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.hv
\(\chi_{9464}(373,\cdot)\) \(\chi_{9464}(445,\cdot)\) \(\chi_{9464}(1101,\cdot)\) \(\chi_{9464}(1173,\cdot)\) \(\chi_{9464}(1829,\cdot)\) \(\chi_{9464}(1901,\cdot)\) \(\chi_{9464}(2629,\cdot)\) \(\chi_{9464}(3285,\cdot)\) \(\chi_{9464}(4013,\cdot)\) \(\chi_{9464}(4085,\cdot)\) \(\chi_{9464}(4741,\cdot)\) \(\chi_{9464}(4813,\cdot)\) \(\chi_{9464}(5469,\cdot)\) \(\chi_{9464}(5541,\cdot)\) \(\chi_{9464}(6197,\cdot)\) \(\chi_{9464}(6269,\cdot)\) \(\chi_{9464}(6925,\cdot)\) \(\chi_{9464}(6997,\cdot)\) \(\chi_{9464}(7653,\cdot)\) \(\chi_{9464}(7725,\cdot)\) \(\chi_{9464}(8381,\cdot)\) \(\chi_{9464}(8453,\cdot)\) \(\chi_{9464}(9109,\cdot)\) \(\chi_{9464}(9181,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2367,4733,2705,9297)\) → \((1,-1,e\left(\frac{1}{3}\right),e\left(\frac{29}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 9464 }(373, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{3}{26}\right)\) |