Basic properties
| Modulus: | \(338130\) | |
| Conductor: | \(13005\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(816\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{13005}(79,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 338130.byf
\(\chi_{338130}(79,\cdot)\) \(\chi_{338130}(2029,\cdot)\) \(\chi_{338130}(2419,\cdot)\) \(\chi_{338130}(3199,\cdot)\) \(\chi_{338130}(5539,\cdot)\) \(\chi_{338130}(6709,\cdot)\) \(\chi_{338130}(7099,\cdot)\) \(\chi_{338130}(8269,\cdot)\) \(\chi_{338130}(9049,\cdot)\) \(\chi_{338130}(12949,\cdot)\) \(\chi_{338130}(13729,\cdot)\) \(\chi_{338130}(14899,\cdot)\) \(\chi_{338130}(15289,\cdot)\) \(\chi_{338130}(16459,\cdot)\) \(\chi_{338130}(18799,\cdot)\) \(\chi_{338130}(19579,\cdot)\) \(\chi_{338130}(19969,\cdot)\) \(\chi_{338130}(21919,\cdot)\) \(\chi_{338130}(22309,\cdot)\) \(\chi_{338130}(23089,\cdot)\) \(\chi_{338130}(25429,\cdot)\) \(\chi_{338130}(26599,\cdot)\) \(\chi_{338130}(26989,\cdot)\) \(\chi_{338130}(28159,\cdot)\) \(\chi_{338130}(28939,\cdot)\) \(\chi_{338130}(32839,\cdot)\) \(\chi_{338130}(33619,\cdot)\) \(\chi_{338130}(34789,\cdot)\) \(\chi_{338130}(35179,\cdot)\) \(\chi_{338130}(38689,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{816})$ |
| Fixed field: | Number field defined by a degree 816 polynomial (not computed) |
Values on generators
\((262991,67627,104041,145081)\) → \((e\left(\frac{2}{3}\right),-1,1,e\left(\frac{167}{272}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 338130 }(79, a) \) | \(-1\) | \(1\) | \(e\left(\frac{271}{816}\right)\) | \(e\left(\frac{643}{816}\right)\) | \(e\left(\frac{81}{136}\right)\) | \(e\left(\frac{611}{816}\right)\) | \(e\left(\frac{337}{816}\right)\) | \(e\left(\frac{701}{816}\right)\) | \(e\left(\frac{191}{272}\right)\) | \(e\left(\frac{263}{816}\right)\) | \(e\left(\frac{377}{408}\right)\) | \(e\left(\frac{115}{204}\right)\) |