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.gg
\(\chi_{9464}(75,\cdot)\) \(\chi_{9464}(563,\cdot)\) \(\chi_{9464}(803,\cdot)\) \(\chi_{9464}(1291,\cdot)\) \(\chi_{9464}(1531,\cdot)\) \(\chi_{9464}(2019,\cdot)\) \(\chi_{9464}(2259,\cdot)\) \(\chi_{9464}(2747,\cdot)\) \(\chi_{9464}(2987,\cdot)\) \(\chi_{9464}(3475,\cdot)\) \(\chi_{9464}(3715,\cdot)\) \(\chi_{9464}(4443,\cdot)\) \(\chi_{9464}(4931,\cdot)\) \(\chi_{9464}(5171,\cdot)\) \(\chi_{9464}(5659,\cdot)\) \(\chi_{9464}(5899,\cdot)\) \(\chi_{9464}(6387,\cdot)\) \(\chi_{9464}(6627,\cdot)\) \(\chi_{9464}(7115,\cdot)\) \(\chi_{9464}(7355,\cdot)\) \(\chi_{9464}(7843,\cdot)\) \(\chi_{9464}(8083,\cdot)\) \(\chi_{9464}(8571,\cdot)\) \(\chi_{9464}(9299,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2367,4733,2705,9297)\) → \((-1,-1,e\left(\frac{5}{6}\right),e\left(\frac{71}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 9464 }(75, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{3}{26}\right)\) |