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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 335.w
\(\chi_{335}(2,\cdot)\) \(\chi_{335}(7,\cdot)\) \(\chi_{335}(12,\cdot)\) \(\chi_{335}(13,\cdot)\) \(\chi_{335}(18,\cdot)\) \(\chi_{335}(28,\cdot)\) \(\chi_{335}(32,\cdot)\) \(\chi_{335}(48,\cdot)\) \(\chi_{335}(57,\cdot)\) \(\chi_{335}(63,\cdot)\) \(\chi_{335}(78,\cdot)\) \(\chi_{335}(87,\cdot)\) \(\chi_{335}(98,\cdot)\) \(\chi_{335}(108,\cdot)\) \(\chi_{335}(113,\cdot)\) \(\chi_{335}(117,\cdot)\) \(\chi_{335}(118,\cdot)\) \(\chi_{335}(128,\cdot)\) \(\chi_{335}(147,\cdot)\) \(\chi_{335}(152,\cdot)\) \(\chi_{335}(162,\cdot)\) \(\chi_{335}(168,\cdot)\) \(\chi_{335}(178,\cdot)\) \(\chi_{335}(182,\cdot)\) \(\chi_{335}(197,\cdot)\) \(\chi_{335}(203,\cdot)\) \(\chi_{335}(208,\cdot)\) \(\chi_{335}(212,\cdot)\) \(\chi_{335}(213,\cdot)\) \(\chi_{335}(232,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((202,136)\) → \((-i,e\left(\frac{19}{66}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 335 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{132}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{5}{66}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{49}{132}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{73}{132}\right)\) | \(e\left(\frac{95}{132}\right)\) |