Basic properties
Modulus: | \(1521\) | |
Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{169}(18,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1521.bm
\(\chi_{1521}(73,\cdot)\) \(\chi_{1521}(109,\cdot)\) \(\chi_{1521}(190,\cdot)\) \(\chi_{1521}(226,\cdot)\) \(\chi_{1521}(307,\cdot)\) \(\chi_{1521}(343,\cdot)\) \(\chi_{1521}(424,\cdot)\) \(\chi_{1521}(460,\cdot)\) \(\chi_{1521}(541,\cdot)\) \(\chi_{1521}(658,\cdot)\) \(\chi_{1521}(694,\cdot)\) \(\chi_{1521}(811,\cdot)\) \(\chi_{1521}(892,\cdot)\) \(\chi_{1521}(928,\cdot)\) \(\chi_{1521}(1009,\cdot)\) \(\chi_{1521}(1045,\cdot)\) \(\chi_{1521}(1126,\cdot)\) \(\chi_{1521}(1162,\cdot)\) \(\chi_{1521}(1243,\cdot)\) \(\chi_{1521}(1279,\cdot)\) \(\chi_{1521}(1360,\cdot)\) \(\chi_{1521}(1396,\cdot)\) \(\chi_{1521}(1477,\cdot)\) \(\chi_{1521}(1513,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{52})$ |
Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((677,847)\) → \((1,e\left(\frac{31}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
\( \chi_{ 1521 }(694, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{1}{26}\right)\) |