Basic properties
| Modulus: | \(9464\) | |
| Conductor: | \(4732\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4732}(55,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9464.ho
\(\chi_{9464}(55,\cdot)\) \(\chi_{9464}(503,\cdot)\) \(\chi_{9464}(783,\cdot)\) \(\chi_{9464}(1231,\cdot)\) \(\chi_{9464}(1511,\cdot)\) \(\chi_{9464}(1959,\cdot)\) \(\chi_{9464}(2239,\cdot)\) \(\chi_{9464}(2687,\cdot)\) \(\chi_{9464}(2967,\cdot)\) \(\chi_{9464}(3415,\cdot)\) \(\chi_{9464}(4143,\cdot)\) \(\chi_{9464}(4423,\cdot)\) \(\chi_{9464}(4871,\cdot)\) \(\chi_{9464}(5151,\cdot)\) \(\chi_{9464}(5879,\cdot)\) \(\chi_{9464}(6327,\cdot)\) \(\chi_{9464}(6607,\cdot)\) \(\chi_{9464}(7055,\cdot)\) \(\chi_{9464}(7335,\cdot)\) \(\chi_{9464}(7783,\cdot)\) \(\chi_{9464}(8063,\cdot)\) \(\chi_{9464}(8511,\cdot)\) \(\chi_{9464}(8791,\cdot)\) \(\chi_{9464}(9239,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2367,4733,2705,9297)\) → \((-1,1,-1,e\left(\frac{28}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 9464 }(55, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{1}{13}\right)\) |