Basic properties
| Modulus: | \(335\) | |
| Conductor: | \(335\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | 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 335.x
\(\chi_{335}(17,\cdot)\) \(\chi_{335}(23,\cdot)\) \(\chi_{335}(33,\cdot)\) \(\chi_{335}(47,\cdot)\) \(\chi_{335}(73,\cdot)\) \(\chi_{335}(77,\cdot)\) \(\chi_{335}(83,\cdot)\) \(\chi_{335}(88,\cdot)\) \(\chi_{335}(93,\cdot)\) \(\chi_{335}(102,\cdot)\) \(\chi_{335}(103,\cdot)\) \(\chi_{335}(122,\cdot)\) \(\chi_{335}(123,\cdot)\) \(\chi_{335}(127,\cdot)\) \(\chi_{335}(132,\cdot)\) \(\chi_{335}(138,\cdot)\) \(\chi_{335}(153,\cdot)\) \(\chi_{335}(157,\cdot)\) \(\chi_{335}(167,\cdot)\) \(\chi_{335}(173,\cdot)\) \(\chi_{335}(183,\cdot)\) \(\chi_{335}(188,\cdot)\) \(\chi_{335}(207,\cdot)\) \(\chi_{335}(217,\cdot)\) \(\chi_{335}(218,\cdot)\) \(\chi_{335}(222,\cdot)\) \(\chi_{335}(227,\cdot)\) \(\chi_{335}(237,\cdot)\) \(\chi_{335}(248,\cdot)\) \(\chi_{335}(257,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((202,136)\) → \((-i,e\left(\frac{20}{33}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 335 }(73, a) \) | \(-1\) | \(1\) | \(e\left(\frac{47}{132}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{91}{132}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{79}{132}\right)\) | \(e\left(\frac{101}{132}\right)\) |