Basic properties
Modulus: | \(845\) | |
Conductor: | \(845\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(52\) | 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 845.be
\(\chi_{845}(18,\cdot)\) \(\chi_{845}(47,\cdot)\) \(\chi_{845}(83,\cdot)\) \(\chi_{845}(112,\cdot)\) \(\chi_{845}(148,\cdot)\) \(\chi_{845}(177,\cdot)\) \(\chi_{845}(213,\cdot)\) \(\chi_{845}(242,\cdot)\) \(\chi_{845}(278,\cdot)\) \(\chi_{845}(307,\cdot)\) \(\chi_{845}(343,\cdot)\) \(\chi_{845}(372,\cdot)\) \(\chi_{845}(473,\cdot)\) \(\chi_{845}(502,\cdot)\) \(\chi_{845}(538,\cdot)\) \(\chi_{845}(567,\cdot)\) \(\chi_{845}(603,\cdot)\) \(\chi_{845}(632,\cdot)\) \(\chi_{845}(668,\cdot)\) \(\chi_{845}(697,\cdot)\) \(\chi_{845}(733,\cdot)\) \(\chi_{845}(762,\cdot)\) \(\chi_{845}(798,\cdot)\) \(\chi_{845}(827,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{52})$ |
Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((677,171)\) → \((-i,e\left(\frac{31}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(14\) |
\( \chi_{ 845 }(18, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{23}{26}\right)\) |