Basic properties
| Modulus: | \(1014\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1014.s
\(\chi_{1014}(31,\cdot)\) \(\chi_{1014}(73,\cdot)\) \(\chi_{1014}(109,\cdot)\) \(\chi_{1014}(151,\cdot)\) \(\chi_{1014}(187,\cdot)\) \(\chi_{1014}(229,\cdot)\) \(\chi_{1014}(265,\cdot)\) \(\chi_{1014}(307,\cdot)\) \(\chi_{1014}(343,\cdot)\) \(\chi_{1014}(385,\cdot)\) \(\chi_{1014}(421,\cdot)\) \(\chi_{1014}(463,\cdot)\) \(\chi_{1014}(499,\cdot)\) \(\chi_{1014}(541,\cdot)\) \(\chi_{1014}(619,\cdot)\) \(\chi_{1014}(655,\cdot)\) \(\chi_{1014}(697,\cdot)\) \(\chi_{1014}(733,\cdot)\) \(\chi_{1014}(811,\cdot)\) \(\chi_{1014}(853,\cdot)\) \(\chi_{1014}(889,\cdot)\) \(\chi_{1014}(931,\cdot)\) \(\chi_{1014}(967,\cdot)\) \(\chi_{1014}(1009,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((677,847)\) → \((1,e\left(\frac{7}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 1014 }(31, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(-i\) | \(-1\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{8}{13}\right)\) |