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.hu
\(\chi_{9464}(283,\cdot)\) \(\chi_{9464}(355,\cdot)\) \(\chi_{9464}(1011,\cdot)\) \(\chi_{9464}(1083,\cdot)\) \(\chi_{9464}(1739,\cdot)\) \(\chi_{9464}(1811,\cdot)\) \(\chi_{9464}(2467,\cdot)\) \(\chi_{9464}(2539,\cdot)\) \(\chi_{9464}(3195,\cdot)\) \(\chi_{9464}(3267,\cdot)\) \(\chi_{9464}(3923,\cdot)\) \(\chi_{9464}(3995,\cdot)\) \(\chi_{9464}(4651,\cdot)\) \(\chi_{9464}(4723,\cdot)\) \(\chi_{9464}(5379,\cdot)\) \(\chi_{9464}(5451,\cdot)\) \(\chi_{9464}(6179,\cdot)\) \(\chi_{9464}(6835,\cdot)\) \(\chi_{9464}(7563,\cdot)\) \(\chi_{9464}(7635,\cdot)\) \(\chi_{9464}(8291,\cdot)\) \(\chi_{9464}(8363,\cdot)\) \(\chi_{9464}(9019,\cdot)\) \(\chi_{9464}(9091,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2367,4733,2705,9297)\) → \((-1,-1,e\left(\frac{1}{6}\right),e\left(\frac{17}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 9464 }(283, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{15}{26}\right)\) |