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.hx
\(\chi_{9464}(725,\cdot)\) \(\chi_{9464}(1213,\cdot)\) \(\chi_{9464}(1453,\cdot)\) \(\chi_{9464}(1941,\cdot)\) \(\chi_{9464}(2181,\cdot)\) \(\chi_{9464}(2669,\cdot)\) \(\chi_{9464}(2909,\cdot)\) \(\chi_{9464}(3397,\cdot)\) \(\chi_{9464}(3637,\cdot)\) \(\chi_{9464}(4125,\cdot)\) \(\chi_{9464}(4365,\cdot)\) \(\chi_{9464}(4853,\cdot)\) \(\chi_{9464}(5581,\cdot)\) \(\chi_{9464}(5821,\cdot)\) \(\chi_{9464}(6309,\cdot)\) \(\chi_{9464}(6549,\cdot)\) \(\chi_{9464}(7037,\cdot)\) \(\chi_{9464}(7277,\cdot)\) \(\chi_{9464}(7765,\cdot)\) \(\chi_{9464}(8005,\cdot)\) \(\chi_{9464}(8493,\cdot)\) \(\chi_{9464}(8733,\cdot)\) \(\chi_{9464}(9221,\cdot)\) \(\chi_{9464}(9461,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2367,4733,2705,9297)\) → \((1,-1,e\left(\frac{2}{3}\right),e\left(\frac{29}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 9464 }(725, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{21}{26}\right)\) |