Basic properties
Modulus: | \(471\) | |
Conductor: | \(471\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 471.u
\(\chi_{471}(11,\cdot)\) \(\chi_{471}(17,\cdot)\) \(\chi_{471}(35,\cdot)\) \(\chi_{471}(47,\cdot)\) \(\chi_{471}(71,\cdot)\) \(\chi_{471}(89,\cdot)\) \(\chi_{471}(113,\cdot)\) \(\chi_{471}(176,\cdot)\) \(\chi_{471}(194,\cdot)\) \(\chi_{471}(197,\cdot)\) \(\chi_{471}(209,\cdot)\) \(\chi_{471}(257,\cdot)\) \(\chi_{471}(263,\cdot)\) \(\chi_{471}(266,\cdot)\) \(\chi_{471}(272,\cdot)\) \(\chi_{471}(278,\cdot)\) \(\chi_{471}(281,\cdot)\) \(\chi_{471}(311,\cdot)\) \(\chi_{471}(323,\cdot)\) \(\chi_{471}(344,\cdot)\) \(\chi_{471}(395,\cdot)\) \(\chi_{471}(440,\cdot)\) \(\chi_{471}(446,\cdot)\) \(\chi_{471}(461,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((158,319)\) → \((-1,e\left(\frac{7}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 471 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{3}{13}\right)\) |