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 \(\chi_{4732}(103,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9464.hm
\(\chi_{9464}(103,\cdot)\) \(\chi_{9464}(311,\cdot)\) \(\chi_{9464}(831,\cdot)\) \(\chi_{9464}(1039,\cdot)\) \(\chi_{9464}(1559,\cdot)\) \(\chi_{9464}(1767,\cdot)\) \(\chi_{9464}(2287,\cdot)\) \(\chi_{9464}(2495,\cdot)\) \(\chi_{9464}(3015,\cdot)\) \(\chi_{9464}(3223,\cdot)\) \(\chi_{9464}(3743,\cdot)\) \(\chi_{9464}(3951,\cdot)\) \(\chi_{9464}(4471,\cdot)\) \(\chi_{9464}(4679,\cdot)\) \(\chi_{9464}(5199,\cdot)\) \(\chi_{9464}(5927,\cdot)\) \(\chi_{9464}(6135,\cdot)\) \(\chi_{9464}(6655,\cdot)\) \(\chi_{9464}(6863,\cdot)\) \(\chi_{9464}(7383,\cdot)\) \(\chi_{9464}(7591,\cdot)\) \(\chi_{9464}(8319,\cdot)\) \(\chi_{9464}(8839,\cdot)\) \(\chi_{9464}(9047,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2367,4733,2705,9297)\) → \((-1,1,e\left(\frac{5}{6}\right),e\left(\frac{25}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 9464 }(103, a) \) | \(1\) | \(1\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{9}{13}\right)\) |