Basic properties
| Modulus: | \(471\) | |
| Conductor: | \(157\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{157}(34,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 471.x
\(\chi_{471}(34,\cdot)\) \(\chi_{471}(43,\cdot)\) \(\chi_{471}(55,\cdot)\) \(\chi_{471}(61,\cdot)\) \(\chi_{471}(70,\cdot)\) \(\chi_{471}(73,\cdot)\) \(\chi_{471}(85,\cdot)\) \(\chi_{471}(88,\cdot)\) \(\chi_{471}(91,\cdot)\) \(\chi_{471}(94,\cdot)\) \(\chi_{471}(97,\cdot)\) \(\chi_{471}(133,\cdot)\) \(\chi_{471}(136,\cdot)\) \(\chi_{471}(139,\cdot)\) \(\chi_{471}(142,\cdot)\) \(\chi_{471}(151,\cdot)\) \(\chi_{471}(163,\cdot)\) \(\chi_{471}(172,\cdot)\) \(\chi_{471}(175,\cdot)\) \(\chi_{471}(178,\cdot)\) \(\chi_{471}(181,\cdot)\) \(\chi_{471}(217,\cdot)\) \(\chi_{471}(220,\cdot)\) \(\chi_{471}(223,\cdot)\) \(\chi_{471}(226,\cdot)\) \(\chi_{471}(229,\cdot)\) \(\chi_{471}(241,\cdot)\) \(\chi_{471}(244,\cdot)\) \(\chi_{471}(253,\cdot)\) \(\chi_{471}(259,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((158,319)\) → \((1,e\left(\frac{25}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 471 }(34, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{25}{156}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{5}{13}\right)\) |