Basic properties
| Modulus: | \(9464\) | |
| Conductor: | \(9464\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | 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 9464.gf
\(\chi_{9464}(165,\cdot)\) \(\chi_{9464}(893,\cdot)\) \(\chi_{9464}(1381,\cdot)\) \(\chi_{9464}(1621,\cdot)\) \(\chi_{9464}(2109,\cdot)\) \(\chi_{9464}(2349,\cdot)\) \(\chi_{9464}(2837,\cdot)\) \(\chi_{9464}(3077,\cdot)\) \(\chi_{9464}(3565,\cdot)\) \(\chi_{9464}(3805,\cdot)\) \(\chi_{9464}(4293,\cdot)\) \(\chi_{9464}(4533,\cdot)\) \(\chi_{9464}(5021,\cdot)\) \(\chi_{9464}(5749,\cdot)\) \(\chi_{9464}(5989,\cdot)\) \(\chi_{9464}(6477,\cdot)\) \(\chi_{9464}(6717,\cdot)\) \(\chi_{9464}(7205,\cdot)\) \(\chi_{9464}(7445,\cdot)\) \(\chi_{9464}(7933,\cdot)\) \(\chi_{9464}(8173,\cdot)\) \(\chi_{9464}(8661,\cdot)\) \(\chi_{9464}(8901,\cdot)\) \(\chi_{9464}(9389,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2367,4733,2705,9297)\) → \((1,-1,e\left(\frac{2}{3}\right),e\left(\frac{20}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 9464 }(165, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{7}{26}\right)\) |