Basic properties
| Modulus: | \(1014\) | |
| Conductor: | \(507\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{507}(107,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1014.v
\(\chi_{1014}(29,\cdot)\) \(\chi_{1014}(35,\cdot)\) \(\chi_{1014}(107,\cdot)\) \(\chi_{1014}(113,\cdot)\) \(\chi_{1014}(185,\cdot)\) \(\chi_{1014}(263,\cdot)\) \(\chi_{1014}(269,\cdot)\) \(\chi_{1014}(341,\cdot)\) \(\chi_{1014}(347,\cdot)\) \(\chi_{1014}(419,\cdot)\) \(\chi_{1014}(425,\cdot)\) \(\chi_{1014}(497,\cdot)\) \(\chi_{1014}(503,\cdot)\) \(\chi_{1014}(575,\cdot)\) \(\chi_{1014}(581,\cdot)\) \(\chi_{1014}(659,\cdot)\) \(\chi_{1014}(731,\cdot)\) \(\chi_{1014}(737,\cdot)\) \(\chi_{1014}(809,\cdot)\) \(\chi_{1014}(815,\cdot)\) \(\chi_{1014}(887,\cdot)\) \(\chi_{1014}(893,\cdot)\) \(\chi_{1014}(965,\cdot)\) \(\chi_{1014}(971,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((677,847)\) → \((-1,e\left(\frac{25}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 1014 }(107, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{67}{78}\right)\) |