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 \(\chi_{4732}(87,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9464.hb
\(\chi_{9464}(87,\cdot)\) \(\chi_{9464}(159,\cdot)\) \(\chi_{9464}(815,\cdot)\) \(\chi_{9464}(887,\cdot)\) \(\chi_{9464}(1615,\cdot)\) \(\chi_{9464}(2271,\cdot)\) \(\chi_{9464}(2999,\cdot)\) \(\chi_{9464}(3071,\cdot)\) \(\chi_{9464}(3727,\cdot)\) \(\chi_{9464}(3799,\cdot)\) \(\chi_{9464}(4455,\cdot)\) \(\chi_{9464}(4527,\cdot)\) \(\chi_{9464}(5183,\cdot)\) \(\chi_{9464}(5255,\cdot)\) \(\chi_{9464}(5911,\cdot)\) \(\chi_{9464}(5983,\cdot)\) \(\chi_{9464}(6639,\cdot)\) \(\chi_{9464}(6711,\cdot)\) \(\chi_{9464}(7367,\cdot)\) \(\chi_{9464}(7439,\cdot)\) \(\chi_{9464}(8095,\cdot)\) \(\chi_{9464}(8167,\cdot)\) \(\chi_{9464}(8823,\cdot)\) \(\chi_{9464}(8895,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2367,4733,2705,9297)\) → \((-1,1,e\left(\frac{1}{6}\right),e\left(\frac{2}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 9464 }(87, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{1}{13}\right)\) |