Basic properties
| Modulus: | \(338130\) | |
| Conductor: | \(33813\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(816\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{33813}(11,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 338130.bzh
\(\chi_{338130}(11,\cdot)\) \(\chi_{338130}(821,\cdot)\) \(\chi_{338130}(1931,\cdot)\) \(\chi_{338130}(3101,\cdot)\) \(\chi_{338130}(3191,\cdot)\) \(\chi_{338130}(6701,\cdot)\) \(\chi_{338130}(7031,\cdot)\) \(\chi_{338130}(8201,\cdot)\) \(\chi_{338130}(9041,\cdot)\) \(\chi_{338130}(10121,\cdot)\) \(\chi_{338130}(11351,\cdot)\) \(\chi_{338130}(12551,\cdot)\) \(\chi_{338130}(14801,\cdot)\) \(\chi_{338130}(14861,\cdot)\) \(\chi_{338130}(15221,\cdot)\) \(\chi_{338130}(17201,\cdot)\) \(\chi_{338130}(20711,\cdot)\) \(\chi_{338130}(21821,\cdot)\) \(\chi_{338130}(22991,\cdot)\) \(\chi_{338130}(23081,\cdot)\) \(\chi_{338130}(26591,\cdot)\) \(\chi_{338130}(26921,\cdot)\) \(\chi_{338130}(28091,\cdot)\) \(\chi_{338130}(28931,\cdot)\) \(\chi_{338130}(30011,\cdot)\) \(\chi_{338130}(31241,\cdot)\) \(\chi_{338130}(32441,\cdot)\) \(\chi_{338130}(34691,\cdot)\) \(\chi_{338130}(34751,\cdot)\) \(\chi_{338130}(35111,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{816})$ |
| Fixed field: | Number field defined by a degree 816 polynomial (not computed) |
Values on generators
\((262991,67627,104041,145081)\) → \((e\left(\frac{1}{6}\right),1,e\left(\frac{7}{12}\right),e\left(\frac{23}{272}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 338130 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{155}{816}\right)\) | \(e\left(\frac{53}{272}\right)\) | \(e\left(\frac{41}{408}\right)\) | \(e\left(\frac{427}{816}\right)\) | \(e\left(\frac{19}{272}\right)\) | \(e\left(\frac{281}{816}\right)\) | \(e\left(\frac{809}{816}\right)\) | \(e\left(\frac{715}{816}\right)\) | \(e\left(\frac{385}{408}\right)\) | \(e\left(\frac{19}{51}\right)\) |