Basic properties
Modulus: | \(1600\) | |
Conductor: | \(1600\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1600.cq
\(\chi_{1600}(29,\cdot)\) \(\chi_{1600}(69,\cdot)\) \(\chi_{1600}(109,\cdot)\) \(\chi_{1600}(189,\cdot)\) \(\chi_{1600}(229,\cdot)\) \(\chi_{1600}(269,\cdot)\) \(\chi_{1600}(309,\cdot)\) \(\chi_{1600}(389,\cdot)\) \(\chi_{1600}(429,\cdot)\) \(\chi_{1600}(469,\cdot)\) \(\chi_{1600}(509,\cdot)\) \(\chi_{1600}(589,\cdot)\) \(\chi_{1600}(629,\cdot)\) \(\chi_{1600}(669,\cdot)\) \(\chi_{1600}(709,\cdot)\) \(\chi_{1600}(789,\cdot)\) \(\chi_{1600}(829,\cdot)\) \(\chi_{1600}(869,\cdot)\) \(\chi_{1600}(909,\cdot)\) \(\chi_{1600}(989,\cdot)\) \(\chi_{1600}(1029,\cdot)\) \(\chi_{1600}(1069,\cdot)\) \(\chi_{1600}(1109,\cdot)\) \(\chi_{1600}(1189,\cdot)\) \(\chi_{1600}(1229,\cdot)\) \(\chi_{1600}(1269,\cdot)\) \(\chi_{1600}(1309,\cdot)\) \(\chi_{1600}(1389,\cdot)\) \(\chi_{1600}(1429,\cdot)\) \(\chi_{1600}(1469,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1151,901,577)\) → \((1,e\left(\frac{1}{16}\right),e\left(\frac{1}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 1600 }(1029, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{80}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{19}{80}\right)\) | \(e\left(\frac{1}{80}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{53}{80}\right)\) |