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.z
\(\chi_{845}(8,\cdot)\) \(\chi_{845}(57,\cdot)\) \(\chi_{845}(73,\cdot)\) \(\chi_{845}(122,\cdot)\) \(\chi_{845}(138,\cdot)\) \(\chi_{845}(187,\cdot)\) \(\chi_{845}(203,\cdot)\) \(\chi_{845}(252,\cdot)\) \(\chi_{845}(317,\cdot)\) \(\chi_{845}(333,\cdot)\) \(\chi_{845}(382,\cdot)\) \(\chi_{845}(398,\cdot)\) \(\chi_{845}(447,\cdot)\) \(\chi_{845}(463,\cdot)\) \(\chi_{845}(512,\cdot)\) \(\chi_{845}(528,\cdot)\) \(\chi_{845}(593,\cdot)\) \(\chi_{845}(642,\cdot)\) \(\chi_{845}(658,\cdot)\) \(\chi_{845}(707,\cdot)\) \(\chi_{845}(723,\cdot)\) \(\chi_{845}(772,\cdot)\) \(\chi_{845}(788,\cdot)\) \(\chi_{845}(837,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((677,171)\) → \((-i,e\left(\frac{1}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(14\) |
| \( \chi_{ 845 }(8, a) \) | \(1\) | \(1\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{15}{26}\right)\) |