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.el
\(\chi_{3724}(15,\cdot)\) \(\chi_{3724}(71,\cdot)\) \(\chi_{3724}(127,\cdot)\) \(\chi_{3724}(155,\cdot)\) \(\chi_{3724}(211,\cdot)\) \(\chi_{3724}(547,\cdot)\) \(\chi_{3724}(603,\cdot)\) \(\chi_{3724}(659,\cdot)\) \(\chi_{3724}(743,\cdot)\) \(\chi_{3724}(827,\cdot)\) \(\chi_{3724}(1135,\cdot)\) \(\chi_{3724}(1191,\cdot)\) \(\chi_{3724}(1219,\cdot)\) \(\chi_{3724}(1359,\cdot)\) \(\chi_{3724}(1611,\cdot)\) \(\chi_{3724}(1723,\cdot)\) \(\chi_{3724}(1751,\cdot)\) \(\chi_{3724}(1807,\cdot)\) \(\chi_{3724}(1891,\cdot)\) \(\chi_{3724}(2143,\cdot)\) \(\chi_{3724}(2199,\cdot)\) \(\chi_{3724}(2283,\cdot)\) \(\chi_{3724}(2339,\cdot)\) \(\chi_{3724}(2423,\cdot)\) \(\chi_{3724}(2675,\cdot)\) \(\chi_{3724}(2731,\cdot)\) \(\chi_{3724}(2787,\cdot)\) \(\chi_{3724}(2815,\cdot)\) \(\chi_{3724}(2871,\cdot)\) \(\chi_{3724}(2955,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((1863,3041,3137)\) → \((-1,e\left(\frac{4}{7}\right),e\left(\frac{7}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 3724 }(71, a) \) | \(1\) | \(1\) | \(e\left(\frac{8}{63}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{16}{63}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{101}{126}\right)\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{11}{63}\right)\) | \(e\left(\frac{125}{126}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{8}{21}\right)\) |