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.gd
\(\chi_{9464}(467,\cdot)\) \(\chi_{9464}(1195,\cdot)\) \(\chi_{9464}(1403,\cdot)\) \(\chi_{9464}(1923,\cdot)\) \(\chi_{9464}(2131,\cdot)\) \(\chi_{9464}(2651,\cdot)\) \(\chi_{9464}(2859,\cdot)\) \(\chi_{9464}(3587,\cdot)\) \(\chi_{9464}(4107,\cdot)\) \(\chi_{9464}(4315,\cdot)\) \(\chi_{9464}(4835,\cdot)\) \(\chi_{9464}(5043,\cdot)\) \(\chi_{9464}(5563,\cdot)\) \(\chi_{9464}(5771,\cdot)\) \(\chi_{9464}(6291,\cdot)\) \(\chi_{9464}(6499,\cdot)\) \(\chi_{9464}(7019,\cdot)\) \(\chi_{9464}(7227,\cdot)\) \(\chi_{9464}(7747,\cdot)\) \(\chi_{9464}(7955,\cdot)\) \(\chi_{9464}(8475,\cdot)\) \(\chi_{9464}(8683,\cdot)\) \(\chi_{9464}(9203,\cdot)\) \(\chi_{9464}(9411,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2367,4733,2705,9297)\) → \((-1,-1,e\left(\frac{5}{6}\right),e\left(\frac{15}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 9464 }(467, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{3}{26}\right)\) |