Basic properties
| Modulus: | \(212\) | |
| Conductor: | \(212\) | 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 212.k
\(\chi_{212}(3,\cdot)\) \(\chi_{212}(19,\cdot)\) \(\chi_{212}(27,\cdot)\) \(\chi_{212}(31,\cdot)\) \(\chi_{212}(35,\cdot)\) \(\chi_{212}(39,\cdot)\) \(\chi_{212}(51,\cdot)\) \(\chi_{212}(55,\cdot)\) \(\chi_{212}(67,\cdot)\) \(\chi_{212}(71,\cdot)\) \(\chi_{212}(75,\cdot)\) \(\chi_{212}(79,\cdot)\) \(\chi_{212}(87,\cdot)\) \(\chi_{212}(103,\cdot)\) \(\chi_{212}(111,\cdot)\) \(\chi_{212}(127,\cdot)\) \(\chi_{212}(139,\cdot)\) \(\chi_{212}(147,\cdot)\) \(\chi_{212}(151,\cdot)\) \(\chi_{212}(167,\cdot)\) \(\chi_{212}(171,\cdot)\) \(\chi_{212}(179,\cdot)\) \(\chi_{212}(191,\cdot)\) \(\chi_{212}(207,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((107,161)\) → \((-1,e\left(\frac{1}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 212 }(55, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{31}{52}\right)\) |