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 \(\chi_{4732}(199,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9464.hn
\(\chi_{9464}(199,\cdot)\) \(\chi_{9464}(439,\cdot)\) \(\chi_{9464}(927,\cdot)\) \(\chi_{9464}(1167,\cdot)\) \(\chi_{9464}(1655,\cdot)\) \(\chi_{9464}(1895,\cdot)\) \(\chi_{9464}(2383,\cdot)\) \(\chi_{9464}(2623,\cdot)\) \(\chi_{9464}(3111,\cdot)\) \(\chi_{9464}(3351,\cdot)\) \(\chi_{9464}(3839,\cdot)\) \(\chi_{9464}(4567,\cdot)\) \(\chi_{9464}(4807,\cdot)\) \(\chi_{9464}(5295,\cdot)\) \(\chi_{9464}(5535,\cdot)\) \(\chi_{9464}(6023,\cdot)\) \(\chi_{9464}(6263,\cdot)\) \(\chi_{9464}(6751,\cdot)\) \(\chi_{9464}(6991,\cdot)\) \(\chi_{9464}(7479,\cdot)\) \(\chi_{9464}(7719,\cdot)\) \(\chi_{9464}(8207,\cdot)\) \(\chi_{9464}(8447,\cdot)\) \(\chi_{9464}(9175,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2367,4733,2705,9297)\) → \((-1,1,e\left(\frac{1}{6}\right),e\left(\frac{67}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 9464 }(199, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) |