Basic properties
Modulus: | \(212\) | |
Conductor: | \(53\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{53}(8,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 212.l
\(\chi_{212}(5,\cdot)\) \(\chi_{212}(21,\cdot)\) \(\chi_{212}(33,\cdot)\) \(\chi_{212}(41,\cdot)\) \(\chi_{212}(45,\cdot)\) \(\chi_{212}(61,\cdot)\) \(\chi_{212}(65,\cdot)\) \(\chi_{212}(73,\cdot)\) \(\chi_{212}(85,\cdot)\) \(\chi_{212}(101,\cdot)\) \(\chi_{212}(109,\cdot)\) \(\chi_{212}(125,\cdot)\) \(\chi_{212}(133,\cdot)\) \(\chi_{212}(137,\cdot)\) \(\chi_{212}(141,\cdot)\) \(\chi_{212}(145,\cdot)\) \(\chi_{212}(157,\cdot)\) \(\chi_{212}(161,\cdot)\) \(\chi_{212}(173,\cdot)\) \(\chi_{212}(177,\cdot)\) \(\chi_{212}(181,\cdot)\) \(\chi_{212}(185,\cdot)\) \(\chi_{212}(193,\cdot)\) \(\chi_{212}(209,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{52})$ |
Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((107,161)\) → \((1,e\left(\frac{3}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 212 }(61, a) \) | \(-1\) | \(1\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{41}{52}\right)\) |