Basic properties
| Modulus: | \(1014\) | |
| Conductor: | \(507\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{507}(317,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1014.r
\(\chi_{1014}(5,\cdot)\) \(\chi_{1014}(47,\cdot)\) \(\chi_{1014}(83,\cdot)\) \(\chi_{1014}(125,\cdot)\) \(\chi_{1014}(161,\cdot)\) \(\chi_{1014}(203,\cdot)\) \(\chi_{1014}(281,\cdot)\) \(\chi_{1014}(317,\cdot)\) \(\chi_{1014}(359,\cdot)\) \(\chi_{1014}(395,\cdot)\) \(\chi_{1014}(473,\cdot)\) \(\chi_{1014}(515,\cdot)\) \(\chi_{1014}(551,\cdot)\) \(\chi_{1014}(593,\cdot)\) \(\chi_{1014}(629,\cdot)\) \(\chi_{1014}(671,\cdot)\) \(\chi_{1014}(707,\cdot)\) \(\chi_{1014}(749,\cdot)\) \(\chi_{1014}(785,\cdot)\) \(\chi_{1014}(827,\cdot)\) \(\chi_{1014}(863,\cdot)\) \(\chi_{1014}(905,\cdot)\) \(\chi_{1014}(941,\cdot)\) \(\chi_{1014}(983,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((677,847)\) → \((-1,e\left(\frac{51}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 1014 }(317, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(-i\) | \(1\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{7}{26}\right)\) |