Basic properties
| Modulus: | \(3969\) | |
| Conductor: | \(3969\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(378\) | 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 3969.dh
\(\chi_{3969}(20,\cdot)\) \(\chi_{3969}(41,\cdot)\) \(\chi_{3969}(83,\cdot)\) \(\chi_{3969}(104,\cdot)\) \(\chi_{3969}(167,\cdot)\) \(\chi_{3969}(209,\cdot)\) \(\chi_{3969}(230,\cdot)\) \(\chi_{3969}(272,\cdot)\) \(\chi_{3969}(335,\cdot)\) \(\chi_{3969}(356,\cdot)\) \(\chi_{3969}(398,\cdot)\) \(\chi_{3969}(419,\cdot)\) \(\chi_{3969}(461,\cdot)\) \(\chi_{3969}(482,\cdot)\) \(\chi_{3969}(524,\cdot)\) \(\chi_{3969}(545,\cdot)\) \(\chi_{3969}(608,\cdot)\) \(\chi_{3969}(650,\cdot)\) \(\chi_{3969}(671,\cdot)\) \(\chi_{3969}(713,\cdot)\) \(\chi_{3969}(776,\cdot)\) \(\chi_{3969}(797,\cdot)\) \(\chi_{3969}(839,\cdot)\) \(\chi_{3969}(860,\cdot)\) \(\chi_{3969}(902,\cdot)\) \(\chi_{3969}(923,\cdot)\) \(\chi_{3969}(965,\cdot)\) \(\chi_{3969}(986,\cdot)\) \(\chi_{3969}(1049,\cdot)\) \(\chi_{3969}(1091,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{189})$ |
| Fixed field: | Number field defined by a degree 378 polynomial (not computed) |
Values on generators
\((2108,3727)\) → \((e\left(\frac{25}{54}\right),e\left(\frac{13}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 3969 }(20, a) \) | \(1\) | \(1\) | \(e\left(\frac{229}{378}\right)\) | \(e\left(\frac{40}{189}\right)\) | \(e\left(\frac{109}{189}\right)\) | \(e\left(\frac{103}{126}\right)\) | \(e\left(\frac{23}{126}\right)\) | \(e\left(\frac{61}{378}\right)\) | \(e\left(\frac{131}{378}\right)\) | \(e\left(\frac{80}{189}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{13}{18}\right)\) |