Basic properties
Modulus: | \(6001\) | |
Conductor: | \(353\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(352\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{353}(3,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6001.eh
\(\chi_{6001}(52,\cdot)\) \(\chi_{6001}(69,\cdot)\) \(\chi_{6001}(103,\cdot)\) \(\chi_{6001}(154,\cdot)\) \(\chi_{6001}(205,\cdot)\) \(\chi_{6001}(239,\cdot)\) \(\chi_{6001}(273,\cdot)\) \(\chi_{6001}(290,\cdot)\) \(\chi_{6001}(341,\cdot)\) \(\chi_{6001}(358,\cdot)\) \(\chi_{6001}(409,\cdot)\) \(\chi_{6001}(443,\cdot)\) \(\chi_{6001}(460,\cdot)\) \(\chi_{6001}(477,\cdot)\) \(\chi_{6001}(494,\cdot)\) \(\chi_{6001}(511,\cdot)\) \(\chi_{6001}(528,\cdot)\) \(\chi_{6001}(545,\cdot)\) \(\chi_{6001}(596,\cdot)\) \(\chi_{6001}(732,\cdot)\) \(\chi_{6001}(783,\cdot)\) \(\chi_{6001}(851,\cdot)\) \(\chi_{6001}(885,\cdot)\) \(\chi_{6001}(936,\cdot)\) \(\chi_{6001}(970,\cdot)\) \(\chi_{6001}(1004,\cdot)\) \(\chi_{6001}(1072,\cdot)\) \(\chi_{6001}(1174,\cdot)\) \(\chi_{6001}(1191,\cdot)\) \(\chi_{6001}(1208,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{352})$ |
Fixed field: | Number field defined by a degree 352 polynomial (not computed) |
Values on generators
\((2825,3180)\) → \((1,e\left(\frac{1}{352}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6001 }(3180, a) \) | \(-1\) | \(1\) | \(e\left(\frac{41}{88}\right)\) | \(e\left(\frac{1}{352}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{309}{352}\right)\) | \(e\left(\frac{15}{32}\right)\) | \(e\left(\frac{9}{32}\right)\) | \(e\left(\frac{35}{88}\right)\) | \(e\left(\frac{1}{176}\right)\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{15}{88}\right)\) |