Basic properties
| Modulus: | \(338130\) | |
| Conductor: | \(169065\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(816\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169065}(97,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 338130.byv
\(\chi_{338130}(97,\cdot)\) \(\chi_{338130}(193,\cdot)\) \(\chi_{338130}(3607,\cdot)\) \(\chi_{338130}(5947,\cdot)\) \(\chi_{338130}(6793,\cdot)\) \(\chi_{338130}(7963,\cdot)\) \(\chi_{338130}(8257,\cdot)\) \(\chi_{338130}(9457,\cdot)\) \(\chi_{338130}(11767,\cdot)\) \(\chi_{338130}(11893,\cdot)\) \(\chi_{338130}(13063,\cdot)\) \(\chi_{338130}(14107,\cdot)\) \(\chi_{338130}(14983,\cdot)\) \(\chi_{338130}(17617,\cdot)\) \(\chi_{338130}(19663,\cdot)\) \(\chi_{338130}(19987,\cdot)\) \(\chi_{338130}(20083,\cdot)\) \(\chi_{338130}(23497,\cdot)\) \(\chi_{338130}(24763,\cdot)\) \(\chi_{338130}(25837,\cdot)\) \(\chi_{338130}(26683,\cdot)\) \(\chi_{338130}(27853,\cdot)\) \(\chi_{338130}(28147,\cdot)\) \(\chi_{338130}(31657,\cdot)\) \(\chi_{338130}(31783,\cdot)\) \(\chi_{338130}(32953,\cdot)\) \(\chi_{338130}(33997,\cdot)\) \(\chi_{338130}(34873,\cdot)\) \(\chi_{338130}(37507,\cdot)\) \(\chi_{338130}(39877,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{816})$ |
| Fixed field: | Number field defined by a degree 816 polynomial (not computed) |
Values on generators
\((262991,67627,104041,145081)\) → \((e\left(\frac{2}{3}\right),i,e\left(\frac{5}{12}\right),e\left(\frac{189}{272}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 338130 }(97, a) \) | \(-1\) | \(1\) | \(e\left(\frac{55}{272}\right)\) | \(e\left(\frac{461}{816}\right)\) | \(e\left(\frac{127}{408}\right)\) | \(e\left(\frac{55}{272}\right)\) | \(e\left(\frac{563}{816}\right)\) | \(e\left(\frac{275}{816}\right)\) | \(e\left(\frac{655}{816}\right)\) | \(e\left(\frac{155}{272}\right)\) | \(e\left(\frac{39}{136}\right)\) | \(e\left(\frac{133}{204}\right)\) |