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.gr
\(\chi_{9464}(131,\cdot)\) \(\chi_{9464}(859,\cdot)\) \(\chi_{9464}(1067,\cdot)\) \(\chi_{9464}(1587,\cdot)\) \(\chi_{9464}(1795,\cdot)\) \(\chi_{9464}(2315,\cdot)\) \(\chi_{9464}(2523,\cdot)\) \(\chi_{9464}(3251,\cdot)\) \(\chi_{9464}(3771,\cdot)\) \(\chi_{9464}(3979,\cdot)\) \(\chi_{9464}(4499,\cdot)\) \(\chi_{9464}(4707,\cdot)\) \(\chi_{9464}(5227,\cdot)\) \(\chi_{9464}(5435,\cdot)\) \(\chi_{9464}(5955,\cdot)\) \(\chi_{9464}(6163,\cdot)\) \(\chi_{9464}(6683,\cdot)\) \(\chi_{9464}(6891,\cdot)\) \(\chi_{9464}(7411,\cdot)\) \(\chi_{9464}(7619,\cdot)\) \(\chi_{9464}(8139,\cdot)\) \(\chi_{9464}(8347,\cdot)\) \(\chi_{9464}(8867,\cdot)\) \(\chi_{9464}(9075,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2367,4733,2705,9297)\) → \((-1,-1,e\left(\frac{5}{6}\right),e\left(\frac{12}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 9464 }(131, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{23}{26}\right)\) |