Basic properties
| Modulus: | \(338130\) | |
| Conductor: | \(169065\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(408\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169065}(59,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 338130.buv
\(\chi_{338130}(59,\cdot)\) \(\chi_{338130}(5159,\cdot)\) \(\chi_{338130}(5969,\cdot)\) \(\chi_{338130}(5999,\cdot)\) \(\chi_{338130}(12929,\cdot)\) \(\chi_{338130}(14159,\cdot)\) \(\chi_{338130}(17699,\cdot)\) \(\chi_{338130}(18029,\cdot)\) \(\chi_{338130}(19949,\cdot)\) \(\chi_{338130}(25049,\cdot)\) \(\chi_{338130}(25859,\cdot)\) \(\chi_{338130}(25889,\cdot)\) \(\chi_{338130}(32819,\cdot)\) \(\chi_{338130}(34049,\cdot)\) \(\chi_{338130}(37589,\cdot)\) \(\chi_{338130}(37919,\cdot)\) \(\chi_{338130}(39839,\cdot)\) \(\chi_{338130}(44939,\cdot)\) \(\chi_{338130}(45749,\cdot)\) \(\chi_{338130}(45779,\cdot)\) \(\chi_{338130}(52709,\cdot)\) \(\chi_{338130}(53939,\cdot)\) \(\chi_{338130}(57479,\cdot)\) \(\chi_{338130}(57809,\cdot)\) \(\chi_{338130}(59729,\cdot)\) \(\chi_{338130}(64829,\cdot)\) \(\chi_{338130}(65639,\cdot)\) \(\chi_{338130}(65669,\cdot)\) \(\chi_{338130}(72599,\cdot)\) \(\chi_{338130}(77369,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{408})$ |
| Fixed field: | Number field defined by a degree 408 polynomial (not computed) |
Values on generators
\((262991,67627,104041,145081)\) → \((e\left(\frac{5}{6}\right),-1,e\left(\frac{11}{12}\right),e\left(\frac{117}{136}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 338130 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{107}{408}\right)\) | \(e\left(\frac{5}{136}\right)\) | \(e\left(\frac{32}{51}\right)\) | \(e\left(\frac{277}{408}\right)\) | \(e\left(\frac{5}{136}\right)\) | \(e\left(\frac{269}{408}\right)\) | \(e\left(\frac{365}{408}\right)\) | \(e\left(\frac{79}{408}\right)\) | \(e\left(\frac{19}{204}\right)\) | \(e\left(\frac{23}{204}\right)\) |