Basic properties
| Modulus: | \(338130\) | |
| Conductor: | \(169065\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(204\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169065}(103,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 338130.biu
\(\chi_{338130}(103,\cdot)\) \(\chi_{338130}(5407,\cdot)\) \(\chi_{338130}(12037,\cdot)\) \(\chi_{338130}(13363,\cdot)\) \(\chi_{338130}(19993,\cdot)\) \(\chi_{338130}(25297,\cdot)\) \(\chi_{338130}(31927,\cdot)\) \(\chi_{338130}(33253,\cdot)\) \(\chi_{338130}(45187,\cdot)\) \(\chi_{338130}(51817,\cdot)\) \(\chi_{338130}(53143,\cdot)\) \(\chi_{338130}(59773,\cdot)\) \(\chi_{338130}(65077,\cdot)\) \(\chi_{338130}(71707,\cdot)\) \(\chi_{338130}(73033,\cdot)\) \(\chi_{338130}(79663,\cdot)\) \(\chi_{338130}(91597,\cdot)\) \(\chi_{338130}(92923,\cdot)\) \(\chi_{338130}(99553,\cdot)\) \(\chi_{338130}(104857,\cdot)\) \(\chi_{338130}(111487,\cdot)\) \(\chi_{338130}(112813,\cdot)\) \(\chi_{338130}(119443,\cdot)\) \(\chi_{338130}(124747,\cdot)\) \(\chi_{338130}(131377,\cdot)\) \(\chi_{338130}(132703,\cdot)\) \(\chi_{338130}(139333,\cdot)\) \(\chi_{338130}(144637,\cdot)\) \(\chi_{338130}(151267,\cdot)\) \(\chi_{338130}(159223,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{204})$ |
| Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((262991,67627,104041,145081)\) → \((e\left(\frac{1}{3}\right),-i,-1,e\left(\frac{4}{17}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 338130 }(103, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{204}\right)\) | \(e\left(\frac{25}{102}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{79}{204}\right)\) | \(e\left(\frac{25}{102}\right)\) | \(e\left(\frac{29}{102}\right)\) | \(e\left(\frac{41}{68}\right)\) | \(e\left(\frac{41}{102}\right)\) | \(e\left(\frac{155}{204}\right)\) | \(e\left(\frac{23}{204}\right)\) |