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 \(\chi_{169065}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 338130.byc
\(\chi_{338130}(29,\cdot)\) \(\chi_{338130}(1049,\cdot)\) \(\chi_{338130}(2369,\cdot)\) \(\chi_{338130}(3389,\cdot)\) \(\chi_{338130}(3539,\cdot)\) \(\chi_{338130}(5879,\cdot)\) \(\chi_{338130}(6899,\cdot)\) \(\chi_{338130}(7049,\cdot)\) \(\chi_{338130}(8069,\cdot)\) \(\chi_{338130}(9389,\cdot)\) \(\chi_{338130}(10409,\cdot)\) \(\chi_{338130}(14069,\cdot)\) \(\chi_{338130}(15089,\cdot)\) \(\chi_{338130}(15239,\cdot)\) \(\chi_{338130}(19919,\cdot)\) \(\chi_{338130}(22259,\cdot)\) \(\chi_{338130}(23279,\cdot)\) \(\chi_{338130}(23429,\cdot)\) \(\chi_{338130}(24449,\cdot)\) \(\chi_{338130}(25769,\cdot)\) \(\chi_{338130}(26789,\cdot)\) \(\chi_{338130}(26939,\cdot)\) \(\chi_{338130}(27959,\cdot)\) \(\chi_{338130}(29279,\cdot)\) \(\chi_{338130}(30299,\cdot)\) \(\chi_{338130}(33959,\cdot)\) \(\chi_{338130}(34979,\cdot)\) \(\chi_{338130}(35129,\cdot)\) \(\chi_{338130}(36149,\cdot)\) \(\chi_{338130}(39809,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{816})$ |
| Fixed field: | Number field defined by a degree 816 polynomial (not computed) |
Values on generators
\((262991,67627,104041,145081)\) → \((e\left(\frac{1}{6}\right),-1,e\left(\frac{1}{3}\right),e\left(\frac{125}{272}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 338130 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{816}\right)\) | \(e\left(\frac{19}{272}\right)\) | \(e\left(\frac{41}{408}\right)\) | \(e\left(\frac{121}{816}\right)\) | \(e\left(\frac{257}{272}\right)\) | \(e\left(\frac{383}{816}\right)\) | \(e\left(\frac{95}{816}\right)\) | \(e\left(\frac{613}{816}\right)\) | \(e\left(\frac{283}{408}\right)\) | \(e\left(\frac{127}{204}\right)\) |