Basic properties
| Modulus: | \(3756\) | |
| Conductor: | \(939\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{939}(617,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3756.by
\(\chi_{3756}(317,\cdot)\) \(\chi_{3756}(545,\cdot)\) \(\chi_{3756}(617,\cdot)\) \(\chi_{3756}(797,\cdot)\) \(\chi_{3756}(1133,\cdot)\) \(\chi_{3756}(1169,\cdot)\) \(\chi_{3756}(1337,\cdot)\) \(\chi_{3756}(1421,\cdot)\) \(\chi_{3756}(1433,\cdot)\) \(\chi_{3756}(1577,\cdot)\) \(\chi_{3756}(1673,\cdot)\) \(\chi_{3756}(1757,\cdot)\) \(\chi_{3756}(1889,\cdot)\) \(\chi_{3756}(2141,\cdot)\) \(\chi_{3756}(2165,\cdot)\) \(\chi_{3756}(2261,\cdot)\) \(\chi_{3756}(2501,\cdot)\) \(\chi_{3756}(2561,\cdot)\) \(\chi_{3756}(2741,\cdot)\) \(\chi_{3756}(2801,\cdot)\) \(\chi_{3756}(2921,\cdot)\) \(\chi_{3756}(2993,\cdot)\) \(\chi_{3756}(3269,\cdot)\) \(\chi_{3756}(3365,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1879,1253,949)\) → \((1,-1,e\left(\frac{67}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 3756 }(617, a) \) | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{19}{78}\right)\) |