Basic properties
Modulus: | \(229\) | |
Conductor: | \(229\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(57\) | 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 229.i
\(\chi_{229}(3,\cdot)\) \(\chi_{229}(9,\cdot)\) \(\chi_{229}(14,\cdot)\) \(\chi_{229}(19,\cdot)\) \(\chi_{229}(20,\cdot)\) \(\chi_{229}(25,\cdot)\) \(\chi_{229}(37,\cdot)\) \(\chi_{229}(48,\cdot)\) \(\chi_{229}(51,\cdot)\) \(\chi_{229}(55,\cdot)\) \(\chi_{229}(75,\cdot)\) \(\chi_{229}(81,\cdot)\) \(\chi_{229}(82,\cdot)\) \(\chi_{229}(83,\cdot)\) \(\chi_{229}(91,\cdot)\) \(\chi_{229}(111,\cdot)\) \(\chi_{229}(126,\cdot)\) \(\chi_{229}(129,\cdot)\) \(\chi_{229}(130,\cdot)\) \(\chi_{229}(132,\cdot)\) \(\chi_{229}(144,\cdot)\) \(\chi_{229}(149,\cdot)\) \(\chi_{229}(151,\cdot)\) \(\chi_{229}(153,\cdot)\) \(\chi_{229}(158,\cdot)\) \(\chi_{229}(159,\cdot)\) \(\chi_{229}(167,\cdot)\) \(\chi_{229}(171,\cdot)\) \(\chi_{229}(173,\cdot)\) \(\chi_{229}(180,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 57 polynomial |
Values on generators
\(6\) → \(e\left(\frac{13}{57}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 229 }(171, a) \) | \(1\) | \(1\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{25}{57}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{20}{57}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{50}{57}\right)\) | \(e\left(\frac{8}{57}\right)\) | \(e\left(\frac{18}{19}\right)\) |