Basic properties
Modulus: | \(1681\) | |
Conductor: | \(1681\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(41\) | 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 1681.i
\(\chi_{1681}(42,\cdot)\) \(\chi_{1681}(83,\cdot)\) \(\chi_{1681}(124,\cdot)\) \(\chi_{1681}(165,\cdot)\) \(\chi_{1681}(206,\cdot)\) \(\chi_{1681}(247,\cdot)\) \(\chi_{1681}(288,\cdot)\) \(\chi_{1681}(329,\cdot)\) \(\chi_{1681}(370,\cdot)\) \(\chi_{1681}(411,\cdot)\) \(\chi_{1681}(452,\cdot)\) \(\chi_{1681}(493,\cdot)\) \(\chi_{1681}(534,\cdot)\) \(\chi_{1681}(575,\cdot)\) \(\chi_{1681}(616,\cdot)\) \(\chi_{1681}(657,\cdot)\) \(\chi_{1681}(698,\cdot)\) \(\chi_{1681}(739,\cdot)\) \(\chi_{1681}(780,\cdot)\) \(\chi_{1681}(821,\cdot)\) \(\chi_{1681}(862,\cdot)\) \(\chi_{1681}(903,\cdot)\) \(\chi_{1681}(944,\cdot)\) \(\chi_{1681}(985,\cdot)\) \(\chi_{1681}(1026,\cdot)\) \(\chi_{1681}(1067,\cdot)\) \(\chi_{1681}(1108,\cdot)\) \(\chi_{1681}(1149,\cdot)\) \(\chi_{1681}(1190,\cdot)\) \(\chi_{1681}(1231,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{41})$ |
Fixed field: | Number field defined by a degree 41 polynomial |
Values on generators
\(6\) → \(e\left(\frac{38}{41}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1681 }(1313, a) \) | \(1\) | \(1\) | \(e\left(\frac{18}{41}\right)\) | \(e\left(\frac{20}{41}\right)\) | \(e\left(\frac{36}{41}\right)\) | \(e\left(\frac{27}{41}\right)\) | \(e\left(\frac{38}{41}\right)\) | \(e\left(\frac{4}{41}\right)\) | \(e\left(\frac{13}{41}\right)\) | \(e\left(\frac{40}{41}\right)\) | \(e\left(\frac{4}{41}\right)\) | \(e\left(\frac{39}{41}\right)\) |