)\) \(\chi_{3724}(3131,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((1863,3041,3137)\) → \((-1,e\left(\frac{16}{21}\right),e\left(\frac{5}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 3724 }(1115, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{63}\right)\) | \(e\left(\frac{34}{63}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{67}{126}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{52}{63}\right)\) | \(e\left(\frac{1}{126}\right)\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{13}{21}\right)\) |