Basic properties
| Modulus: | \(8450\) | |
| Conductor: | \(845\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{845}(57,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8450.br
\(\chi_{8450}(57,\cdot)\) \(\chi_{8450}(593,\cdot)\) \(\chi_{8450}(707,\cdot)\) \(\chi_{8450}(1243,\cdot)\) \(\chi_{8450}(1357,\cdot)\) \(\chi_{8450}(1893,\cdot)\) \(\chi_{8450}(2007,\cdot)\) \(\chi_{8450}(2543,\cdot)\) \(\chi_{8450}(2657,\cdot)\) \(\chi_{8450}(3193,\cdot)\) \(\chi_{8450}(3307,\cdot)\) \(\chi_{8450}(3843,\cdot)\) \(\chi_{8450}(4607,\cdot)\) \(\chi_{8450}(5143,\cdot)\) \(\chi_{8450}(5257,\cdot)\) \(\chi_{8450}(5793,\cdot)\) \(\chi_{8450}(5907,\cdot)\) \(\chi_{8450}(6443,\cdot)\) \(\chi_{8450}(6557,\cdot)\) \(\chi_{8450}(7093,\cdot)\) \(\chi_{8450}(7207,\cdot)\) \(\chi_{8450}(7743,\cdot)\) \(\chi_{8450}(7857,\cdot)\) \(\chi_{8450}(8393,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((677,3551)\) → \((i,e\left(\frac{11}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 8450 }(57, a) \) | \(1\) | \(1\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(i\) | \(e\left(\frac{45}{52}\right)\) | \(i\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{25}{26}\right)\) |